If a researcher is standing in a corner (point c) of a triangle plot. the angle to point a is S76E . the distance between point A and point B is 210 ft.
How to find the distance between point A and point B?To find the distance between points A and B, we can use the Law of Cosines. Let's first label the angles of the triangle:
Angle ACB = 180 - (76 + 32) = 72 degrees
Angle BAC = 76 degrees
Angle ABC = 32 degrees
Using the Law of Cosines, we have:
AB^2 = AC^2 + BC^2 - 2(AC)(BC)cos(ACB)
where;
AB is the distance between points A and B
AC is the distance between points A and C (210 ft
BC is the distance between points B and C (150 ft)
ACB is the angle between AC and BC (72 degrees)
Plugging in the values, we get:
AB^2 = 210^2 + 150^2 - 2(210)(150)cos(72)
AB^2 = 44100
AB = sqrt(44100)
AB = 210 ft
Therefore, the distance between point A and point B is 210 ft.
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Find an equation of the osculating plane and an equation of the normal
plane of the curve x = sin 2t, y = t, z = cos 2t at the point (0, π, 1).
The equation of the normal plane is 4y = 4π, or equivalently, y = π.
What is osculating plane?The word osculate comes from the Latin osculatus, which is a past participle of the verb osculari, which means "to kiss." Thus, an osculating plane is one that "kisses" a submanifold.
To find the osculating plane and normal plane of the curve x = sin 2t, y = t, z = cos 2t at the point (0, π, 1), we need to follow these steps:
Find the first and second derivatives of the curve with respect to t.Evaluate the derivatives at t = π to get the velocity, acceleration, and curvature vectors at the point (0, π, 1).Use the velocity and acceleration vectors to find the normal vector of the osculating plane.Use the normal vector and the point (0, π, 1) to find the equation of the osculating plane.Use the curvature vector to find the normal vector of the normal plane.Use the normal vector and the point (0, π, 1) to find the equation of the normal plane.Step 1: Find the first and second derivatives of the curve with respect to t.
x' = 2cos2t
y' = 1
z' = -2sin2t
x'' = -4sin2t
y'' = 0
z'' = -4cos2t
Step 2: Evaluate the derivatives at t = π.
x'(π) = 2cos2π = 2
y'(π) = 1
z'(π) = -2sin2π = 0
x''(π) = -4sin2π = 0
y''(π) = 0
z''(π) = -4cos2π = -4
So the velocity vector at the point (0, π, 1) is v = ⟨2, 1, 0⟩, the acceleration vector is a = ⟨0, 0, -4⟩, and the curvature vector is κv = ⟨0, 4, 0⟩.
Step 3: Use the velocity and acceleration vectors to find the normal vector of the osculating plane.
The normal vector of the osculating plane is given by the cross product of the velocity and acceleration vectors:
n = v × a = ⟨2, 1, 0⟩ × ⟨0, 0, -4⟩ = ⟨4, 0, 0⟩
Step 4: Use the normal vector and the point (0, π, 1) to find the equation of the osculating plane.
The equation of the osculating plane is given by:
4(x - 0) + 0(y - π) + 0(z - 1) = 0
Simplifying, we get:
4x - 4 = 0
So the equation of the osculating plane is 4x = 4, or equivalently, x = 1.
Step 5: Use the curvature vector to find the normal vector of the normal plane.
The normal vector of the normal plane is given by the curvature vector:
n' = κv = ⟨0, 4, 0⟩
Step 6: Use the normal vector and the point (0, π, 1) to find the equation of the normal plane.
The equation of the normal plane is given by:
0(x - 0) + 4(y - π) + 0(z - 1) = 0
Simplifying, we get:
4y - 4π = 0
So, the equation of the normal plane is 4y = 4π, or equivalently, y = π.
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ii) The door is 0.9 m wide and 2.1 m high. Each of the four windows is 1.5 m wide and 1.2 m high work out the toral area of the door and the four windows
Answer: The area of the door can be calculated as:
Area of door = width x height
= 0.9 m x 2.1 m
= 1.89 square meters
The area of one window can be calculated as:
Area of window = width x height
= 1.5 m x 1.2 m
= 1.8 square meters
Since there are four windows, the total area of the four windows is:
Total area of four windows = 4 x Area of window
= 4 x 1.8 square meters
= 7.2 square meters
Therefore, the total area of the door and the four windows is:
Total area = Area of door + Total area of four windows
= 1.89 square meters + 7.2 square meters
= 9.09 square meters
Hence, the total area of the door and the four windows is 9.09 square meters.
