unit 11: volume & surface area homework 8

Answer:

12

Step-by-step explanation:

Differentiate the equation. It will give you -1/6x + 2 = dy/dx.

Let dy/dx = 0 (you do this because the highest point is usually the turning point. The gradient is zero at the turning point, meaning that you'd have to set dy/dx to be zero to figure out the highest point).

Then rearrage for x

-1/6x+2=0

1/6x = 2

x = 12

Circumference = 2× pie × r

Circumference = 6pie

Thus ;

2pie × r = 6pie

r = 3

____________________________________________

[tex]r = \frac{1}{2} \sqrt{ ({ - 6})^{2} + {2}^{2} - c} \\ [/tex]

[tex]3 = \frac{1}{2} \sqrt{ 36 + 4 - c} \\ [/tex]

[tex]6 = \sqrt{40 - c} [/tex]

[tex]( {6})^{2} = ({ \sqrt{40 - c} })^{2} [/tex]

[tex]36 = 40 - c[/tex]

[tex]c = 4[/tex]

Answer:

2064

Step-by-step explanation:

18 + 21 + 24 + ...

This is an arithmetic series with first term 18 and common difference 3.

The nth term is

18 + 3(n - 1)

The 32nd term is the number of seats in the 32nd row:

18 + 3(32 - 1) = 18 + 3(31) = 18 + 93 = 111

The sum of the series is:

n/2(a + L) = (32/2)(18 + 111) = 2064

The function which is the vertex form of the equation whose first three steps shown in writing is  f(x)=5(x +4)²- 80.

Vertex form of parabola is the equation form of quadratic equation, which is used to find the coordinate of vertex points at which the parabola crosses its symmetry.

The standard equation of the vertex form of parabola is given as,

[tex]y=a(x-h)^2+k[/tex]

Here, (h, k) is the vertex point.

The first three steps in writing the function in vertex form are shown.

[tex]f(x) = 40x +5x^2[/tex]

Write the function in standard form.

[tex]f(x) = 5x^2+ 40x[/tex]

Factor out of the first two terms by taking out the common number 5 from the equation,

[tex]f(x) = 5(x^2 +8x)[/tex]

Form a perfect square trinomial with (8/2)² = 16,

[tex]f(x) = 5(x^2 +8x+ 16) - 5(16)\\f(x) = 5(x+4)^2 - 80[/tex]

Hence, the function which is the vertex form of the equation whose first three steps shown in writing is  f(x)=5(x +4)²- 80.

Learn more about the vertex form of the parabola here;

https://brainly.com/question/17987697

Answer:

c

Step-by-step explanation:

We will see that the length of the browser window is 4.9 inches, and the screen is a square of sidelength 10.2 in

We know that the area of the browser window is 24 in^2, we will assume that the window is a perfect square, then the area is equal to the square of the length x, we have:

x^2 = 24 in^2

x = √(24 in^2) = 4.9 in

We know that the browser covers 3/13 of the screen, so the area of the screen is 13/3 times the area of the browser:

A = (13/3)*24 in^2 = 104 in^2

Again, if the screen is square of sidelength s, we have:

s^2 = 104 in^2

s = √(104 in^2)  = 10.2 in

If you want to learn more about areas, you can read:

https://brainly.com/question/24487155

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{24\% of 48.06}}{\left( \cfrac{24}{100} \right)48.06}\implies 11.5344~\hfill \underset{total}{\stackrel{48.06~~ + ~~11.53}{\approx 59.59}}[/tex]

Answer:

59.59$

Step-by-step explanation:

24% of $48.06=11.5344

Total=11.5+48.06=$59.59

[tex]~~~~~~~~~~~~\textit{angle between two vectors } \\\\ cos(\theta)=\cfrac{\stackrel{\textit{dot product}}{u \cdot v}}{\underset{\textit{magnitude product}}{||u||~||v||}} \implies \measuredangle \theta = cos^{-1}\left(\cfrac{u \cdot v}{||u||~||v||}\right) \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} 6i-4j\\ 2i-6j \end{cases}\implies \stackrel{\qquad a~\hfill b\qquad }{\begin{array}{llll} < 6~~,~~-4 > \\ < 2~~,~~-6 > \end{array}}[/tex]

