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Stels [109]
2 years ago
10

Please help asap! brainliest to best answer! how do you do this???? and what are the answers!

Mathematics
2 answers:
Angelina_Jolie [31]2 years ago
8 0

Answer:

8953.5 seconds

Step-by-step explanation:

Since the challenger descends at a rate of 4 feet per second, divide 35,814 by 4 to get the answer

OLEGan [10]2 years ago
8 0

Answer:

it took James 8953.5 seconds

Step-by-step explanation:

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What is the relationship between these 2 angles
AlekseyPX
The answer is D. Alternate Interior
4 0
2 years ago
More Calculus! (I'm so sorry)
Olenka [21]
Recall that converting from Cartesian to polar coordinates involves the identities

\begin{cases}y(r,\phi)=r\sin\phi\\x(r,\phi)=r\cos\phi\end{cases}

As a function in polar coordinates, r depends on \phi, so you can write r=r(\phi).

Differentiating the identities with respect to \phi gives

\begin{cases}\dfrac{\mathrm dy}{\mathrm d\phi}=\dfrac{\mathrm dr}{\mathrm d\phi}\sin\phi+r\cos\phi\\\\\dfrac{\mathrm dx}{\mathrm d\phi}=\dfrac{\mathrm dr}{\mathrm d\phi}\cos\phi-r\sin\phi\end{cases}

The slope of the tangent line to r(\phi) is given by

\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm d\phi}}{\frac{\mathrm dx}{\mathrm d\phi}}=\dfrac{\frac{\mathrm dr}{\mathrm d\phi}\sin\phi+r\cos\phi}{\frac{\mathrm dr}{\mathrm d\phi}\cos\phi-r\sin\phi}

Given r(\phi)=3\cos\phi, you have \dfrac{\mathrm dr}{\mathrm d\phi}=-3\sin\phi. So the tangent line to r(\phi) has a slope of

\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{-3\sin^2\phi+3\cos^2\phi}{-3\sin\phi\cos\phi-3\cos\phi\sin\phi}=\dfrac{3\cos2\phi}{-3\sin2\phi}=-\cot2\phi

When \phi=120^\circ=\dfrac{2\pi}3\text{ rad}, the tangent line has slope

\dfrac{\mathrm dy}{\mathrm dx}=-\cot\dfrac{4\pi}3=-\dfrac1{\sqrt3}

This line is tangent to the point (r,\phi)=\left(-\dfrac32,\dfrac{2\pi}3\right) which in Cartesian coordinates is equivalent to (x,y)=\left(\dfrac34,-\dfrac{3\sqrt3}4\right), so the equation of the tangent line is

y+\dfrac{3\sqrt3}4=-\dfrac1{\sqrt3}\left(x-\dfrac34\right)

In polar coordinates, this line has equation

r\sin\phi+\dfrac{3\sqrt3}4=-\dfrac1{\sqrt3}\left(r\cos\phi-\dfrac34\right)
\implies r=-\dfrac{3\sqrt3}{2\sqrt3\cos\phi+6\sin\phi}

The tangent line passes through the y-axis when x=0, so the y-intercept is \left(0,-\dfrac{\sqrt3}2\right).

The vector from this point to the point of tangency on r(\phi) is given by the difference of the vector from the origin to the y-intercept (which I'll denote \mathbf a) and the vector from the origin to the point of tangency (denoted by \mathbf b). In the attached graphic, this corresponds to the green arrow.

\mathbf b-\mathbf a=\left(\dfrac34,-\dfrac{3\sqrt3}4\right)-\left(0,-\dfrac{\sqrt3}2\right)=\left(\dfrac34,-\dfrac{\sqrt3}4\right)

The angle between this vector and the vector pointing to the point of tangency is what you're looking for. This is given by

\mathbf b\cdot(\mathbf b-\mathbf a)=\|\mathbf b\|\|\mathbf b-\mathbf a\|\cos\theta
\dfrac98=\dfrac{3\sqrt3}4\cos\theta
\implies\theta=\dfrac\pi6\text{ rad}=30^\circ

The second problem is just a matter of computing the second derivative of \phi with respect to t and plugging in t=2.

\phi(t)=2t^3-6t
\phi'(t)=6t^2-6
\phi''(t)=12t
\implies\phi''(2)=24

6 0
3 years ago
Lucy is saving money to buy a game. The game costs $21, and so far she has saved one-third of this cost. How much money has Lucy
Svetach [21]

Answer:

$7

Step-by-step explanation:

just did 21 divided by three since it says she has saved one third of the $21.

5 0
3 years ago
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Help me please. It’s Alagrabra
poizon [28]

The area of the rectangle will be 36√3 square cm. Then the correct option is C.

<h3>What is the area of the rectangle?</h3>

Let L be the length and W be the width of the rectangle.

Then the area of the rectangle will be

Area of the rectangle = L × W square units

The dimensions of the rectangle are 6 cm and 6√3 cm.

Then the area of the rectangle will be

Area of the rectangle = L × W

Area of the rectangle = 6 × 6√3

Area of the rectangle = 36√3 square cm

The area of the rectangle will be 36√3 square cm.

Then the correct option is C.

More about the area of the rectangle link is given below.

brainly.com/question/20693059

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7 0
1 year ago
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What is the y-intercept of the linear equation x-3y=-6?
IceJOKER [234]

To find the y-intercept, let x = 0.

0 - 3y = -6

-3y = -6

y = 2

The y-intercept of the equation is the point (0, 2).

7 0
3 years ago
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