Perpendicular lines have negative reciprocal slop to each other.
So first solve for y.
Slope will be the coefficient of x in y=mx+c form.
m is the slope. Then negative reciprocal this slope and in this case the answer is -1/5
Answer:
A = 1701,38 ft²
Dimensions :
x (north and south sides ) = 38.89 ft
y ( east and west sides ) = 43,75 ft
Step-by-step explanation:
North and south (sides of same length) equal "y" cost (4 + 5 ) = 4,5 $/ft²
East and west (sides of same length) equal "x" cost ( 3 + 5 ) = 4 $ /ft²
Equation of cost is
C = Cost of (north + south ) + Cost (east + west)
C = 2 * 4,5 * x + 4*2* y
C = 9x + 8y
700 = 9x + 8y ⇒ y = ( 700- 9x)/ 8
A = x*y
A(x) = x * ( 700 - 9x ) /8
A(x) = ( 700 x -9x²) / 8 A´(x) = ( 700 - 18 x )/ 8 A´(x) = 0
( 700 - 18 x )/ 8 = 0 ⇒ 700 - 18 x = 0 ⇒ x = 700/18
x = 38.89 ft
y = ( 700 - 9x )/8 ⇒ y = 349.99 / 8 ⇒ y = 43.75
And maximum ara is
A = x*y A = 38.89 * 43.75 = 1701,38 ft²
Answer:
x = 10
Step-by-step explanation:
You can try the answers to see which works. (The first one does.)
Or, you can solve for the variable:
Divide by 75
... (1/5)^(x/5) = 3/75 = 1/25
Recognize that 25 = 5^2, so ...
... (1/5)^(x/5) = (1/5)^2
Equating exponents, you have
... x/5 = 2
... x = 10 . . . . . multiply by 5
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You can also start by taking logarithms:
... log(75) +(x/5)log(1/5) = log(3)
... (x/5)log(1/5) = log(3) -log(75) = log(3/75) = log(1/25) . . . . simplify the log
... x/5 = log(1/25)/log(1/5) = 2 . . . . . simplify (or evaluate) the log expression
... x = 10 . . . . . multiply by 5
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"Equating exponents" is essentially the same as taking logarithms.
It would be 10 miles since we use Pythagorean Theorem
