Answer:
<h2>-11 and 1</h2>
Step-by-step explanation:
Put the values of x to the given expression:
for x = -3:
2(-3) - 5 = -6 - 5 = -11
for x = 3
2(3) - 5 = 6 - 5 = 1
Answer:
- Base Length of 68cm
- Height of 34 cm.
Step-by-step explanation:
Given a box with a square base and an open top which must have a volume of 157216 cubic centimetre. We want to minimize the amount of material used.
Step 1:
Let the side length of the base =x
Let the height of the box =h
Since the box has a square base
Volume 
Surface Area of the box = Base Area + Area of 4 sides
Step 2: Find the derivative of A(x)
Step 3: Set A'(x)=0 and solve for x
![A'(x)=\dfrac{2x^3-628864}{x^2}=0\\2x^3-628864=0\\2x^3=628864\\x^3=314432\\x=\sqrt[3]{314432}\\ x=68](https://tex.z-dn.net/?f=A%27%28x%29%3D%5Cdfrac%7B2x%5E3-628864%7D%7Bx%5E2%7D%3D0%5C%5C2x%5E3-628864%3D0%5C%5C2x%5E3%3D628864%5C%5Cx%5E3%3D314432%5C%5Cx%3D%5Csqrt%5B3%5D%7B314432%7D%5C%5C%20x%3D68)
Step 4: Verify that x=68 is a minimum value
We use the second derivative test
Since the second derivative is positive at x=68, then it is a minimum point.
Recall:
Therefore, the dimensions that minimizes the box surface area are:
- Base Length of 68cm
- Height of 34 cm.
I'm pretty sure it a 3 to 8 and 32 to 12
h(t) = -46t² + 40t + 3
We can think this graph by t being the x-axis and h being y-axis
So we want the maximum value to y.
We know by math that the vertex of a parabola is (-b/2a, -Δ/4a)
So the y value of the vertex is -Δ/4a
Let's calculate:
Δ = b² - 4.a.c
Δ = 40² - 4.(-46).3
Δ = 2152
Yvertex = -2152/4.(-46)
Yvertex = 2152/184
Yvertex = 269/23
Now we have the value of y we need to equal it to the equation
269/23 = -46t² + 40t + 3
-46t² + 40t + 3 - 269/23 = 0
-46t² + 40t - 200/23 = 0
Δ = b² - 4.a.c
Δ = 40² - 4 . -46 . (-200/23)
Δ = 1600 - 4. -46 . (-200/23)
Δ = 0
There's 1 real root.
In this case, x' = x'':
x = (-b +- √Δ)/2a
x' = (-40 + √0)/2.-46
x'' = (-40 - √0)/2.-46
x' = -40 / -92
x'' = -40 / -92
x' = 0,43478260869565216
x'' = 0,43478260869565216
So, after approximately 0,4348 seconds the balloon will reach the highest point.
B) height after 2 seconds
h(2) = -46.2² + 40.2 + 3
h(2) = -46.4 + 80 + 3
h(2) = -184 + 83
h(2) = -101
Not sure how it's possible but it would be -101.
