The Flash runs 100 km in 25 seconds. What is the Flash's velocity

For the integrals in (a), (b), and (e), you'll end up integrating by parts.

(a)

[tex]\displaystyle \int_0^\infty t e^{-st} \, dt[/tex]

Let

[tex]u = t \implies du = dt[/tex]

[tex]dv = e^{-st} \, dt \implies v = -\dfrac1s e^{-st}[/tex]

Then

[tex]\displaystyle \int_0^\infty t e^{-st} \, dt = uv\bigg|_{t=0}^{t\to\infty} - \int_0^\infty v\, du[/tex]

[tex]\displaystyle \int_0^\infty t e^{-st} \, dt = \left(-\frac1s te^{-st}\right)\bigg|_0^\infty + \frac1s \int_0^\infty e^{-st} \, dt[/tex]

[tex]\displaystyle \int_0^\infty t e^{-st} \, dt = -\frac1s \left(\lim_{t\to\infty} te^{-st} - 0\right) + \frac1s \int_0^\infty e^{-st} \, dt[/tex]

[tex]\displaystyle \int_0^\infty t e^{-st} \, dt = \frac1s \int_0^\infty e^{-st} \, dt[/tex]

[tex]\displaystyle \int_0^\infty t e^{-st} \, dt = -\frac1{s^2} e^{-st} \bigg|_0^\infty e^{-st} \, dt[/tex]

[tex]\displaystyle \int_0^\infty t e^{-st} \, dt = -\frac1{s^2} \left(\lim_{t\to\infty}e^{-st} - 1\right) = \boxed{\frac1{s^2}}[/tex]

(b)

[tex]\displaystyle \int_0^\infty t e^{-t} e^{-st} \, dt = \int_0^\infty t e^{-(s+1)t} \, dt[/tex]

Let

[tex]u = t \implies du = dt[/tex]

[tex]dv = e^{-(s+1)t} \, dt \implies v = -\dfrac1{s+1} e^{-(s+1)}t[/tex]

Then

[tex]\displaystyle \int_0^\infty t e^{-(s+1)t} \, dt = -\dfrac1{s+1} te^{-(s+1)t} \bigg|_0^\infty + \frac1{s+1} \int_0^\infty e^{-(s+1)t} \, dt[/tex]

[tex]\displaystyle \int_0^\infty t e^{-(s+1)t} \, dt = -\dfrac1{s+1} \left(\lim_{t\to\infty}te^{-(s+1)t} - 0\right) + \frac1{s+1} \int_0^\infty e^{-(s+1)t} \, dt[/tex]

[tex]\displaystyle \int_0^\infty t e^{-(s+1)t} \, dt = \frac1{s+1} \int_0^\infty e^{-(s+1)t} \, dt[/tex]

[tex]\displaystyle \int_0^\infty t e^{-(s+1)t} \, dt = -\frac1{(s+1)^2} e^{-(s+1)t} \bigg|_0^\infty[/tex]

[tex]\displaystyle \int_0^\infty t e^{-(s+1)t} \, dt = -\frac1{(s+1)^2} \left(\lim_{t\to\infty}e^{-(s+1)t} - 1\right) = \boxed{\frac1{(s+1)^2}}[/tex]

(e)

[tex]\displaystyle \int_0^\infty t^2 e^{-st} \, dt[/tex]

Let

[tex]u = t^2 \implies du = 2t \, dt[/tex]

[tex]dv = e^{-st} \, dt \implies v = -\dfrac1s e^{-st}[/tex]

Then

[tex]\displaystyle \int_0^\infty t^2 e^{-st} \, dt = -\frac1s t^2 e^{-st} \bigg|_0^\infty + \frac2s \int_0^\infty t e^{-st} \, dt[/tex]

[tex]\displaystyle \int_0^\infty t^2 e^{-st} \, dt = -\frac1s \left(\lim_{t\to\infty} t^2 e^{-st} - 0\right) + \frac2s \int_0^\infty t e^{-st} \, dt[/tex]

[tex]\displaystyle \int_0^\infty t^2 e^{-st} \, dt = \frac2s \int_0^\infty t e^{-st} \, dt[/tex]

The remaining integral is the transform we found in (a), so

[tex]\displaystyle \int_0^\infty t^2 e^{-st} \, dt = \frac2s \times \frac1{s^2} = \boxed{\frac2{s^3}}[/tex]

Computing the integrals in (c) and (d) is much more immediate.

