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3 years ago

13

A cable TV company has a $35 installation fee and a $15 monthly rate. Write an equation in slope-intercept form to describe the

cost of cable TV for any number of months. Use x for the number of months and y for the total cost.

1 answer:

Komok [63]3 years ago

7 0

Answer:

y=15x+35

Step-by-step explanation:

15 every month and 35 for instant charge

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Identify the x-intercept and y-intercept of the equation below.

Lady_Fox [76]

Divide by 21 to put the equation in intercept form.
x/(21/9) + y/(-21/7) = 1
x/(7/3) + y/(-3) = 1

The x-intercept is (7/3, 0)
The y-intercept is (0, -3)

The 3rd choice is appropriate.

8 0

3 years ago

Find the absolute extrema for f(x,y)=4-x^2-y^4+1/2y^2 over the closed disk D:x^2+y^2 is less than or equal to 1

algol [13]

Find the critical points of $f(x,y)$ :

$\dfrac{\partial f}{\partial x}=-2x=0\implies x=0$

$\dfrac{\partial f}{\partial y}=y-4y^3=y(1-4y^2)=0\implies y=0\text{ or }y=\pm\dfrac12$

All three points lie within $D$ , and $f$ takes on values of

$\begin{cases}f(0,0)=4\\f\left(0,-\frac12\right)=\frac{65}{16}\\f\left(0,\frac12\right)=\frac{65}{16}\end{cases}$

Now check for extrema on the boundary of $D$ . Convert to polar coordinates:

$f(x,y)=f(\cos t,\sin t)=g(t)=4-\cos^2-\sin^4t+\dfrac12\sin^2t=3+\dfrac32\sin^2t-\sin^4t$

Find the critical points of $g(t)$ :

$\dfrac{\mathrm dg}{\mathrm dt}=3\sin t\cos t-4\sin^3t\cos t=\sin t\cos t(3-4\sin^2t)=0$

$\implies\sin t=0\text{ or }\cos t=0\text{ or }\sin t=\pm\dfrac{\sqrt3}2$

$\implies t=n\pi\text{ or }t=\dfrac{(2n+1)\pi}2\text{ or }\pm\dfrac\pi3+2n\pi$

where $n$ is any integer. There are some redundant critical points, so we'll just consider $0\le t< 2\pi$ , which gives

$t=0\text{ or }t=\dfrac\pi3\text{ or }t=\dfrac\pi2\text{ or }t=\pi\text{ or }t=\dfrac{3\pi}2\text{ or }t=\dfrac{5\pi}3$

which gives values of

$\begin{cases}g(0)=3\\g\left(\frac\pi3\right)=\frac{57}{16}\\g\left(\frac\pi2\right)=\frac72\\g(\pi)=3\\g\left(\frac{3\pi}2\right)=\frac72\\g\left(\frac{5\pi}3\right)=\frac{57}{16}\end{cases}$

So altogether, $f(x,y)$ has an absolute maximum of 65/16 at the points (0, -1/2) and (0, 1/2), and an absolute minimum of 3 at (-1, 0).

5 0

3 years ago

F) As a truck driver, Roland averages 400 miles every 6 hours of driving. How long will it take him to drive

liubo4ka [24]

Answer:

31.5 hours

Step-by-step explanation:

time * speed = distance

speed=400/6=66.67 miles per hour

2100/(400/6)=31.5 hours

6 0

4 years ago

Jane had $7 and her sister had $2. Their parents gave each of them an equal amount of money . Then, Jane had twice as much money

slega [8]

Answer:

They each got $3.00

Step-by-step explanation:

7+x = 2(2+x)

7+x = 4 + 2x

-x = -3

x=3

3 0

4 years ago

Read 2 more answers

I would like to know what is the value of z

Brrunno [24]

From the chord theorem we know that:

$\overline{TW}\cdot\overline{UW}=\overline{CW}\cdot\overline{VW}$

so:

$\overline{TW}\cdot\overline{UW}=\overline{CW}\cdot\overline{VW}\\\\3\cdot\overline{UW}=x\cdot6\\\\3\cdot(\overline{TU}-\overline{TW})=x\cdot6\\\\
3\cdot(x+7-3)=x\cdot6\\\\3\cdot(x+4)=x\cdot6\\\\3x+12=6x\\\\12=6x-3x\\\\3x=12\qquad|\div3\\\\\boxed{x=4}$

Answer C.

3 0

4 years ago