Anita is 42 1/2 feet below jared. Steph is 67 3/7 feet above anita. What is stephs position compared to jared. Explain

The Laplace transform of the non-homogeneous second order differential equation is [tex]\mathcal {L} \{f(t)\} = \frac{4\cdot (s+6)}{s\cdot (s-4)\cdot (s+1)\cdot (s-5)} +\frac{1}{s} -\frac{1}{s\cdot (s-5)}[/tex].

A Laplace transform is a frequency-based algebraic substitution method used to determine the solutions of differential equations in a quick and efficient manner.

In this question we shall use the following Laplace transforms:

[tex]\mathcal {L} \{f(t) + g(t)\} = \mathcal {L} \{f(t)\} + \mathcal {L}\{g(t)\}[/tex]   (1)

[tex]\mathcal {L} \{\alpha\cdot f(t)\} = \alpha\cdot \mathcal {L} \{f(t)\}[/tex]   (2)

[tex]\mathcal{L} \left\{y^{(n)} \right\} = s^{n}\cdot \matcal {L}\{f(t)\}-s^{n-1}\cdot y(0) -...-y^{(n)}(0)[/tex]   (3)

[tex]\mathcal {L} \{e^{-a\cdot t}\} = \frac{1}{s+a}[/tex]   (4)

Now we proceed to derive an expression fo the Laplace transform of the solution of the differential equation:

[tex]y'' -5\cdot y' = 8\cdot e^{4\cdot t}-4\cdot e^{-t}[/tex]

[tex]s^{2}\cdot \mathcal {L}\{f(t)\}-5\cdot y(0) - y'(0) - 5\cdot s \cdot \mathcal {L} \{f(t)\} +5\cdot y(0) = \frac{8}{s-4}-\frac{4}{s+1}[/tex]

[tex]\mathcal {L} \{f(t)\} = \frac{4\cdot (s+6)}{s\cdot (s-4)\cdot (s+1)\cdot (s-5)} +\frac{1}{s} -\frac{1}{s\cdot (s-5)}[/tex]

The Laplace transform of the non-homogeneous second order differential equation is [tex]\mathcal {L} \{f(t)\} = \frac{4\cdot (s+6)}{s\cdot (s-4)\cdot (s+1)\cdot (s-5)} +\frac{1}{s} -\frac{1}{s\cdot (s-5)}[/tex]. [tex]\blacksquare[/tex]

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The Laplace transform Y'' − 5y' = 8e4t − 4e−t when y(0) = 1, y'(0) = −1 for f(t) = 8e4t − 4e−t would be  [tex]\frac{4(s+6)}{s.(s-4)(s+1).(s-5)} + \frac{1}{s} - \frac{1}{s.(s-5)}[/tex].

A Laplace transform is a frequency-based algebraic substitution method used to determine the solutions of differential equations quickly and efficiently.

The Laplace transform

L[ f(t) + g(t) ] = Lf(t) + Lg(t)

Also,

L [[tex]y^{n}[/tex]] = [tex]s^{n} . L[ f(t) ] - s^{n-1} .y(0) .....y^{n}(0)[/tex]

We have

Y'' − 5y' = 8 . e^4t − 4 . e−t

[tex]s^{2} . L[ f(t) ] - 5. y(0)- y'(0) .....y^{n}(0)[/tex]

y(0) = 1, y'(0) = −1  

for f(t) = 8e4t − 4e−t.

= [tex]\frac{8}{s-4} - \frac{4}{s+1}[/tex]

L [f(t)] = [tex]\frac{4(s+6)}{s.(s-4)(s+1).(s-5)} + \frac{1}{s} - \frac{1}{s.(s-5)}[/tex]

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Answer:

[tex]\boxed{\text{Slope = 5}}[/tex]

[tex]\boxed{\text{y-intercept = 1}}[/tex]

Step-by-step explanation:

To find the slope of the line, we must pick any two points on the line. Using those two points, we will calculate the Rise and the Run. Then, we will use the slope formula (Rise/Run) to find the slope. The y-intercept is the intersection of the point on the y-axis.

