Answer:
A(max) = (9/2)*L² ft²
Dimensions:
x = 3*L feet
y = (3/2)*L ft
Step-by-step explanation:
Let call "x" and " y " sides of the rectangle. The side x is parallel to the wall of the house then
Area of the rectangle is
A(r) = x*y
And total length of fence available is 6*L f , and we will use the wall as one x side then, perimeter of the rectangle which is 2x + 2y becomes x + 2*y
Then
6*L = x + 2* y ⇒ y = ( 6*L - x ) /2
And the area as function of x is
A(x) = x* ( 6*L - x )/2
A(x) = ( 6*L*x - x² ) /2
Taking derivatives on both sides of the equation we get:
A´(x) = 1/2 ( 6*L - 2*x )
A´(x) = 0 ⇒ 1/2( 6*L - 2*x ) = 0
6*L - 2*x = 0
-2*x = - 6*L
x = 3*L feet
And
y = ( 6*L - x ) /2 ⇒ y = ( 6*L - 3*L )/ 2
y = ( 3/2)*L feet
And area maximum is:
A(max) = 3*L * 3/2*L
A(max) = (9/2)*L² f²
Answer:
x = +2√21 and y = +2√30
Step-by-step explanation:
The two marked sides of the smaller triangle are x and y. The third side has length equal to 14 - 8, or 6.
We can thus write two equations in x and y:
x^2 = y^2 + 6^2
and
y 6
-- = ---
8 y
Solving the first equation for y^2 yields y^2 = 36 - x^2. Solving the second equation for y^2 yields 48. Thus 36 - x^2 = 48, and
x^2 = 84. Thus, x = +√7*√4*√3, or x = +2√21.
We now find y. y^2 = 36 = x^2, which here becomes
y^2 = 36 + 4(21) = 36 + 84 = 120. Thus, y = +√4*√30, or y = +2√30.
<u>Answer:</u> The final answer must have only one decimal place.
<u>Step-by-step explanation:</u>
Significant figures are defined as the figures present in a number that expresses the magnitude of a quantity to a specific degree of accuracy.
We are given:
An addition problem having values (34.530 g + 12.1 g + 1222.34 g)
<u>The rule that is applied for the addition and subtraction is:</u>
The least precise number present after the decimal point determines the number of significant figures in the answer.
For the given problem, the least precise number after the decimal is '1'
Evaluating the value: (34.530 g + 12.1 g + 1222.34 g) = 1268.97 ≈ 1269.0
Hence, the final answer must have only one decimal place.
The answer is going to be 3.5 more than 52.5 so the answer is 56.