(c)

[tex]\displaystyle \int_0^\infty \sinh(bt) e^{-st} \, dt = \int_0^\infty \frac{e^{bt}-e^{-bt}}2 \times e^{-st} \, dt[/tex]

[tex]\displaystyle \int_0^\infty \sinh(bt) e^{-st} \, dt = \frac12 \int_0^\infty \left(e^{(b-s)t} - e^{(b+s)t}\right) \, dt[/tex]

[tex]\displaystyle \int_0^\infty \sinh(bt) e^{-st} \, dt = \frac12 \left(\frac1{b-s} e^{(b-s)t} - \frac1{b+s} e^{(b+s)t}\right) \bigg|_0^\infty[/tex]

[tex]\displaystyle \int_0^\infty \sinh(bt) e^{-st} \, dt = \frac12 \left[\lim_{t\to\infty}\left(\frac1{b-s} e^{(b-s)t} - \frac1{b+s} e^{(b+s)t}\right) - \left(\frac1{b-s} - \frac1{b+s}\right)\right][/tex]

[tex]\displaystyle \int_0^\infty \sinh(bt) e^{-st} \, dt = \frac12 \left(\frac1{b+s} - \frac1{b-s}\right) = \boxed{\frac{s}{s^2-b^2}}[/tex]

(d)

[tex]\displaystyle \int_0^\infty (e^{2t} - 3e^t) e^{-st} \, dt = \int_0^\infty \left(e^{(2-s)t} - 3e^{(1-s)t}\right) \, dt[/tex]

[tex]\displaystyle \int_0^\infty (e^{2t} - 3e^t) e^{-st} \, dt = \left( \frac1{2-s} e^{(2-s)t} - \frac3{1-s} e^{(1-s)t} \right) \bigg|_0^\infty[/tex]

[tex]\displaystyle \int_0^\infty (e^{2t} - 3e^t) e^{-st} \, dt = \lim_{t\to\infty} \left( \frac1{2-s} e^{(2-s)t} - \frac3{1-s} e^{(1-s)t} \right) - \left( \frac1{2-s} - \frac3{1-s} \right)[/tex]

[tex]\displaystyle \int_0^\infty (e^{2t} - 3e^t) e^{-st} \, dt = \frac3{1-s} - \frac1{2-s} = \boxed{-\frac{2s-5}{s^2-3s+2}}[/tex]

Answer:it would be 88 because of the co efficient due to the process of mingus in china which made it a law to not pursue dreams within country borders

Step-by-step explanation:

Answer:

v < -5

Step-by-step explanation:

Add 3 to both sides. This gives -8+(-3)>v-3+3, or -5>v. Rewriting the inequality gives v < -5.

"This is non response bias because many customers may choose to not fill out the cards"
Not everyone will chose to leave a review when leaving the store, and those that do were probably in some way inconvenienced, and felt inclined to leave one, while the others left and went about their day.

Answer:

[tex]\huge\boxed{\sf acute\ and \ scalene}[/tex]

Step-by-step explanation:

In terms of sides:

Since, all of the sides of the triangles are unequal (As indicated), it is a scalene triangle.

In terms of angles:

All the angles are less than 90 degrees (acute), hence, it is an acute triangle.

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

5 x - 4

Step-by-step explanation:

Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=x5+45 f - 1 ( x ) = x 5 + 4 5 is the inverse of f(x)=5x−4 f ( x ) = 5 x - 4 .

Answer:

The length of the other diagonal is 42 cm.

Step-by-step explanation:

Area of Rhombus = 966 cm^2 (squared)

one length of diagonal(d2) =46cm

The are of rhombus= d1 x d2/2  

*substitution from equation above* = 966= 46 x d2/2 *plug answer in* :  966=23 x d2  *divide next*

d2=966/23

d2=42cm

I don't know if that makes sense hopefully it helps.

