The cost c of producing q units of a product is given by c=0.1q^(2)+6q+1000 If the price per unit p is given by the equation q=500-1.5p, use the chain rule to find the rate of change of cost with respect to price per unit ((dc)/(dp)) when p=50.
Answers
A. The rate of change of cost with respect to price per unit when p = 50 is approximately $105.75.
B. To find the rate of change of cost with respect to price per unit, we need to apply the chain rule, which states that for two functions u and v, if y = u(v), then dy/dx = du/dv * dv/dx.
In this case, we have c as a function of q, and q as a function of p.
1. Find the derivative of c with respect to q:
dc/dq = d/dq (0.1q^2 + 6q + 1000)
= 0.2q + 6
2. Find the derivative of q with respect to p:
dq/dp = d/dp (500 - 1.5p)
= -1.5
3. Apply the chain rule:
dc/dp = (dc/dq) * (dq/dp)
= (0.2q + 6) * (-1.5)
4. Substitute the value of q when p = 50:
q = 500 - 1.5p
= 500 - 1.5(50)
= 500 - 75
= 425
5. Calculate the rate of change of cost with respect to the price per unit when p = 50:
dc/dp = (0.2q + 6) * (-1.5)
= (0.2(425) + 6) * (-1.5)
= (85 + 6) * (-1.5)
= 91 * (-1.5)
≈ -136.5
Therefore, the rate of change of cost with respect to price per unit when p = 50 is approximately $105.75 (rounded to two decimal places).
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Related Questions
please help
tou is working on the stage scenery for a play. he needs to know the area of a circle with a radius of 7 feet. use the formula A=3.14r² to find the area
Answers
Answer:
Step-by-step explanation:
\(\lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right]\)
A=153.86
Explanation:
In your equation the radius plugs into the r
A=3.14(7)^2
A=3.14(49)
A=153.86
Need help on this question help please
Answers
A model of a house is 6 inch wide and 8 inches long. If the actual house is
20 yards long, how wide is the actual house?
OA) 2.4 yd
OB) 4.8 yd
OC) 15 yd
OD 26 yd
Answers
Answer:
its 15 <3
Step-by-step explanation:
i did the quiz.
Help hurry !2. What is the value of the expression? (V5)?
B) V125
C) 5
A) V5
D) 25
Answers
Find the Dy/Dx of y=7/x using first principle
Answers
By using first principle, the value of Dy/Dx is,
⇒ Dy/Dx = - 7 / x²
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ y = 7 / x
Now, Differentiate the function with respect to x, we get;
⇒ y = 7 / x
⇒ Dy/ Dx = D / Dx (7 / x)
= 7 D/Dx (1/x)
= 7 (- 1 × x⁻¹⁻¹ )
= 7 (- x⁻²)
= - 7 / x²
⇒ Dy/Dx = - 7 / x²
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Type the correct answer in each box. Use numerals instead of words.
Consider the given circle with the shaded sector XY and central angle, 225°. The circumference of the circle is 30
units.
A circle with center C has two lines C X, and C Y drawn from the center of the circle to the circle wall such that the exterior angle of X C Y is 225 degrees.
Use the given information to complete the statements. Round any non-integer answers to the hundredths place.
Answers
The correct answer is Length of arc XY: 15.03 units.Area of shaded sector XY: 15.73 square units.
To complete the statements, we can use the properties of circles and the given information.
The length of the arc XY, denoted as "s," can be found using the formula:
s = (θ/360) * 2πr
where θ is the central angle in degrees and r is the radius of the circle.
Given that the central angle is 225° and the circumference of the circle is 30 units, we can solve for the radius (r):
Circumference = 2πr
30 = 2πr
r = 30 / (2π) ≈ 4.77 units (rounded to the hundredths place)
Now we can calculate the length of the arc XY:
s = (225/360) * 2π * 4.77 ≈ 15.03 units (rounded to the hundredths place)
Therefore, the length of the arc XY is approximately 15.03 units.
The area of the shaded sector XY, denoted as "A," can be found using the formula:
A = (θ/360) * πr²
Using the same values for θ and r as above, we can calculate the area:
A = (225/360) * π * (4.77)² ≈ 15.73 square units (rounded to the hundredths place)
Therefore, the area of the shaded sector XY is approximately 15.73 square units.
Note: Please double-check the formulas and calculations with the provided information to ensure accuracy.
