The model represents an equation. What value of x makes the equation true?
A) -3
B) -9
C) 3
D) 9

Answer:

a. L{t} = 1/s² b. L{1} = 1/s

Step-by-step explanation:

Here is the complete question

The The Laplace Transform of a function ft), which is defined for all t2 0, is denoted by Lf(t)) and is defined by the improper integral Lf))s)J" e-st . f(C)dt, as long as it converges. Laplace Transform is very useful in physics and engineering for solving certain linear ordinary differential equations. (Hint: think of s as a fixed constant) 1. Find Lft) (hint: remember integration by parts) A. None of these. B. O C. D. 1 E. F. -s2 2. Find L(1) A. 1 B. None of these. C. 1 D.-s E. 0

Solution

a. L{t}

L{t} = ∫₀⁰⁰[tex]e^{-st}t[/tex]

Integrating by parts  ∫udv/dt = uv - ∫vdu/dt where u = t and dv/dt = [tex]e^{-st}[/tex] and v = [tex]\frac{e^{-st}}{-s}[/tex] and du/dt = dt/dt = 1

So, ∫₀⁰⁰udv/dt = uv - ∫₀⁰⁰vdu/dt w

So,  ∫₀⁰⁰[tex]e^{-st}t[/tex] =  [[tex]\frac{te^{-st}}{-s}[/tex]]₀⁰⁰ -  ∫₀⁰⁰ [tex]\frac{e^{-st}}{-s}[/tex]

∫₀⁰⁰[tex]e^{-st}t[/tex] =  [[tex]\frac{te^{-st}}{-s}[/tex]]₀⁰⁰ -  ∫₀⁰⁰ [tex]\frac{e^{-st}}{-s}[/tex]

= -1/s(∞exp(-∞s) - 0 × exp(-0s)) + [tex]\frac{1}{s}[/tex] [[tex]\frac{e^{-st} }{-s}[/tex]]₀⁰⁰

= -1/s[(∞exp(-∞) - 0 × exp(0)] - 1/s²[exp(-∞s) - exp(-0s)]

= -1/s[(∞ × 0 - 0 × 1] - 1/s²[exp(-∞) - exp(-0)]

= -1/s[(0 - 0] - 1/s²[0 - 1]

= -1/s[(0] - 1/s²[- 1]

= 0 + 1/s²

= 1/s²

L{t} = 1/s²

b. L{1}

L{1} = ∫₀⁰⁰[tex]e^{-st}1[/tex]

= [[tex]\frac{e^{-st} }{-s}[/tex]]₀⁰⁰

= -1/s[exp(-∞s) - exp(-0s)]

= -1/s[exp(-∞) - exp(-0)]

= -1/s[0 - 1]

= -1/s(-1)

= 1/s

L{1} = 1/s

[tex] y = 1 + \sqrt{x + 2} [/tex]

the root must at least be 0 to have a solution. the "1+" makes it at least 1 instead of zero

Answer:

25 miles (The pattern is m = 25g where m is miles and g is gallons.)

Answer:

A

Step-by-step explanation:

The volume of prism is b*h, base area is (2.5)*(3.24*(1.1)=8.91. Hence volume is 8.91*6.17=54.97

Answer:

-15 < x < -5

Step-by-step explanation:

-3 < x/5  < -1

Multiply all sides by 5

-3*5 < x/5 *5  < -1*5

-15 < x < -5

Answer:

[tex]\frac{a+3}{6}[/tex]

Step-by-step explanation:

Treat it like any other math problem with a equals sign:

6x + 3 = a

subtract 3 from both sides: 6x = a + 3

divide both sides by 6: [tex]x = \frac{a+3}{6}[/tex]

swap the ≥ back in: [tex]x \geq \frac{a+3}{6}[/tex]

the only time the sign flips is if you divide by a negative

9514 1404 393

Answer:

  zero

Step-by-step explanation:

3(2x) = x/2

5.5x = 0 . . . . subtract x/2

x = 0 . . . . . . . divide by 5.5

The number is zero.

Answer:

2/10 = 1/5

Step-by-step explanation:

To figure out the probability of something, we can take

(number of outcomes of that something) / (number of total outcomes)

Here, we are trying to find the probability that the ball is white. The number of outcomes that are possible with the ball being white is 2, as there are two white balls and you can only pick one. You can pick either of the two white balls, but there is no way to pick one of them two times, pick two of them at once, or pick any other ball and have it be white.