Step-by-step explanation:

Use the Distributive Property:

[tex]1/5(5x+9)+4/5(1-9x)[/tex]

[tex]x+1.8+4/5-7.2x[/tex]

Combine Like-Terms:

[tex]-6.2x+2.6[/tex]

Answer:

  a. 1

  b. 5

Step-by-step explanation:

Ordered pairs are (x, f(x)). You want f(2), so you look for an ordered pair that lists 2 as the first number. That one is (2, 1). This means f(2) = 1.

__

f(2) is plotted as the point (2, f(2)). That is, the x-coordinate of the point will be 2. The point that has x-coordinate 2 is (2, 5).

As above, this means f(2) = 5.

Answer:

its c just so u know

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

the surface area of the rectangular prism is 142cm³

Step-by-step explanation:

35+15+21+21+35+15

Step-by-step explanation:

the number is represented by x. you need to add -2 first then multiply by 5.

thus, the correct expression will be:

( x + -2) *5 = (x-2) *5 = 5(x-2)

for e.g, let x be 3.

acc to the puzzle,

3+-2 = 3-2=1

1*5= 5

using Kiran's expression:

x-10; 3-10= -7

here you can see the answer is wrong.

using the "correct expression" :

5(x-2) = 5( 3-2)

= 5(1)

= 5.

hope this helped you!

-s.

Answer:

A=4. B=5. C=24

Answer:

35x + 14

Step-by-step explanation:

multiply in the brackets

5x × 7 = 35x

(+)2 × 7 = (+)14

Answer:

Step-by-step explanation:

14 times 14 then do 15 times 15 then add both answers up and take that answer and square route it

Answer:

ok so we need to first find the amount of black squares vs white squares

top row: 2 black 3 white

2nd top row: 1 black 4 white

middle row: 3 black 2 white

2nd bottom row: 1 black 4 white

bottom row: 2 black 3 white

so lets add that up

9 black 16 white

so then each one is 5 meters so

9*5=45

45m^2

Hope This Helps!!!

Answer:

area of the given figure: 58 m²

Explanation:

area of rectangle: length * width

total area:

( 2 * 5 + 12 * 4 )

58 m²

Answer:

The area of the given figure is 58 m².

Step-by-step explanation:

Dividing the given figure into two parts :

———————————————————————

Firstly, finding the area of bigger rectangle by substituting the values in the formula :

[tex]\longrightarrow{\pmb{\sf{A_{(Rectangle)} = l \times b}}}[/tex]

[tex]\begin{gathered} \qquad\longrightarrow{\sf{A_{(Rectangle)} = l \times b}}\\\\\qquad{\longrightarrow{\sf{A_{(Rectangle)} = 12\times 4}}}\\\\\qquad{\longrightarrow{\sf{A_{(Rectangle)} =48}}}\\\\\qquad{\star{\underline{\boxed{\sf{\pink{A_{(Rectangle)} =48 \: {m}^{2}}}}}}} \end{gathered}[/tex]

Hence, the area of bigger rectangle is 48 m².

———————————————————————

Secondly, finding the area of smaller rectangle by substituting the values in formula :

[tex]\longrightarrow{\pmb{\sf{A_{(Rectangle)} = l \times b}}}[/tex]

[tex]\begin{gathered} \qquad\longrightarrow{\sf{A_{(Rectangle)} = l \times b}}\\\\\qquad{\longrightarrow{\sf{A_{(Rectangle)} = 5\times 2}}}\\\\\qquad{\longrightarrow{\sf{A_{(Rectangle)} =10}}}\\\\\qquad{\star{\underline{\boxed{\sf{\purple{A_{(Rectangle)} =10 \: {m}^{2}}}}}}} \end{gathered}[/tex]

Hence, the area of smaller rectangle is 10 m².

———————————————————————

Now, finding the total area of given figure by substituting the values in the formula :

[tex]\longrightarrow{\pmb{\sf{Total \: Area = A_{(Big)} + A_{(Small)}}}}[/tex]

[tex] \begin{gathered} \qquad{\longrightarrow{\sf{Total \: Area = A_{(Big)} + A_{(Small)}}}} \\ \\ \quad{\longrightarrow{\sf{Total \: Area = 48 + 10}}} \\ \\ \quad{\longrightarrow{\sf{Total \: Area = 58}}} \\ \\ \quad{\star{\underline{\boxed{\sf{\red{Total \: Area =58\: {m}^{2}}}}}}} \end{gathered}[/tex]

Hence, the total area of the given figure is 58 m².