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Help my math homework
Answers
Answer:
the question dear sister
NM=x+5, ML=6x+2, JK=8, JL=24. NL = ___ units?
Answers
Answer:
is approximately 10.092 units long.
Step-by-step explanation:
NM + ML = JL
Substituting the given values:
x + 5 + 6x + 2 = 24
7x + 7 = 24
Subtracting 7 from both sides:
7x = 17
Dividing by 7:
x = 2.43 (rounded to two decimal places)
Now that we know x, we can find the length of segment NM:
NM = x + 5
NM = 2.43 + 5
NM = 7.43
Finally, we can find the length of segment NL by using the Pythagorean theorem:
NL^2 = NM^2 + ML^2
Substituting the given values and the value we found for NM:
NL^2 = (7.43)^2 + (6x + 2)^2
NL^2 = 55.2049 + (6(2.43) + 2)^2
NL^2 = 55.2049 + 46.6564
NL^2 = 101.8613
Taking the square root of both sides:
Find the value of y. Y squared=169 I wrote 13 and I tried -13 but it’s saying it wrong PLEASE HELP
Answers
The value of y from the equation given in the task content; y squared = 169 is; ±13 and hence should be expressed as such.
What is the value of the variable according to the equation given in the task content; y squared = 169?It follows from the task content that the value of the variable y according to the equation given y squared = 169 as in the task content.
Since the equation given in the task content is;
y² = 169
To determine the value of y, take the square root of both sides so that we have;
√y² = ± √169
y = ± 13 ( This follows from the fact that 169 is a perfect square).
Therefore, the value of y which satisfies the equation given can be either of -13 and 13 and hence, the answer should be expressed as; ±13.
Ultimately, the value of y from the equation given in the task content; y squared = 169 is; ±13 and hence should be expressed as such.
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For the following frequency distribution of quiz scores, how many individuals took the quiz (N)?
X f
5 6
4 5
3 5
2 3
1 2
ANSWERS:
A. 5
B. 15
C. Cannot determine
D. 21
Answers
The number of individuals who took the quiz is D) 21.
To determine the total number of individuals who took the quiz (N), we need to sum up the frequencies (f) in the given frequency distribution. The frequency (f) represents the number of individuals who obtained each score.
Let's add up the frequencies:
6 + 5 + 5 + 3 + 2 = 21
The total frequency is 21, which means that 21 individuals took the quiz. Each score represents a certain number of individuals who obtained that score, and by adding up all the frequencies, we get the total number of individuals.
Therefore, the correct answer is D. 21.
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Factorise x squared - 2x - 35
Answers
x^2 + 5x -7x - 35
Factor out x from the expression
x(x+5) -7x - 35
Factor out (x+5) from the expression
(x+5) (x-7)
Tell whether the value is a solution of the inequality.
yes
no
Answers
Answer:
Yes I believe so, not 100% sure.
Step-by-step explanation:
a portion or part of a population is called a:
Answers
Answer:
Step-by-step explanation:
The answer is Samples. A sample is a random selection of members of a population. It is a smaller group drawn from the people with the entire population's characteristics.
I hope I have helped.
Find x and input that value in the text box. (The lines that appear to be parallel are indeed parallel.) (4x12) 120° x = ?
Answers
We can see that the angle (4x-12) and 120 are supplementary. That is, they add 180 degrees.
We can conclude that because the supplementary angle for (4x-12) is similar to the angle of 120 degrees.
Then, we can work from this equality:
\(\begin{gathered} (4x-12)+120=180 \\ 4x-12=180-120=60 \\ 4x=60+12 \\ 4x=72 \\ x=\frac{72}{4} \\ x=18 \end{gathered}\)The value of x is 18 degrees.
15. A famer has 100 pigs and 180 sheep.
What is the ratio of pigs to sheep in the form 1:n
Answers
Answer:
5:9
Step-by-step explanation:
100:180 can be simplified by dividing by 20, which results in the ratio 5:9
Answer:
1 : 1.8
Step-by-step explanation:
ratio of pigs : sheep = 100 : 180 ( divide both parts of the ratio by 100 )
= 1 : 1.8
our boss is a biologist who needs wood samples from long-leaf pine trees with a fungal disease which is only visible under a microscope, and she sends you on an assignment to collect the samples. She wants at least 50 different diseased samples. She tells you that approximately 28% of long-leaf pine trees currently have the fungal disease. If you sample 160 long-leaf pine trees at random, what is the probability you’ll have at least 50 diseased samples to return to your boss? (Use the normal approximation to calculate this probability and chose the closest answer to the question.)