Step-by-step explanation:
Chloe claims that Point A=−6 and Point B=1 . Which of the following statements provide support for Chloe's claim? Select ALL that apply. A A<0 because A is to the left of zero B A>0 because A is to the left of zero C A 0 because B is to the left of zero F B>0 because B is to the right of zero
The statements that provide support for Chloe's claim are A<0 because A is to the left of zero, B>0 because B is to the right of zero. So correct option is A and F.
Describe Comparison Algebra?Comparison algebra is a branch of algebra that deals with inequalities and comparisons between different quantities or expressions. In comparison algebra, the goal is to determine the relationships between different expressions or quantities, such as whether one expression is greater than, less than, or equal to another expression.
Comparison algebra involves the use of comparison symbols, such as "<" (less than), ">" (greater than), and "=" (equal to), to express these relationships. For example, if we have two expressions, A and B, we can use the "<" symbol to express the relationship that A is less than B, as in A < B.
In comparison algebra, we can also manipulate inequalities and equations in similar ways as we do with regular algebraic expressions. For instance, we can add, subtract, multiply, or divide both sides of an inequality or equation by the same number or expression, while maintaining the inequality's direction.
The statements that provide support for Chloe's claim are:
A. A<0 because A is to the left of zero.
F. B>0 because B is to the right of zero.
Statement A supports Chloe's claim because Point A is to the left of zero on the number line, which means its value is negative. Statement F also supports Chloe's claim because Point B is to the right of zero on the number line, which means its value is positive.
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Write 80cm to 2km as rate
One per 2,500 can be used to represent the rate of 80cm to 2km.
Writing measures as a rate.To write 80cm to 2km as a rate, we need to convert the units to the same system. We can convert 80cm to kilometers by dividing by 100,000 (since there are 100,000 centimeters in a kilometer):
80 cm/100,000 = 0.0008 km
Now we can express the rate as:
0.0008 km per 2 km
Or we can simplify it by dividing both the numerator and denominator by 0.0008:
1 per 2,500
Therefore, 80cm to 2km can be expressed as a rate of 1 per 2,500.
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Determine the circumference and approximate area of the
given circle, using 3.14 for pie.
The circumference and approximate area of the given circle is 69.08 inches & 380.14 square inches.
What is circumference?
Circumference is the distance around the edge of a circular object or a round shape. It is the length of the boundary or perimeter of the circle. The formula is given by C = 2πr, where C is the circumference, r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14.
The circumference of a circle is given by the formula:
C = 2πr
where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14.
Using this formula and plugging in the given value of radius:
C = 2 x 3.14 x 11
C = 69.08 inches (rounded to two decimal places)
So the circumference of the circle with 11 inches radius is approximately 69.08 inches.
The area of a circle is given by the formula:
A = πr²
Again, using the given value of radius and approximating π to 3.14:
A = 3.14 x 11²
A = 3.14 x 121
A = 380.14 square inches (rounded to two decimal places)
So the approximate area of the circle with 11 inches radius is approximately 380.14 square inches.
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Write an absolute value equation that has the following solution set.
-8 and -2
Thank you!
The absolute value equation that has -8 and -2 as the solution set is |x + 5| = 3
What is an absolute value equation?
An absolute value equation can be written as |expression| = value
To have -8 and -2 as the solution set, we need an absolute value equation that produces these two values when the expression inside the absolute value is either positive or negative.
We can write,
|x + 5| = 3
To solve for x, we have two cases,
Case 1: x + 5 is positive
If x + 5 is positive, then the equation becomes x + 5 = 3
Solving for x,
x = -2
This matches one of the solutions we want.
Case 2: x + 5 is negative
If x + 5 is negative, then the equation becomes -(x + 5) = 3
Solving for x,
x = -8
This also matches the other solution we want.
Therefore, the absolute value equation that has -8 and -2 as the solution set is |x + 5| = 3.
