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3 years ago

Find the angle between the given vectors to the nearest tenth of a degree. u = <8, 4>, v = <9, -9> (5 points)

Mathematics

1 answer:

alexdok [17]3 years ago

6 0

There are a number of ways to do this. One way is to use a graphics program to measure it.

The angle is 71.6°.

Another way is to divide the vectors and look at the angle of the result.
(8 +4i)/(9 -9i) = (8 +4i)(9 +9i)/162
= 36 +108i
So the angle is
arctan(108/36) ≈ 71.565° ≈ 71.6°

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For $7.52, you purchased 8 pens and highlighters from a local bookstore. Each highlighter cost $1.09 and each pen cost $.69. How

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2 years ago

Find the values of x for which the combined function h(x) = is undefined if f(x) = 5x + 1 and g(x) = x2 - 9.

Rama09 [41]

We need to know the definition of the "combined function" h(x). I'm going to guess--by looking at answers--that the function is $h(x)=\frac{f(x)}{g(x)}$ making it

$h(x)=\frac{5x+1}{x^2-9}$

This function is undefined wherever the denominator is equal to 0 (division by zero is undefined). Factor the denominator.

$h(x)=\frac{5x+1}{(x+3)(x-3)}$

The two values of x that make the denominator 0 are 3 and -3, otherwise written $x=\pm 3$ .

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2 years ago

A cylinder has a 12-inch diameter and is 15 inches tall. It is filled to the top with water. A 6-inch-diameter ball is placed wi

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The volume of the cylinder is the space occupied by the cylinder. The volume of the water in the cylinder is 1583.36266 in³.

<h3>What is the volume of a cylinder?</h3>

The volume of the cylinder is the space occupied by the cylinder. It is calculated with the help of the formula,

$\text{Volume of the cyllinder}= \pi r^2h$

As it is given that the diameter of the cylinder is 12 inches while the height of the cylinder is 15 inches, also, it has a ball of the diameter of 6 inches placed inside the cylinder, therefore, the volume of the water that is inside the cylinder is the difference in the volume of the cylinder and the volume of the spherical ball.

$\text{Volume of the cyllinder}= \pi r^2h = \dfrac{\pi}{4}d^2 h$

Substitute the values,

$\begin{aligned}\text{Volume of the cyllinder}&= \dfrac{\pi}{4}d^2 h\\& = \dfrac{\pi}{4} \times (12^2) \times 15\\ &=1696.46\rm\ in^3\end{aligned}$

Now, the volume of the ball is equal to the volume of the sphere therefore, the volume of the ball can be written as,

$\text{Volume of the sphere} = \dfrac{4}{3}\pi r^3$

$= \dfrac{4}{3}\pi r^3\\\\= \dfrac{4}{3}\times \pi \times (3^3)\\\\= 113.097\rm\ in^3$

Further, the volume of the water that is inside the cylinder can be written as,

The volume of water = Volume of the cylinder - Volume of the sphere

= 1696.46 - 113.097

= 1583.36266 in³

Hence, the volume of the water in the cylinder is 1583.36266 in³.

Learn more about Volume of the Cylinder:

brainly.com/question/1780981

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