Answers
Answer:
Step-by-step explanation:
In this scenario, the probability of success, p is 28% = 28/100 = 0.28
Number of samples, n = 160
Probability of failure, q = 1 - p = 1 - 0.28 = 0.72
Mean,µ = np = 0.28 × 160 = 44.8
Standard deviation, σ = √npq = √160 × 0.28 × 0.72 = 5.68
Let x be the random variable representing the number of wood samples from long-leaf pine trees with a fungal disease. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
the probability that you’ll have at least 50 diseased samples to return to your boss is expressed as
P(x ≥ 50) = 1 - P(x < 50)
For P(x < 50)
z = (50 - 44.8)/5.68 = 0.91
Looking at the normal distribution table, the probability corresponding to the z score is 0.819
Therefore,
P(x ≥ 50) = 1 - 0.819 = 0.181
( pls help i’ll give the brainliest and quick) In the equation (x-3)2+(y-2)2=16, the center of the circle is...
(3,2)
(-2-3)
(-3,-2)
Answers
The denominator of a fraction is 4 more than its numerator. If the fraction equals 1/3, what is the fraction?
Answers
Answer:
Hello,
Here is your answer:
2/6
Which statements are true regarding the transformation? Select three options. The rule for the transformation is (x, y) → (–x, –y). The coordinates of L' are (–2,–2). The coordinates of M' are (–4,4). The coordinates of N' are (6,–1). The coordinates of N' are (–1,–6).
Answers
Answer: A, B, and E
Step-by-step explanation:
On edgenuity
Answer:
A B and E is correct on edge 2021
Step-by-step explanation:
trust me i got it correct on edge
Lambert invests $20,000 for a 1/3 interest in a partnership in which the other partners have capital totaling $34,000 before admitting Lambert. After distribution of the bonus, what is Lambert's capital?
Answers
Lambert's initial investment of $20,000 gave him a 1/3 interest in the partnership. Bonus is distributed, it would be added to the partnership's capital.
Here's a step-by-step explanation:
1. Determine the total capital before Lambert's investment: The other partners have a combined capital of $34,000.
2. Calculate the capital after Lambert's investment: Lambert invests $20,000, so the new total capital becomes $34,000 + $20,000 = $54,000.
3. Determine the value of 1/3 interest: Since Lambert has a 1/3 interest in the partnership, we need to find 1/3 of the total capital after his investment. (1/3) * $54,000 = $18,000.
4. Calculate the bonus: The difference between Lambert's initial investment ($20,000) and his 1/3 interest ($18,000) is the bonus. $20,000 - $18,000 = $2,000.
5. Determine Lambert's capital after the bonus distribution: Since the bonus is distributed, we subtract the bonus from Lambert's initial investment. $20,000 - $2,000 = $18,000.
So, after the distribution of the bonus, Lambert's capital in the partnership is $18,000.
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If p is prime, then there exists a field of order p². O True False
Answers
The statement "If p is prime, then there exists a field of order p²" is true. For any prime number p, there exists a finite field of order p².
Is it true that if p is prime, there exists a field of order p²?Yes, it is true that if p is a prime number, then there exists a field of order p². In mathematics, a field is a specific type of algebraic structure with two operations, addition and multiplication, that satisfy certain properties. The order of a field refers to the number of elements in the field. For any prime number p, there exists a unique finite field of order p², often denoted as GF(p²) or Fp². This field consists of p² elements and is crucial in various areas of mathematics, such as number theory, cryptography, and coding theory.
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Determine whether the sequence 1/117659, 1/16807, 1/2401...converges or diverges. If it converges, give the limit.
Answers
The sequence is a geometric sequence with a common ratio of 7. Since, the common ratio is greater than 1, the sequence diverges.
What is the sequence converges or diverges?A convergent series is a series whose partial sums tend to a specific number, also called a limit. A divergent series is a series whose partial sums, by contrast, don't approach a limit. Divergent series typically go to ∞, go to −∞, or don't approach one specific number.
The given sequence is 1/117659, 1/16807, 1/2401...
Here, common ratio is
1/16807 ÷ 1/117659
= 1/16807 × 117659/1
= 117659/16807
= 7
Now, 1/2401 ÷ 1/16807
= 1/2401 × 16807/1
= 16807/2401
= 7
Hence, the sequence is a geometric sequence with a common ratio of 7. Since, the common ratio is greater than 1, the sequence diverges.
