To solve this you would use the pythagorean theorem since the brace is making the frame look like two right triangles. The theorem states that for a triangle with a right angle, A^2+B^2=C^2. A and B are the sides of the frame and C is the brace which is like the hypotenuse of the triangle. It doesn't matter which side is A or B so you can put 6 or 8 in place of either in the equation. 6^2+8^2=C^2. If you simplify this it equals 36+64=C^2, which then simplifies to 100=C^2. Then you take the square root of both sides (what number multiplied by itself = the number you are trying to get, in this case, 100). So then you get C=10 because 10x10=100. So the length of the diagonal brace is 10ft.
Find the area of the cone:
Area of cone: ⅓r^2h
⅓r^2h
= ⅓(3.5)^2(7)
= ⅓(12.25)(7)
= 1/3(85.75)
= 85.75/3
1/3 cup sloshed out:
(85.75/3 )/3
= 29.9 cubic cm
Answer:
The roots are;
x = (2 + i)/5 or (2-i)/5
where the term i is the complex number representing the square root of -1
Step-by-step explanation:
Here, we want to use the completing the square method to solve the quadratic equation;
f(x) = -5x^2 + 4x -1
Set the function to zero
0 = -5x^2 + 4x - 1
So;
-5x^2 + 4x = 1
divide through by the coefficient of x which is -5
x^2 - 4/5x = -1/5
We now take half of the coefficient of x and square it
= -2/5^2 = 4/25
add it to both sides
x^2 - 4x/5 + 4/25= -1/5 + 4/25
(x- 2/5)^2 = -1/5 + 4/25
(x - 2/5)^2 = -1/25
Take the square root of both sides
x - 2/5 = √( -1/25
x - 2/5 = +i/5 or -i/5
x = 2/5 + i/5 or 2/5 - i/5
<span>A new kind of temporary pavilion support for a square roof uses just two poles set at the diagonal corners of a square. The allowable distance between the poles is 18 feet. Find the area of the roof. The sides will have lengths of 18/sqrt(2). Since they are perpendicular, the area of the square will be (18^2)/2 = 81*4/2 = 162 square feet.
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