Find the value of y picture *****
1 answer:
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Answer:
AC =
Step-by-step explanation:
Assuming you require AC
Using Pythagoras' identity in the right triangle
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is
AC² + BC²= AB²
AC² + 7² = 8²
AC² + 49 = 64 ( subtract 49 from both sides )
AC² = 15 ( take square root of both sides )
AC = ≈ 3.87 ( to 2 dec. places )
Answer:
and
.
Step-by-step explanation:
Please find the attachment.
We have been given that a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. The total perimeter is 38 feet.
The perimeter of the window will be equal to three sides of rectangle plus half the perimeter of circle. We can represent our given information in an equation as:
We can see that diameter of semicircle is W. We know that diameter is twice the radius, so we will get:
Let us find area of window equation as:
Now, we will solve for L is terms W from perimeter equation as:
Substitute this value in area equation:
Since we need the area of window to maximize, so we need to optimize area equation.
Let us find derivative of area equation as:
To find maxima, we will equate first derivative equal to 0 as:
Upon substituting in equation
, we will get:
Therefore, the dimensions of the window that will maximize the area would be and
.
