Check all solutions to the equation. If there are no solutions, check 'None."<br> x² = 64

Jobisdone [24]

<h3>Answer: 133</h3>

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Explanation:

The quickest way to get this answer is to add the angles given to get 87+46 = 133

This is through the use of the remote interior angle theorem.

Note how the angles 87 and 46 are interior, or inside the triangle. And also, they are not adjacent to the exterior angle we want to find. So that's where the "remote" portion comes in.

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The slightly longer method involves letting x be the measure of the missing interior angle of the triangle.

The three interior angles add to 180

87+46+x = 180

133+x = 180

x = 180 - 133

x = 47

The missing interior angle of the triangle is 47 degrees.

Angle 1 is adjacent and supplementary to this 47 degree angle, so,

(angle1)+(47) = 180

angle1 = 180-47

angle1 = 133 degrees

This example helps confirm that the remote interior angle theorem is correct.

6 0

2 years ago

What is greater 2yards or5feet

Brilliant_brown [7]

yards, there are 3 feet per yard

7 0

2 years ago

Read 2 more answers

Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circu

Sunny_sXe [5.5K]

Answer:

0.0221 feet per minute.

Step-by-step explanation:

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

If the Base Diameter = Height of the Cone

The radius of the Cone = h/2

Therefore,

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

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

Since gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. Therefore, the Volume of the cone is increasing at a rate of 10 cubic feet per minute.

$\dfrac{dV}{dt}=10$ ft^3/min$

We want to determine how fast is the height of the pile is increasing when the pile is 24 feet high.

We have:

$\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=10\\\\$When h=24$ feet$\\\dfrac{3\pi *24^2}{12}\dfrac{dh}{dt}=10\\144\pi \dfrac{dh}{dt}=10\\ \dfrac{dh}{dt}= \dfrac{10}{144\pi}\\ \dfrac{dh}{dt}=0.0221$ feet per minute$