The average weight of a 7-year old girl is 49 pounds. The average weight of an 11 year old girl is 77 pounds.

A rectangular room is 22 meters longer than it is wide, and its perimeter is 1616 meters. find the dimension of the room.

Eddi Din [679]

W= width; L= length =w+22m; p= perimeter= 2(L+w)
1616 meters= 2 (L+w) substitute for L
1616m+ 2(w+22m+w) divide each side by 2

808m= 2w+22m subtract 22m from each side
786m=2w divide each side by 2
393m=w Anwer: The width is 393 meters
L=w+22m=393m+22m=415m Answer: The length is 415 meters

3 0

3 years ago

Consider the differential equation:

Wewaii [24]

(a) Take the Laplace transform of both sides:

$2y''(t)+ty'(t)-2y(t)=14$

$\implies 2(s^2Y(s)-sy(0)-y'(0))-(Y(s)+sY'(s))-2Y(s)=\dfrac{14}s$

where the transform of $ty'(t)$ comes from

$L[ty'(t)]=-(L[y'(t)])'=-(sY(s)-y(0))'=-Y(s)-sY'(s)$

This yields the linear ODE,

$-sY'(s)+(2s^2-3)Y(s)=\dfrac{14}s$

Divides both sides by $-s$ :

$Y'(s)+\dfrac{3-2s^2}sY(s)=-\dfrac{14}{s^2}$

Find the integrating factor:

$\displaystyle\int\frac{3-2s^2}s\,\mathrm ds=3\ln|s|-s^2+C$

Multiply both sides of the ODE by $e^{3\ln|s|-s^2}=s^3e^{-s^2}$ :

$s^3e^{-s^2}Y'(s)+(3s^2-2s^4)e^{-s^2}Y(s)=-14se^{-s^2}$

The left side condenses into the derivative of a product:

$\left(s^3e^{-s^2}Y(s)\right)'=-14se^{-s^2}$

Integrate both sides and solve for $Y(s)$ :

$s^3e^{-s^2}Y(s)=7e^{-s^2}+C$

$Y(s)=\dfrac{7+Ce^{s^2}}{s^3}$

(b) Taking the inverse transform of both sides gives

$y(t)=\dfrac{7t^2}2+C\,L^{-1}\left[\dfrac{e^{s^2}}{s^3}\right]$

I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that $\frac{7t^2}2$ is one solution to the original ODE.

$y(t)=\dfrac{7t^2}2\implies y'(t)=7t\implies y''(t)=7$

Substitute these into the ODE to see everything checks out:

$2\cdot7+t\cdot7t-2\cdot\dfrac{7t^2}2=14$

5 0

3 years ago

What is the range of a function f(x)=-x+15 when the domain is {-3,-1,11}?

hodyreva [135]

Answer:

The range is the output value or the y value.

You would work backwards to find the domain.

f(x) = 4x - 1 f(x) = 4x - 1

3 = 4x - 1 7 = 4x - 1

add 1 to both sides add 1 to both sides

4 = 4x 8 = 4x

divide both sides by 4 divide both sides by 4

x = 1 x = 2

f(x) = 4x - 1 f(x) = 4x - 1

11 = 4x - 1 15 = 4x - 1

add 1 to both sides add 1 to both sides

12 = 4x 16 = 4x

divide both sides by 4 divide both sides by 4

x = 3 x = 4

Domain { 1, 2, 3, 4}

Step-by-step explanation:

4 0

3 years ago

Since we have computer algebra systems that can solve polynomial division problems for us, why is it necessary to learn how to d

hjlf

Answer:

Because simply, we need to be smarter and we can’t let computers take over humans.

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

You want to buy a $203,000 home. You plan to pay 10% as a down payment, and take out a 30 year loan for the rest. or a) How much

Darina [25.2K]

Answer:

The amount of the loan is going to be $ 182,700, and the monthly payments, if the interest is 6%, are going to be $ 537.95, while if the interest is 7%, are going to be $ 543.02.

Step-by-step explanation:

Given that you want to buy a $ 203,000 home, and you plan to pay 10% as a down payment, and take out a 30 year loan for the rest, for A) determine how much is the loan amount going to be, B) determine what will your monthly payments be if the interest rate is 6%, and C) determine what will your monthly payments be if the interest rate is 7%, the following calculations must be made:

A) 100 - 10 = 90

203,000 x 0.90 = X

182,700 = X

B) (182,700 x 1.06) / (30 x 12) = X

193,662 / 360 = X

537.95 = X

C) (182,700 x 1.07) / (30 x 12) = X

195,489 / 360 = X

543.025 = X

Therefore, the amount of the loan is going to be $ 182,700, and the monthly payments, if the interest is 6%, are going to be $ 537.95, while if the interest is 7%, are going to be $ 543.02.

5 0

3 years ago