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3 years ago

Write the exact value solution and an approximation for 10^4x=25

Mathematics

1 answer:

Murrr4er [49]3 years ago

6 0

Answer:

exact value: $x= \frac{log25}{4}$

approximate: x=0.349485

Step-by-step explanation:

Exact Value:

$10^{4x} = 25$

$log (10^{4x})= log 25$

$4x = log 25$

$x= \frac{log25}{4}$

Approximate:

$x= \frac{log25}{4}$

$x=1.39794/4\\$

$x=0.349485$

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A restaurant manager has the option of a 30-year loan of $417,000 at an annual interest rate of 3.85% or the same interest rate

victus00 [196]

a) The monthly payment for each loan is as follows:

30-year $1,954.93

15-year $3,053.25

b) The savings in interest by using the 15-year loan is <u>$154,189,20</u> ($286,774.20 - $132,585).

c) No. the monthly payment for the 15-year loan is <u>not twice</u> that of the 30-year loan as the loan term.

d) The interest savings for the 15-year loan are <u>more</u> than one-half of the interest paid on the 30-year loan.

<h3>How are the calculations for periodic payments done?</h3>

The calculations for the monthly payments, including interests can be carried out using an online finance calculator, as follows:

N (# of periods) = 360 months (12 x 30 years)

I/Y (Interest per year) = 3.85%

PV (Present Value) = $417000

FV (Future Value) = $0

<u>Results</u>:

PMT = $1,954.93

Sum of all periodic payments = $703,774.80 ($1,954.93 x 360)

Total Interest = $286,774.20 ($703,774.80 - $417,000)

N (# of periods) = 180 months (12 x 15 years)

I/Y (Interest per year) = 3.85%

PV (Present Value) = $417000

FV (Future Value) = $0

<u>Results</u>:

PMT = $3,053.25

Sum of all periodic payments = $549,585 ($3,053.25 x 180)

Total Interest = $132,585 ($549,585 - $417,000)

Learn more about periodic payments at brainly.com/question/13098072

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3 years ago

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3 years ago

Find the surface area of a cylinder with a base radius of 2 yd and a height of 3 yd.

kherson [118]

Answer:

20 π

Step-by-step explanation:

The surface area of a cylinder is made up of 2 circles and its side.

To find the circles' areas, use the area formula for a circle: A = π $r^2$ .

Since our radius is 2 yd, we can substitute r = 2 into this formula.

A = π $2^2$ = 4π

Now remember, this is only the area of once circle. Multiply 4π by 2 to get the area of both circles: 8π.

Now we need to find the surface area of the side.

If we flatten it out, we can see that the side is actually a curled up rectangle.

The length is the circumference of the circle and the width is the height of the cylinder.

To find the circumference, use the circumference formula for a circle: C = 2πr.

Substitute r = 2 into the formula.

C = 2π2 = 4π

Now that we know that the length is 4π, we can multiply the length by the width to find the area of the cylinder's side.

l = 4π

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A = lw = 4π * 3 = 12π

Finally, we can add the areas of the circles and the side to get the total surface area.

8π + 12π = 20π

And that is your answer!

Please mark as Brainliest! :)

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3 years ago