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Given the graphs of y = f(x) and y = g(x), what is the value of f(x)-g(x) where the two graphs intersect?
Answers
Answer:
0
Step-by-step explanation:
If they want the values of where the graphs intersect, that means the values are both = to each other, meaning subtracting the same value by the same value is 0
Tell me the coordinates to graph it plz
Answers
Answer:
x=2, y=3
Step-by-step explanation:
Solve equation.
a-7=9
Answers
To solve the equation, add 7 to both sides. The solution is a = 16.
A linear equation is an equation of which the highest degree of its variables is 1.
Steps to solve linear equations:
Simplify the expressions. If there are parentheses, remove them by multiplying the corresponding terms.Combine the same terms.Isolate the variable on one side by using subtraction or addition.Use division or multiplication to find the value of the variable.Recall that if we subtract or add the same number to both sides of an equation, it does not change the equality.
The given problem:
Solve a-7=9
The variable is a. To isolate a, remove -7 by adding 7 to both sides:
a-7 +7 = 9 +7
a = 16 (solved)
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Predict whether atoms of chlorine or atoms of sulfur would be more likely to attract electrons and, therefore, be more reactive. Explain your reasoning.
Answers
Chlorine will be more reactive.
Reactivity of elementsFrom the question, we are to predict whether the atoms of chlorine or atoms of sulfur would be more likely to attract electrons
The electronic configuration of chlorine (Cl) is
2,8,7
This means Cl needs only one electron to complete its octet configuration
and
The electronic configuration of sulfur (S) is
2,8,6
This means sulfur needs two more electrons to complete its octet configuration
Since chlorine needs fewer electrons to complete its octet configuration, then it will be more likely to attract electrons.
Thus, chlorine will be more reactive.
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a pond is in the shape of a semi-circle. the diameter of the pond is 11 feet. what is the perimeter of the pond? use 3.14 for pi. round your answer to the nearest hundredth.
Answers
The perimeter of the pond is 28.21 feet.
The perimeter of a semi-circle pond having a diameter of 11 feet should be calculated as follows: The perimeter of a semi-circle is equal to the sum of its straight and curved sides.
The diameter of the pond is 11 feet, so the radius of the pond is half that, or:
11/2 = 5.5 feet
The length of the curved side of the pond is half the circumference of a circle having a diameter of 11 feet, or:
πd/2 = 3.14 × 11/2 = 17.21 feet
The length of the straight side of the pond is equal to the diameter, or: 11 feet
The perimeter of the pond is the sum of these two values: 17.21 + 11 = 28.21 feet
Therefore, the perimeter of the pond is 28.21 feet, rounded to the nearest hundredth.
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Rebecca's boss pays her time and a half for overtime work at the comic book store. If her regular wage is $8.50, what is Rebecca paid for overtime work?
Answers
The amount that Rebecca will be paid for overtime work is $12.75.
How to calculate the value?From the information, Rebecca's boss pays her time and a half for overtime work at the comic book store. Her regular wage is $8.50.
The amount for overtime will be:
= (1.5 × $8.50)
= $12.75
Therefore, the amount that Rebecca will be paid for overtime work is $12.75.
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what is an inequality that represents this sentence?
if seven times a number is decreased by three, the result is less than thirty.
Answers
Answer:
7x-3<30
Step-by-step explanation:
7 times a number = 7x
is decreased by 3 = -3
the result is less than 30 = <30
Answer:
7x - 3 < 30
Step-by-step explanation:
We can put "seven times a number" as 7x since a number is unknown -->
now decreased is subraction so we have 7x - 3 -->
the result is less than thirty is that the difference must be less then 30.
so, 7x - 3 < 30.
Hope this helps!
an equation for loudness, in decibles, is L=10log10 R where R is the relative intensity of the sound. Sounds that reach levels of 120 decibles or more are painful to humans what is the relative intensity of 120 decibles
Answers
Considering the logarithmic loudness equation, the relative intensity of 120 decibels is of \(R = 10^{12}\).
What is the logarithmic loudness equation?The equation is:
\(L = 10\log{R}\)
In which:
L is the loudness, in decibels.R is the relative intensity.For this problem, we have that L = 120, hence the relative intensity is found as follows:
\(120 = 10\log{R}\)
\(\log{R} = 12\)
\(R = 10^{12}\)
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