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Strike441 [17]
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.
Mathematics
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
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