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IRISSAK [1]
3 years ago
8

(xm.x2)3(k3)5 = x21k15 Find the Value of M

Mathematics
1 answer:
Svet_ta [14]3 years ago
8 0

Answer:

m=5

Step-by-step explanation:

Given:

([(x^m) (x^2)]^3) ([k^3)^5]= (x^21)(k^15)

we can simplify this equation by understanding what operation that was applied to the x and k variables

we can pridect that they were using the multiplication method of exponents by distribution as follows:

if we look at x^21 at the right side of the equation then we shold have the same nuber of x multiples such that:

21= (3)(7) but if we look at the right hand side we have some missing information but we can still use the multiplication of the exponent and subtract it from the right hand side as follows:

first distribute 3 for both x's in the left hand side:

(x^m)^3= x^(3)(m)

and

(x^2)^3= x^(2)(3)

⇒will give us:

(x^3m)(x^6)=(x^21)

let us now check by ignoring the x's and use the exponents in the form of an equation:

(3m)+(6)=21

move 6 to the right side

3m = 21-6

3m=15

m= 15/3

m=5

so, by substituting 5 with m at the original equation we will get:

(x^5(3)) (x^6) = x^21

(x^15)(x^6)=x^21

that applies the same rule to the variable k

k^3(5)=k^15

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If Mia Wong invests $73,000 at 7 1/2% annual simple interest on March 1, when will her investment be worth $75,760?
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<h3>Answer:   September 1st</h3>

=========================================================

Work Shown::

1/2 = 0.5

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7.5% = (7.5)/100 = 0.075

She invests P = 73000 dollars at an interest rate of r = 0.075

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--------------------------------

Apply the simple interest formula to help solve for x

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Due to rounding error, that 1 at the very end likely shouldn't be there. So it looks like exactly 184 days must elapse so that she earns that amount of money.

If she started on March 1, then adding on 184 days leads to September 1.

I recommend looking at a "Day of Year Calendar". Note on this calendar there are numbers for each day. In this case, march 1st occurs on the 60th day of the year while September 1st occurs on the 244th day of the year. Then note how 60+184 = 244. The day of year calendar is a quick way to scroll forward or backward in time on any day. Many online calculators provide an even faster method. The slowest method is to count the number of days on a traditional calendar, but I don't recommend this.

5 0
2 years ago
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