All categories

3 years ago

PRE CALC QUESTION

Mathematics

1 answer:

Oksi-84 [34.3K]3 years ago

5 0

Answer:

-5 $x^{3}$ + 65x + 60

<h3>Step-by-step explanation:</h3>

You might be interested in

The following table shows the weights, in hundreds of pounds, for six selected cars. Also shown is the corresponding fuel eff

Reika [66]

Answer:

Step-by-step explanation:

Given is a table showing the weights, in hundreds of pounds, for six selected cars. Also shown is the corresponding fuel efficiency, in miles per gallon (mpg), for the car in city driving.

Weight Fuel eff. x^2 xy y^2

X Y

28 20 784 560 400

3 22 9 66 484

35 19 1225 665 361

32 22 1024 704 484

30 23 900 690 529

29 21 841 609 441

Mean 26.16666667 21.16666667 797.1666667 549 449.8333333

Variance 112.4722222 1.805555556

Covariance -553.8611111

r -0.341120235

Correlaton coefficient =cov (xy)/S_x S_y

Covariance (x,y) = E(xy)-E(x)E(y)

The correlation coefficient between the weight of a car and the fuel efficiency is -0.341

8 0

3 years ago

Hich points are reflections of each other across the y-axis?

Serhud [2]

Answer:

(- 7, - 3) and (7, - 3)

Step-by-step explanation:

The best way to do this is to sketch the graph...when dealing with reflection in the y axis, the value for y remains the same and the value for x becomes negative if it was positive or becomes positive if it was negative

4 0

3 years ago

Read 2 more answers

Which set of side lengths form a right triangle?

Reil [10]

I just took the test and the answer was D
50 in, 48 in, 14 in are the side lengths that form a right triangle

4 0

3 years ago

Read 2 more answers

Which of these absolute values is the greatest? a. |140| b. |-104| c. |104| d. |-20

Wewaii [24]

Answer: a

/////////////////

5 0

2 years ago

Read 2 more answers

The graphs of the polar curves r = 4 and r = 3 + 2cosθ are shown in the figure above. The curves intersect at θ = π/3 and θ = 5π

Gennadij [26K]

(a)

$\displaystyle \frac{1}{2} \cdot \int_{\frac{\pi}{3}}^{\frac{5\pi}{3}} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta$

or, via symmetry

$\displaystyle\frac{1}{2} \cdot 2 \int_{\frac{\pi}{3}}^{\pi} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta$

____________

(b)

By the chain rule:

$\displaystyle \frac{dy}{dx} = \frac{ dy/ d\theta}{ dx/ d\theta}$

For polar coordinates, x = rcosθ and y = rsinθ. Since
<span>r = 3 + 2cosθ, it follows that

$x = (3 + 2\cos\theta) \cos \theta \\ 
y = (3 + 2\cos\theta) \sin \theta$

Differentiating with respect to theta

$\begin{aligned}
\displaystyle \frac{dy}{dx} &= \frac{ dy/ d\theta}{ dx/ d\theta} \\
&= \frac{(3 + 2\cos\theta)(\cos\theta) + (-2\sin\theta)(\sin\theta)}{(3 + 2\cos\theta)(-\sin\theta) + (-2\sin\theta)(\cos\theta)} \\ \\
\left.\frac{dy}{dx}\right_{\theta = \frac{\pi}{2}}
&= 2/3
\end{aligned}$

2/3 is the slope

____________

(c)

"</span><span>distance between the particle and the origin increases at a constant rate of 3 units per second" implies dr/dt = 3

A</span>ngle θ and r are related via <span>r = 3 + 2cosθ, so implicitly differentiating with respect to time

</span><span /> $\displaystyle\frac{dr}{dt} = -2\sin\theta \frac{d\theta}{dt} \quad \stackrel{\theta = \pi/3}{\implies} \quad 3 = -2\left( \frac{\sqrt{3}}{2}}\right) \frac{d\theta}{dt} \implies \\ \\ \frac{d\theta}{dt} = -\sqrt{3} \text{ radians per second}$

5 0

3 years ago