If Riders have to climb a m staircase to board the ride at its lowest point.
a. sine function for the height of Emma, who is at the very top of the ride when t = 0 is: h(t) = 60 sin(π/6 t).
b. a cosine function for Eva, who is just boarding the ride is: h(t) = m + 60 cos(π/6 t).
c. a sine function for Matthew is: h(t) = 30 sin(π/6 t).
What is the sine function for the height of Emma?(a) Let's assume that the Ferris wheel completes one full revolution in 12 minutes. The height of the Ferris wheel can be modeled by a sine function as it moves up and down periodically. When the Ferris wheel completes one revolution, it returns to its original position, so the period of the sine function is 12 minutes.
The maximum height of the Ferris wheel is 60 m, so the amplitude of the sine function is 60 m. When t = 0, Emma is at the very top of the ride, which means she is at the maximum height of the Ferris wheel. Therefore, the sine function for Emma's height, h(t), can be written as:
h(t) = 60 sin(2π/12 t)
Simplifying this equation, we get:
h(t) = 60 sin(π/6 t)
(b) Eva is just boarding the ride, which means she is at the lowest point of the ride when t = 0. The cosine function is ideal for modeling this situation, as it starts at its maximum value and reaches its minimum value after one-fourth of the period. Therefore, the cosine function for Eva's height, h(t), can be written as:
h(t) = m + 60 cos(2π/12 t)
Simplifying this equation, we get:
h(t) = m + 60 cos(π/6 t)
where m is the height of the staircase that Eva has to climb to board the ride.
(c) Matthew is at the same height as the central axle of the Ferris wheel, which means he is halfway between the maximum and minimum height of the ride. Therefore, the sine function for Matthew's height, h(t), can be written as:
h(t) = 30 sin(2π/12 t)
Simplifying this equation, we get:
h(t) = 30 sin(π/6 t)
Therefore sine function for the height of Emma, who is at the very top of the ride when t = 0 is: h(t) = 60 sin(π/6 t).
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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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In triangle BC, point D is on AC such that AD = 12 and CD = 12. If angle ABC = angle BDC = 90 degrees, then what is BD?
Answer:
Step-by-step explanation:
BD is craxking treys and cracking treys is gd dissing bd you can look it up i ffrom o block and bd is the opps im telling so you wont lose yo life so please play right if you gdk be gdk if u gd be gd we aint bd ofn
An economy is operating with output $400 billion above its natural level, and fiscal policymakers want to close this expansionary gap. The central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. The marginal propensity to consume is 3/4, and the price level is completely fixed in the short run.
to close the expansionary gap, the government would need to increase or decrease spending by $ billion.
Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.
To close the expansionary gap, the government would need to decrease spending by $100 billion.
The formula to calculate the change in equilibrium output due to a change in government spending is:
∆Y = (∆G / (1 - MPC))
Where:
∆Y = change in equilibrium output
∆G = change in government spending
MPC = marginal propensity to consume
Here, the output is $400 billion above its natural level, and the central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. Therefore, we can assume that the change in government spending (∆G) would have a one-to-one effect on the equilibrium output (∆Y).
Given that MPC = 3/4, we can plug in the values into the formula:
400 = (∆G / (1 - 3/4))
∆G = (1 - 3/4) * 400
∆G = (1/4) * 400
∆G = 100
Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.
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Prove: DC = 6 units
A
6 units
D
Statements
AD || BC
ZDAC ZBCA
C
?
DC BA
DC = BA
given
alternate interior angles theorem
AC AC
reflexive property of congruence
ZDCA ZBAC alternate interior angles theorem
DC = 6 units
Which step is missing?
B
O A. ADAC
OB. ADCA
O C. ADCA
Reasons
?
CPCTC
definition of congruent sides
substitution property of equality
ABCA by SAS
ABCA by ASA
ABCA by SAS
The missing step in the proof is: D. ADCA
What is the missing step and reason of the proof?In the statements, we are given that AD || BC and ZDAC = ZBCA (alternate interior angles theorem), so we can conclude that triangle ADCA is similar to triangle BCA (by AA similarity criterion).
