The volume of a cylinder with a height of 4 feet is 144n cubic feet what is the radius of the base of the cylinder V=nr2h

Mathematics

1 answer:

geniusboy [140]2 years ago

6 0

Answer: 6 ft

Step-by-step explanation:

$144\pi =\pi(r^{2})(4)\\\\144\pi=4\pi r^{2}\\\\36=r^{2}\\\\r=\boxed{6 \text{ ft}}$

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An isosceles triangle has angle measures 50°, 50°, and 80°. The side across from the 80° angle is 10 inches long. How long are t

djverab [1.8K]

Answer: The value of other side is 7.8 inch.

Explanation:

It is given that the isosceles triangle has angle measures 50°, 50°, and 80°. The side across from the 80° angle is 10 inches long.

Let the given length of other equal sides be x.

The side across from the 50° angle is x inches long.

Law of sine,

$\frac{a}{\sin A}= \frac{b}{\sin B} =\frac{c}{\sin C}$

$\frac{x}{\sin (50)}= \frac{10}{\sin (80)}$

$\frac{x}{0.766} =\frac{10}{0.9848}$

$x =\frac{10}{0.9848}\times (0.766)$

$x =7.778229 \approx 7.8$

Therefore, the value of other side is 7.8 inch.

3 0

3 years ago

Read 2 more answers

Let f be a continuous function defined on the interval [0,1] such that f(0) = f(1). Show that there exists a number 0 <= a &l

Leni [432]

Explanation:

In order to prove that affirmation, we define the function g over the interval [0, 1/2] with the formula $g(x) = f(x+1/2)-f(x) .$

If we evaluate g at the endpoints we have

g(0) = f(1/2)-f(0) = f(1/2) - f(1) (because f(0) = f(1))

g(1/2) = f(1) - f(1/2) = -g(0)

Since g(1/2) = -g(0), we have one chance out of three

g(0) > 0 and g(1/2) < 0
g(0) < 0 and g(1/2) > 0
g(0) = g(1/2) = 0

We will prove that g has a zero on [0,1/2]. If g(0) = 0, then it is trivial. If g(0) ≠ 0, then we are in one of the first two cases, and therefore g(0) * g(1/2) < 0. Since f is continuous, so is g. Bolzano's Theorem assures that there exists c in (0,1/2) such that g(c) = 0. This proves that g has at least one zero on [0,1/2].

Let c be a 0 of g, then we have

$0 = g(c) = f(c+1/2)-f(c)$