What is the EXACT volume of this composite figure?

324 pie in^3
468 pie in^3
684 pie in^3
828 pie in^3

Step-by-step explanation:

the usual line equation is

y = mx + b

I personally rather write it

y = ax + b

but really, all letters are possible as needed (particularly, if certain letters are already used for other parts of the problem definition).

what is important is to understand the messaging of the parts of such equations independently of what letter is used for what.

the factor of x (usually m in these equations) is the slope of the line, its incline. it is expressed as the ratio "y coordinate change / x coordinate change" when going from one point on the line to another.

the constant term (often called b in these equations) is the y-intercept (the y value when x = 0, indicating where the line is intercepting the y-axis).

I guess the equation in your problem actually looks like

2 + 3x + 5 - 2x = y

so, let's combine similar terms

3x - 2x + 2 + 5 = y

x + 7 = y

and now compare this to the general line equation, and we find

m = 1

b = 7

Decompose each given F(s) into partial fractions.

[tex]F(s) = \dfrac{s+1}{s(s-1)(s-3)}[/tex]

has partial fraction decomposition

[tex]\dfrac{s+1}{s(s-1)(s-3)} = \dfrac as + \dfrac b{s-1} + \dfrac c{s-3}[/tex]

Combine the rational terms on the right and solve for the coefficients:

[tex]\dfrac{s+1}{s(s-1)(s-3)} = \dfrac{a(s-1)(s-3) + b s(s-3) + c s(s-1)}{s (s-1) (s-3)}[/tex]

[tex]1 = a(s-1)(s-3) + bs(s-3) + c s(s-1)[/tex]

[tex]1 = 3 a + (-4 a - 3 b - c) s + (a + b + c) s^2[/tex]

[tex]\begin{cases}3a=1 \\ -4a-3b-c = 0 \\ a+b+c=0 \end{cases} \implies a=\dfrac13, b=-\dfrac12, c=\dfrac16[/tex]

Then

[tex]F(s) = \dfrac13 \times \dfrac1s - \dfrac12 \times \dfrac1{s-1} + \dfrac16 \times \dfrac1{s-3}[/tex]

Using the frequency-shifting property, the inverse transform is

[tex]\boxed{f(t) = \dfrac13 - \dfrac{e^t}2 + \dfrac{e^{3t}}6}[/tex]

The other transform can be dealt with in the same manner.

[tex]F(s) = \dfrac1{(s-1)(s-2)(s-3)} = \dfrac a{s-1} + \dfrac b{s-2} + \dfrac c{s-3}[/tex]

[tex]\implies 1 = a(s-2)(s-3) + b(s-1)(s-3) + c(s-1)(s-2)[/tex]

[tex]\implies 1 = 6 a + 3 b + 2 c + (-5 a - 4 b - 3 c) s + (a + b + c) s^2[/tex]

[tex]\implies \begin{cases}6 a + 3 b + 2 c=1 \\ -5a-4b-3c = 0 \\ a+b+c=0\end{cases} \implies a=\dfrac12, b=-1, c=\dfrac12[/tex]

[tex]\implies F(s) = \dfrac12 \times \dfrac1{s-1} - \dfrac1{s-2} + \dfrac12 \times \dfrac1{s-3}[/tex]

[tex]\implies \boxed{f(t) = \dfrac{e^t}2 - e^{2t} + \dfrac{e^{3t}}2}[/tex]

Answer:

A, B, E

Step-by-step explanation:

Positive,

because 2*12 equals to 24, and 24 is positive!

Answer:

Step-by-step explanation:

Answered here: https://brainly.com/question/26774005

Answer:

-6 5/7

Multiply the denominator by the number that doesn't exceed -47. Here, it would be -6.

7 x (-6) = -42

Then, subtract the difference to get the mixed number.

-42-5 = -47

The numbers used are found in the improper fraction: -6 5/7

Answer:

[tex]-6\frac{5}{7}[/tex]

Step-by-step explanation:

Given the following question:

[tex]-\frac{47}{7}[/tex]

To convert an improper fraction into a mixed number we simply have to divide the numerator by the denominator.

[tex]-\frac{47}{7}[/tex]
[tex]-\frac{47}{7}=47\div7=-6\frac{5}{7}[/tex]
[tex]=-6\frac{5}{7}[/tex]

Let 6 represent how many times 7 does into 47
Let 5 represent the remainder
Let 7 represent the denominator which remains the same.

Hope this helps.

Answer:

You find the range by subtracting the smallest value from the highest in the set. So in this case, it would be 5-0=0

Step-by-step explanation:

Hope This Helps

Have A Great Day

~Zero~

Answer:

Option A

Step-by-step explanation:

Both fractions have common denominators (x - 4). So, we can add the numerators.

