Answer:
Zero Property of Addition
Step-by-step explanation:
Click the heart button, will you?
Answer:
17) MC(x) = 35 − 12/x²
18) R(x) = -0.05x² + 80x
Step-by-step explanation:
17) The marginal average cost function (MC) is the derivative of the average cost function (AC).
AC(x) = C(x) / x
MC(x) = d/dx AC(x)
First, find the average cost function:
AC(x) = C(x) / x
AC(x) = (5x + 3)(7x + 4) / x
AC(x) = (35x² + 41x + 12) / x
AC(x) = 35x + 41 + 12/x
Now find the marginal average cost function:
MC(x) = d/dx AC(x)
MC(x) = 35 − 12/x²
18) x is the demand, and p(x) is the price at that demand. Assuming the equation is linear, let's use the points to find the slope:
m = (40 − 50) / (800 − 600)
m = -0.05
Use point-slope form to find the equation of the line:
p(x) − 50 = -0.05 (x − 600)
p(x) − 50 = -0.05x + 30
p(x) = -0.05x + 80
The revenue is the product of price and demand:
R(x) = x p(x)
R(x) = x (-0.05x + 80)
R(x) = -0.05x² + 80x
Answer:
8 balloons
Step-by-step explanation:
We want to find how many she kept for herself.
She brought 24 balloons to the picnic.
She gave 1/3 to Karen.
She will be left with 2/3 of the balloons:
2/3 * 24 = 16
She will be left with 16 balloons.
She gave 1/2 of what was left to Tim. She will be left with 1/2 of the balloons:
1/2 * 16 = 8
She will be left with 8 balloons.
Maximum weight the bridge can support in kilograms is 101696
Step-by-step explanation:
- Step 1: Given capacity of bridge = 100 British tons. Find how many kilograms are equivalent to 1 British ton.
1 British ton = 2240 pounds
1 pound = 0.454 kg
⇒ 1 British ton = 2240 × 0.454 kg = 1016.96 kg
- Step 2: Find how many kilograms are in 100 British tons.
⇒ 100 × 1016.96 = 101696
Answer:
<u>5π/6</u>
Step-by-step explanation:
<u>Given</u> :
<u>Solving</u> :
- We know that : cos⁻¹ cosθ = θ
- But we can't just do that in this case
- Because the range of cos values is [0, π]
- Clearly, our value does not lie in this range
- We have to take a different Quadrant other than the 3rd Quadrant which gives cos a negative value
- The 2nd Quadrant also has cos values negative
- Therefore,
- cos⁻¹ cos (π - π/6)
- cos⁻¹ cos (5π/6)
- ⇒ <u>5π/6</u> ∈ [0, π] ⇒ It lies in the range!