[tex]\text{My chosen points: (0,1) and (1,6)}[/tex]

[tex]\text{Rise = 5; Run = 1}[/tex]

≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

[tex]\text{Slope}= \dfrac{\text{Rise}}{\text{Run}}[/tex]

➡ [tex]\bold{Slope = \frac{5}{1} = \underline{5}} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Rise = 5; Run = 1}][/tex]

[tex]\underline{........................................................................................................................}[/tex]

[tex]\text{Intersection on y-axis:} \ (0,1)[/tex]

➡ [tex]\text{y-intercept} \rightarrow (0,\bold{ 1}) \rightarrow \bold{\underline{{1}}}}[/tex]

≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

Answer:

33.3333333333

Step-by-step explanation:

we see that there are 6 candies in total

we also see that there is a 50% chance that someone will take out 3 candies of the same color,

50/3 = 16.66666666666667

so the chance of getting 2 marbles of the same color is 16.66666666666667 + 16.66666666666667 which is 33.3333333333

I hope I could help

Answer:

13.75 is your answer

Step-by-step explanation:

find area of whole triangle 5.5*7*1/2=19.25

Find area of blank spot 5.5*2*1/2=5.5

Subtract 19.25-5.5=13.75

Answer:

(6-5)/5=20% increase

Step-by-step explanation:

Answer:

$1.5

Step-by-step explanation:

12 x 1.75 + 6c = 30

21 + 6c = 30

6c = 30 - 21

6c = 9

c = 9/6

c = 1.5

Answer:

do face reveal

Step-by-step explanation:

we don't talk about bruno

Answer:

[tex]\pi (\frac{diameter}{2} )^{2}[/tex]

Step-by-step explanation:

The formula is pretty similar to the standard equation, π·r², since the diameter is just the radius times two.

Hope that helps! :)

Answer:

Step-by-step explanation:

The radious is 7 inches, that means the diameter is 14 inches.

The height is 18 inches. so...

V=πr2h=π·72·18≈2770.88472

So hence, your answer is

-------------------------------------------------------------------------------------------------------------

Always keep more than 2 smiles so that you can share! Me happy! You happy! EVERYONE HAPPY!

Thanks!

Have a great day!

:D

The cosine function for the ferris wheel ride is an illustration of a sinusoidial function

The equation of the Ferris wheel is y = -190cos(π / 120 t) + 195

A cosine function is represented as:

y = Acos(Bt - C) + D

From the complete question, the diameter of the ferris wheel is 380 feet.

The amplitude represents the radius, and this is calculated as:

A = 380/2

A = 190

The function becomes:

y = 190cos(Bt - C) + D

The period of the function is:

T = 2π / B

From the complete question, one full rotation is completed in 4 minutes.

Convert the time to seconds

T = 4 * 60

T = 240.

So, we have:

240 = 2π / B

Divide both sides by 2

120 = π / B

Make B the subject

B = π / 120

The function becomes

y = 190cos(π / 120 t - C) + D

From the question, the ferris wheel is 195 feet above the ground.

This represents the vertical shift.

So, we have:

D = 195

The function becomes

y = 190cos(π / 120 t - C) + 195

Also, we have:

The lowest point is at t = 0 and the function is a negative cosine function

So, we have:

C = 0

The function becomes

y = -190cos(π / 120 t) + 195

Hence, the cosine function is y = -190cos(π / 120 t) + 195

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Answer:

Add 509 and 476; The Roman Era lasted for a total of 985 years from 509 B.C to 476 A.D.

Step-by-step explanation:

Answer:

Delta does not have a relative extreme in the equation, so it is variable y It can not be true

Step-by-step explanation:

[tex]s = 5x + 3y[/tex]

There is an answer

The rest of the equation that has no substituted delta is not true, so the prime variables have relative extremes.

Answer: 25

Step-by-step explanation: because 50% of 50 is 25

Answer:

a

Step-by-step explanation:

the solution to the system is at the point of intersection of the linear equations.

the lines intersect at (- 4, 3 )

then solution is (- 4, 3 )

The probability helps us to know the chances of an event occurring. The probability of event n occurring is 0.3.