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Suppose that the functions fand g are defined as follows.
f(x)=2x-1
g(x)=√3x-5
The composite functions (f/g)(x) and (f-g)(x) are (2x-1)/√(3x-5) and (2x-1) -√(3x-5)
Calculating the composite functions (f/g)(x) and (f-g)(x)To calculate (f/g)(x), we need to divide f(x) by g(x):
(f/g)(x) = f(x)/g(x) = (2x-1)/√(3x-5)
The domain of (f/g)(x) is the set of all x-values for which the denominator √(3x-5) is not equal to zero and non-negative
3x-5 ≥ 0, or x ≥ 5/3
Therefore, the domain of (f/g)(x) is x ≥ 5/3.
To calculate (f-g)(x), we need to subtract g(x) from f(x):
(f-g)(x) = f(x) - g(x) = (2x-1) - √(3x-5)
The domain of (f-g)(x) is the set of all x-values for which the expression inside the square root is non-negative:
3x-5 ≥ 0, or x ≥ 5/3
Therefore, the domain of (f-g)(x) is x ≥ 5/3.
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50pts!!!!
Many investors use interest-only loans to buy shares or property. For such loans the principal stays constant and only the interest is paid back each month.
She buys an investment property for $300 000 and borrows the full amount at 7% p.a. simple interest. She rents out the property at $1500 per month and pays $3000 per year in rates and other costs to keep the property.
Find the amount of interest she needs to pay back every month.
Find her yearly income from rent.
By considering the other costs in keeping the property, calculate her overall loss in a year.
she hopes that the property’s value will increase enough to cover any loss she is making. By what percentage of the original price will the property need to increase in value per year?
Step-by-step explanation:
to find the interest she needs to pay back every month, we need to use this formula:
I = PRT/12
in this case the principle is $300,000, the rate is 7% p.a. and the amount of time is 1 year, if we substitute in our values we:
I = (300,000)(7)(1)/12 = $17,500 in interest every month
to find her yearly income from rent, we have to multiply the monthly rent by 12
1500 × 12 = $18,000
to calculate her loss percentage in a year, we have to subtract 18,000 from 3000 which is 15,000
she said that she hopes the property's value will increase to cover the loss she made.
to cover the loss of $15000 per year, the property needs to increase in value by at least $15000. the percentage increases value can be written as
Percentage increase = (difference in increase/Original price) × 100
so
percentage increase = (15000/300000) × 100 = 5%
so the property needs to increase in value by at least 5% per year to cover the loss.
The woman needs to pay $1750 monthly as interest. Her yearly income from the rent is $18,000. After considering all other costs, she is at a loss of $6000 per year, so the property needs to increase in value by 2% per year to cover this loss.
Explanation:First, let's calculate the monthly interest she needs to pay. 7% of $300,000 is $21,000 for a year. To find the monthly interest, we divide this by 12, resulting in $1750.Her yearly income from rent is $1500 multiplied by 12, giving us $18,000.To calculate her overall loss, we add the yearly interest and the costs to keep the property, then subtract the yearly rent income. So, $21,000 + $3000 - $18,000 = $6000 loss per year.Lastly, to find out by what percentage the property value needs to increase, we divide the loss by the original price and multiply by 100, giving us 2% increase per year.Learn more about Interest and Profit Calculation here:https://brainly.com/question/32651816
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I need help
A population of bacteria is growing according to the equation p(t)=800e^0.14t Estimate when the population will exceed 1151.
t= ---------
Answer: t=2.59
Step-by-step explanation:
This is a matter of clearing out the equation
set 1151=800e^0.14t
1151/800=e^0.14t
ln(1151/800)/0.14=t
t=2.59
help please! state the key features for the graph
Answer:
Axis of symmetry =1
vertex =(1,2)
y intercept =0
min/max= -6,2
domain= 0,1,2
range =y≥1,2
) Rewrite as an exponential equation.
log8 1/64 =2
(b) Rewrite as a logarithmic equation.
3 0=1
a) the exponential equation equivalent to log8 1/64 = 2 is 1/64 = [tex]8^{(-2)}[/tex]
b) the logarithmic equation equivalent to 3^0 = 1 is log3 1 = 0.
What is exponential equation?
An exponential equation is one in which the exponent contains a variable.
