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Mathematics

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Pie2 years ago

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<h2>This is your answer :</h2>

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What is the volume of a cone that has a height of 10 feet and a base with a diameter of 2 and half feet?

lyudmila [28]

Volume of a cone: 1/3 $\pi$ r²h
r is the radius (diameter ÷ 2) and h is the height.

Find the radius first using the diameter: 2 $\frac{1} {2}$ ÷ 2 = 1.25

Now plug in the numbers into the formula.

1/3 $\pi$ 1.25²10 = <span>16.4
</span>
The volume of the cone is 16.4 cubic feet.

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2 years ago

state the coordinate of the image of the given point B (-10, -6) under a dilation with a center at the orgin with the given scal

JulijaS [17]

Answer:

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Step-by-step explanation:

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2 years ago

Find the roots of h(t) = (139kt)^2 − 69t + 80

Sonbull [250]

Answer:

The positive value of $k$ will result in exactly one real root is approximately 0.028.

Step-by-step explanation:

Let $h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80$ , roots are those values of $t$ so that $h(t) = 0$ . That is:

$19321\cdot k^{2}\cdot t^{2}-69\cdot t + 80=0$ (1)

Roots are determined analytically by the Quadratic Formula:

$t = \frac{69\pm \sqrt{4761-6182720\cdot k^{2} }}{38642}$

$t = \frac{69}{38642} \pm \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }$

The smaller root is $t = \frac{69}{38642} - \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }$ , and the larger root is $t = \frac{69}{38642} + \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }$ .

$h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80$ has one real root when $\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} = 0$ . Then, we solve the discriminant for $k$ :