The probability helps us to know the chances of an event occurring.

[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

We know that for two independent events the probability of the two events occurring simultaneously is written as,

[tex]P(A \cap B) = P(A)\cdot P(B)[/tex]

Now, as we know the probability of event m occurring also we know the probability of both events occurring simultaneously, therefore, the probability of event n occurring can be written as,

[tex]P(A \cap B) = P(A)\cdot P(B)\\\\P(m \cap n) = P(m)\cdot P(n)\\\\0.138 = 0.46 \times P(n)\\\\P(n) = 0.3[/tex]

Hence, the probability of event n occurring is 0.3.

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Answer:

Step-by-step explanation:

29-9=20

9-(-11)=20

50×-20=-1000

-1000+29=-971

Answer:

c = 40degrees

Step-by-step explanation:

the sum of a triangle should be 180 degrees

you need to ad 80+60 which is 140 then minus 140 from 180 which is 40 so 40 degrees is the measurement of angle c

Answer:

yes

Step-by-step explanation:

The answer is: Reject H0. There is convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds.

The difference between group 1 and group 2 is the species of group 1 are vertebrates and species of group 2 are invertebrates.

Vertebrates are those animals that have a spinal cord.

Invertebrates are those who do not have a spinal cord or vertebrae.

The animals, of group 1 are alligator, fish, frog, bird, and zebra, all are vertebrates.

The animals of group 2 are jellyfish, octopus, tarantula, and earthworms.

Thus, the correct option is C, group 1 are vertebrates, and group 2 is invertebrates.

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Using it's concept, it is found that the domain and range of the function are given by:

D: [–4, ∞) and R: [0, ∞)

In this problem, the function is:

[tex]g(x) = \sqrt{x + 4}[/tex]

The square root function does not exist for negative values, hence the domain is represented by:

[tex]x + 4 \geq 0 \rightarrow x \geq -4[/tex]

The range of the square root function is [tex]x \geq 0[/tex], which remains the same as there are no vertical translations.

Hence the correct option is given by:

D: [–4, ∞) and R: [0, ∞)

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Answer: C) D: [–4, ∞) and R: [0, ∞)

Step-by-step explanation:

Answer:

[tex] \frac{ \alpha + \beta + \gamma }{ - d} [/tex]

Step-by-step explanation:

If we simplify that fraction, we get

[tex] \frac{ \alpha + \beta + \gamma }{ \alpha \beta \gamma } [/tex]

Keep that in mind.

If y, a ,b are zeroes of the cubic polynomial, then that means

[tex](x - \alpha )(x - \beta )(x - \gamma )[/tex]

make up the polynomial.

Notice that leading xoeffeicent will be 1, so the roots will multiply to

[tex] - d[/tex]

so

[tex] \alpha \beta \gamma = - d[/tex]

which gives us

[tex] \frac{ \alpha + \beta + \gamma }{ - d} [/tex]

Proof:

Consider the function

[tex](x - 2)(x - 3)(x - 5)[/tex]

The roots are 2, 3, 5.

D is -30 so we get

Using the value,

[tex] \frac{2 + 3 + 5}{ 30} = \frac{1}{3} [/tex]

If we use the orginal equation, we get

[tex] \frac{1}{6} + \frac{1}{10} + \frac{1}{15} = \frac{10}{30} = \frac{1}{3} [/tex]

Answer:

Hey,mate

Notice that leading xoeffeicent will be 1, so the roots will multiply to

The roots are 2, 3, 5.