(a) We can rewrite the logarithmic equation as an exponential equation by using the definition of logarithms. The logarithmic equation
log8 1/64 = 2
means that 8 raised to the power of 2 is equal to 1/64:
[tex]8^2 = 1/64[/tex]
Thus, we can write the exponential equation as:
[tex]1/64 = 8^{(-2)}[/tex]
Therefore, the exponential equation equivalent to log8 1/64 = 2 is 1/64 = [tex]8^{(-2)}.[/tex]
(b) We can rewrite the exponential equation as a logarithmic equation by using the definition of logarithms. The exponential equation
[tex]3^0 = 1[/tex]
means that the logarithm of 1 to the base 3 is equal to 0:
log3 1 = 0
Therefore, the logarithmic equation equivalent to 3^0 = 1 is log3 1 = 0.
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complete the equatiotin 3 over 4 x 6 =
PLEASE HELP
Answer:
1/8
Step-by-step explanation:
If "over" refers to (4 * 6) as a whole,
[tex]\frac{3}{4*6}\\\\=\frac{3}{24}\\\\=\frac{1}{8}[/tex]
If "over" refers to division,
[tex]3 \div 4 \times 6\\= 0.75 \times 6\\= 4.5[/tex]
I would suppose it's the first one, so, ignore the second one if you haven't learnt BODMAS yet.
Hope this helps and be sure to mark this as brainliest! :)
Help Please...
You have 67 coins consisting of half-dollars and quarters. The number of quarters is 7 more than three times the number of half-dollars.
How many quarters do you have?
How many half -dollars do you have?
There are 52 quarters and 15 half-dollars
To solve this problem
Let's represent the number of half-dollars as "x" and the number of quarters as "y".
From the problem statement, we know that:
x + y = 67 (because there are a total of 67 coins)
y = 3x + 7 (because the number of quarters is 7 more than three times the number of half-dollars)
We can use substitution to solve for x:
x + (3x + 7) = 67
4x + 7 = 67
4x = 60
x = 15
So there are 15 half-dollars. We can use this to find the number of quarters:
y = 3x + 7
y = 3(15) + 7
y = 52
So there are 52 quarters.
Therefore, there are 52 quarters and 15 half-dollars.
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HELP ME PLEASE!!! HELPPP!!! A backyard pool is in the shape of a rectangle. The pool has a perimeter of 90 feet and an area of 500 ft2. Which of the following could be the pool's length and width? 15 feet and 30 feet, 10 feet and 35 feet ,50 feet and 10 feet, 25 feet and 20 feet
Answer:
(d) 25 feet and 20 feet
Step-by-step explanation:
You want the possible dimensions of a pool with an area of 500 square feet and a perimeter of 90 feet.
AreaThe area is the product of the length and width. The area of the pools offered in the answer choices are ...
(a) 15·30 = 450 . . . square feet
(b) 10·35 = 350 . . . square feet
(c) 50·10 = 500 . . . square feet
(d) 25·20 = 500 . . . square feet
The area requirement eliminates answer choices A and B.
PerimeterThe perimeter is twice the sum of length and width. The perimeters of the possible pools are ...
(c) 2(50 +10) = 120 . . . feet
(d) 2(25 +20) = 90 . . . feet
The perimeter requirement eliminates answer choice C.
The pool's possible length and width are 25 feet and 20 feet, choice D.
__
Additional comment
You could write a quadratic equation for the pool dimensions, but doing that will generally involve more work than checking the given answer choices.
If x is the width, then 45-x is the length, and the area is ...
x(45 -x) = 500
x² -45x +506.25 = -500 +506.25 . . . multiply by -1, complete the square
x = 22.5 -√6.25 = 20 . . . . take the square root; width is the smaller dimension
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(a) What is the value of x? Show your work.
(b) What is the measure of angle C? Show your work.
In triangle ABC
a) The value of x = 29⁰
b) The angle c equal to 93⁰
What is a triangle?A triangle is a closed plane figure that is formed by connecting three line segments, also known as sides, at their endpoints. The three endpoints, or vertices, where the sides of the triangle meet are not collinear. Triangles are important in mathematics and geometry because they are the simplest polygon that can exist in two-dimensional space.
According to the given informationIn a triangle, the sum of all interior angles is always 180 degrees. Therefore, we can use this fact to find the value of x and angle c.
We know that:
angle a = 35⁰
angle b = 52⁰
angle c = 3(x+2)⁰
Using the fact that the sum of all interior angles in a triangle is 180 degrees, we can write:
angle a + angle b + angle c = 180
Substituting the values we know, we get:
35 + 52 + 3(x+2) = 180
Simplifying the equation, we get:
87 + 3x + 6 = 180
3x + 93 = 180
3x = 87
x = 29
Therefore, x = 29⁰
To find angle c, we can substitute the value of x into the equation we were given for angle c:
angle c = 3(x+2)
angle c = 3(29+2)
angle c = 3(31)
angle c = 93
Therefore, angle c is equal to 93⁰.