Therefore, we have the following proportional sides:
DC/AC = AC/BC
Given that DC = BA (given statement), we can substitute BA for DC in the proportion:
BA/AC = AC/BC
Now, we can cross-multiply to get:
BA * BC = AC²
Using the given statement that AC = AC (reflexive property of congruence), we can substitute AC for AC in the equation:
BA * BC = AC * AC
Use the definition of congruent sides to replace BA with DC:
DC * BC = AC * AC
And finally, use the substitution property of equality to replace BC with 6 units (given statement):
DC * 6 = AC * AC
From this equation, we can see that DC = 6 units, which completes the proof. Therefore, the missing step is statement D. ADCA.
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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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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:
3. How many ways can you line up 7 books on a shelf?
Answer:
There are 5040 different ways to arrange the 7 books on a shelf.------------------------------
Use the formula for permutations:
n! = n × (n - 1) × (n - 2) × ... × 1, where n is the number of objects and ! denotes a factorial.The number of objects is n = 7 books.
Calculate the factorial:
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040Find the area of a rectangle with length 4.3 cm and breadth 3.9 cm
Answer:
16.77 cm²
Step-by-step explanation:
Area of rectangle = L x W
L = 4.3 cm
Width = 3.9 cm
Let' solve
4.3 x 3.9 = 16.77 cm²
So, the area of the rectangle is 16.77 cm²
3√b in exponential form
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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What is the perimeter of the triangle?
Answer:
40 units
Step-by-step explanation:
a = 8
b = 15
To find c, we can use the formula: [tex]a^{2} +b^{2} =c^{2}[/tex]
[tex]8^{2} +15^{2} =x^{2}[/tex]
64 + 225 = c^2
289 = c^2
c = 17
a + b + c = perimeter
8 + 15 + 17 = 40
Answer:
40 units
Step-by-step explanation:
You want the perimeter of the triangle shown in the graph.
DimensionsYou can count the grid squares to find the horizontal and vertical dimensions of the triangle. You find they are 8 units and 15 units, respectively.
The length of the slant side is the hypotenuse of a right triangle with sides 8 and 15. If you don't recognize this {8, 15, 17} Pythagorean triple, you can find the hypotenuse using the Pythagorean theorem:
c² = a² +b²
c² = 8² +15² = 64 +225 = 289
c = √289 = 17
The long side of the triangle is 17 units.
PerimeterThe perimeter of the triangle is the sum of the lengths of its sides:
P = 8 + 15 + 17 = 40
The perimeter is 40 units.
__
Additional comment
A "Pythagorean triple" is a set of three integer side lengths that form a right triangle. The triple is "primitive" if the numbers have no common factor. There are a few Pythagorean triples that regularly show up in algebra, trig, and geometry problems. Some of them are ...
{3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}
You will also see multiples of these, for example, 2·{3, 4, 5} = {6, 8, 10}.
The smallest is {3, 4, 5}, and it is the only set that is an arithmetic sequence (has constant differences between lengths). In every case, the sum of the numbers is even. (A right triangle cannot have integer side lengths and an odd perimeter value.)
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
1:20 - salesman allows a 5% discount for cash payment. What will be the discount allowed for a ash payment of GH¢5,600.00? A. GH 250.00
The discount allowed for a cash payment of GH 5,600.00 is given as follows:
GHC 280.00.
How to obtain the discount?The discount allowed for a cash payment of GH 5,600.00 is obtained applying the proportions in the context of the problem.
There is a 5% discount, hence the value of the discount is obtained as follows:
0.05 x 5600 = GHC 280.00.
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On the Y axis, we have the profit from the trucking company and on the X axis, we have the miles the truck has traveled. The company decided that they needed to start paying for a driver at a price of 0.25 cents a mile. After this change what will happen to the x and y axis/slope?