[tex]\sqrt{2} \sqrt{3} \sqrt{5}[/tex]

D is -30

Answer: 83 degrees

Step-by-step explanation:

In order to find theta, you must take the arccosine of both sides. The arccosine eliminates the cosine, and extracts the argument. Therefore:

[tex]cos(x)=\frac{2}{16} =\frac{1}{8}[/tex]

[tex]arccos(cos(x))=arccos(\frac{1}{8} )=x[/tex]

Use a calculator the find the arccosine of 1/8. Its nearly impossible to find the exact answer without one:

[tex]x=arccos(\frac{1}{8} )[/tex]

[tex]x=83[/tex]

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &250\\ r=rate\to 16\%\to \frac{16}{100}\dotfill &0.16\\ t=\textit{elapsed time} \end{cases} \\\\\\ A=250(1 + 0.16)^{t}\implies A=250(1.16)^t \\\\[-0.35em] ~\dotfill[/tex]

[tex]A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill &1000\\ P=\textit{initial amount}\dotfill &250\\ r=rate\to 16\%\to \frac{16}{100}\dotfill &0.16\\ t=\textit{elapsed time} \end{cases} \\\\\\ 1000=250(1.16)^t\implies \cfrac{1000}{250}=1.16^t\implies 4=1.16^t \\\\\\ \log(4)=\log(1.16^t)\implies \log(4)=t\log(1.16) \\\\\\ \cfrac{\log(4)}{\log(1.16)}=t\implies \stackrel{\textit{about 9 years and 4 months}}{9.34\approx t}[/tex]

Answer:

1. Find the circumference, then multiply that by 120 turns.

Formula for circumference;

C = 2πr

But, we need to find the radius which is 1/2(half) of the diameter, so,

D/2 = R

D = Diameter

R = Radius

20/2 = 10 is the radius.

Plug in values now:-

C = 2(3.14) x 10

C = 6.28 x 10

C = 62.8 is the circumference, now we multiply this by 120 to get the total amount of centimetres it'll go.

62.8(120)

= 7,536 cm it'll go.

2. Find the circumference, then multiply that by 750 turns/revolutions.

C = 2πr

Find radius,

D/2 = R

50/2 = 25 is the radius.

Plug in values now:-

C = 2(3.14) x 25

C = 6.28 x 25

C = 157 cm it'll go.

3. Same thing, find circumference then compare values.

Given that radius is 10,

Use the formula for circumference;

C = 2πr

Replace values:-

C = 2(3.14) x 10

C = 6.28 x 10

C = 62.8 cm is the circumference of the first circle.

Now the second circle, (use same formula)

C = 2πr

Find radius,

D/2 = R

10/2 = 5 is the radius.

Replace values:-

C = 2(3.14) x 5

C = 6.28 x 5

C = 31.4 cm is the circumference for the second circle.

Now subtract the second circle's circumference from the first:

62.8 - 31.4

= 31.4, 31.4 cm is how much greater the second circle is than the first.

4 - 5. Find circumference, (using circumference formula)

C = 2πr

Find radius,

D/2 = R

760/2 = 380

Replace values:-

C = 2(3.14) x 380

C = 6.28 x 380

C = 2,386.4 km is the distance he'll travel.

If he wants to travel around it with 2,000 km, he'll need to travel at least once.

Answer:

[tex]A_{Circle} \approx 39.24\: units^2[/tex]

Step-by-step explanation:

Square ABCD is inscribed in a circle with center P such that BC = 5 units.

BD will be diagonal of the square as well as diameter of the circle.

[tex]BD = BC\times\sqrt 2[/tex]

[tex]\implies BD = 5\sqrt 2[/tex]

-> Diameter of the circle [tex](d) = 5\sqrt 2[/tex]

-> Radius of the circle [tex](r) = 2.5\sqrt 2=3.535\: units[/tex]

[tex]A_{Circle} =\pi(r)^2[/tex]

[tex]\implies A_{Circle} =3.14(3.535)^2[/tex]

[tex]\implies A_{Circle} =3.14(3.535)^2[/tex]

[tex]\implies A_{Circle} =39.2381465[/tex]

[tex]\implies A_{Circle} \approx 39.24\: units^2[/tex]

Answer:

160 000

Step-by-step explanation:

400 000 - 240 000 = 160 000

Answer:

0.1 or 10%

Step-by-step explanation:

Cost: 500

Sell: 550

550-500 = 50

50/500 = 0.1 OR 10%

Therefore, the percentage profit for each sale is 10% of the original wholesale price.

Answer:

10%

Step-by-step explanation:

profit=buyingpirce _selling price

550_500=50

%profit=profit\buyingprice×100

50\500×100=10%