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Which expresion has the greatest value when n is equal to 4
The expression that has the greatest value when n is equal to 4 is option B, n + 30, with a value of 34.
How do we calculate?To determine which mathematical expression has the greatest value when n is equal to 4, we can simply substitute 4 for n in each expression and compare the results.
A. 5n = 5(4) = 20
B. n + 30 = 4 + 30 = 34
C. 50 - n = 50 - 4 = 46
D. 80 ÷ n = 80 ÷ 4 = 20
The complete question is: Which expression has the greatest value when n is equal to 4? A. 5n B. n + 30 C. 50 – n D. 80 ÷ n
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find the area and perimeter of each figure below.
Answer:
finding the perimeter, you sumthe distance all round that is 7+7.5+17.8+6=38.3
38.3 is the perimeter
Find the compound interest on Rs. 3,500 for 2 years at the rate of 8% per annum.
Answer: The formula for compound interest is:
A = P(1 + R/100)^t
where A is the amount after t years, P is the principal amount, R is the rate of interest per annum, and t is the time period in years.
Here, P = Rs. 3,500, R = 8%, and t = 2 years.
So, the amount after 2 years will be:
A = 3,500(1 + 8/100)^2
= 3,500(1.08)^2
= 3,892.32
Therefore, the compound interest for 2 years will be:
CI = A - P
= 3,892.32 - 3,500
= 392.32
Hence, the compound interest on Rs. 3,500 for 2 years at the rate of 8% per annum is Rs. 392.32.
Step-by-step explanation:
A drawer contains 10 blue pens, 12 black pens, and 3 red pens. Without looking, Mr. Lopez is going to take one pen from the drawer, use it, and then put it back into the drawer. Then he is going to take another pen from the drawer to use. What is the probability of Mr. Lopez taking a red pen first and then taking a blue pen?
Answer: 4.8%
Step-by-step explanation: the total amount of pens in the drawer is (10+12+3) = 25
the amount of red pens in the drawer is 3
the probability of picking out a red pen from the drawer = 3/25
the amount of blue pens in the drawer is 10
the probability of picking out a red pen from the drawer = 10/25
the probability of picking out a red pen then a blue pen afterwards = (10/25 x 3/25) = 4.8%
PLEASE HURRY DUE TODAY WILL MARK BRAINLESTIS RIGHT
what is √29 Place a dot on the number line at the BEST approximation
Answer:
5.4
Step-by-step explanation:
square of 29 = 5.385164807
5.385164807 estimated is 5.4
solve y''+y=t using laplace inverse with y(0)=1 and y'(0)=-2
The solution of the differential equation y'' + y = t with the initial conditions y(0)=1 and y'(0)=-2 is y(t)= 1-2t+te-t.
What is equation?Equation is a mathematical statement that expresses the equality of two expressions. It shows the relationship between two or more variables and can be written using symbols, numbers, and operations. Equations are used to describe physical laws, to make calculations, and to solve problems. Examples of equations include the Pythagorean theorem, Newton's laws of motion, and linear equations.
We solve this differential equation using Laplace inverse, with the initial conditions y(0)=1 and y'(0)=-2. First, we take the Laplace transform of the equation:
L[y''+y]=L[t]
Using the properties of Laplace transform, we can write this as:
s2Y(s)-sy(0)-y'(0)+Y(s)= (1/s)
Substituting the initial conditions and rearranging terms, we have:
Y(s)= (1/s) + (2/s2) + (1/s2)
We can then invert the Laplace transform to get the solution of the original equation:
y(t)= 1-2t+te-t
Therefore, the solution of the differential equation y'' + y = t with the initial conditions y(0)=1 and y'(0)=-2 is y(t)= 1-2t+te-t.
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Rectangle MPAT has vertices M(1,2) , P(1, 3), A(3, 3), and T(3, 2) . Rectangle M’P’A’T . Which coordinates describe the vertices of the image?
The coordinates of the vertices of the image rectangle M'P'A'T' are:
M'(2,1), P'(3,1), A'(3,3), T'(2,3).