The number of total outcomes is 10. There are 10 balls, and you can only pick one ball at a time. There are only 10 options to choose from.

Therefore, we can plug our numbers into the formula above and get 2/10 = 1/5 as our probability

Answer:

25, 33

Step-by-step explanation:

let the length of the one with equal sides be x

third side = x+8

x+x+x+8 = 83

3x+8 = 83

3x = 75

x = 25

x+8 = 25+8 = 33

Answer:

48degrees

Step-by-step explanation:

From the circle geometry shown, traingle BDC is an isosceles triangle which shows means that their base angels are the same. Hence;

<B = <C

<CBD + <BCD + <D = 180

<BCD + <BCD + <D =180

2<BCD + <BDC = 180

Get <BCD;

<BCD+ <ECB = 90

<BCD + 48 = 90

<BCD = 90 - 48

<BCD = 42degrees

Get <BDC

2<BCD + <BDC = 180

2(42)+ <BDC = 180

84 + <BDC = 180

<BDC = 180 - 84

<BDC = 96

Since angle at the centre is twice that at the circumference, then;

<BAC = 1/2(<BDC )

<BAC = 96/2

<BAC = 48degrees

Answer: Choice A)  y - 10 = 2(x - 3)

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

Explanation:

We can rule out choices C and D because this diagonal line has a positive slope (as it moves uphill when moving to the right).

So m = 2 must be the slope.

---------

Recall that

y - y1 = m(x - x1)

represents the point slope form of a linear equation.

The point shown on this graph is (3,10) meaning that x1 = 3 and y1 = 10 pair up together.

So,

y - y1 = m(x - x1)

y - 10 = 2(x - 3)

which points to choice A as the final answer

Answer:

I could be wrong but I calculated 2 years 8 months and 15 days.

2 years

8 months

15 days

Answer:

c = 4√2

Step-by-step explanation:

From the question given above, the following data were obtained:

Angle θ = 30

Opposite = 2√2

Hypothenus = c =?

We can obtain the value of c by using the sine ratio as illustrated below:

Sine θ = Opposite / Hypothenus

Sine 30 = 2√2 / c

½ = 2√2 / c

Cross multiply

c = 2 × 2√2

c = 4√2

Therefore, the value of c is 4√2.

Answer:

a)2x+y=1

b) 6x+12y=16

c) y=-x+3 (I was a bit confused on this one but I believe this is correct)

d) 4x-2y=-8

Answer:

a. -2x - y + 1 = 0

b. 6x + 12y -16 = 0

c. x - 3 = 0

d. -4x + 2y - 8 = 0

Step-by-step explanation:

Answer:

It's How much did you spend at the movies today?

Step-by-step explanation:

The question can the manager asks "How much did you spend at the movies today?". Then the correct option is C.

A discrete quantitative parameter has a clear mathematical explanation but could only take certain integer values (instead of every value in intervals).

The manager of a movie theater is standing outside the theater complex one evening.

He will be asking the moviegoers questions.

Then the questions can the manager ask that will result in discrete quantitative data will be

How much did you spend at the movies today?

The question can the manager asks "How much did you spend at the movies today?"

Then the correct option is C.

More about the discrete quantitative data link is given below.

https://brainly.com/question/12831013

#SPJ2

Answer:

Factorise out x and y terms:

[tex]{ \tt{ = \frac{ {x}^{2} {y}^{4} (5x - 3y)}{45} }} \\ [/tex]

Answer:

A=3.1

B=4.2

C=2.7

Step-by-step explanation:

Answer:

2x+16

Step-by-step explanation:

PEMDAS

Answer:

10 + 40 + 30

Step-by-step explanation:

Commutative property states that the order in which we add numbers does not affect the answer, so we just need to change the order of numbers

Answered by Gauthmath

Answer:

Bonsoir,

f'(-5)=-4/3

f'(-1) =3/4

Step-by-step explanation:

f'(-5) = ?

2 points : (-6,9) and (-3,5)

f'(-5)=(9-5)/(-6-(-3))=-4/3

f'(-1) = ?

2 points : (-3,5) and (1,8)

f'(-1)=(5-8)/(-3-1)=3/4

The lines are perpendicular

The derivative at the points -5 and -1 are:

f’(-5)  = -4/3

f’(-1) = 3/4

The slope of the tangent line to the graph of a function at a point is called the derivative of the function at that point.

We consider the line on which where the x coordinate -5 lies.

It is the line with points (-3, 5) and (-6, 9).

