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3 years ago

7

Sylvester plans to rent a car to tour the West Coast. The cost of the rental is $53 per day. The cost of the deposit is $99 for

as long as Sylvester needs the car. Write a linear equation that represents this scenario.

2 answers:

My name is Ann [436]3 years ago

8 0

Amount Due when he returns car = $53 x Days - Deposit

Luda [366]3 years ago

4 0

Answer:

C = 53D + 99

Step-by-step explanation:

The cost (C) is equal to $53 per day (53 multiplied by the number of days, D) plus the fixed deposit (+ 99)

Expressed as a linear equation below

C = 53D + 99

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R (-3,1) and S (-1,3) are points on a circle. If RS is a diameter, find the equation of the circle.

ELEN [110]

Answer:

$\sf (x+2)^2+(y-2)^2=2$

Step-by-step explanation:

If RS is the diameter of the circle, then the midpoint of RS will be the center of the circle.

$\sf midpoint=\left(\dfrac{x_s-x_r}{2}+x_r,\dfrac{y_s-y_r}{2}+y_r \right)$

$\sf =\left(\dfrac{-1-(-3)}{2}+(-3),\dfrac{3-1}{2}+1 \right)$

$\sf =(-2, 2)$

Equation of a circle: $\sf (x-h)^2+(y-k)^2=r^2$

(where (h, k) is the center and r is the radius)

Substituting found center (-2, 2) into the equation of a circle:

$\sf \implies (x-(-2))^2+(y-2)^2=r^2$

$\sf \implies (x+2)^2+(y-2)^2=r^2$

To find $\sf r^2$ , simply substitute one of the points into the equation and solve:

$\sf \implies (-3+2)^2+(1-2)^2=r^2$

$\sf \implies 1+1=r^2$

$\sf \implies r^2=2$

Therefore, the equation of the circle is:

$\sf (x+2)^2+(y-2)^2=2$

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2 years ago

After unloading 96 pounds of mulch from the truck, there were still 24 pounds

Dennis_Churaev [7]

Answer:

120

Step-by-step explanation:

To find the answer you just have to add 24 and 96 together to get 120.

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3 years ago

A cylindrical soup can has a diameter of 3.6 in. and is 6.4 in. tall. Find the volume of the can.

arsen [322]

<h2>⚘Your Answer:------</h2>

<h3><u>Given</u><u> </u><u>Information</u><u>:</u></h3>

<u>Diameter of can</u>:- 3.6 cm
<u>Height of</u><u> </u><u>can</u><u>:</u><u>-</u> 6.4 cm

<h3><u>To</u><u> </u><u>Find</u><u> </u><u>Out</u><u>:</u></h3>

<u>Volume</u><u> </u><u>of</u><u> </u><u>the</u><u> </u><u>Can</u><u>.</u>

<h3><u>Solution</u><u>:</u></h3>

Radius = (Diameter/2)

ㅤㅤㅤㅤ3.6 cm/2

ㅤㅤㅤㅤ1.8 cm

<u>So</u><u>,</u><u> </u><u>Radius</u><u> </u><u>of</u><u> </u><u>the</u><u> </u><u>soup</u><u> </u><u>can</u><u> </u><u>is</u> 1.8 cm.

Volume øf cylinder = Volume øf can

Volume of cylinder = π r²h

(π = 22/7)

(r = radius = 1.8 cm)

(h = height = 6.4 cm

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ= 22/7×(1.8 cm)²× 6.4 cm

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ= 22/7× 3.24 cm² × 6.4 cm

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ= 22/7 × 20.736 cm³

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ= (456.192/7) cm³

ㅤㅤㅤㅤㅤㅤㅤㅤㅤ= 65.17 cm³

So, the Volume of the soup can is 65.17 cm³

ㅤㅤㅤㅤㅤㅤㅤㅤ⚘Thank You

7 0

2 years ago

Consider the following equation. f(x, y) = y3/x, P(1, 2), u = 1 3 2i + 5 j (a) Find the gradient of f. ∇f(x, y) = Correct: Your

BaLLatris [955]

$f(x,y)=\dfrac{y^3}x$

a. The gradient is

$\nabla f(x,y)=\dfrac{\partial f}{\partial x}\,\vec\imath+\dfrac{\partial f}{\partial y}\,\vec\jmath$

$\boxed{\nabla f(x,y)=-\dfrac{y^3}{x^2}\,\vec\imath+\dfrac{3y^2}x\,\vec\jmath}$

b. The gradient at point P(1, 2) is

$\boxed{\nabla f(1,2)=-8\,\vec\imath+12\,\vec\jmath}$

c. The derivative of $f$ at P in the direction of $\vec u$ is

$D_{\vec u}f(1,2)=\nabla f(1,2)\cdot\dfrac{\vec u}{\|\vec u\|}$

It looks like

$\vec u=\dfrac{13}2\,\vec\imath+5\,\vec\jmath$

so that

$\|\vec u\|=\sqrt{\left(\dfrac{13}2\right)^2+5^2}=\dfrac{\sqrt{269}}2$

Then

$D_{\vec u}f(1,2)=\dfrac{\left(-8\,\vec\imath+12\,\vec\jmath\right)\cdot\left(\frac{13}2\,\vec\imath+5\,\vec\jmath\right)}{\frac{\sqrt{269}}2}$

$\boxed{D_{\vec u}f(1,2)=\dfrac{16}{\sqrt{269}}}$

7 0

3 years ago

What is 2,400 milliliters converted into liters

BARSIC [14]

Answer:

2.4 liters

Step-by-step explanation:

5 0

4 years ago

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