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3 years ago

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jacks mom purchased a savings bond for jack. the value of the savings bond increases by 5% each year. one year after it was purc

hased, the value of the savings bond was $210. find the value of the bond when jacks mom purchased it.

1 answer:

aalyn [17]3 years ago

4 0

Answer:

Step-by-step explanation:

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If f(x, y) = esin(x + y) and D = [−π, π] × [−π, π], show the following. 1 e ≤ 1 4π2 D f(x, y) dA ≤ e The area of the region D is

Digiron [165]

I'm guessing the purpose of this exercise is to find the average value of $f(x,y)=e^{\sin(x+y)}$ over the region $D$ ,

$D=\left\{(x,y)\mid (x,y)\in[-\pi,\pi]^2\right\}$

which is

$\displaystyle\frac{\displaystyle\iint_Df(x,y)\,\mathrm dx\,\mathrm dy}{\displaystyle\iint_D\mathrm dx\,\mathrm dy}$

The denominator is the measure (area) of $D$ , which is easy to compute:

$\displaystyle\iint_D\mathrm dx\,\mathrm dy=\int_{-\pi}^\pi\int_{-\pi}^\pi\mathrm dx\,\mathrm dy=(2\pi)^2=4\pi^2$

Not to be confused with the integral in the numerator:

$\displaystyle\iint_Df(x,y)\,\mathrm dx\,\mathrm dy=\int_{-\pi}^\pi\int_{-\pi}^\pi e^{\sin(x+y)}\,\mathrm dx\,\mathrm dy$

but this integral is difficult to compute, hence the inequalities. We have

$-1\le\sin(x+y)\le1$

$\implies\dfrac1e\le e^{\sin(x+y)}\le e$

$\implies\displaystyle\iint_D\frac{\mathrm dx\,\mathrm dy}e\le\iint_De^{\sin(x+y)}\,\mathrm dx\,\mathrm dy\le\iint_De\,\mathrm dx\,\mathrm dy$

$\implies\displaystyle\frac{4\pi^2}e\le\iint_De^{\sin(x+y)}\,\mathrm dx\,\mathrm dy\le4\pi^2e$

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3 years ago

The volume of a cone is 141.3 cubic inches. The height of the cone is 15 inches. What is the radius of the cone, rounded to the

kkurt [141]

Answer:

3

Step-by-step explanation:

V=πr²h/3 = π3²·15/3 = 141.37167

-hope it helps

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2 years ago

A line intersects the point (0,3) and has a slope of 0. What is the slope intercept equation for this line?

deff fn [24]

the slope intercept form is y=mx+b

since the line intersects at (0,3) b= 3

since the slope is 0 m= 0

so the equation would be y=0x+3 or y=3

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3 years ago

Which of the following is an example of a quadratic equation?

REY [17]

Answer:

B. x^2 - 64 = 0

Step-by-step explanation:

A. x+10 = 33

B. x^2 - 64 = 0

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A quadratic has an term with a power of two

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3 years ago

Read 2 more answers

Find the slope of the line passing through the points (4, 4) and (4, - 4) .

sveticcg [70]

Answer:

Slope = undefined

Step-by-step explanation:

<u>We know that:</u>

Slope Formula = y₂ - y₁/x₂ - x₁

<u>Solution:</u>

y₂ - y₁/x₂ - x₁ = -4 - 4/4 - 4
=> -8/0 = undefined

Since the slope of the line is un-defined, the line is vertical. Please look at my graph to understand better.

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