Answer:
3 ft
Step-by-step explanation:
The volume of the box is given by the formula ...
V = Bh
where B is the base area and h is the height. Solving for h, we get ...
h = V/B
Filling in the numbers gives us the height:
h = (20 1/4 ft^3)/(6 3/4 ft^2) = (81/4)·(4/27) ft = 3 ft
The height of the box is 3 feet.
Answer:
- 8) 4 + 2q²/p² - 4r/p + r²/p²
- 9) (3/4, -9/4)
- 10) (3/8, 41/16)
Step-by-step explanation:
8. ============
Given
- α and β are roots of px² + qx + r = 0
The sum of the roots is α + β = -q/p, the product of then roots αβ = r/p
- (2 + α²)(2 + β²) =
- 4 + 2(α² + β²) + (αβ)² =
- 4 + 2((α + β)² -2αβ) + (αβ)² =
- 4 + 2((-q/p)² - 2r/p) + (r/p)² =
- 4 + 2q²/p² - 4r/p + r²/p²
------------------------------
9. ============
<u>Given function</u>
The minimum point is reached at vertex
<u>The vertex is:</u>
- x = -b/2a
- x = -(-3)/2*2 = 3/4
<u>The corresponding y-coordinate is:</u>
- y = 2(3/4)² - 3(3/4) - 1 = 9/8 - 9/4 - 1 = 1/8(9 - 18 - 9) = - 18/8 = - 9/4
<u>So the point is: </u>
---------------
10. ============
<u>Given function</u>
The maximum is reached at vertex
<u>The vertex is:</u>
- x = -b/2a
- x = -(-3)/2(-4) = -3/8
<u>The corresponding y-coordinate is:</u>
- y = 2 - 3(-3/8) -4(-3/8)² = 2 + 9/8 - 9/16 = 1/16(32 + 18 - 9) = 41/16
<u>So the maximum point is:</u>
The value of x in the triangle is (a) 22
<h3>How to solve for x?</h3>
The complete question is in the attached image.
From the attached image of the triangle, we have:
Evaluate sin(45)
Solve for x
Divide
x = 22
Hence, the value of x is (a) 22
Read more about special triangles at:
brainly.com/question/654982
#SPJ1
Answer:
3x-6
Step-by-step explanation:
