Find all the values of x where the tangent line is horizontal. 2x^3+36x^2+192x+12

1 answer:

3 0

At x = -4 and -8
Take the derivative of the given equation to find rate of change of the graph.
f'(x) = 6x^2 + 72x + 192
At a horizontal tangent, f'(x) = 0, so set the equation equal to 0 and solve. Eventually you get x = -4 and -8

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Mark is cutting construction paper into rectangles for a project. He needs to cut one rectangle that is 12 inches × 13 1/3 inche

Anna11 [10]

Answer: 265.9167 square inches (rounded)

Step-by-step explanation:

Shoot, okay if this is wrong, shame on me:

All you do is find the areas of each rectangle and add them together.

(12 × 13 1/3) + (10 1/4 x 10 1/3) = 265.9167 (rounded) square inches. Or as a fraction: 3191/12

4 0

3 years ago

Will a truck that is 10 feet wide carrying a load that reaches 12 feet above the ground clear the semielliptical arch on the one

beks73 [17]

Figure is missing, so i have attached it.

Answer:

it will clear the arch because the height of the archway of the bridge 5 feet from the center is approximately 12.76 ft

Step-by-step explanation:

The standard form of equation of an ellipse is;

x²/a² + y²/b² = 1

From the figure in the image attached, we can see that the radius is; a = 52/2 = 26 ft

While the value of b = 13 ft

Thus;

x²/26² + y²/13² = 1

x²/676 + y²/169 = 1

We want to find the height of the archway of the bridge 5 feet from the center.

Thus, we will plug in 5 for x to get;

5²/676 + y²/169 = 1

(25/676) + (y²/169) = 1

Multiply through by 676 to get;

25 + 4y² = 676

4y² = 676 - 25

y² = 651/4

y² = 162.75

y = 12.76 ft

Thus height of the truck is 12 ft and so it will clear the arch because the height of the archway of the bridge 5 feet from the center is approximately 12.76 ft