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Answer:
B. When the amount of lemonade produced is 10 gallons, the cost is increasing at a rate of $1.15 per gallon.
Step-by-step explanation:
For C(x) = (dollar cost of producing x gallons of lemonade), the derivative C'(x) has units of dollars per gallon. It is the rate of change in cost when x gallons have been produced.
Then C'(10) is the rate of increase of cost, in dollars per gallon, when 10 gallons have been produced. (matches choice B)
Answer:
x = 0.59 to the nearest hundredth
Step-by-step explanation:
Look at the attached figure
- The equation is 2x + = 3
- The red curve represents the left side of the equation
- The blue line represents the right side of the equation
- The solution of the equation is the point of intersection of the two graphs
∵ There are 5 small squares between every 2 numbers on the x-axis
∴ Each square represents 0.2
∵ There are 5 small squares between every 2 numbers on the y-axis
∴ Each square represents 0.2
∵ The point of intersection between the 2 graphs is nearest to
the 3rd small square after the zero on the x-axis
∵ 0.2 × 3 = 0.6
∴ The x-coordinate of the point is approximately located at 0.59
∴ x = 0.59 to the nearest hundredth
Answer:
B(4, - 3 )
Step-by-step explanation:
We have A(2, - 7) and C(7, 3 )
Using the section formula to calculate the coordinates of B
= = = = 4
= = = = - 3
Hence B(4, - 3 )
Answer:
x = 4 + sqrt(38) or x = 4 - sqrt(38)
Step-by-step explanation using the quadratic formula:
Solve for x over the real numbers:
2 (x^2 - 8 x - 22) = 0
Divide both sides by 2:
x^2 - 8 x - 22 = 0
x = (8 ± sqrt((-8)^2 - 4 (-22)))/2 = (8 ± sqrt(64 + 88))/2 = (8 ± sqrt(152))/2:
x = (8 + sqrt(152))/2 or x = (8 - sqrt(152))/2
sqrt(152) = sqrt(8×19) = sqrt(2^3×19) = 2sqrt(2×19) = 2 sqrt(38):
x = (2 sqrt(38) + 8)/2 or x = (8 - 2 sqrt(38))/2
Factor 2 from 8 + 2 sqrt(38) giving 2 (sqrt(38) + 4):
x = 1/22 (sqrt(38) + 4) or x = (8 - 2 sqrt(38))/2
(2 (sqrt(38) + 4))/2 = sqrt(38) + 4:
x = sqrt(38) + 4 or x = (8 - 2 sqrt(38))/2
Factor 2 from 8 - 2 sqrt(38) giving 2 (4 - sqrt(38)):
x = 4 + sqrt(38) or x = 1/22 (4 - sqrt(38))
(2 (4 - sqrt(38)))/2 = 4 - sqrt(38):
Answer: x = 4 + sqrt(38) or x = 4 - sqrt(38)