Is y – 4x = 9 a function?

the radius of a cylindrical construction pipe is 3 ft . If the pipe is 25ft long , what is it’s volume ?

ki77a [65]

Given:

radius of a cylindrical construction pipe is 3 ft

lenghtis 25ft long

Required:

what is it’s volume

Explanation:

volume of cylinder:

$\begin{gathered} V=\pi r^2h \\ \\ here\text{ h is the length of the pipe} \\ \\ V=3.14\times(3)^2\times25 \\ \\ V=3.14\times9\times25 \\ \\ V=707\text{ ft}^3 \end{gathered}$

Required answer:

$V=707\text{ ft}^3$

7 0

9 months ago

A bag contains the two tiles shown below. One tile is drawn at random from the bag. The tile is returned to the bag and again a

BaLLatris [955]

<span>From the given ((E) (U)), the sample space for the experiment</span> is {EE, EU, UE, UU}. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.

6 0

3 years ago

Find the magnitude and direction in degrees of the vector v=6i+2 seq31

masha68 [24]

Answer:

Please check the explanation.

Step-by-step explanation:

Given the vector

v = 6i + 2√3j

The Magnitude of a vector:

$\mathrm{Computing\:the\:Euclidean\:Length\:of\:a\:vector}:\quad \left|\left(x_1\:,\:\:\ldots \:,\:\:x_n\right)\right|=\sqrt{\sum _{i=1}^n\left|x_i\right|^2}$

$=\sqrt{6^2+\left(2\sqrt{3}\right)^2}$

$=\sqrt{36+12}$

$=\sqrt{48}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}$

$=\sqrt{3}\sqrt{2^4}$

$=4\sqrt{3}$

The Direction of a vector:

tan Ф = y/x

y=2√3

x = 6

tan Ф = y/x

= 2√3 / 6

= √3 / 3

$\theta \:=tan\:^{-1}\left(\frac{\sqrt{3}}{3}\right)$

$\:\theta \:=\frac{\pi \:}{6}=30^{\circ \:}$

6 0

3 years ago

What is the function f(x) = 2(x + 6), find x if f(x) = 22

lord [1]

Answer:

Step-by-step explanation:

f(x) = 2(x + 6)

f(x) = 22

thereofre we have the equation:

2(x + 6) = 22 <em>use distributive property</em>

2x + 12 = 22 <em>subtract 12 from both sides</em>

2x = 10 <em>divide both sides by 2</em>

x = 5

3 0

3 years ago

You are jumping off the 12 foot diving board at the municipal pool. You bounce up at 6 feet per second and drop to the water you

NARA [144]

Answer:

When do you hit the water?

1.075 seconds after you jump.

What is your maximum height?

the maximum height is 12.5626 ft

Step-by-step explanation:

The equation:

h(t) = -16*t^2 + 6*t + 12

Is the height as a function of time.

We know that the initial height is the height when t = 0s

h(0s) = 12

and we know that the diving board is 12 foot tall.

Then the zero in h(t)

h(t) = 0

Represents the surface of the water.

When do you hit the water?

Here we just need to find the value of t such that:

h(t) = 0 = -16*t^2 + 6*t + 12

Using the Bhaskara's formula, we get:

$t = \frac{-6 \pm \sqrt{6^2 - 4*(-16)*12} }{2*(-16)} = \frac{-6 \pm 28.4}{-32}$

Then we have two solutions, and we only care for the positive solution (because the negative time happens before the jump, so that solution can be discarded)

The positive solution is:

t = (-6 - 28.4)/-32 = 1.075

So you hit the water 1.075 seconds after you jump.

What is your maximum height?

The height equation is a quadratic equation with a negative leading coefficient, then the maximum of this parabola is at the vertex.

We know that the vertex of a general quadratic:

a*x^2 + b*x + c

is at

x = -b/2a

Then in the case of our equation:

h(t) = -16*t^2 + 6*t + 12

The vertex is at:

t = -6/(2*-16) = 6/32 = 0.1875

Evaluating the height equation in that time will give us the maximum height, which is:

h(0.1875) = -16*(0.1875 )^2 + 6*(0.1875) + 12 = 12.5626

And the height is in feet, then the maximum height is 12.5626 ft

6 0

3 years ago