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2 years ago

Ellie wants to double her savings of £8000 by investing her money for 16 years.

Mathematics

1 answer:

Tanya [424]2 years ago

5 0

Answer:

She need a interest rate of 6.25%

Step-by-step explanation:

we know that

The simple interest formula is equal to

$A=P(1+rt)$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest

t is Number of Time Periods

in this problem we have

$t=16\ years\\ P=\£8,000\\ A=\£8,000*2=\£16,000\\r=?$

substitute in the formula above and solve for r

$16,000=8,000(1+16r)$

$16r=2-1$

$r=1/16$

$r=0.0625$

Convert to percentage

$r=0.0625*100=6.25\%$

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Let 'x' be the distance from THE far bank where 700 is the distance to the NEAR bank

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3 years ago

A ride on the roller coaster costs 4 tickets while the boat ride only costs 3 tickets. Michael went on the two rides a total of

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Let x = roller coaster ticket
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3 years ago

How do you do this question?

ElenaW [278]

x*y' + y = 8x

y' + y/x = 8 .... divide everything by x

dy/dx + y/x = 8

dy/dx + (1/x)*y = 8

We have something in the form

y' + P(x)*y = Q(x)

which is a first order ODE

The integrating factor is $u(x) = e^{\int P(x)dx} = e^{\int (1/x) dx} = e^{\ln(x)} = x$

Multiply both sides by the integrating factor (x) and we get the following:

dy/dx + (1/x)*y = 8

x*dy/dx + x*(1/x)*y = x*8

x*dy/dx + y = 8x

y + x*dy/dx = 8x

Note the left hand side is the result of using the product rule on xy. We technically didn't need the integrating factor since we already had the original equation in this format, but I wanted to use it anyway (since other ODE problems may not be as simple).

Since (xy)' turns into y + x*dy/dx, and vice versa, this means

y + x*dy/dx = 8x turns into (xy)' = 8x

Integrating both sides with respect to x leads to

xy = 4x^2 + C

y = (4x^2 + C)/x

y = (4x^2)/x + C/x

y = 4x + Cx^(-1)

where C is a constant. In this case, C = -5 leads to a solution

y = 4x - 5x^(-1)

you can check this answer by deriving both sides with respect to x

dy/dx = 4 + 5x^(-2)

Then plugging this along with y = 4x - 5x^(-1) into the ODE given, and you should find it satisfies that equation.

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