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3 years ago

WHICH VALUE IS AN EXTRANEOUS SOLUTION X=-3X+12

Mathematics

1 answer:

Rina8888 [55]3 years ago

8 0

<span>X=-3X+12
4X = 12
X = 3

answer
X = 3</span>

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If you invest $4000 at 9% interest compounded annually, in how many years will you have $20,000. Give your answer the nearest te

Masteriza [31]

Answer:

18.7 years

Step-by-step explanation:

This is a compound interest problem and the following variables have been given;

Principal = 4000; this is the amount o be invested

APR = 9%; this is the compound interest to be earned

Accumulated amount = 20,000

We are required to determine the duration in years. We apply the compound interest formula;

$A=P(1+r)^{n}$

$20000=4000(1+\frac{9}{100})^{n}\\20000=4000(1.09)^{n}\\5=(1.09)^{n}$

The next step is to introduce natural logarithms in order to determine n;

$ln5=nln(1.09)\\n=\frac{ln5}{ln(1.09)}\\n= 18.675$

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4 years ago

A laptop computer is purchased for 3100. Each year, its value is 75% of its value the year before. After how many years will the

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3 years ago

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3 years ago

Find the exact value of the given expression.<br> sin(2cos^-1(5/13))

xeze [42]

Answer:

+120/169 or -120/169

Step-by-step explanation:

let $cos^{-1}[\frac{5}{13} ] = \alpha$

where, alpha is some angle that satisfies the assumed condition.

so, $cos\alpha= 5/13$

[ taking cos to the other side or applying cos on both sides]

now, substitute this in the given expression

$sin(2cos^-1(5/13)) = sin(2\alpha )$

as sin $\beta$ = $+ or -\sqrt{1-(cos\beta) ^{2}$

[by general trigonometry formula: $cos^{2}[\beta] +sin^{2}[\beta]=1$ ]

so if $cos\alpha= 5/13$ , we can get sin $\alpha$ from the above formula as + or - 12/13

(because, after taking square root on both sides we keep + or -]

as, sin $2\beta = 2*sin[\beta ]*cos[\beta ]$

[by general trigonometry formula]

here, now $sin[2\alpha ]=2*(+or- 12/13)*5/13\\$

so, the final value can be 120/169 or -120/169.

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3 years ago