The equation for the volume of a cone is:

where V = volume of the cone, r = radius of the circular base, and h = height of the cone.
You are told that the height, h = 25.5 cm. You are also told that the diameter is <span>12 centimeters. Remember that the diameter of a circle is just twice the radius. Divide 12 by 2 to get the radius: r =12/2 = 6 cm.
Since you know </span>h = 25.5 cm and r = 6 cm, plug these values into your equation for volume of a cone and solve for V, volume:

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Answer: B) <span>
961.33 cm³ </span>
V = s²h
<span>150 = s²h </span>
<span>150 = s²(3/2)s </span>
<span>(2/3)150 = s³ </span>
<span>100 = s³ </span>
<span>s = ∛100 (approx 4.642 in) </span>
I would say that the third one is false.
Answer:
No.
Step-by-step explanation:
As x increases 2^x will grow faster than 5 x^2. This is because the x in 2^x is an exponent and its graph grows very steeply compared with 5x^2 , as x increases.
For example when x = 10
5x^2 = 5*10^2 = 500
2^x = 2^10 =1024
When x = 11:
5x^2 = 605
2^x = 2048 and the difference will continue to increase.
This is a linear differential equation of first order. Solve this by integrating the coefficient of the y term and then raising e to the integrated coefficient to find the integrating factor, i.e. the integrating factor for this problem is e^(6x).
<span>Multiplying both sides of the equation by the integrating factor: </span>
<span>(y')e^(6x) + 6ye^(6x) = e^(12x) </span>
<span>The left side is the derivative of ye^(6x), hence </span>
<span>d/dx[ye^(6x)] = e^(12x) </span>
<span>Integrating </span>
<span>ye^(6x) = (1/12)e^(12x) + c where c is a constant </span>
<span>y = (1/12)e^(6x) + ce^(-6x) </span>
<span>Use the initial condition y(0)=-8 to find c: </span>
<span>-8 = (1/12) + c </span>
<span>c=-97/12 </span>
<span>Hence </span>
<span>y = (1/12)e^(6x) - (97/12)e^(-6x)</span>