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3 years ago

James got 5 questions wrong out of 40 questions what percent of the questions did he get correct

Mathematics

1 answer:

Arte-miy333 [17]3 years ago

8 0

8% of them right, 40/5

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Find the height of a cylinder with a volume of 12157 mm3 and a radius of 9 mm.

Ivahew [28]

Volume of a Cylinder = pi * r^2 * h

V / (pi*r^2) = h

12157 / (pi * 9^2) = h = 47.774

5 0

2 years ago

(x^2y+e^x)dx-x^2dy=0

klio [65]

It looks like the differential equation is

$\left(x^2y + e^x\right) \,\mathrm dx - x^2\,\mathrm dy = 0$

Check for exactness:

$\dfrac{\partial\left(x^2y+e^x\right)}{\partial y} = x^2 \\\\ \dfrac{\partial\left(-x^2\right)}{\partial x} = -2x$

As is, the DE is not exact, so let's try to find an integrating factor µ(x, y) such that

$\mu\left(x^2y + e^x\right) \,\mathrm dx - \mu x^2\,\mathrm dy = 0$

*is* exact. If this modified DE is exact, then

$\dfrac{\partial\left(\mu\left(x^2y+e^x\right)\right)}{\partial y} = \dfrac{\partial\left(-\mu x^2\right)}{\partial x}$

We have

$\dfrac{\partial\left(\mu\left(x^2y+e^x\right)\right)}{\partial y} = \left(x^2y+e^x\right)\dfrac{\partial\mu}{\partial y} + x^2\mu \\\\ \dfrac{\partial\left(-\mu x^2\right)}{\partial x} = -x^2\dfrac{\partial\mu}{\partial x} - 2x\mu \\\\ \implies \left(x^2y+e^x\right)\dfrac{\partial\mu}{\partial y} + x^2\mu = -x^2\dfrac{\partial\mu}{\partial x} - 2x\mu$

Notice that if we let µ(x, y) = µ(x) be independent of y, then ∂µ/∂y = 0 and we can solve for µ :

$x^2\mu = -x^2\dfrac{\mathrm d\mu}{\mathrm dx} - 2x\mu \\\\ (x^2+2x)\mu = -x^2\dfrac{\mathrm d\mu}{\mathrm dx} \\\\ \dfrac{\mathrm d\mu}{\mu} = -\dfrac{x^2+2x}{x^2}\,\mathrm dx \\\\ \dfrac{\mathrm d\mu}{\mu} = \left(-1-\dfrac2x\right)\,\mathrm dx \\\\ \implies \ln|\mu| = -x - 2\ln|x| \\\\ \implies \mu = e^{-x-2\ln|x|} = \dfrac{e^{-x}}{x^2}$

The modified DE,

$\left(e^{-x}y + \dfrac1{x^2}\right) \,\mathrm dx - e^{-x}\,\mathrm dy = 0$

is now exact:

$\dfrac{\partial\left(e^{-x}y+\frac1{x^2}\right)}{\partial y} = e^{-x} \\\\ \dfrac{\partial\left(-e^{-x}\right)}{\partial x} = e^{-x}$

So we look for a solution of the form F(x, y) = C. This solution is such that

$\dfrac{\partial F}{\partial x} = e^{-x}y + \dfrac1{x^2} \\\\ \dfrac{\partial F}{\partial y} = e^{-x}$

Integrate both sides of the first condition with respect to x :

$F(x,y) = -e^{-x}y - \dfrac1x + g(y)$

Differentiate both sides of this with respect to y :

$\dfrac{\partial F}{\partial y} = -e^{-x}+\dfrac{\mathrm dg}{\mathrm dy} = e^{-x} \\\\ \implies \dfrac{\mathrm dg}{\mathrm dy} = 0 \implies g(y) = C$

Then the general solution to the DE is

$F(x,y) = \boxed{-e^{-x}y-\dfrac1x = C}$

5 0

3 years ago

Nine scores have an average of 8. Scores x and x+1 are added, and these increase the average to 9. Find x

Degger [83]

Answer:

x must be 13

Step-by-step explanation:

Represent the nine scores by a, b, c, d, e, f, g, h, i.

Write the following equation to indicate that the average of these nine scores is 8:

a+b+c+d+e+f+g+h+i

----------------------------- = 8, or a+b+c+d+e+f+g+h+i = 72 if we multiply both

9 sides of this equation by 9.

Next, we add scores x and x+ 1 to

a+b+c+d+e+f+g+h+i + x + x + 1

and divide the result by 11, as there are now 11 scores instead of just 9:

a+b+c+d+e+f+g+h+i + x + x + 1

----------------------------------------------

Earlier, we saw that a+b+c+d+e+f+g+h+i = 72. We can now replace

a+b+c+d+e+f+g+h+i in the above fraction by 72:

72 + 2x + 1

------------------- = 9 (as the new average is 9)

Multiplying both sides of this equation by 11 results in:

73 + 2x = 99, or 2x = 26.

Then x must be 13, and x + 1 must be 14.

3 0

2 years ago

Which inequality is equivalent to 8 < 3x – 4(2x – 5)?

oksian1 [2.3K]

8<-5x+20 is one possible answer. it depends on how they are writing it. you need to do the distributed property.

5 0

3 years ago

Nina opened a savings account and deposited $300.00. The account earns 4% interest, compounded monthly. If she wants to use the

mylen [45]

Answer:

up to $338.18

Step-by-step explanation:

Use the compound amount formula:

A = P(1 + r/n)^(n*t), where r is the interest rate as a decimal fraction and n is the number of compounding periods per year.

Here, A = $300(1 + 0.04/12)^(12*3), or

A = $300(1.0033333)^*36, or

A = $300(1.127) = $338.18

Nina will be able to spend up to $338.18 on a new bike.

5 0

2 years ago

Read 2 more answers