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Jill earned 40$ from a carpool plus 9$ per hour (h) babysitting this week. turn into an Expression

nadya68 [22]

Answer:

9h + 40

Step-by-step explanation:

You use 9h, because you don't know how many hours Jill worked, she already had 40$ so 40 is the constant.

7 0

3 years ago

You are given the polar curve r = e^θ

galina1969 [7]

The tangent to $r(\theta)=e^\theta$ has slope $\frac{\mathrm dy}{\mathrm dx}$ , where

$\begin{cases}x(\theta)=r(\theta)\cos\theta\\y(\theta)=r(\theta)=\sin\theta\end{cases}$

By the chain rule, we have

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}$

and by the product rule,

$\dfrac{\mathrm dx}{\mathrm d\theta}=\dfrac{\mathrm dr}{\mathrm d\theta}\cos\theta-r(\theta)\sin\theta$

$\dfrac{\mathrm dy}{\mathrm d\theta}=\dfrac{\mathrm dr}{\mathrm d\theta}\sin\theta+r(\theta)\cos\theta$

so that with $\frac{\mathrm dr}{\mathrm d\theta}=e^\theta$ , we get

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{e^\theta\sin\theta+e^\theta\cos\theta}{e^\theta\cos\theta-e^\theta\sin\theta}=\dfrac{\sin\theta+\cos\theta}{\cos\theta-\sin\theta}=-\dfrac{1+\sin(2\theta)}{\cos(2\theta)}$

The tangent line is horizontal when the slope is 0; this happens for

$-\dfrac{1+\sin(2\theta)}{\cos(2\theta)}=0\implies\sin(2\theta)=-1\implies2\theta=-\dfrac\pi2+2n\pi\implies\theta=-\dfrac\pi4+n\pi$

where $n$ is any integer. In the interval $0\le\theta\le2\pi$ , this happens for $n=1,2$ , or

$\theta=\dfrac{3\pi}4\text{ and }\theta=\dfrac{7\pi}4$

i.e at the points

$(r,\theta)=\left(e^{3\pi/4},\dfrac{3\pi}4\right)$

and

$(r,\theta)=\left(e^{7\pi/4},\dfrac{7\pi}4\right)$

8 0

3 years ago

SPENDING ALL MY POINTS FOR THIS PLEASE LOOK AT PHOTO AND HELP! Please

Iteru [2.4K]

Answer:

1a - reduction

2a- enlargement

3a- reduction

4a- enlargement

Step-by-step explanation:

when the scale factor is greater than 100% it is making it larger, when less than 100% size it is making it smaller. for every answer do the original number (ex #1 would be 48 inches) and multiply it by the scale factor in decimal form, by moving the decimal over two places (ex #1 the 25% would become .25 or 1/4). therefore #1 would be an equation like 48 x 0.25= 12

5 0

3 years ago

If the measure of angle 4 is 43 degrees, then the measure of angle 6 is -------

marta [7]

Answer:

degrees and the measure of angle 5 is -------- degrees. The measure of angl

Step-by-step explanation:

3 0

3 years ago

AB passes through A(-3,0) and B(-6,5). what is the equation of the line that passes through the origin and is parallel to AB?

vaieri [72.5K]

Answer:

y = -5/3x or 5x +3y = 0

Step-by-step explanation:

To write the equation of a line through the origin, we need only find its slope. It is parallel to the line through the given points, so will have the same slope.

<h3>Slope</h3>

The slope of a line through points (x1, y1) and (x2, y2) is given by the formula ...

m = (y2 -y1)/(x2 -x1)

For the given points, the slope is ...

m = (5 -0)/(-6 -(-3)) = 5/(-3) = -5/3

<h3>Equation</h3>

The line trough the origin has a y-intercept of zero, so its equation will be ...

y = mx

For the slope we found, the desired equation is ...

y = -5/3x

<h3>Standard form</h3>

If we multiply by 3 and add 5x, we have ...

3y = -5x

5x +3y = 0 . . . . . . standard form equation of the line

3 0

1 year ago