[tex]\rule{300}{2.5}[/tex]

Answer:

4

Step-by-step explanation:

You can set up the equation as 5x-3=2x+9. Subtract 2x from both sides, then add three to both sides which gives you 3x=12. Divide both sides by 3, and you get x=4.

Answer:

Tennnnnnnnnnnnn.............

Answer:

$35.00

Step-by-step explanation:

I just did it rn

Answer:

9 apples, 21 oranges, 9 bananas.

Step-by-step explanation:

i did the math

Answer:

It would be 39 fruits

Step-by-step explanation:

If you add up 3+7+3=13 which makes 4 smothies. So 4×3=12 then you would do 13×3=39

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

Explanation:

You can use your calculator to make short work of this problem. Simply plot the parabola and use the "minimum" feature on the calculator to spot the lowest point (specifically the coordinates of that point).

However, I have a feeling your teacher wants you to use a bit of math here. So I'll focus on another approach instead.

---------

The parabolic equation is of the form y = ax^2+bx+c

In this case, we have

Use the values of 'a' and b to find the x coordinate of the vertex h

h = -b/(2a)

h = -(-192)/(2*0.3)

h = 320

The x coordinate of the vertex is 320.

Plug this into the original equation to find the y coordinate of the vertex.

y = 0.3x^2 - 192x + 40357

y = 0.3(320)^2 - 192(320) + 40357

y = 9637 which is the minimum unit cost, in dollars.

The vertex is (h,k) = (320, 9637). It is the lowest point on this parabola.

Interpretation: If the company made 320 cars, then the unit cost (aka cost per car) is the smallest at $9637 per car.

Answer:

12

Step-by-step explanation:

regular implies that all sides are equal
8 sides
total of 96
96/8
12

Answer:

5.1%

Step-by-step explanation:

percent = part/whole × 100%

percent = 85/1675 × 100%

percent = 5.1%

The percentage of earnings that Charlotte spends on cosmetics to the nearest tenth of a per cent is 5.1%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Charlotte earns $1675 every month of which she spends $85 on cosmetics.

The percentage will be calculated as,

Percent = part/whole × 100%

Percent = 85/1675 × 100%

Percent = 5.1%

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Answer:

The answer is 4x² + 2x + 11

Step-by-step explanation:

4x⁴ – 2x³ + 5x² + 2x ÷ x² – x – 1

Now,

[tex]4 {x}^{2} + 2x + 11\\ x² - x - 1 \sqrt{4 x⁴ - 2x³ + 5x² + 2x} \\ \: \: \: \: \: \: 4 {x}^{4} - 4 {x}^{3} - {4x}^{2} \\ \frac{ \: \: \: - \: \: \: \: \: \: + \: \: \: \: \: \: \: \: + \: \: }{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2x {}^{3} + 9x {}^{2} + 2x } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2 {x}^{3} - {2x}^{2} - 2x \\ \frac{ \: \: \: \: \: - \: \: \: \: \: \: + \: \: \: \: + }{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 11 {x}^{2} + 4x } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 11 {x}^{2} - 11x - 11 \\ \frac{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - \: \: \: \: \: \: + \: \: \: \: \: \: \: \: + }{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 15x + 11} [/tex]

Thus, The answer is 4x² + 2x + 11

-TheUnknownScientist 72

Answer:

4x² + 2x + 11

Step-by-step explanation:

hope it's helpful

Answer:

I think the answer is B or C

Answer:

135 is the amount of that she has for now

Answer:

52 x 4 = (50 + 2) x 4

= 50 x 4 + 2 x 4

=200 + 8

=208

this should be right!

brainliest?

The correct the correct multiple of ( 52 x 4 ) is 208.

The number you obtain when you multiple a certain number by an integer. Multiple as like consisting of, including, or involving more than one.

Assume the multiplication of 52 x 4 is A.

To find the value of A

52 x 4 = ( 50 + 2 ) x 4

52 x 4 = 50 x ( 4 ) + ( 2 ) x 4

52 x 4 = ( 200 ) + 8

52 x 4 = ( 208 ).

A = 208.

Therefore, the correct multiple of ( 52 x 4 ) is 208.

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