A. Y intercept will be less and X will be less
B. Y intercept will be less and X intercept will be greater
C. Y intercept will be greater and X will be greater
D. Y intercept will be greater and X will be less
Answer:
B.
Step-by-step explanation:
Answer:
B.
Step-by-step explanation:
the description is very confusing and lacks any hint about the behavior of the curve before the change.
but ok, let's assume that the curve (line ?) is in general going up. in other words, if the traveled miles go up, so does the profit.
I also don't know how they could drive the miles without paying the driver, but again, let's assume they did.
now they pay the driver. $0.25 per mile.
this has to come out of their profit.
so, the Y (profit) values all go down by 0.25.
therefore, the y-intercept is going down too.
that eliminates C. and D.
for this to be true they have to have some overhead costs that apply even if there are 0 miles traveled (which is the meaning of the y-intercept : the y-value when x = 0).
so, the line must be in a form
y = ax + b
with "b" <> 0.
and since we assumed the line to go up (positive slope), a "sinking" line means that the x-intercept (the break-even point, where the line goes from below the x-axis and therefore negative (y) profit up into positive profit) will move to the right (become greater).
because now that they have additional costs (paying the driver), it takes longer (more driven miles) to make a positive profit.
and that eliminates A, leaving B. as the right answer.
Jeremy and Aksa were finding the volume of this prism. They agreed that 4 layers can be added together to find the volume. Jeremy says that he can see on the end of the prism that each layer will have 16 cubes in it. Aksa says that each layer has 24 cubes in it. Who is right? Explain your answer.
Both Jeremy and Aksa could be right, depending on how they are counting the cubes for finding the volume of a prism.
What is a prism?A prism is a three-dimensional solid shape with a constant cross-section, usually a polygon. It is characterized by two identical end faces, parallel and congruent bases, and straight lateral faces connecting the bases.
According to the given information:Both Jeremy and Aksa could be right, depending on how they are counting the cubes.
If the prism has a square base with 4 cubes along each side, then there would be 16 cubes in each layer. If there are 4 layers, then the total volume would be 16 x 4 = 64 cubic units.
However, if the prism has a rectangular base with 6 cubes along one side and 4 cubes along the other side, then there would be 24 cubes in each layer. If there are 4 layers, then the total volume would be 24 x 4 = 96 cubic units.
Therefore, the answer depends on the shape of the prism and how the layers are counted.
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^4√p7
in exponential form.
Answer:1111
Step-by-step explanation:
Triangle PQR is rotated 180 degrees clockwise about the origin to produce the image Triangle P’Q’R’. Which of the following statements is TRUE abóyate Triangle P’Q’R’.
Answer:
Step-by-step explanation:
We get triangle PQR by plotting the point P (1, 4), Q (3, 1), R (2, -1) on the graph paper when rotated through 180° about the origin. The new position of the point is: P (1, 4) → P' (-1, -4) Q (3, 1) → Q' (-3, -1) R (2, -1) → R' (-2, 1) Thus, the new position of ∆PQR is ∆P’Q’R’.
Please help and hurry
The equation of the parabola with vertex at point (2, -11) and passes through the point (0, 5) is y = 4(x - 2)² - 11.
What is linear and quadratic equation?A straight line can be used to symbolise a function that is linear, meaning that for each unit change in the input, the output (y) changes by a fixed amount (x). While a parabola can be used to depict a function, a quadratic function has an output (y) that changes by a non-constant amount for each unit change in the input (x). In other words, a quadratic function curves because of the squared term in its equation.
Given, the parabola has vertex at point (2, -11) and passes through the point (0, 5).
Thus, the equation of parabola in vertex form is:
y = a(x - 2)² - 11
Now, the parabola passes through the point (0, 5) we have:
5 = a(0 - 2)² - 11
5 = 4a - 11
16 = 4a
a = 4
Hence, the equation of the parabola with vertex at point (2, -11) and passes through the point (0, 5) is y = 4(x - 2)² - 11.
