Find the volume of this rectangular
prism.

Continue the given solution and solve for B and C :

[tex](s+1)\dfrac{s^2+1}{(s-1)(s+1)(s-2)} = (s+1)\left(-\dfrac1{s-1} + \dfrac B{s+1} + \dfrac C{s-2}\right)[/tex]

[tex]\dfrac{s^2+1}{(s-1)(s-2)} = -\dfrac{s+1}{s-1} + B + \dfrac{C(s+1)}{s-2}[/tex]

[tex]s=-1 \implies B = \dfrac13[/tex]

Similar steps lead to C = 5/3, and so

[tex]\dfrac{s^2+1}{(s-1)(s+1)(s-2)} = -\dfrac1{s-1} + \dfrac13\times\dfrac1{s+1} + \dfrac53\times\dfrac1{s-2}[/tex]

Now take the inverse transform of each term.

[tex]Y(s) = -\dfrac1{s-1} \implies y(t) = -e^t L^{-1}\left\{\dfrac1s\right\} = -e^t[/tex]

[tex]Y(s) = \dfrac13\times\dfrac1{s+1} \implies y(t) = \dfrac{e^{-t}}3 L^{-1}\left\{\dfrac1s\right\} = \dfrac{e^{-t}}3[/tex]

[tex]Y(s) = \dfrac53\times\dfrac1{s-2} \implies y(t) = \dfrac53e^{2t} L^{-1}\left\{\dfrac1s\right\} = \dfrac{5e^{2t}}3[/tex]

Then the inverse transform of F(s) is

[tex]F(s) = \dfrac{s^2+1}{(s-1)(s+1)(s-2)} \implies f(t) = -e^t + \dfrac{e^{-t}+5e^{2t}}3[/tex]

[tex]\implies f(t) = \boxed{\dfrac{5e^{3t} - 3e^{2t} + 1}{3e^t}}[/tex]

Answer: For this question, the answers are as follows:

a) d = 3.6t

b) 10.8 miles

c) 1.2 hours

Step-by-step explanation:

Part A: The slope of a line is y=mx+b

equation for this part would be : d=mt

plug in the value: d=3.6t

Part B: The value of t is 3 hours

Plug everything in: 3.6 (3)= 10.8 miles

Part C: The Distance given is 4.32 miles.

4.32 miles = 3.6 hours

then divide both sides by 3.6

you get  t=1.2 hours

Hope this helped and didn't confuse you!

We have the identity

[tex]\left(\sqrt x + \dfrac1{2^n}\right)^2 = x + \dfrac1{2^{n-1}} \sqrt x + \dfrac1{2^{2n}}[/tex]

Take the square root of both sides and rearrange terms on the right to get

[tex]\sqrt x + \dfrac1{2^n} = \sqrt{x + \dfrac1{2^{n-1}} \left(\sqrt{x} + \dfrac1{2^{n+1}}\right)}[/tex]

Decrementing n gives

[tex]\sqrt x + \dfrac1{2^{n-1}} = \sqrt{x + \dfrac1{2^{n-2}} \left(\sqrt{x} + \dfrac1{2^{n}}\right)}[/tex]

and substituting the previous expression into this, we have

[tex]\sqrt x + \dfrac1{2^{n-1}} = \sqrt{x + \dfrac1{2^{n-2}} \sqrt{x + \dfrac1{2^{n-1}} \left(\sqrt x + \dfrac1{2^{n+1}}\right) } }[/tex]

Continuing in this fashion, after k steps we would have

[tex]\sqrt x + \dfrac1{2^{n-k}} = \sqrt{x + \dfrac1{2^{n-(k+1)}} \sqrt{x + \dfrac1{2^{n-k}} \sqrt{x + \dfrac1{2^{n-(k-1)}} \sqrt{\cdots \dfrac1{2^{n-1}} \left(\sqrt x + \dfrac1{2^{n+1}}\right)}}}}[/tex]

After a total of n - 2 steps, we arrive at

[tex]\sqrt x + \dfrac14 = \sqrt{x + \dfrac12 \sqrt{x + \dfrac1{2^2} \sqrt{x + \dfrac1{2^3} \sqrt{\cdots \dfrac1{2^{n-1}} \left(\sqrt x + \dfrac1{2^{n+1}}\right)}}}}[/tex]

Then as n goes to infinity, the first nested radical converges to √x + 1/4. Similar reasoning can be used to show the other nested radical converges to √x - 1/4. Then the integral reduces to

[tex]\displaystyle \int_e^{e^2} \left(\sqrt x - \frac14\right) + \left(\sqrt x + \frac14\right) \, dx = 2 \int_e^{e^2} \sqrt x \, dx = \boxed{\frac43 \left(e^3 - e^{\frac32}\right)}[/tex]

Answer:

9/8

27 divided by 3 = 9

24 divided by 3 = 8

I hope this helps!