[tex]\stackrel{\textit{\Large dot product}}{ < 6~~,~~-4 > \cdot < 2~~,~~-6 > \implies (6\cdot 2)+(-4\cdot -6)}\implies 12+24\implies 36 \\\\\\ \stackrel{\textit{\Large magnitudes}}{|| < 6~~,~~-4 > ||\implies \sqrt{6^2+(-4)^2}\implies \sqrt{52}} \\\\\\ || < 2~~,~~-6 > ||\implies \sqrt{2^2+(-6)^2}\implies \sqrt{40} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\measuredangle \theta =cos^{-1}\left( \cfrac{36}{\sqrt{52}\cdot \sqrt{40}} \right)\implies \measuredangle \theta =cos^{-1}\left( \cfrac{36}{\sqrt{52}\cdot \sqrt{40}} \right) \\\\\\ \measuredangle \theta =cos^{-1}\left( \cfrac{36}{\sqrt{2080}} \right)\implies \measuredangle \theta \approx 37.9^o[/tex]

Formula for the area of a triangle = 1/2 x base x height

Base = 24

Height = 7

Area = 1/2 x 24 x 7 = 12 x 7 = 84

Answer: 84 yd^2

Hope this helps!

Answer:

6.167

Step-by-step explanation:

1 + 2/3 - (-9/2)

1 + 2/3 + 9/2

Taking LCM (1 x 2 x 3)

6/6 + 4/6 + 27/6

6 + 4 + 27/6

37/6

6.167 Ans

The quadratic regression equation of company X sales would have a degree of 2

To determine the quadratic regression equation, we make use of a graphing calculator

From the graphing calculator,we have the following calculation summary

A quadratic regression equation is represented as:

y = ax^2 + bx + c

So, we have:

y = -507.61x^2 +23372.94x -170697.85

Hence, the quadratic regression equation is y = -507.61x^2 +23372.94x -170697.85

This means that:

x = 22.75

So, we have:

y = -507.61 * 22.75^2 + 23372.94 * 22.75 -170697.85

Evaluate

y = 98316.63

Hence, the profit for selling at $22.75 is $98316.63

Read more about quadratic regression equation at:

https://brainly.com/question/14279500

Answer: 1.a equal 158 over 33 1.b equals 34 over 33

1.c equals negative 31 over 15

3.a equals 106 over 35

3.b equals negative 293 over 72 .

Step-by-step explanation: I am very sorry but I answered what I know . Hope it helps you . Sorryyy. Thanks . .

Answer:

1

Step-by-step explanation:

because if you do 1 1/2 - 1/2 = 1

Answer:

Step-by-step explanation:

The total number of marbles is 6 + 8 + 4 = 18]

If the first marble drawn is yellow, that happens with a probability of 8/18

So the important thing to note is that now there are 17 marbles,

Now a red marble is drawn. We didn't replace the yellow.

There are 6 red marbles.

So the chances of getting a red marble is 6/17

Answer. P(Y then R) = 8/18 * 6/17 = 48/306

48 / 306 reduces down to 8/51  = 0.156

points: (3, 7) and (-1, -1)

slope (m) :

[tex]\sf \dfrac{y_2-y_1}{x_2-x_1}[/tex]

========

[tex]\hookrightarrow \dfrac{-1-7}{-1-3}[/tex]

[tex]\hookrightarrow \dfrac{-8}{-4}[/tex]

[tex]\hookrightarrow 2[/tex]

Equation:

[tex]\sf y-y_1 = m(x-x_1)[/tex]

==============

[tex]\rightarrow \sf y-7 = 2(x-3)[/tex]

[tex]\rightarrow \sf y = 2x-6+7[/tex]

[tex]\rightarrow \sf y = 2x+1[/tex]

Answer:

[tex]y = 2x- 1[/tex]

Step-by-step explanation:

To determine which equation passes through the points (3, 7) and (-1, -1), we need to determine the slope of the equation. Then, we shall use point slope form to determine the equation of the line.

Determining the slope of the line:

[tex]\text{Slope} = \dfrac{\text{Rise}}{\text{Run} } =\dfrac{\text{y}_{2} - \text{y}_{1} }{\text{x}_{2} - \text{x}_{1} }[/tex]

Substituting the points in the slope formula:

[tex]\text{Slope} =\dfrac{-1 - 7 }{-1- 3 }[/tex]

Simplifying the slope:

[tex]\text{Slope} =\dfrac{-1 - 7 }{-1- 3 }[/tex]

[tex]\text{Slope} =\dfrac{-8}{-4 } = 2[/tex]

Determining the equation of the line:

We shall use point slope form to determine the equation of the line.

[tex]\text{Point slope form:} \ y - y_{1} = m(x- x_{1} )[/tex]

Substitute the slope and the coordinates of any two points stated above.

