Answer:
x = 2.81 and 2.096
Step-by-step explanation:
Given the expression
10(2^x) + 7(3^x) = 6^x + 70
This can also be expressed as;
10(2^x) + 7(3^x) = (2*3)^x + 70
10(2^x) + 7(3^x) = 2^x*3^x + 70
Let a = 2^x and b = 3^x
10a + 7b = ab + 70
10a + 7b - ab = 70
10a-ab + 7b - 70 = 0
a(10-b)+7(b-10) = 0
a(10-b)-7(10-b) = 0
a-7 = 0 and 10-b = 0
a = 7 and b = 10
Since a = 2^x
7 = 2^x
log 7 = log2^x
log7 = xlog2
x = log7/log2
x = 2.81
Similarly
10 = 3^x
log 10 = log 3^x
log 10 = xlog3
x = log 10/log 3
x = 1/0.4771
x = 2.096
Hence the values of x that satisfies the equation are 2.81 and 2.096
10 pancakes produces 8 inches in diameter.
The area of 1 pancake is
Area = pi * r^2
Area = pi * 4^2
Area = 50.27 in^2
Then multiply it by 10
Total area = 502.65 in^2
A smaller pancake
Area = pi * r^2
Area = pi * 2^2
<span>Area = 12.56 in^2
Divide 502.65 by 12.56
= 502.65 / 12.65
= 39.74
So there are 39 pancakes.
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Answer:
x = 2 , 3/2
Step-by-step explanation:
Answer:
or 5.5√2
Step-by-step explanation:
We can see that this is a 45-45-90 triangle
refer to the image below to see what that means
we can see that (in the image) 11=x√2
which means that x= 11/√2
to rationalize this fraction we mulitply both sides by √2 to get
or 5.5√2
