Can someone please answer 5, 6 and 7? Thank you.

Use Euler’s Formula to find the missing number. Edges: 37 Faces: 25 Vertices: ?

matrenka [14]

Answer:

Step-by-step explanation:

Comment

The formula that relates edges faces and vertices is F + V = E + 2

Givens

Edges (E): 37

Faces (F) = 25

Vertices: x

Solution

25 + x = 37 + 2 Subtract 25 from both sides.

25-25 +x= 37 - 25 + 2 Combine

x = 12 + 2

x = 14

Answer: The vertices = 14

7 0

2 years ago

Kacie has a balance of $10,000 on a loan with an annual interest rate of 8%. To pay off the $10,000 in four years, Kacie will ha

SOVA2 [1]

Kacie has a balance of $10,000 on a loan with an annual interest rate of 8%. To pay off the $10,000 in four years, Kacie will have to make a minimum payment is $244.13 per month. How much will kacie pay in interest over the four year period?

A.) $1.088.20

B.) $1,718.24

C.) $2,971.99

D.) $11,718.24

8 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.