Answer:
The value of t that will satisfy the equation is π/6 (which is 30 degrees)
Step-by-step explanation:
The function that models the movement of the particle is given as;
S(t) = 2 sin(t) + 3 cos (t)
Now we want to the value of t between 0 and pi/2 that satisfies the equation;
s(t) = (2+ 3√3)/2 = 1 + 3√3/2
What we do here is simply find that value of t that would ensure that;
2sin(t) + 3cos(t) = 1 + 3√3/2
Without any need for rigorous calculations, this value of t can be gotten by inspection.
From our regular trigonometry, we know that the sin of angle 30 is 1/2 and its cos value is √3/2
We can make a substitution for it in this equation.
We obtain the following;
2 sin(30) + 3cos (30) and that is exactly equal to 1 + 3√3/2
Do not forget however that we have a range. And the range in question is between 0 and π/2
Kindly that π/2 in degrees is 90 degrees
So our range of values here is between 0 and 90 degrees.
So to follow the notation in the question, the value within the range that will satisfy the equation is π/6
“a railroad bridge spans a gorge 40 feet wide and connects two cliffs at heights of 98 and 158 feet above the bottom of the gorge. a train is crossing this gorge from the higher cliff to the lower. when the front of the train has traveled three-fourths of the bridge's length, how many feet is it above the bottom of the bottom of the gorge?”
Answer:
Height above the bottom gorge is 113 feet
Step-by-step explanation:
The width of the gorge = 40 feet
The height of the higher cliff = 158 feet
The height of the lower cliff = 98 feet
The length of the bridge = √((158-98)² + 40²) = 72.11 feet
The slope of the bridge = (158-98)/40 = 1.5
The length of 1/4 of the bridge from the lower cliff =72.11 - 3/4×72.11 = 18.03 feet
The angle of inclination of the bridge = tan⁻¹(1.5) = 56.31°
The height above the bottom at 3/4 from the higher cliff = The height above the bottom at 1/4 from the lower cliff = 98+ 18.03×sin(56.31 ) = 113 feet
Which can also be found directly from the heights of the two cliffs knowing that 3/4 from the higher cliff = 1/4 from the lower cliff giving;
Height above the bottom gorge = 98 + 1/4×(158 - 98) = 113 feet.
With steps... Thanks..
Answer:
[tex]\boxed{-25x-y}[/tex]
[tex]\boxed{-p^2q +5pq^2}[/tex]
Step-by-step explanation:
[tex](-15x+6y)-(10x+7y)[/tex]
Distribute negative sign.
[tex]-15x+6y-10x-7x[/tex]
Combine like terms.
[tex]\boxed{-25x-y}[/tex]
[tex]2pq(p+q)- (3pq(p-q))[/tex]
Expand brackets.
[tex]2p^2 q+2pq^2 -(3p^2q-3pq^2)[/tex]
Distribute negative sign.
[tex]-3p^2q+3pq^2+2p^2q+2pq^2[/tex]
Combine like terms.
[tex]\boxed{-p^2q +5pq^2}[/tex]
Answer:
a. -25x - yb. pq ( - p + 5q )Step-by-step explanation:
a.
[tex] - 15x + 6y - (10x + 7y)[/tex]
When there is a (-) in front of an expression in parentheses, change the sign of each term in the expression
[tex] - 15x + 6y - 10x - 7y[/tex]
Collect like terms
[tex] - 15x - 10x + 6y - 7y[/tex]
[tex] - 25x - y[/tex]
b.
[tex]2pq(p + q) - 3pq(p - q)[/tex]
Factor out pq from the expression
[tex]pq(2(p + q) - 3(p - q))[/tex]
Distribute 2 through the parentheses
[tex]pq \: (2p + 2q - 3(p - q)[/tex]
Distribute -3 through the parentheses
[tex]pq \: (2p + 2q - 3p + 3q)[/tex]
Collect like terms
[tex]pq( - p + 5q)[/tex]
Hope this helps...