[tex]\dfrac{x-9}{x-4}+\dfrac{x^{2}-x+5}{x-4}=\dfrac{x-9 +x^{2}-x +5}{x-4}\\\\\\=\dfrac{x -x +x^{2}-9+5}{x-4}\\\\\\=\dfrac{x^{2}-4}{x-4}[/tex]

Answer:

10/11

Step-by-step explanation:

The required equation that can be used to figure out how many miles Hugh and his brothers have traveled based on the number of miles they have driven is y = 65x

Given the following variables

Time taken to travel is x

Mils traveled is y

Using the coordinate points (2, 130) and (4, 260)

The standard linear equation is y = mx + b

slope m = 260-130/4-2
m = 130/2

m = 65

For the intercept

130 = 65(2) + b

b = 0

The required equation that can be used to figure out how many miles Hugh and his brothers have traveled based on the number of miles they have driven is y = 65x

Learn more on linear functions here; https://brainly.com/question/14323743

Answer:

The slope-intercept form of a linear equation is y = mx + b. In the equation, x and y are the variables. The numbers m and b give the slope of the line (m) and the value of y when x is 0 (b). The value of y when x is 0 is called the y-intercept because (0,y) is the point at which the line crosses the y-axis.

Answer:

The answer is 55.

m=55

Step-by-step explanation:

we know that a straight line is 180
We know that m+125 is a straight line.
This means that we will subtract 125 from 180
When you do that, you get 55.

We can check our answer by doing 125+55
That will get you 180.

Answer:

<

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf{b=55\:(b=y-intercept\:;)}}[/tex]

Step-by-step explanation:

Hello.

The y-intercept of a line is a point where the graph touches the y-axis.

Y-intercepts always have an x-coordinate of 0.

Now, what is the y-intercept?

If we have a point (0, b) then b is the y-intercept.

This is just a formula, so don't think that the y-intercept is b, okay?

The y-intercept is b, but only in formulae. :)

Using the formula, we can deduce that

the y-intercept is 55.

I hope it helps.

Have a great day.

[tex]\boxed{imperturbability}[/tex]

Answer:

If he earns (e) $7.75 per hour, this implies e = 7.75h.

Step-by-step explanation:

If you wanted to solve that-

e = 7.75h

193.75 = 7.75h

Divide both sides by 7.25  

h = 25

Answer:

300

Step-by-step explanation:

60 * 5 = 300

Answer:

Ernie has $10.50 saved.

Step-by-step explanation:

1.5 x $7 = 10.5

OR

(1 x $7) + (0.5 x $7) = $7 + $3.50 = $10.50

Hope this helps!

We need slope

[tex]\\ \rm\Rrightarrow m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\\ \rm\Rrightarrow m=\dfrac{2-1}{6-3}[/tex]

[tex]\\ \rm\Rrightarrow m=\dfrac{1}{3}[/tex]

This can be solved using two methods:

Method #1:

The slope is 1/3.

Method #2:

The slope is 1/3.

Looking at the two methods, we can conclude that:

The slope of the line is 1/3.

Answer:The y intercept would be 55.

Step-by-step explanation:Wherever the y-axis is touched at with the x-value at 0 (in this case, its 55) that would be the y-intercept.

Answer:

[tex]\huge\boxed{\sf{55}}[/tex]

Step-by-step explanation:

Hello.

In order to determine the y-intercept, just look at the y-coordinate (If we have a point like (0, b)

b --> y-intercept

Therefore, b (the y-intercept) is equal to 55.

I hope it helps.

Have a great day.

[tex]\boxed{imperturbability}[/tex]

Answer:

it is a geometrical net

Answer:

the 1st

Step-by-step explanation:

no need to explain

Answer:

Step-by-step explanation:

x-axis and y-axis meet at (0, 0), that is the origin

[tex]f(x)=cos(x)x^{-2}\implies f(x)=\cfrac{cos(x)}{x^2}\implies \cfrac{df}{dx}=\stackrel{\textit{quotient rule}}{\cfrac{-sin(x)\cdot x^2-cos(x)\cdot 2x}{(x^2)^2}} \\\\\\ \cfrac{df}{dx}=\cfrac{-x[x\cdot sin(x)+2cos(x)]}{x^4}\implies \cfrac{df}{dx}=\cfrac{-[xsin(x)+2cos(x)]}{x^3}[/tex]

Answer:

h = b - a

Step-by-step explanation:

Answer:

A/b = h

Step-by-step explanation:

A=bh

1) divide both sides by b

A/b = h

Answer: proportional

Step-by-step explanation: just took the quiz

Answer:

T = 31

Step-by-step explanation:

(T + 8) + T = 70

subtract 8 from both sides

T+T = 62

Rewrite

2T = 62

divide both sides by 2

T = 31

In hexadecimal/base-16, we have B₁₆ = 11, C₁₆ = 12, and D₁₆ = 13, so

4D₁₆ = 4 × 16¹ + 13 × 16⁰ = 77

and

BC2₁₆ = 11 × 16² + 12 × 16¹ + 2 × 16⁰ = 3010