What is rectangle?
A rectangle is a geometric shape that has four sides and four right angles (90 degrees) with opposite sides being parallel and equal in length.
To find the coordinates of the vertices of the image rectangle M'P'A'T', we need to apply a transformation to each vertex of the original rectangle MPAT.
We can see that the original rectangle MPAT has sides parallel to the x and y-axes, which suggests that it is aligned with the coordinate axes. We can also see that the length of its sides are equal, which means it is a square.
To transform this square, we can use a combination of translations, rotations, and reflections. However, since we don't have any information about the type of transformation that is being applied, we can assume that the simplest transformation is a reflection across the line y=x.
To reflect a point (x,y) across the line y=x, we swap its x and y coordinates to get the reflected point (y,x). Therefore, the coordinates of the vertices of the image rectangle M'P'A'T' are:
M'(2,1)
P'(3,1)
A'(3,3)
T'(2,3)
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Help corrections due in 3 hours! giving 25 points and brainlist
The value of GH in the right angle triangle, given FH and Angle FHG is 22.46 inches.
How to find the value of GH ?Since we have the adjacent side (FH) and want to find the hypotenuse (GH), we can use the cosine function.
cos(35°) = adjacent side (FH) / hypotenuse (GH)
We know that FH = 18.4 in. So, we can write the equation as:
cos(35°) = 18.4 / GH
GH = 18.4 / cos(35°)
GH = 18.4 / 0.81915
= 22.46 inches
So, the length of GH, the hypotenuse, is approximately 22.46 inches.
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Suppose a supermarket ordered 13 cases of organic vegetable soup with a list price of $18.90 per case and 4 cases of organic baked beans with a list price of $33.50 per case. The wholesaler offered the supermarket a 39% trade discount. (Round your answers to the nearest cent.)
What is the total net amount (in $) the supermarket owes the wholesaler for the order?
The total net amount the supermarket owes the wholesaler for the order is $231.31.
What does discount mean?A discount is a reduction in the price of a product or service. It is often offered by businesses to encourage customers to buy more or to make a purchase they might not otherwise make. A discount can be expressed as a percentage or a specific dollar amount, and it is usually subtracted from the original price of the item or service.
According to the given informationTo find the total net amount the supermarket owes the wholesaler for the order, we need to first calculate the cost of each case of soup and baked beans after the 39% trade discount is applied, and then multiply those costs by the number of cases ordered.
The trade discount rate is 39%, which means the supermarket will receive a discount of 39% off the list price of each case of soup and baked beans. To calculate the cost of each case after the discount is applied, we can use the following formula:
Discounted cost = List price - (Discount rate x List price)
For the soup, the discounted cost per case is:
$18.90 - (0.39 x $18.90) = $11.51
For the baked beans, the discounted cost per case is:
$33.50 - (0.39 x $33.50) = $20.42
Now we can calculate the total net amount owed by the supermarket to the wholesaler:
Total net amount = (Number of cases of soup x Cost per case) + (Number of cases of baked beans x Cost per case)
Total net amount = (13 x $11.51) + (4 x $20.42)
Total net amount = $149.63 + $81.68
Total net amount = $231.31
Therefore, the total net amount the supermarket owes the wholesaler for the order is $231.31.
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I need help solving this thank you
The negation is the fourth option.
6 + 3 ≠ 9 or 6 - 3 ≠ 9
How to write the negation?The negation of an equation is an inequality such that we just change the equal sign, by the "≠" sign.
Here we start with the two equations.
6 + 3 = 9 or 6 - 3 = 9
Just change the equal signs for different signs:
6 + 3 ≠ 9 or 6 - 3 ≠ 9
That is the negation, fourth option.
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3) Given the formula F=ma where * F represents force, *m represents mass and has units of kilograms (kg), and • a represents acceleration and has units of meters per second squared (). Select an appropriate measurement unit for force.
The appropriate measurement unit for force is kg.m/s²
What is the appropriate measurement unit for force?A force is simply referred to as either a push or pull of an object resulting from the object's interaction with another object.
From Newton's Second Law, force is expressed as;
F = m × a
Where is mass of object and a is the acceleration
One Newton is defined as the force required to accelerate a mass of one kilogram at a rate of one meter per second squared.
Since F = m × a
Plug in m = kg and a = m/s²
F = kg × m/s²
F = kg.m/s²
Therefore, the unit of measurement is kg.m/s².