Best regards!!
The right isosceles triangle shown is rotated about line k with the base forming perpendicular to k. The perimeter of the triangle is 58 units. Which best describes the resulting three-dimensional shape?
Answer:
The new shape will be cone with a radius of 17 units, tilt height 24 and units of height k.
Step-by-step explanation:
The image related to the exercise is necessary, to be able to solve therefore the attached one.
We have the following information:
Perimeter of the triangle = 58 units
Hypotenuse = 24 units
We have that the other two sides are equal and have x units, therefore we have the following:
x + x + 24 = 58
2 * x = 58-24
2 * x = 34
x = 34/2
x = 17
Now the triangle rotates around line k , and then it will result in a cone, which is a three-dimensional shape.
Therefore, the new shape will be cone with a radius of 17 units, tilt height 24 and units of height k.
Answer:
Cone with a radius of 17 units
If a test has 40 questions and you get 200 points for the whole test, how many points are each question worth?
Answer:
5
Step-by-step explanation:
To find the points for each question, you must divide the number of points (200) by the number of questions (40) to get the number of points for each question
[tex]\frac{200}{40}[/tex]
Divide 200 by 40 to get
[tex]\frac{5}{1}[/tex] or [tex]5[/tex]
Hope this helps. If you have any follow-up questions, feel free to ask.
Have a great day!
Answer:
5 points
Step-by-step explanation:
200points / 40 questions = 5points/1question
then:
1 questión worths 5 points
Example 2
A black die and a white die are thrown at the same
time. Display all the possible outcomes. Find the
probability of obtaining:
a) a total of 5
b) a total of 11
c) a 'two' on the black die and a six' on the white die.
It is convenient to display all the possible outcomes
on a grid. This is called a possibility diagram
It’s example 2 please help:)
Answer:
Total possible outcomes = 6×6 = 36
a) P(5) = 1/9
b) P(11) = 1/18
c) P(two and six) = 1/36
Step-by-step explanation:
A black die and a white die are thrown at the same time.
Each die has six sides so total possible outcomes are
Total possible outcomes = 6×6 = 36
The possible outcomes are given below:
(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
a) Find the probability of obtaining a total of 5
Number of ways to get a total of 5 = (1, 4) (2, 3) (3, 2) (4, 1)
Number of ways to get a total of 5 = 4
The probability is given by
P = Number of desired outcomes/total number of outcomes
P(5) = 4/36
P(5) = 1/9
b) Find the probability of obtaining a total of 11
Number of ways to get a total of 11 = (5, 6) (6, 5)
Number of ways to get a total of 11 = 2
The probability is given by
P(11) = 2/36
P(11) = 1/18
c) a 'two' on the black die and a six' on the white die.
There is only one way to get a two on the black die.
Probability of obtaining a two on the black die = 1/6
There is only one way to get a six on the white die.
Probability of obtaining a six on the white die = 1/6
P(two and six) = 1/6×1/6
P(two and six) = 1/36
A stick has a length of $5$ units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are longer than $1$ unit?
Answer:
4/25 = 0.16
Step-by-step explanation:
The shortest stick must be between 0 and 5/3. The probability that it is longer than 1 is therefore:
(5/3 − 1) / (5/3 − 0)
(2/3) / (5/3)
2/5
So the probability that both of the shortest sticks are longer than 1 is (2/5)² = 4/25.
Find the value of x.
x = 64°
Step-by-step Explanation
x = 1/2[(360° - 2*58°)-2*58°]
x = 1/2[(360° - 2*58°) - 2*58°]
x = 1/2[(360° - 116°) - 116°]
x = 1/2[244° - 116°]
x = 1/2[128°]
x = 64°
label missing angles 1, 2, 3, 4, and 5 if lines ‘m’ and ‘n’ are parallel
Answer:
see attached diagram
Step-by-step explanation:
1. 1 and 70 are angles on a line (supplementary)
2. vertical angles with 70
3. angles on a line are supplementary
4. 2 and 4 are supplementary interior angles between parallel lines m & n
5. corresponding angle with 70
Explain how you would decide whether to use a dot plot or a box plot to display a data set. Give some strengths and weaknesses of each type of display to support your explanation.
