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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)
The answer is -10
Explanation: -9+(-1)=-10
Answer:
Step-by-step explanation:
It is 76 degrees F at the 6000-foot level of a mountain, and 49 degrees
F at the 12000-foot level of a mountain.
Write a linear equation to find the temperature T at an elevation e on the
mountain, where e is in thousands of feet.:
:
Find the slope using the slope formula: m = %28y2-y1%29%2F%28x2-x1%29
Assign the given values as follows
x1 = 6 (for 6000 ft); y1 = 76
x2 = 12(for 12000ft); y2 = 49
:
m = %2849-76%29%2F%2812-6%29 = %28-27%29%2F6 = -9%2F2
;
Use the point slope equation y - y1 = m(x - x1) so create the equation
y - 76 = -9%2F2(x - 6)
y - 76 = -9%2F2x - (-27)
y - 76 = -9%2F2x + 27 + 76
y = -9%2F2x + 103; is the equation
Using e and T
T = -9%2F2e + 103
:
where elevation is the horizontal and Temp is the vertical
;
Since segment AC bisects (aka cuts in half) angle A, this means the two angles CAB and CAD are the same measure. I'll refer to this later as "fact 1".
Triangles ABC and ADC have the shared segment AC between them. By the reflexive property AC = AC. Any segment is equal in length to itself. I'll call this "fact 2" later on.
Similar to fact 1, we have angle ACB = angle ACD. This is because AC bisects angle BCD into two smaller equal halves. I'll call this fact 3
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To summarize so far, we have these three facts
- angle CAB = angle CAD
- AC = AC
- angle ACB = angle ACD
in this exact order, we can use the ASA (angle side angle) congruence property to prove the two triangles are congruent. Facts 1 and 3 refer to the "A" parts of "ASA", while fact 2 refers to the "S" of "ASA". The order matters. Notice how the side is between the angles in question.
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Once we prove the triangles are congruent, we use CPCTC (corresponding parts of congruent triangles are congruent) to conclude that AB = AD and BC = BD. These pair of sides correspond, so they must be congruent in order for the entire triangles to be congruent overall.
It's like saying you had 2 identical houses, so the front doors must be the same. The houses are the triangles (the larger structure) and the door is an analogy to the sides (which are pieces of the larger structure).