Which of the following are solutions to the quadratic equation? Check all that apply x^2 + 12x + 36 = 7

Mathematics

1 answer:

garik1379 [7]2 years ago

5 0

Answer:

x = -6 + $\sqrt{7}$ , x = -6 - $\sqrt{7}$

Step-by-step explanation:

(x + 6)² = 7

x + 6 = + or - $\sqrt{7}$

x = -6 + $\sqrt{7}$ , x = -6 - $\sqrt{7}$

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A flagpole has a height of 16 yards. It will be supported by three cables, each of which is attached to the flagpole at a point

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Cables are forming 3 right angled triangles the pole being the shared height of them;

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12^2 + 9^2 = 225
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11Alexandr11 [23.1K]

Answer:

0.25 feet per minute

Step-by-step explanation:

Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min. Since we are told that the shape formed is a cone, the rate of change of the volume of the cone.

$\dfrac{dV}{dt}=20$ ft^3/min$

$\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h$

Since base diameter = Height of the Cone

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Therefore,

$\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}$

$\text{Rate of Change of the Volume}, \dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}$

Therefore: $\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=20$

We want to determine how fast is the height of the pile is increasing when the pile is 10 feet high.

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