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Rus_ich [418]
2 years ago
5

Peter invests $1000 at 4% compounded annually for 10 years and Jose invests $900 compounded annually at 5% for 11 years. Who end

s up with more money? And how much more money?
Mathematics
1 answer:
Nesterboy [21]2 years ago
6 0

Answer:

Jose ends up with more money with $59 more than Peter.

Step-by-step explanation:

To determine the amount they will have, you have to use the formula to calculate the future value:

FV=PV(1+r)^n

FV= future value

PV= present value

r= rate of interest

n= number of periods of time

-Peter:

FV=1,000*(1+0.04)^10

FV=1,000*1.48

FV=1,480

-Jose:

FV=900*(1+0.05)^11

FV=900*1.71

FV=1,539

Difference: $1,539-$1,480=$59

According to this, the answer is that Jose ends up with more money with $59 more than Peter.

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Celine is Drake’s granddaughter. Her age is 4 years greater than of Drake’s age. If Celine is 28 years old, how old is Drake?
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3 years ago
Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2/3 + y2/3 = 4 (−3 3 , 1)
vovikov84 [41]

Answer with Step-by-step explanation:

We are given that an equation of curve

x^{\frac{2}{3}}+y^{\frac{2}{3}}=4

We have to find the equation of tangent line to the given curve at point (-3\sqrt3,1)

By using implicit differentiation, differentiate w.r.t x

\frac{2}{3}x^{-\frac{1}{3}}+\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=0

Using formula :\frac{dx^n}{dx}=nx^{n-1}

\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=-\frac{2}{3}x^{-\frac{1}{3}}

\frac{dy}{dx}=\frac{-\frac{2}{3}x^{-\frac{1}{3}}}{\frac{2}{3}y^{-\frac{1}{3}}}

\frac{dy}{dx}=-\frac{x^{-\frac{1}{3}}}{y^{-\frac{1}{3}}}

Substitute the value x=-3\sqrt3,y=1

Then, we get

\frac{dy}{dx}=-\frac{(-3\sqrt3)^{-\frac{1}{3}}}{1}

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Slope of tangent=m=\frac{1}{\sqrt3}

Equation of tangent line with slope m and passing through the point (x_1,y_1) is given by

y-y_1=m(x-x_1)

Substitute the values then we get

The equation of tangent line is given by

y-1=\frac{1}{\sqrt3}(x+3\sqrt3)

y-1=\frac{x}{\sqrt3}+3

y=\frac{x}{\sqrt3}+3+1

y=\frac{x}{\sqrt3}+4

This is required equation of tangent line to the given curve at given point.

8 0
3 years ago
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