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Julli [10]
3 years ago
12

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.
Mathematics
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

3 0
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

8 0
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

5 0
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

C. Y-776

D. y = 4x + 6

A quadratic has an term with a power of two

3 0
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.

3 0
3 years ago
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