Slope of the line =  [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] = [tex]\frac{9-5}{-6+3} = \frac{-4}{3}[/tex]

f'(-5) = -4/3

We consider the line on which where the x coordinate -1 lies.

It is the line with points (-3, 5) and (1, 8).

Slope of the line =  [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] = [tex]\frac{8-5}{1+3} = \frac{3}{4}[/tex]

f'(-1) = 3/4

Learn more about derivative at a point here

https://brainly.com/question/1111011

#SPJ2

Answer:

[tex]A(x) = 12500(1.054)^x[/tex]

Step-by-step explanation:

Exponential equation for population growth:

Considering a constant growth rate, the population, in x years after 2005, is given by:

[tex]A(x) = A(0)(1 + r)^x[/tex]

In which A(0) is the population in 2005 and r is the growth rate, as a decimal.

The initial population of the town was estimated to be 12,500 in 2005.

This means that [tex]A(0) = 12500[/tex]

The population has increased by about 5.4% per year since 2005.

This means that [tex]r = 0.054[/tex]

So

[tex]A(x) = A(0)(1 + r)^x[/tex]

[tex]A(x) = 12500(1 + 0.054)^x[/tex]

[tex]A(x) = 12500(1.054)^x[/tex]

Answer:

2x-1 = 5x-14

Step-by-step explanation:

5(2x−1) = 5(5x−14)

Divide each side by 5

5/5(2x−1) = 5/5(5x−14)

2x-1 = 5x-14

Answer:

A.

Step-by-step explanation:

5(2x−1) = 5(5x−14)

10x - 5 = 25x - 70

65 = 15x

x = 13/3.

Take Option A.

2x - 1 = 5x - 14

3x = 13

x = 13/3 so its this one.

B: 10x - 5 = 5x - 14

5x = -9

x = -9/5 so NOT B.

C. simplifies to x = 3. so NOT C.

Answer:

128.57 degrees

Step-by-step explanation:

To find the measure of an interior angle of a regular polygon with [tex]n[/tex] sides, we can use the formula: [tex]\frac{180(n-2)}{n}[/tex]

To find the measure of an interior angle of a polygon with 7 sides, all we have to do is plug in 7 into the formula:

[tex]\frac{180(7-2)}{7}[/tex]

7 minus 2 equals 5, so the answer is

[tex]180(5)[/tex]÷[tex]7[/tex]

180 times 5 is equal to 900, and 900 divided by 7 is approximately 128.57

9514 1404 393

Answer:

  3. 42.21 in

  4. 4.38 cm

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationships between an angle in a right triangle and the basic trig functions. The triples of letters stand for ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

where the terms "opposite" and "adjacent" refer to sides of the triangle that are opposite the angle of interest or adjacent to it, respectively.

In these problems, the measure of the hypotenuse is shown, and the problem requests the measure of the side opposite the given angle. The sine function is relevant.

__

3. sin(79°) = GE/GB = GE/(43 in)

   GE = (43 in)sin(79°) ≈ (43 in)(0.981627) ≈ 42.21 in

__

4. sin(26°) = BC/BA = BC/(10 cm)

  BC = (10 cm)sin(26°) ≈ (10 cm)(0.438371) ≈ 4.38 cm

Answer:

the since ratio is 5/4

Step-by-step explanation:

Answer:

Kindly check explanation

Step-by-step explanation:

Given that :

The hypothesis :

H0 : σ²= 47.1

H1 : σ² > 47.1

α = 5% = 0.05

Population variance, σ² = 47.1

Sample variance, s² = 83.2

Sample size, n = 15

The test statistic = (n-1)*s²/σ²

Test statistic, T = [(15 - 1) * 83.2] ÷ 47.1

Test statistic = T = [(14 * 83.2)] * 47.1

Test statistic = 1164.8 / 47.1

Test statistic = 24.73

The degree of freedom, df = n - 1 ; 10 = 9

Critical value (0.05, 9) = 16.92 (Chisquare distribution table)

Reject H0 ; If Test statistic > Critical value

Since ; 24.73 > 16.92 ; Reject H0 and conclude that variance is greater.

Answer:

Product of the zeroes of polynomial 3x²-2x-4 is ?

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Answer:

here's the answer to your question

Answer:

for B : he spend 30 minutes jogging and 45 minutes riding his bike

Step-by-step explanation:

75-15=60

60/2=30

jogging (x) =30

30+15=45

riding bike (y) =45

hopefully it help you