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3 years ago

13

Bill and 10 friends are planning for a pizza party.They purchased 3 quarts of juice.If each glass holds 8 ounces will everyone g

et at least one glass of juice?Show your work.

1 answer:

Naily [24]3 years ago

7 0

Yes. all the friends will get at least one cup of juice

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The tangents to the curve with equation y = x^3-3x at the points A and B with x coordinates −1 and 4 respectively meet at the po

sladkih [1.3K]

Answer:

$\displaystyle C=\left(\frac{26}{9}, 2\right)$

Step-by-step explanation:

We need to find the equation of the tangent lines of Points A and B.

Differentiate the equation:

$\displaystyle \frac{dy}{dx}=3x^2-3$

Point A has an <em>x-</em>coordinate of -1. Hence, the slope of its tangent line is:

$\displaystyle \frac{dy}{dx}\Big|_{x=-1}=3(-1)^2-3=0$

Find the <em>y-</em>coordinate of Point A using the original equation:

$y(-1)=(-1)^3-3(-1)=2$

Hence, Point A is (-1, 2).

Thus, the tangent line at Point A is:

$y-2=0(x-(-1))$

Simplify:

$y=2$

Point B has an <em>x-</em>coordinate of 4. Hence, the slope of its tangent line is:

$\displaystyle \frac{dy}{dx}\Big|_{x=4}=3(4)^2-3=45$

Find the <em>y-</em>coordinate of Point B:

$y(4)=(4)^3-3(4)=52$

Thus, Point B is at (4, 52).

So, the tangent line at Point B is:

$y-52=45(x-4)$

Simplify:

$y=45x-128$

Point C occurs at the intersections of the tangent lines of Points A and B. Set the two equations equal to each other and solve for <em>x: </em>

$2=45x-128$

We acquire:

$\displaystyle x=\frac{26}{9}$

Since one of our equations is <em>y</em> = 2, the <em>y-</em>coordinate is 2.

Hence, Point C is:

$\displaystyle C=\left(\frac{26}{9}, 2\right)$

5 0

3 years ago

Read 2 more answers

Use the elimination method to solve the system of equations. 3x+2y=16 2x-2y=4

Masteriza [31]

Answer:

x = 4; y = 2

Step-by-step explanation:

(1) 3x + 2y = 16

(2) 2x – 2y = 4 Add (1) and (2)

5x = 20 Divide each side by 5

(3) x = 4 Substitute (3) into (2)

2×4 – 2y = 4

8 - 2y = 4 Subtract 16 from each side

-2y = -4 Divide each side by -2

y = 2

<em>Check: </em>

(1) 3×4 + 2×2 = 16

12 + 4 = 16

16 = 16

(2) 2×4 – 2×2 = 4

8 - 4 = 4

4 = 4

5 0

3 years ago

Read 2 more answers

Joe is riding his bicycle. He rides for 3 hours at a speed of 4.8 kilometers per hour. For how many kilometers does he ride?

eduard

Answer:

14.4km

Step-by-step explanation:

<h2>Speed = distance / time </h2>

speed = 4.8 km/h
time = 3 hrs
distance = ?

Distance = speed * time

Distance = 4.8 * 3 = 14.4km

5 0

2 years ago

What adds to 1 and multiplies to 2

kicyunya [14]

-2 and 1.

Hope this helps!

3 0

3 years ago

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The line that passes through the given point and has the given slope for (-1,-4), m = -2

alisha [4.7K]

Answer:

y = -2x - 6

Step-by-step explanation:

y = -2x + b

-4 = -2(-1) + b

-4 = 2 + b

-6 = b

y = -2x - 6

3 0

2 years ago