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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:
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! :)
The sum of a number and three is no more than eight
Answer:5
Step-by-step explanation: hope this helps
whats the answer to 102-38x14 divided by 7+162= help plss
Answer:
-2.5
Step-by-step explanation:
follow BIMDAS.
like my answer if you find it helpful
Which of the numbers 0, 1, 2, 3 or 4 make the equation 8/y2 + 2 true?
None of the given numbers make the equation 8/y² + 2 true.
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
To solve this problem, we can substitute each of the given numbers (0, 1, 2, 3, 4) for y in the equation 8/y² + 2 and see if the equation is true.
Substituting y=0 would make the denominator of the fraction zero, which is undefined, so y=0 is not a valid choice.
Substituting y=1 would give us:
8/1² + 2 = 8 + 2 = 10
So, 1 is not the answer.
Substituting y=2 would give us:
8/2² + 2 = 8/4 + 2 = 2 + 2 = 4
So, 2 is not the answer.
Substituting y=3 would give us:
8/3² + 2 = 8/9 + 2 = 0.888 + 2 = 2.888
So, 3 is not the answer.
Substituting y=4 would give us:
8/4² + 2 = 8/16 + 2 = 0.5 + 2 = 2.5
So, 4 is not the answer.
Therefore, none of the given numbers make the equation 8/y² + 2 true.
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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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1. You go to the ice cream shop with your friends and you can choose an ice cream, a topping
and sprinkles. How many different sundaes can you make when you order one flavor of ice
cream, one topping and one color of sprinkles from the chart below? Show all possible
outcomes in a tree diagram.
Ice Cream
Chocolate
Vanilla
Strawberry
Topping
Fudge
Marshmallow
Sprinkles
Chocolate
Rainbow
How many sample spaces are there? HINT: How many possible combinations?
b. P (Chocolate, Fudge, Rainbow)
Answer:
Step-by-step explanation:
Answer:
You can make 12 possible sundaes with these toppings.
Step-by-step explanation:
Chocolate, Vanilla, and Strawberry all have 4 possible outcomes:
1. Fudge & Chocolate Sprinkles
2. Fudge & Rainbow Sprinkles
3. Marshmallow & Chocolate Sprinkles
4. Marshmallow & Rainbow Sprinkles
-------------------------------------------------------------------------------------------------------------
4 x 3 will equal 12, the total possible sundaes you can make with these toppings and ice cream flavors.
Will mark brainliest if answer is correct
Answer:
[tex]3( {2}^{2} ) - {2}^{2} + 4 = 12[/tex]
[tex] {2}^{3} + b( {2}^{2} ) + 43(2) - 126 = 4b - 204[/tex]
[tex]4b - 32 = 12[/tex]
[tex]4b = 44[/tex]
[tex]b = 11[/tex]
For this value of b, these graphs will intersect at (2, 12). Please use your graphing calculator to confirm that this is the only point of intersection.
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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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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The sum of 2 vector forces is <5, -3>. What is the magnitude of the resulting force?
According to the question the magnitude of the resulting force is 5.83.
What is magnitude?Magnitude is a measure of the size or intensity of a physical quantity. It is an expression of how large or small a quantity is in comparison to a reference value. Magnitude is typically used in physics and astronomy, but it can also be used in other areas such as engineering and seismology. Magnitude is not an absolute measurement; rather, it is a relative measure of how much larger or smaller one quantity is compared to another. For example, the magnitude of a star's brightness is a measure of how much brighter it is compared to other stars.
The magnitude of the resulting force can be calculated using the Pythagorean theorem. The formula for calculating the magnitude of a vector is:
[tex]\sqrt[]{(x2 + y2)}[/tex]
In this case, x = 5 and y = -3, which gives us:
[tex]\sqrt{(52 + (-3)2)}[/tex] = [tex]\sqrt{(25 + 9)}[/tex] = √[tex]\sqrt{(34)}[/tex] = 5.83.
Therefore, the magnitude of the resulting force is 5.83.
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