Answer:
A box plot should be used in a situation when you need the median and quartiles. A dot plot should be used when you need exact numbers. The strengths of a box plot is that it shows a big data sets into a rounded form. The strengths of a data set is that you can show the exact numbers but it would work best with small numbers.
Hope this helped?
aljebra questions anum counted the money she had in her purse and money box . When she doubbled the amount in her purse and add it to the amount in money box she gets rs 1700 . When she triples the amount in her purse and add in to money box she gets rs 2200. How much money does she have in her purse
Answer:
Money in her purse is Rs. 500.
Step-by-step explanation:
Let the money in her purse = Rs. [tex]x\\[/tex]
Let the money in her Money box = Rs. [tex]y[/tex]
As per question statement,
Double the money in her purse (i.e. [tex]2 \times x[/tex]) and add it to the amount in money box, she gets Rs. 1700.[tex]2x+y=1700[/tex] ........ (1)
Triple the money in her purse (i.e. [tex]3\times x[/tex]) and add it to amount in money box ([tex]y[/tex]), she gets Rs. 2200.[tex]3x+y=2200[/tex] ....... (2)
To find: Money in her purse = ? i.e. [tex]x=?[/tex]
Let us solve for [tex]x[/tex] using the two linear equations.
We can use substitution method here i.e. find value of one variable from one equation and then substitute that value in other equation.
Using equation (1), we get the value of [tex]y[/tex] as follows:
[tex]y=1700-2x[/tex]
Now, let us put this value of y in equation (2) to find the value of [tex]x[/tex]:
[tex]3x+1700-2x=2200\\\Rightarrow x+1700 = 2200\\\Rightarrow x=2200-1700\\\Rightarrow x = Rs.\ 500[/tex]
Money in her purse is Rs. 500.
1. A test-tube has a diameter of 3cm. How many turns would a piece of thread of length
90.42cm make round the test tube. (Taken= =).
(3marks)
So if we think of a test tube, it looks sort of like a cylinder. This means that its cross-section would be a circle. To find out how many turns a piece of thread would make around the test tube, we need to find the circumference of the test tube, then divide the length of the string by the circumference.
Step 1) Find the circumference
C = pi x diameter
C = 3.14 x 3
C = 9.42
Step 2) Divide the length of the string by the circumference
90.42 / 9.42 = 9.5987
The string would make approximately 9.60 turns around the test tube.
Hope this helps!! :)
Please answer the question correct only if you know the answer
Use the law of cosines to solve for side g.
g^2 = e^2 + f^2 - 2*e*f*cos(G)
g^2 = 10^2 + 8^2 - 2*10*8*cos(57)
g^2 = 76.85775 ... make sure your calc is in degree mode
g = sqrt(76.85775)
g = 8.766855
g = 8.8
PLEASE HELP I NEED HELP FAST ILL ALSO THANK AND MARK AS BRAINLIEST IF U ANSWER ALL OF THEM WITH AT LEAST MOST OF THEM CORRECT Find the original price if the price was: $3b after a 70% discount. What number : Increased by 75% is 35? Find the original price if the price was: $8a after a 60% increase?
Answer:
1) $10b
2) 20
3) $5a
Around which line would the following cross-section need to be revolved to create a sphere? circle on a coordinate plane with center at 1 on the y-axis and a radius of 1
Answer:
y= 1
Step-by-step explanation:
A circle forms a sphere only when it goes around a straight line throughout the center so y= 1 because it's (1,0).
The y = 1 is the axis around which the circle cross-section needs to be revolve to create a sphere.
