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Vika [28.1K]
3 years ago
9

Solve the equation. show all work 18^(r-10)=93

Mathematics
1 answer:
Elina [12.6K]3 years ago
3 0
Recall the logarithm rules :

a^y = x  is the same as log_a x = y

In this case, 

a = 18
y = r - 10
x = 93

So,

18^ (r-10) = 93

is the same as

log_18  93 = r - 10

Solve for r to get :

10 + log_18  93 = r
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Analyze the diagram below and complete the instructions that follow.
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Law of Cosines says


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\cos B = \dfrac{16^2 + 16^2 - 11^2}{2(16)(16)} = \dfrac{ 391}{512}


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Number of pounds of dough used = 3/5 pounds.

Number of pounds of sugar used = 3/4 pounds

Number of pounds of sprinkles used = 2/3 pounds.

Total number of pounds of donuts = Number of pounds of dough used + Number of pounds of sugar used + Number of pounds of sprinkles used.

Plugging values.

Total number of pounds of donuts = 3/5 + 3/4 + 2/3.

We need to add all those fractions.

In order to add fracions, we need to find common denominator (lcd).

We have 5,4 and 3 in denominators.

Least common denominator(lcd) of 5, 4 and 3 is 60.

We need to make each denominator equals 60.

Multiplying first fracion by 12 in top and bottom, we get

3*12/5*12 = 36/60

Multiplying first fracion by 5 in top and bottom, we get

3*15/4*15 = 45/60

Multiplying first fracion by 20 in top and bottom, we get

2*20/3*20 = 40/60.

Therefore,

3/5 + 3/4 + 2/3 = 36/60 + 45/60 + 40/60

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Let us convert 121/60 into mixed fraction.

Dividing 121 by 60 we get quotient =2 and remainder =1.

So, the mixed fraction is 2 1/60.

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