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pav-90 [236]
3 years ago
7

Someone please help me answer this!!

Mathematics
1 answer:
Scrat [10]3 years ago
4 0

Answer:

b = 9cm is the answer.

Step-by-step explanation:

a = 12cm

b = ?

c = 15cm

By using the Pythagoras theorem,

a² + b² = c²

12² + b² = 15²

144 + b² = 225

b² = 225 - 144

b² = 81

b = 9cm.

∴ b = 9cm is the length of the missing leg.

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Solve this problem by using variation of parameters method.<br> y''-y=coshx.
Gekata [30.6K]
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For the nonhomogeneous ODE

y''-y=\underbrace{\cosh x}_{f(x)}

we're looking for a particular solution of the form

y_p=u_1y_1+u_2y_2

where

u_1=-\displaystyle\int\frac{y_2(x)f(x)}{W(y_1(x),y_2(x))}\,\mathrm dx
u_2=\displaystyle\int\frac{y_1(x)f(x)}{W(y_1(x),y_2(x))}\,\mathrm dx

and W(y_1,y_2) is the Wronskian of the two fundamental solutions.

We have

W(y_1,y_2)=\begin{vmatrix}\cosh x&\sinh x\\\sinh x&\cosh x\end{vmatrix}=\cosh^2x-\sinh^2x=1

so we're left with

u_1=-\displaystyle\int\sinh x\cosh x\,\mathrm dx=-\dfrac12\cosh^2x
u_2=\displaystyle\int\cosh^2x\,\mathrm dx=\dfrac12x+\dfrac14\sinh2x

so that the particular solution is

y_p=-\dfrac12\cosh^3x+\dfrac12x\sinh x+\dfrac14\sinh x\sinh2x
y_p=-\dfrac12\cosh x+\dfrac12x\sinh x

As y_1 already accounts for the \cosh x term in y_p, we're left with the general solution

y=C_1\cosh x+C_2\sinh x+\dfrac12x\sinh x
3 0
3 years ago
2x + 3 = 5 . Solve for x
STALIN [3.7K]

Answer:

x = 1

Step-by-step explanation:

2x + 3 = 5

=> 2x = 5 - 3

=> 2x = 2

=> x = 2/2

=> x = 1

4 0
3 years ago
Read 2 more answers
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Liula [17]
Given that <span>a bag contains 26 tiles marked with the letters A through Z.

The probability of picking a letter from the name JACK is 4 / 26

The probability of picking a letter from the name BEN is 3 / 26.

Therefore, the probability of picking a letter from the name JACK or from the name BEN iis given by 4 / 26 + 3 / 26 = 7 / 26 </span>
6 0
3 years ago
!! AP CALCULUS AB !!<br> find the limit of [(secx*sinx) + (cscx*cosx)]/(3secx) as x approaches 3pi/2
uysha [10]

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So,

\lim_{x \rightarrow \frac{3\pi}{2}}{f(x)=f(\frac{3\pi}{2})=\frac{1}{3\sin{\frac{3\pi}{2}}}=-\frac{1}{3}

6 0
4 years ago
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sertanlavr [38]

Answer:

i think you solved it

Step-by-step explanation:

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