The ratio in the simplest form of 27 to 24 is equal to 9:8 or 9/8.

When comparing two or more numbers, the phrase ratio is used in mathematics. When one quantity is related to another, it can be used to show how big or tiny it is. Division is used to compare two quantities in a ratio. The term "antecedent" in this context refers to the dividend, and "resultant" to the divisor.

From the given information in the question,

To find the simplest form, divide numerator and denominator with the same number.

Numerator = 27 feet

In simple form = 27/3 = 9

Denominator = 24 yards = 72 feet

In simple form = 72/3 = 24

= 9/24

= 3/8 is the simplest form.

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volume: 113.1 and SA:138.23

Answer:

b = 4, or -4

Step-by-step explanation:

b^2 - 4*4*1 = 0

b^2 = 16

b = 4, or -4

Answer:

x=[tex]\sqrt{\frac{7y+8}{5} }[/tex]

Step-by-step explanation:

Answer:

$18.75

Step-by-step explanation:

25/4 = 6.25

25-6.25=18.75

$18.75

Solution:

Given that:

Substitute the value of y into equation #2.

Since the equation has no variable and is false, this system has no solution.

[tex] \Large{\boxed{\sf Option \ A) \ Slope = -2 }} [/tex]

[tex] \\ [/tex]

To find the value of the slope of the line that passes through the points (5 , -11) and (-9 , 17), we will have to use the slope formula.

[tex] \\ [/tex]

[tex] \Large{\left[ \begin{array}{c c c} \underline{\tt Slope \ formula \text{:}} \\~ \\ \tt m = \dfrac{rise}{run} = \dfrac{\Delta y}{\Delta x} = \dfrac{y_2 - y_1}{x_2 - x_1}\end{array} \right] } [/tex]

Where m is the slope of the line.

[tex] \\ [/tex]

To apply the above formula, we first need to identify our values.

[tex] \sf (\underbrace{\sf 5}_{x_1} \ , \ \overbrace{\sf -11}^{y_1} ) \ \ and \ \ (\underbrace{\sf -9}_{x_2} \ , \ \overbrace{\sf 17}^{y_2} ) [/tex]

[tex] \\ [/tex]

Let's substitute these values into the formula:

[tex] \longrightarrow \sf m = \dfrac{17 - (-11)}{-9 - 5} \\ \\ \\ \longrightarrow \sf m = \dfrac{17 + 11}{-14} \\ \\ \\ \longrightarrow \sf m = \dfrac{28}{-14} \\ \\ \\ \longrightarrow \sf m = \dfrac{7 \cdot 4}{7 \cdot (-2)} \\ \\ \\ \longrightarrow \sf m = -\dfrac{4}{2} \\ \\ \\ \longrightarrow \boxed{\boxed{\sf m = - 2}} [/tex]

[tex] \\ [/tex]

[tex] \hrulefill [/tex]

[tex] \\ [/tex]

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Gradient (m) of a Line :

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

Substituting the known values ,

➱ [tex]\rm{m=\dfrac{17-(-11)}{-9-5}}[/tex]

➱ [tex]\rm{m=\dfrac{17+11}{-14}}[/tex]

➱ [tex]\rm{m=\dfrac{28}{-14}}[/tex]

➱ [tex]\rm{m=-2}[/tex]

Henceforth, Gradient = -2

Step-by-step explanation:

first lets do the bottom rectangular prism

v = l * w * h

l = 9

w = 3

h = 3

can you work out the volume and answer in the comments

Answer:

I think its D

Step-by-step explanation:

x2+y2+8x+6y=0

x2+8x+6y+y=0

9x2+7y2

15x2y2

Answer:

protecting your personal belongings as a renter.

Step-by-step explanation:

your TVs, laptops, furniture, jewelry, etc.

Answer:

10

Step-by-step explanation:

Mr. Ford selects 5 people who tried out.

He then chooses 5 more people to assist with the show.

