parallel lines r and s are cut by two transversals, parallel lines t and u. Which angles are corresponding angles with angle 8?

assume the camera is placed 6 feet from the center of the merry-go-round and the diameter of the merry-go-round is 6 feet. build

LenKa [72]

The trigonometric function that models the distance (feet) of the rider from the camera as a function of time (seconds) is γ(t) = ωt, where ω is the angular velocity of merry-go-round.

Let, center of the merry-go-round is C and camera is placed at point A. B(t) define the position of the rider at any time t. The angle between these three-point A, C and B is y(t). Radius (r) of the merry-go-round is 3 feet and distance (d) of the rider from the camera is 6 and the angular velocity of the rider is ω.

Assume the rider is at the edge of the merry-go-round (as the position is not specified). So, the length of CB(t) is r. To solve this problem lets consider that angular velocity of merry-go-round is constant, ω = 0 and y(t) = 0.

Therefore, we have y(t) = ωt

So, the the distance (feet) of the rider from the camera is (from the triangle AB(t)C)

C(t) = √(r² + d² - 2rdcos(y(t)) = √(45 - 36cos(ωt) = 3√(5 - 4cos(ωt))

Learn more about angular velocity here:

brainly.com/question/14769426

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8 0

2 years ago

At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 6 cubic feet per minute. The dia

Alla [95]

Answer:

$0.2122\text{ ft per min}$

Step-by-step explanation:

Let r be the radius ( in feet ) of the cone,

So, the diameter of the cone = 2 × radius = 2r feet,

∵ The diameter of the base of the cone is three times the height,

If h represents the height of the cone,

⇒ 2r = 3 × h,

⇒ $r=\frac{3h}{2}$ feet,

∵ Volume of a cone,

$V=\frac{1}{3}\pi R^2 H$

Where,

R = radius, H = height,

Thus, the volume of the given cone is,

$V=\frac{1}{3}\pi r^2 h$

$=\frac{1}{3}\pi (\frac{3h}{2})^2 h$

$=\frac{3}{4}\pi h^3$

Differentiating with respect to t ( time )

$\frac{dV}{dt}=\frac{9}{4}\pi h^2\frac{dh}{dt}$

We have,

$\frac{dV}{dt}=6\text{ cubic ft per min},h=2\text{ feet}$

$6=\frac{9}{4}\pi (2)^2 \frac{dh}{dt}$

$6=9\pi \frac{dh}{dt}$

$\implies \frac{dh}{dt}=\frac{6}{9\pi }\approx 0.2122\text{ ft per min}$

4 0

4 years ago

Either use technology to find the P-value or use

Akimi4 [234]

Answer:

The first step is calculate the degrees of freedom, on this case:

$df=n-1=21-1=20$

Since is a one side left tailed test the p value would be:

$p_v =P(t_{(20)}$

And we can use the following excel code to find it: "=T.DIST(-0.024,20,TRUE)"

Step-by-step explanation:

Data given and notation

$\bar X$ represent the mean

$s$ represent the sample standard deviation

$n=21$ sample size

$\mu_o =140$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t=-0.024 would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean for the widths of tornadoes is lower than 140 yd, the system of hypothesis would be:

Null hypothesis: $\mu \geq 140$

Alternative hypothesis: $\mu < 140$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

The statistic is given by: $t = -0.024$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=21-1=20$

Since is a one side left tailed test the p value would be:

$p_v =P(t_{(20)}$

And we can use the following excel code to find it: "=T.DIST(-0.024,20,TRUE)"

Based on the p value obtained we can conclude that we FAIL to reject the null hypothesis at any significance level selected $\alpah=0.01,0.05,0.1$

7 0

4 years ago

I need help please

devlian [24]

I am pretty sure its B (minimum at -1, -4) because that would be were the first point would be at. The Graphing of this equation would be a "upside down u" shape.

4 0

3 years ago

Which of the following measurements, in centimeters (cm), could be the lengths of the sides of a triangle? Select all that apply

natima [27]

5cm I think or you can try 7cm

6 0

3 years ago