Option B is the correct answer.
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As seen in the diagram below, Austin is building a walkway with a width of x feet to go around a swimming pool that measures 8 feet by 10 feet. If the total area of the pool and the walkway will be 360 square feet, how wide should the walkway be?
Using the total area of the rectangular pool we know that the required width of the pathway is 3.6 ft respectively.
What is a rectangle?In the Euclidean plane, a rectangle is a quadrilateral with four right angles.
A parallelogram with a right angle or an equiangular quadrilateral, where equiangular means that all of its angles are equal, are other ways to define it.
A rectangle with four equal-length sides is a square.
Squares are not always rectangles, but rectangles are always squares.
So, the pool and walkway together have a 360 square foot total space.
Assume that the walkway is w feet in width.
Since the pool has an additional w feet of width on both sides, the total area's measurements can be expressed as (8 + 2w) by (10 + 2w).
Thus, we can construct the following equation:
(8 + 2w) x (10 + 2w) = 360
By enlarging and condensing the left side, we obtain:
4w² + 36w - 80 = 0
Using the quadratic formula, we can find w:
w = (-b ± √(b² - 4ac)) / 2a
Here, an equals 4, b equals 36, and c equals -80. When these values are added to the formula, we obtain:
w = (-36 ± √(36² - 4(4)(-80))) / 8
w = (-36 ± √(1872)) / 8
w ≈ -5.6 or w ≈ 3.6
We can ignore the first option because the width cannot be negative. Consequently, the pathway should be around 3.6 feet wide.
Therefore, using the total area of the rectangular pool we know that the required width of the pathway is 3.6 ft respectively.
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Solve for x.
A. 7
B. 4
C. 3
D. 5
The correct option -D. 5; Thus, the value of x for the given external secant segment and the tangent on the circle is found as:x = 5.
Explain about the secant of circle:A line that precisely intersects a circle at two points is said to be a secant.
The size of the angle created when two tangents, two secants, or two tangents cross outside of a circle is equal to one-half a positive difference between the sizes of the intercepted arcs.
Using the Theorem:
The square of a length of tangent is equal the the product of such external secant segment and the overall length of the secant if one secant and one tangent both drawn to a circle from a single exterior point:
4(4 + x) = 6²
16 + 4x = 36
4x = 36 - 16
4x = 20
x = 20/4
x = 5
Thus, the value of x for the given external secant segment and the tangent on the circle is found as:x = 5.
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Help please i dont know
The histogram should be modified as follows:
The bin from 6 to 15 should be increased by 2.The bin from 16 to 25 should be increased by one.The bin from 26 to 35 should be increased by one.The bin from 46 to 55 should be increased by one.What is shown by an histogram?A histogram is a type of graphical representation that displays the distribution of a dataset. It is a bar graph-like chart where the data is divided into intervals, called "bins", which are represented by adjacent rectangular bars of varying heights.
Then the height of the histogram gives the number of observations into each data interval.
Hence the histogram should be modified as follows:
The bin from 6 to 15 should be increased by 2. -> two measures of 12.The bin from 16 to 25 should be increased by one. -> measure of 16.The bin from 26 to 35 should be increased by one. -> measure of 26.The bin from 46 to 55 should be increased by one. -> measure of 48.More can be learned about histograms at https://brainly.com/question/25983327
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Problem 7: Find the surface area and round to the nearest tenth.
Answer:
1629.24m
Step-by-step explanation:
starting with the easy ones
1) Rectangle 1:
Surface area of rectangle=Length x width
SAR= 24x21
= 504m
2) Rectangle 2:
SAR= 19x21
=399
3) Rectangle 3
SAR= 21x8
=168
4) Rectangle 4:
SAR= 21x11
=231
*because the top and bottom are trapeziums the formular for it is
A=1/2(a+b)h
although those trapeziums don't have h(Height)
it needs to be broken down into two triangles and a rectangle. to find the height*
5) side/height of triangle A:
formula: C squared= a squared + b squared
in this case we already have C and A. meaning we have to rearrange the formula to:
x = c^2 - a^2
x = 8^2 - 2.5^2
x = sqrt 57.75
x = 7.61
6) Trapezium
SA= 1/2(a+b)h
SA= 1/2(19+24)7.61
=163.62
7) add all surface area together
which should equal 1629.24m