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2 years ago

An investment of $8500 increases in value by 4.5% every year. How long until the investment

Mathematics

1 answer:

Zanzabum2 years ago

4 0

Answer:

At an interest rate of 4.5% compounded annually, it will take 16.17 years to reach $17,323.-

Step-by-step explanation:

Giving the following information:

Present Value (PV)= $8,500

Future value (FV)= $17,323

Interest rate (i)= 4.5%

To calculate the time required for the investment to reach the objective, we need to use the following formula:

n= ln(FV/PV) / ln(1+i)

n= ln(17,323/8,500) / ln(1.045)

n= 16.17 years

At an interest rate of 4.5% compounded annually, it will take 16.17 years to reach $17,323.-

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What is the equation in slope-intercept from of the line that passes through the points (-4,47) and (2,-16

Harrizon [31]

Answer:

Step-by-step explanation:

SLOPE FORMULA:

y₂-y₁/x₂-x₁=rise/run

SLOPE-INTERCEPT FORM:

y=mx+b

m represents the slope.

b represents the y-intercept.

y₂=(-16)

y₁=47

x₂=2

y₁=(-4)

Solve.

$\displaystyle \mathsf{\frac{(-16)-47}{2-(-4)}=\frac{21}{6}=\frac{21}{2}=-\frac{21}{2} }}$

Furthermore, the y-intercept is 5.

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The correct answer is y=-21/2x+5.

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3 years ago

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rjkz [21]

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Step-by-step explanation:

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2 years ago

A hydraulic engineer is studying the pressure in a particular fluid. The pressure is equal to the atmospheric pressure 101 kN/m

miskamm [114]

Answer:

Step-by-step explanation:

The pressure is equal to the atmospheric pressure 101 kN/m plus 8 kN/m for every meter below the surface, therefore;

a. expression for pressure is given by,

$Pressure = 101 + 8d$ ............................... (1)

where d = depth below the surface in meter.

b. to find the depth at any pressure, equation (1) above is rearranged to make depth (d) subject of the formula

$d = \frac{Pressure - 101}{8}$

as an example, to find depth at pressure of 200N/m

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2 years ago

Three numbers form a geometric progression. If the second term is increased by 2, the progression will become arithmetic and if,

Evgesh-ka [11]

In this exercise we have to use the knowledge of geometric progression to find three specific numbers, in this way we can say that these numbers correspond to;

$0.16\\ -0.64\\ 2.56$

Then using the formula of the geometric progression we find that:

$a_1*r = a_2\\a_2*r = a_3 = a_1*r^2$

now, the differences between the terms must be the same:

$a1*r + 2 - a_1 = a_3 - (a_1*r + 2) = a_1*r^2 - (a_1*r + 2)\\a_1*r^2 - 2*a_1*r + a_1 - 4 = 0$

and now, when we increase the third term by 9,so we have:

$(a_1*r^2 + 9)/(a_1*r + 2) = (a_1*r + 2)/a_1\\(a_1^2*r^2 + 9*a_1)/(a_1*r + 2) = a_1*r + 2\\a_1^2*r^2 + 9*a_1 = (a_1*r + 2)^2 = a_1^2*r^2 + 4*a_1*r + 4\\4*a_1*r - 9*a_1 + 4 = 0\\9*a - 4 = 4*a_1*r\\r = (9*a_1 - 4)/(4*a_1)$

Now we use that identity in the first equation :

$a_1*(9*a_1 - 4)^2/(4×a_1)^2 - 2*a_1*(9*a_1 - 4)/(4*a_1) + a_1 - 4 = 0\\(81*a_1^2 - 72*a_1 + 16)/(16*a_1) - (9*a_1 - 4)/2 + a_1 - 4 = 0\\81*a_1^2 - 72*a_1 + 16 - 8*a_1*(9*a_1 - 4) + 16*a_1^2 - 64*a_1 = 0\\25a_1^2 - 104a_1 + 16 = 0$