Since profit can't be negative, the production level that'll maximize profit is approximately equal to 220.
<h3>How to find the production level that'll maximize profit?</h3>
The cost function, C(x) is given by 12000 + 400x − 2.6x² + 0.004x³ while the demand function, P(x) is given by 1600 − 8x.
Next, we would differentiate the cost function, C(x) to derive the marginal cost:
C(x) = 12000 + 400x − 2.6x² + 0.004x³
C'(x) = 400 − 5.2x + 0.012x².
Also, revenue, R(x) = x × P(x)
Revenue, R(x) = x(1600 − 8x)
Revenue, R(x) = 1600x − 8x²
Next, we would differentiate the revenue function to derive the marginal revenue:
R'(x) = 1600 - 8x
At maximum profit, the marginal revenue is equal to the marginal cost:
1600 - 8x = 400 − 5.2x + 0.012x
1600 - 8x - 400 + 5.2x - 0.012x² = 0
1200 - 2.8x - 0.012x² = 0
0.012x² + 2.8x - 1200 = 0
Solving by using the quadratic equation, we have:
x = 220.40 or x = -453.73.
Since profit can't be negative, the production level that'll maximize profit is approximately equal to 220.
Read more on maximized profit here: brainly.com/question/13800671
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<h3>
Answer: -6, 7, -8</h3>
Start with the sequence {1, 2, 3, 4, 5, 6, 7, 8, ...}
Then change the sign of every other term so you'll have the first term positive, the second term negative, and so on.
That updates to {1, -2, 3, -4, 5, -6, 7, -8, ...}
Every odd term (1,3,5,..) is positive while every even term (-2,-4,-6) is negative.
Answer:
a=-20
Step-by-step explanation:
-4(7a+5)=-160
7a+(-20)=-160 Multiply -4 and 5
7a=-140 Subtract -20 from -160
a=-20 Divide 7 by -140
This question is in reverse (in two ways):
<span>1. The definition of an additive inverse of a number is precisely that which, when added to the number, will give a sum of zero. </span>
<span>The real problem, in certain fields, is usually to show that for all numbers in that field, there exists an additive inverse. </span>
<span>Therefore, if you tell me that you have a number, and its additive inverse, and you plan to add them together, then I can tell you in advance that the sum MUST be zero. </span>
<span>2. In your question, you use the word "difference", which does not work (unless the number is zero - 0 is an integer AND a rational number, and its additive inverse is -0 which is the same as 0 - the difference would be 0 - -0 = 0). </span>
<span>For example, given the number 3, and its additive inverse -3, if you add them, you get zero: </span>
<span>3 + (-3) = 0 </span>
<span>However, their "difference" will be 6 (or -6, depending which way you do the difference): </span>
<span>3 - (-3) = 6 </span>
<span>-3 - 3 = -6 </span>
<span>(because -3 is a number in the integers, then it has an additive inverse, also in the integers, of +3). </span>
<span>--- </span>
<span>A rational number is simply a number that can be expressed as the "ratio" of two integers. For example, the number 4/7 is the ratio of "four to seven". </span>
<span>It can be written as an endless decimal expansion </span>
<span>0.571428571428571428....(forever), but that does not change its nature, because it CAN be written as a ratio, it is "rational". </span>
<span>Integers are rational numbers as well (because you can always write 3/1, the ratio of 3 to 1, to express the integer we call "3") </span>
<span>The additive inverse of a rational number, written as a ratio, is found by simply flipping the sign of the numerator (top) </span>
<span>The additive inverse of 4/7 is -4/7 </span>
<span>and if you ADD those two numbers together, you get zero (as per the definition of "additive inverse") </span>
<span>(4/7) + (-4/7) = 0/7 = 0 </span>
<span>If you need to "prove" it, you begin by the existence of additive inverses in the integers. </span>
<span>ALL integers each have an additive inverse. </span>
<span>For example, the additive inverse of 4 is -4 </span>
<span>Next, show that this (in the integers) can be applied to the rationals in this manner: </span>
<span>(4/7) + (-4/7) = ? </span>
<span>common denominator, therefore you can factor out the denominator: </span>
<span>(4 + -4)/7 = ? </span>
<span>Inside the bracket is the sum of an integer with its additive inverse, therefore the sum is zero </span>
<span>(0)/7 = 0/7 = 0 </span>
<span>Since this is true for ALL integers, then it must also be true for ALL rational numbers.</span>
Answer:
g(4) = 157
Step-by-step explanation:
g(x) = 8x^2 + 9x - 7
Let x =4
g(4) = 8 * 4^2 +9*4 -7
=8*16 +36 - 7
=128+36-7
=157
