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3 years ago

Additive invers of -12 + 7

Mathematics

1 answer:

lorasvet [3.4K]3 years ago

3 0

Answer:

The additive inverse of 7 is −7, because 7 + (−7) = 0; The additive inverse of −0.3 is 0.3, because −0.3 + 0.3 = 0.

I hope I'm right and good luck! :)

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Solve the given initial-value problem. x^2y'' + xy' + y = 0, y(1) = 1, y'(1) = 8

Kitty [74]

Substitute $z=\ln x$ , so that

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm dz}\cdot\dfrac{\mathrm dz}{\mathrm dx}=\dfrac1x\dfrac{\mathrm dy}{\mathrm dz}$

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1x\dfrac{\mathrm dy}{\mathrm dz}\right]=-\dfrac1{x^2}\dfrac{\mathrm dy}{\mathrm dz}+\dfrac1x\left(\dfrac1x\dfrac{\mathrm d^2y}{\mathrm dz^2}\right)=\dfrac1{x^2}\left(\dfrac{\mathrm d^2y}{\mathrm dz^2}-\dfrac{\mathrm dy}{\mathrm dz}\right)$

Then the ODE becomes

$x^2\dfrac{\mathrm d^2y}{\mathrm dx^2}+x\dfrac{\mathrm dy}{\mathrm dx}+y=0\implies\left(\dfrac{\mathrm d^2y}{\mathrm dz^2}-\dfrac{\mathrm dy}{\mathrm dz}\right)+\dfrac{\mathrm dy}{\mathrm dz}+y=0$
$\implies\dfrac{\mathrm d^2y}{\mathrm dz^2}+y=0$

which has the characteristic equation $r^2+1=0$ with roots at $r=\pm i$ . This means the characteristic solution for $y(z)$ is

$y_C(z)=C_1\cos z+C_2\sin z$

and in terms of $y(x)$ , this is

$y_C(x)=C_1\cos(\ln x)+C_2\sin(\ln x)$

From the given initial conditions, we find

$y(1)=1\implies 1=C_1\cos0+C_2\sin0\implies C_1=1$
$y'(1)=8\implies 8=-C_1\dfrac{\sin0}1+C_2\dfrac{\cos0}1\implies C_2=8$

so the particular solution to the IVP is

$y(x)=\cos(\ln x)+8\sin(\ln x)$

4 0

3 years ago

Find volume of sphere in cubic yards whose radius is 5 yard<br><br> Use pi = 3.14

enyata [817]

Answer:

523.333 cubic yards

Step-by-step explanation:

The formula for the volume of a sphere is $\frac{4}{3}\pi r^{3}$ where $r$ is the radius.

The radius of the given sphere is $r=5$ yards and $\pi =3.14$ .

Therefore, we can substitute in the radius and solve:

$V_{sphere}= \frac{4}{3}\*\times3.14\times 5^{3} =523.333$ cubic yards

4 0

2 years ago

Read 2 more answers

On a certain route, an airline carries 5000 passengers per month, each paying $70. A market survey indicates that for each $1 in

Mkey [24]

Answer:

$85

Step-by-step explanation:

5000 x $70 = $350,000

4950 x $71 = $351,450

4900 x $72 = $352,800

etc.

Create an equation for the monthly revenue:

f(n) = (5000 - 50n) x (70 + n)

= 350000 + 5000n - 3500n - 50n²

= 350000 + 1500n - 50n²

where n is the amount the ticket price is increased from $70.

Differentiate, equal to zero and solve for n to find the value of n when the monthly revenue is at its maximum:

f'(n) = 1500 - 100n

1500 - 100n = 0

1500 = 100n

15 = n

Therefore, the maximum monthly revenue is when n = 15.

So the cost of the ticket will be 70 + n = 70 + 15 = 85

3 0

2 years ago

Pablo bought 4 CDs that were each the same price. Including sales tax, He paid a total of $70.40. Each CD had a tax of $1.10. Wh

Ann [662]

Answer:

$16.50

Step-by-step explanation:

Total cost: $70.40

Per CD w/ tax: $70.40 ÷ 4 = $17.60

Price of CD w/out tax: $17.60 - $1.10 = $16.50

8 0

3 years ago

What is the value of P(z>−2.05)

blagie [28]

Answer:

0.980

Step-by-step explanation:

Use a calculator with built-in distribution functions.

Example:

normcdf(-2.05, 10000) = 0.980

3 0

3 years ago