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2 years ago

A typical credit card company charges 18% annual interest,

Mathematics

1 answer:

AnnZ [28]2 years ago

3 0

Answer:

$1,519

Step-by-step explanation:

Given that :

Balance = principal = $520

Time (t) = 6 years

Annual. Interest rate (r) = 18% = 0.18

Using the compound interest formula:

A = P(1 + r/n)^nt

n = number of times interest is applied per period ; A = final amount

Since interest is compounded monthly, n = 12

A = 520(1 + 0.18/12)^(12 * 6)

A = 520(1 + 0.015)^72

A = 520(1.015)^72

A = 520(2.9211579)

A = 1519.0021

Hence, final amount = $1519

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Given:

The graph of a proportional relationship.

To find:

The constant of proportionality, the value of y when x is 24 and the value of x when y is 108.

Solution:

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Answer:

The least cost of fencing for the rancher is $1200

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Let x be the width and y the length of the rectangular field.

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Next, we find the critical points of the derivative

$20-\frac{18000}{x^2}=0\\\\20x^2-\frac{18000}{x^2}x^2=0\cdot \:x^2\\\\20x^2-18000=0\\\\20x^2-18000+18000=0+18000\\\\20x^2=18000\\\\\frac{20x^2}{20}=\frac{18000}{20}\\\\x^2=900\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{900},\:x=-\sqrt{900}\\\\x=30,\:x=-30$

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$C'(20)=20-\frac{18000}{20^2} = -25 < 0\\\\C'(40)= 20-\frac{18000}{20^2} = 8.75 >0$

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$C(30)=20(30)+\frac{18000}{30}\\C(30)=1200$

The least cost of fencing for the rancher is $1200

Here’s the diagram:

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