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3 years ago

Find the value of y when x=11 8x+6y=28

Mathematics

1 answer:

kondor19780726 [428]3 years ago

7 0

8*11 + 6y = 28
88 + 6y = 28
6y = 28 - 88
6y = -60
y = -60/6
y = -10

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If a mechanic uses his credit card to pay for a compressor that costs $477.95 and does not pay on it until the second month, wha

Rina8888 [55]

Answer:

A. $7.17

Step-by-step explanation:

We have been given that a mechanic uses his credit card to pay for a compressor that costs $477.95 and does not pay on it until the second month.

We will use compound interest formula to solve our given problem.

$A=P(1+\frac{r}{n})^{nT}$ where,

A = Final amount after T years,

P = Principal amount,

r = Annual interest rate in decimal form,

n = Periods of compounding,

T = Time in years.

Let us multiply our given rate by 12 to get APR and convert it in decimal form.

$APR=12\times 1.5\%$

$APR=18\%$

$18\%=\frac{18}{100}=0.18$

Since 1 year equals 12 months, so 1 month will be 1/12 year.

Upon substituting our given values in above formula we will get,

$A=477.95(1+\frac{0.18}{12})^{12\times\frac{1}{12}}$

$A=477.95(1+0.015)^{1}$

$A=477.95(1.015)$

$A=485.11925$

Now let us subtract principal amount from the final amount to get the monthly interest charge at the end of 1st month.

$\text{The monthly interest charge be at the end of the first month}=485.11925-477.95$

$\text{The monthly interest charge be at the end of the first month}=7.16925\approx 7.17$

Therefore, the monthly interest charge be at the end of the first month will be $7.17 and option A is the correct choice.

4 0

3 years ago

(b) For those values of k, verify that every member of the family of functions y = A sin(kt) + B cos(kt) is also a solution. y =

frutty [35]

Answer:

Check attachment for complete question

Step-by-step explanation:

Given that,

y=Coskt

We are looking for value of k, that satisfies 4y''=-25y

Let find y' and y''

y=Coskt

y'=-kSinkt

y''=-k²Coskt

Then, applying this 4y'"=-25y

4(-k²Coskt)=-25Coskt

-4k²Coskt=-25Coskt

Divide through by Coskt and we assume Coskt is not equal to zero

-4k²=-25

k²=-25/-4

k²=25/4

Then, k=√(25/4)

k= ± 5/2

b. Let assume we want to use this

y=ASinkt+BCoskt

Since k= ± 5/2

y=A•Sin(±5/2t)+ B •Cos(±5/2t)

y'=±5/2ACos(±5/2t)-±5/2BSin(±5/2t)

y''=-25/4ASin(±5/2t)-25/4BCos(±5/2t

Then, inserting this to our equation given to check if it a solution to y=ASinkt+BCoskt

4y''=-25y

For 4y''

4(-25/4ASin(±5/2t)-25/4BCos(±5/2t))

-25A•Sin(±5/2t)-25B•Cos(±5/2t).

Then,

-25y

-25(A•Sin(±5/2t)+ B •Cos(±5/2t))

-25A•Sin(±5/2t) - 25B •Cos(±5/2t)

Then, we notice that, 4y'' is equal to -25y, then we can say that y=Coskt is a solution to y=ASinkt+BCoskt

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