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igomit [66]
3 years ago
13

Jerome will be buying a used car for $11,000 in 4 years. How much money should he ask his parents for now so that, if he invests

it at 8% compounded continuously, he will have enough to buy the car?
Mathematics
1 answer:
hjlf3 years ago
4 0

Answer:

$7,987.64

Step-by-step explanation:

We know,

A = Pe^(rt)

Here,

A = 11000  

interest r = .08

Time t = 4

Now,

11000 = Pe^(.08 * 4)

Or, 11000 = Pe^.32  

Or, 11000 / e^.32 = P

Or, 7987.6394 = P

Or, P= 7,987.64

Jerome will have to ask for $7,987.64 to his parents.  

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Slope formula (12,-18),(-15,-18)
nalin [4]

Answer:

M=0

Step-by-step explanation:

there you go almost sure it is

7 0
3 years ago
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A recipe that will make 3 pies calls for 7 cups of flour? Find how many pies can be made with 42 cups of flour.
sdas [7]
18 pies because 7 times 6 is 42 and 3 times 6 is 18
6 0
3 years ago
Find the value of x^2 + 1 divided by x^2 if x-1 divided by x =5
MrRa [10]

Answer:

x^2+1/x^2

(x+1/x)^2 = x^2+1/x^2 +2

(5)^2 = x^2+1/x^2 + 2

25 = x^2+1/x^2 + 2

25-2 = x^2+1/x^2

23 = x^2+1/x^2

Step-by-step explanation:

6 0
3 years ago
Let f(x,y,z) = ztan-1(y2) i + z3ln(x2 + 1) j + z k. find the flux of f across the part of the paraboloid x2 + y2 + z = 3 that li
Sophie [7]
Consider the closed region V bounded simultaneously by the paraboloid and plane, jointly denoted S. By the divergence theorem,

\displaystyle\iint_S\mathbf f(x,y,z)\cdot\mathrm dS=\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV

And since we have

\nabla\cdot\mathbf f(x,y,z)=1

the volume integral will be much easier to compute. Converting to cylindrical coordinates, we have

\displaystyle\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=\iiint_V\mathrm dV
=\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{z=2}^{z=3-r^2}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta
=\displaystyle2\pi\int_{r=0}^{r=1}r(3-r^2-2)\,\mathrm dr
=\dfrac\pi2

Then the integral over the paraboloid would be the difference of the integral over the total surface and the integral over the disk. Denoting the disk by D, we have

\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-\iint_D\mathbf f\cdot\mathrm dS

Parameterize D by

\mathbf s(u,v)=u\cos v\,\mathbf i+u\sin v\,\mathbf j+2\,\mathbf k
\implies\mathbf s_u\times\mathbf s_v=u\,\mathbf k

which would give a unit normal vector of \mathbf k. However, the divergence theorem requires that the closed surface S be oriented with outward-pointing normal vectors, which means we should instead use \mathbf s_v\times\mathbf s_u=-u\,\mathbf k.

Now,

\displaystyle\iint_D\mathbf f\cdot\mathrm dS=\int_{u=0}^{u=1}\int_{v=0}^{v=2\pi}\mathbf f(x(u,v),y(u,v),z(u,v))\cdot(-u\,\mathbf k)\,\mathrm dv\,\mathrm du
=\displaystyle-4\pi\int_{u=0}^{u=1}u\,\mathrm du
=-2\pi

So, the flux over the paraboloid alone is

\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-(-2\pi)=\dfrac{5\pi}2
6 0
3 years ago
Evaluate the variable expression when a=-4, b=2, c=-3, and d =4. b-3a/bc^2-d​
gtnhenbr [62]

Answer:

Therefore, the variable expression when a=-4, b=2, c=-3, and d =4 is

\dfrac{b-3a}{bc^{2}-d}=1

Step-by-step explanation:

Evaluate:

\dfrac{b-3a}{bc^{2}-d}

When a=-4, b=2, c=-3, and d =4

Solution:

Substitute, a=-4, b=2, c=-3, and d =4 in above expression we get

\dfrac{b-3a}{bc^{2}-d}=\dfrac{2-3(-4)}{2(-3)^{2}-4}\\\\=\dfrac{2+12}{18-4}\\\\

\dfrac{b-3a}{bc^{2}-d}=\dfrac{14}{14}=1

Therefore, the variable expression when a=-4, b=2, c=-3, and d =4 is

\dfrac{b-3a}{bc^{2}-d}=1

6 0
3 years ago
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