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aleksley [76]
3 years ago
8

What is the area of a quarter circle with a radius of 10? (answer needs to be in terms of pi)

Mathematics
2 answers:
Aloiza [94]3 years ago
8 0

Answer:

314.16

Step-by-step explanation:

artcher [175]3 years ago
4 0
The answer is 314.16
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Use the method of undetermined coefficients to find the general solution to the de y′′−3y′ 2y=ex e2x e−x
djverab [1.8K]

I'll assume the ODE is

y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}

Solve the homogeneous ODE,

y'' - 3y' + 2y = 0

The characteristic equation

r^2 - 3r + 2 = (r - 1) (r - 2) = 0

has roots at r=1 and r=2. Then the characteristic solution is

y = C_1 e^x + C_2 e^{2x}

For nonhomogeneous ODE (1),

y'' - 3y' + 2y = e^x

consider the ansatz particular solution

y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x

Substituting this into (1) gives

a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1

For the nonhomogeneous ODE (2),

y'' - 3y' + 2y = e^{2x}

take the ansatz

y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}

Substitute (2) into the ODE to get

b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1

Lastly, for the nonhomogeneous ODE (3)

y'' - 3y' + 2y = e^{-x}

take the ansatz

y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}

and solve for c.

ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16

Then the general solution to the ODE is

\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}

6 0
1 year ago
Solve the following inequality: 3-5x-x^2>=0
Dennis_Churaev [7]

Answer:

-5/2+-1/2√37≤x≤-5/2+1/2√37

Step-by-step explanation:

Step 1: Find the critical points

-x^2-5x+3=0

For this equation: a=-1, b=-5, c=3

−1x^2+−5x+3=0

x=−b±√b2−4ac/2a

x=−(−5)±√(−5)2−4(−1)(3)/2(-1)

x=5±√37 /−2

x=-5/2+1/2√37

Step 2: Check intervals in between critical points

x≤-5/2+1/2 √37 (Doesn't work in original inequality)

-5/2+-1/2√37≤x≤-5/2+1/2√37 (Works in original inequality)

x≥-5/2+1/2 √37 (Doesn't work in original inequality)

5 0
3 years ago
Help! Need by 10:30 to turn in and I'm confused!
JulsSmile [24]

Answer:

21.97 tissues

15.47 cough drops

Step-by-step explanation:

13x1.69=21.97

1.19x15.47

7 0
3 years ago
Pat has nine cards. Frank has two more cards than Steve. Steve has 3 cards how many more cards does Pat have than Frank?
n200080 [17]
4. Pat 9. Frank 5. Steve 3. 9-5=4.
4 0
3 years ago
Read 2 more answers
Gauge ran 12 miles in 20 minutes. What is Gaugue's hourly rate?
nikitadnepr [17]
36 miles per hour if he ran 12 miles in 20 minuets and there are 60 minuets in an hour, then multiply the # by 3
6 0
3 years ago
Read 2 more answers
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