Together he has 5 + 5 = 10 people altogether.

Answer:

the answer for the question is N=6

Answer:

6 laps they will run

Step-by-step explanation:

I say 6 laps because if you do 42/7 then you will get 6 so 6 laps.

Answer:

A soda costed $3.50.

Step-by-step explanation:

Step 1) We know that a slice of pizza and a soda costs $9 (from Kate's order). With a burger added (Billy's order) it would cost $13.50.

So a burger would cost $4.50:

[tex]13.50-9=4.50[/tex]

Step 2) We also know a burger and a soda costs $8. So we subtract the cost of the burger from Louis' order to find the cost of the soda:

[tex]8-4.50=3.50[/tex]

Cost of soda: [tex]\$3.50[/tex]

Answer:

The answer is 8 pi

Step-by-step explanation:

The formula is radius squared times pi!

I hope this helped!!

Answer:

There are 112 cans in each box.

Step-by-step explanation:

You divide 1008 by 9, so that gives you 112.

Hope it helps!

Answer: A: √x+5

Step-by-step explanation:

The parent square root function is √x

Transformations to this graph come in the form y =√(x-h) +k, where h is responsible for left-right movements, and k is responsible for up down movements.

For the image, we can see that f(x) is simply the parent square root function, √x. To get h(x) from f(x), there is a translation of 5 units to the left, which can be algebraically represented by a value of h = -5. Putting this into our form, we get h(x) = √x+5, which is your answer :)

The function h(x) is after transformation is √(x + 5).

Option A is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The square root parent function is f(x) = √x, which starts from the point (0, 0) and increases as x increases.

To transform the parent function to h(x) starting from the point (-5, 0), we need to perform a horizontal translation of 5 units to the right.

This is because if we plug in x = -5 into the parent function,

We get f(-5) = √(-5), which is not a real number.

Therefore, we need to shift the function horizontally so that it starts from

x = -5.

The transformation of the square root parent function with a horizontal translation of 5 units to the right is given by the equation:

h(x) = √(x + 5)

This function starts from the point (-5, 0) and increases as x increases.

We can verify this by plugging in x = -5 to get h(-5) = √(0) = 0, which is the starting point of the function, and by observing that h(x) increases as x increases.

Thus,

The function h(x) is √(x + 5).

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Answer:

35t + 20k

Step-by-step explanation:

Let t = number of toddlers.

Let k = number of kids.

Her pay is

35t + 20k

Answer:

I would do it at your own pace. Find yourself a habit that helps you focus.

Step-by-step explanation:

For some people, like me, music helps me focus. For others, utter silence is best. I would suggest that if you finding a focal point does not help that you get a tutor. You can also come up with multiple ways to study like Quizlets, videos, flashcards, podcasts, depending on what type of learner you are!

Answer:

a four is correct answer

Answer:

A. 4

Step-by-step explanation:

Side AE corresponds to EC, so the scale factor is 3.

12/3=4

Hope this helps :)

Hello.

Let's find the multiplicative inverse of -100.

In order to do that, we need to write -100 as a fraction:

[tex]\bf{\displaystyle\frac{-100}{1}[/tex]

Now, in order to find the multiplicative inverse of -100, we should flop the fraction over:

[tex]\bf{\displaystyle\frac{1}{-100}[/tex]

I hope it helps.

Have an outstanding day. :)

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

Answer:

option C is correct answer.

hope this helps you !

Answer:

It's probably 9+59=68

Step-by-step explanation:

=> 9+59=68

68 - 59 gives you 9

So in order to check if the problem was solved correctly you will add the answer plus the subtraction of one number in the two numbers of subtraction

which means between the options 9 + 59 equals to 68 is absolutely the correct answer

Answer:

Diameter

Step-by-step explanation:

If it was from the middle to the edge it would be a radius,

but since it goes all the way across its a diameter.

Answer:

Step-by-step explanation:

3.Diameter.

Answer: One root

Explanation:

x^3 = -343

x^3 + 343 = 0

x^3 + 7^3 = 0

(x+7)(x^2 - 7x + 7^2) = 0 .... sum of cubes factoring rule

(x+7)(x^2 - 7x + 49) = 0

Set each piece equal to zero and solve for x.

You should find that the first piece x+7 = 0 leads to x = -7 as the only real root.

The other piece x^2-7x+49 = 0 leads to two non-real roots, ie complex roots.