It is given that the circle is on a coordinate plane with the centre at 1 on the y-axis.
It is required to find around which line would the following cross-section need to be revolved to create a sphere.
What is a circle?It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the centre of a circle).
We have a circle on the coordinate plane the centre of the circle lies on the y-axis at 1.
On y=axis the value of x is zero ie. x= 0
The centre of the circle = (0,1)
If a half-circle revovle around the axis which is dividing the circle into two halves.
As we can see in the graph the y-axis and y=1 divide the circle into two halves.
Thus, the line y = 1 is the axis around which the circle cross-section needs to be revolve to create a sphere.
Learn more about circle here:
brainly.com/question/11833983
at the rate of 15 per 6 oz. bar of chocolate, how much would a pound
Answer:
40
Step-by-step explanation:
We know there are 16 oz in a pound
We can use ratios
15 x
----- = ----------
6 oz 16 oz
Using cross products
15 * 16 = 6x
240 = 6x
divide by 6
240/6 = 6x/6
40 =x
3x (4x^2 + 4xy + 5y - 6) = ?
Answer:
12x^3 + 12x^2y + 15xy - 18x
Step-by-step explanation:
I simply expanded the equation by multiplying everything in the parentheses by 3x.
Answer:
12x^3+12x^2y+15xy-18x
Step-by-step explanation:
3x (4x^2 + 4xy + 5y - 6)
Distribute
3x *4x^2 +3x* 4xy + 3x*5y -3x* 6
12x^3+12x^2y+15xy-18x
Please help I’m being timed!! The computer rendering of a mural in a town’s square uses the function represented in the table to define the outline of a mountain in the town’s logo, where x is the distance in feet from the edge of the mural and f(x) is the distance from the ground in feet. How can the point (12, 16) be explained? A) The highest point of the mountain defined by the function is 12 feet. B) The highest point of the mountain defined by the function is 16 feet. C) The width of the base of the mountain defined by the function is 12 feet. D) The width of the base of the mountain defined by the function is 16 feet.
Answer:
The correct option is;
B) The highest point of the mountain defined by the function is 16
Step-by-step explanation:
From the given information, we have;
The distance in feet from the edge of the mountain is given as the independent variable, x
The distance in feet from the ground (which is the height) is given the as the dependent variable f(x)
Therefore, given that the point (12, 16) are the values of x and f(x) such that x = 12 and f(x) = 16 and 16 is the largest value of f(x) in the data, therefore, 16 represents the highest defined point of the mountain.
i need help with this please
Answer:
supplementary
Step-by-step explanation:
Since a and b form a straight line, they will add to 180 degrees
Two angles that add to 180 degrees are supplementary angles
What is the determinant of the coefficient matrix of the system –7 –2 –1 0
Answer:
0
Step-by-step explanation:
Please check attachment for complete solution
Answer:
D. 0
Step-by-step explanation:
last option
Please answer this question now
Answer:
[tex] Area = 400.4 m^2 [/tex]
Step-by-step Explanation:
Given:
∆UVW,
m < U = 33°
m < V = 113°
VW = u = 29 m
Required:
Area of ∆UVW
Solution:
Find side length UV using Law of Sines
[tex] \frac{u}{sin(U)} = \frac{w}{sin(W)} [/tex]
U = 33°
u = VW = 29 m
W = 180 - (33+113) = 34°
w = UV = ?
[tex] \frac{29}{sin(33)} = \frac{w}{sin(34)} [/tex]
Cross multiply
[tex] 29*sin(34) = w*sin(33) [/tex]
Divide both sides by sin(33) to make w the subject of formula
[tex] \frac{29*sin(34)}{sin(33)} = \frac{w*sin(33)}{sin(33)} [/tex]
[tex] \frac{29*sin(34)}{sin(33)} = w [/tex]
[tex] 29.77 = w [/tex]
[tex] UV = w = 30 m [/tex] (rounded to nearest whole number)
Find the area of ∆UVW using the formula,
[tex] area = \frac{1}{2}*u*w*sin(V) [/tex]
[tex] = \frac{1}{2}*29*30*sin(113) [/tex]
[tex] = \frac{29*30*sin(113)}{2} [/tex]
[tex] Area = 400.4 m^2 [/tex] (to nearest tenth).
