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2 years ago

Solve for i in the following equation by means of linear interpolation(1 + i)10 – 1= 25

Mathematics

1 answer:

docker41 [41]2 years ago

4 0

Answer:

$i=1.6$

Step-by-step explanation:

The given equation is

$(1+i)10-1=25$

To solve for $i$ , first, we need to sum 1 unit to each side of the equation.

$(1+i)10-1+1=25+1\\(1+i)10=26$

Then, we divide the equation by 10

$\frac{(1+i)10}{10} =\frac{26}{10} \\1+i=2.6$

Finally, we subtract each side with -1

$1+i-1=2.6-1\\i=1.6$

Therefore, the solution to the given equation is $i=1.6$

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2 years ago

What equation can relate to this sentence 11 is the quotient of a number y and 6 ?

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3 years ago

A. 11/1=165/h B. 11/1=h/165 C. 132/12=h/165 D=12/132=165/h plz help

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3 0

2 years ago

√₂

snow_lady [41]

Answer:

$2000 was invested at 5% and $5000 was invested at 8%.

Step-by-step explanation:

Assuming the interest is simple interest.

Simple Interest Formula

I = Prt

where:

I = interest earned.
P = principal invested.
r = interest rate (in decimal form).
t = time (in years).

Given:

Total P = $7000
P₁ = principal invested at 5%
P₂ = principal invested at 8%
Total interest = $500
r₁ = 5% = 0.05
r₂ = 8% = 0.08
t = 1 year

Create two equations from the given information:

$\textsf{Equation 1}: \quad \sf P_1+P_2=7000$

$\textsf{Equation 2}: \quad \sf P_1r_1t+P_2r_2t=I\implies 0.05P_1+0.08P_2=500$

Rewrite Equation 1 to make P₁ the subject:

$\implies \sf P_1=7000-P_2$

Substitute this into Equation 2 and solve for P₂:

$\implies \sf 0.05(7000-P_2)+0.08P_2=500$

$\implies \sf 350-0.05P_2+0.08P_2=500$

$\implies \sf 0.03P_2=150$

$\implies \sf P_2=\dfrac{150}{0.03}$

$\implies \sf P_2=5000$

Substitute the found value of P₂ into Equation 1 and solve for P₁:

$\implies \sf P_1+5000=7000$

$\implies \sf P_1=7000-5000$

$\implies \sf P_1 = 2000$

$2000 was invested at 5% and $5000 was invested at 8%.

Learn more about simple interest here:

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5 0

1 year ago

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GREYUIT [131]

Answer: D. 13 1/2.

Step-by-step explanation:

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7 0

2 years ago

Solve for i in the following equation by means of linear interpolation(1 + i)10 – 1= 25​

Solve for i in the following equation by means of linear interpolation(1 + i)10 – 1= 25