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2 years ago

8

Your friend borrows $7500 to buy an all-terrain vehicle (ATV). The simple annual interest rate is 6%. She pays off the loan afte

r 5 years of equal monthly payments. How much is each payment?

1 answer:

e-lub [12.9K]2 years ago

6 0

Answer:

$162.50

Explanation:

The total amount to be paid is 7500+5(7500)(0.06)=$9750.

There were a total of (5)(12)=60 payments, so each payment is 9750/60 = $162.50.

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3 years ago

Solve the equation 2 sec² x = 3 - tan x for the domain 0° ≤ x ≤ 360°

vodka [1.7K]

$2 \sec^2 x = 3- \tan x \\\\\implies 2(1 +\tan^2 x) = 3- \tan x \\\\\implies 2 + 2 \tan^2 x +\tan x -3 =0\\\\\implies 2 \tan^2 x + \tan x -1 =0\\\\\implies 2u^2 + u -1 =0~~~ ;[\text{set} \tan x = u]\\\\\implies u = \dfrac{-1\pm \sqrt{1-4\cdot 2 \cdot (-1)}}{2(2)}\\\\\implies u =\dfrac{-1 \pm\sqrt{9}}{4}\\\\\implies u = \dfrac{-1 \pm 3}{4}\\\\\implies u = \dfrac{2}{4}=\dfrac 12~~ \text{or} ~~u =\dfrac{-4}{4} =-1\\\\$

$\implies \tan x = \dfrac 12 ~~ \text{or} ~~ \tan x =-1~~~ ;[\text{Substitute back u =tan x}]\\\\\text{Now,}~ \\\\\tan x = -1,\\\\\implies x = n\pi - \dfrac{\pi}4\\\\\\\text{For interval,}~ [0,2\pi) \\\\x = \dfrac{3\pi}4, \dfrac{7\pi}4\\\\\text{In degrees,}~ x = 135^{\circ}, x =315^{\circ}\\\\\tan x = \dfrac 12\\\\\implies x = n\pi + \tan^{-1} \left(\dfrac 12 \right)\\\\\text{For interval} ~[0,2\pi),\\\\$

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2 years ago

Exponent Laws - difference between product law and product raised to a power (with formula please)

enyata [817]

Answer:

Exponent laws:

1. Product law

$x^{a}\times x^{b}\times x^{c}=x^{a+b+c}$

In product law if bases are same then we add their respective powers.But if bases are different we can't add their powers.

x=base, a,b,c=exponent

If x=2 and a=3, b=5 , and c=10, then

$2^{3}\times2^{5}\times2^{10}=2^{3+5+10}=2^{18}$

2.Product raised to a power

1. $[x^{a}]^{c}=x^{ac}$

2. $[x^{a}\times x^{b}]^{c}=[x^{a+b}]^{c}=x^{ac+bc}$

If product is raised to a certain power , keeping the base same , we just multiply the powers.for example

$[2^{3}]^{4}=2^{3\times4}=2^{12}$ and

$[2^{3}\times3^{2}]^{2}=[2^{3}]^2 \times[3^{2}]^{2}=2^{6}\times3^{4}$

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3 years ago

Six more than 1/5 a number is 12. What is the number

suter [353]

Answer:

Step-by-step explanation:

let x be the number

6+1/5x=12

1/5x=12-6

1/5x=6

x=5*6

x=30

check: 6+(1/5*30)=6+6=12

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