Yesterday, a factory used (2)/(3) of a tub of peanut butter. They use 16 of a tub of peanut butter for each batch of peanut butter cookies. How many batches of peanut butter cookies did the factory make yesterday? help!
Answer:
4 batches
Step-by-step explanation:
1/3=2/6, 2/3=4/6
Which is the correct algebraic expression after combining like terms? 6 + 8 x minus 7 minus x 7 x minus 1 7 x + 13 9 x minus 1 9 x + 13
Answer:
7x-1
Step-by-step explanation:
i did the test
Answer:
7x-1
Step-by-step explanation:
correct answer on edge
I have a lot of questions like this, and I know the formula but I still get it wrong!
Answer: 4
Step-by-step explanation: use pick’s theorem to solve.
I+B/2-1.
We can substitute the variables with our information from the graph:
0+10/2-1=5-1=4 that’s the answe
Hope this helps
(-y^5)(8y^2) and (-7^5)(9y) and (-7^5)(-5)
Answer:
[tex]-8y^{25}\\-9y^6\\5y^5[/tex]
Step-by-step explanation:
First one.
[tex]((-y)^5)(8y^{20})=-y^5*8y^{20}=-8y^{5+20}=-8y^{25}[/tex]
Second one
[tex]((-y)^{5} )(9y)=-y^5*9y=-9y^{5+1}=-9y^6[/tex]
and last one
[tex]((-y)^5)(-5)=-y^5*(-5)=5y^5[/tex]
Which of these r-values represents the strongest correlation?
A. -0.7
B. -0.8
C. -0.6
D. -0.5
I guess the answer is D because it is the most far from -1 rather than the other
Answer: The answer should be D.-0.5
can someone help me with this?
Answer:
-5z^3-z^4+4z^5
Can someone help me with this one too
Answer:
A. [tex] 3 {}^{9} [/tex]
Step-by-step explanation:
[tex]3 {}^{4} \times {3}^{5} = {3}^{4 + 5} = 3 {}^{9} [/tex]
Hope this helps ;) ❤❤❤
Answer:
[tex]\boxed{3^9}[/tex]
Step-by-step explanation:
[tex]3^5 \times 3^4[/tex]
Apply the law of exponents : [tex]a^b \times a^c = a^{b+c}[/tex]
The exponent product rule states that, when multiplying two exponents that have the same base, you can add the exponents.
[tex]3^{5+4}[/tex]
[tex]3^9[/tex]
A professor is grading the final exam. He notices that the mean test score is 61, and the standard deviation is 10. The test scores were normally distributed. if there were 450 students in the data sample, how many would have a test score between 61 and 71? *Round your answer to the nearest full value.
Answer:
66666699999
Step-by-step explanation:
What is the slope of (3,-2) (2,-4)
Answer:
2
Step-by-step explanation:
We can use the slope formula
m = (y2-y1)/(x2-x1)
= ( -4 - -2)/ ( 2-3)
= ( -4+2)/( 2-3)
= -2/ -1
= 2
Find the base in the following problem. Round the answer to a whole number. 12.5% of ____ is 130.
Answer:
1040
Step-by-step explanation:
Answer: The number is 1040.
Step-by-step explanation:
The question says 12.5% of a number is 130 so we can represent it by the equation.
12.5% * x = 130 where x is the number.Solve for x
12.5% * x = 130 convert 12.5% to a decimal
0.125 * x = 130
0.125x = 130 Divide both sides by 0.125
x= 1040
Check.
1040 * 12.5% = 130