[tex]y -7= 2(x- 3 ) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Using the point (3,7)}][/tex]

Simplify the equation and organize it to slope intercept form:

[tex]y -7= 2x- 6[/tex]

[tex]y = 2x- 6 + 7[/tex]

[tex]y = 2x+ 1[/tex]

Answer:

See below

Step-by-step explanation:

I assume you want the quadratic that has these values

Vertex form of this parabola

y = a(x- - 1)^2  + 4     insert the given point to calculate 'a'

8 = a (1 + 1)^2 + 4    shows a = 1

y = (x+1)^2 + 4         expand this  vertex form to get the quadratic form

y = x^2 + 2x + 5

Answer:

B which is b=4

Step-by-step explanation:

POSITIVE FOUR, just to be clear

Answer:

the answer is b

Step-by-step explanation:

The shape represented by this solid figure attached is a triangular prism with two triangle base and three rectangular faces.

A solid figure is a three dimensional shape having length, width and height. Examples of solid figures are cylinders, cone, pyramid and prism.

The shape represented by this solid figure attached is a triangular prism with two triangle base and three rectangular faces.

Find out more on solid figure at: https://brainly.com/question/8774322

Answer:

option c iscorrect

Step-by-step explanation:

Speed

|

|~~~~~~~~~~~~

|

|________________ position

Answer:

Place 2 X's above the 2 column, and Place 1 X above the 2 1/4 column, place 4 X's in the 2 3/4 column, place 2 X's in the 3 column,  place 1 X in the 3 1/4 column, and 1 X in the 3 1/2 column.

Step-by-step explanation:

The key with Line plots is to count the amount of that number. As you can see, there are 2 2's in the 2 columns, 2 3's in the three-column, and so on. And the three main steps of making a line graph are these:

1. Count the Number of what you have

2. Always give your graph a title

3. Keep your graph organized. An unorganized graph can cause confusion.

And you're done! I hope this helped!

Answer:

NY or MZ

Step-by-step explanation:

they are both outside of the parallel lines and on opposite sides of the transverse line

Answer:

500miles

Step-by-step explanation:

use the Pythagorean theory

Answer:

15

Step-by-step explanation:

f(X)= f(5)

meaning X= 5

x²-2x

5²-2(5) = 15

Answer:

If you observer the value of x=0 and x=1, you can conclude that every 1 value of x increased,

the f(x) will be increased by 0.5. The graph function should be: 

f(x)= x/2A positive difference means that the value should be always positive.
To find 3 the positive difference of f(x) with 3 values of x apart, let use x=0 and x=0+3= 3. The difference would be:

f(x+3) - f(x)f(3)- f(0)=1.5 - 0= 1.5The answer would be: 1.5

Answer:

27.25 Years Old

Step-by-step explanation:

Find the total age of the 17 golfers.

52(17) = 884

Find total age of the 9 golfers.

9(74) = 666

Subtract.

884 - 666 = 218

Divide by the 8 golfers.

218/8 = 27.25

Answer:

The graph y = 18x2 + mx + 2= 12

So the answer is 12

The value of m does the graph of y = 18 x² + m x + 2 have exactly one x-intercept is 12.

The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.

We have Equation.

y = 18 x² + m x + 2

Now, to find exactly one intercept we will use Discriminant Method as

D = m² - 4 x 18 x 2 = 0

m² - 144 = 0

m² = 144

m = -12 or m = 12

Thus, the required value of m is 12.

Learn more about Intercept here:

https://brainly.com/question/1530139

#SPJ7

Answer:

n = 7

Step-by-step explanation:

n+ 4 = 11       subtract 4 from both sides of the equation

n + 4 -4 = 11-4

n = 7

Hey there!

n + 4 = 11

SUBTRACT 4 to BOTH SIDES

n + 4 - 4 = 11 - 4

CANCEL out: 4 - 4 because it give you 0

KEEP: 11 - 4 because it help solve for the n-value

NEW EQUATION: n = 11 - 4

SIMPLIFY IT!
n = 7

Therefore, your answer is: n = 7

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The range of the dot plot can be from zero to seven because it covers the given data set. Then the correct options are A, B, and C.

The element which appears a number of times are called frequency.

The data set shown below represents the number of times some families went out for dinner the previous week.

The data set is given as:

4, 2, 2, 0, 1, 6, 3, 2, 5, 1, 2, 4, 0, 1

Rearrange in ascending order

0, 0, 1, 1, 2, 2, 2, 2, 4, 4, 5, 6

Data     Frequency

0               2

1                2

2                4

3               0

4               2

5               1

6               1

Because the median is 2, and the data points to the left and right are not symmetrical, the data set is not symmetrical.

From the given data set

4 has a frequency of 2

5 has a frequency of 1

Then the range of the dot plot can be from zero to seven because it covers the given data set.

More about the frequency link is given below.

https://brainly.com/question/4264055

Answer:

109 - -37 = 146

Step-by-step explanation:

since you are subtracting a negative, the negative number and the sign cancel each other out. So all you have to do is add.