Answers
Answer:
3x
Step-by-step explanation
Related Questions
Triangle Z Y X is shown with its exterior angles. Point Z extends to point L, point X extends to point N, and point Y extends to point M.
Analyze the diagram to complete the statements.
The m∠MXN is
the m∠YZX.
The m∠LZX is
the m∠ZYX + m∠YXZ.
The m∠MYL is
180° − m∠ZYX.
Answers
The completed statements, obtained from the relationship between the exterior angles of a triangle and supplementary angles are;
The m∠MXN is greater than m∠YZX
The m∠LZX is equal to m∠ZYX + m∠YXZ
The m∠MYL is equal to 180° - m∠ZYX
What are supplementary angles?Supplementary angles are angles that form a linear pair and when added together are equivalent to 180°
The exterior angle of a triangle theorem indicates, that we get;
m∠MXN = m∠YZX + m∠ZYX
Therefore; m∠MXN > m∠YZXm∠LZX = m∠ZYX + m∠YXZ∠MYL is a supplementary angle to the angle ∠ZYX
Therefore; m∠MYL + m∠ZYX = 180°
m∠MYL = 180° - m∠ZYXThe completed statements are therefore;
m∠MXN is greater than m∠YZX
m∠LZX equal to m∠ZYX + m∠YXZ
m∠MYL equal to 180° - m∠ZYX
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Question 2 of 10
What are the dimensions of AB?
A. 3x2
B. 3x3
C. 2x3
D. 2 x 2
Answers
Answer:
Based on the image, we can see that matrix A is a 3x2 matrix, and matrix B is a 2x3 matrix. In order to multiply matrices A and B, the number of columns in matrix A must match the number of rows in matrix B.
Since matrix A has 2 columns and matrix B has 2 rows, we can multiply them together, resulting in a 3x3 matrix. Therefore, the answer is B. The dimensions of AB are 3x3.
I DONT NEED BRAINLEST JUST STAY FUN AND SAFEAns. (c) 2X3
Dimension of matrix is given by row x column
list the elements of U
Answers
Unit 7: Right Triangles & Trigonometry Homework 4: Trigonometry Ratios & Finding Missing Sides #’s 10&11
Answers
The value of the sides are;
x = 20.4
x = 13.84
How to determine the valueThere are six different trigonometric identities. They include;
sinetangentcosinecosecantsecantcotangentGiven that the ratios are;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
Using the tangent identity, we have;
tan 64 = 42/x
cross multiply the values
x = 42/2. 050
x = 20. 4
Using the sine identity;
sin 70 = 13/x
cross multiply the values
x = 13/0. 939
x = 13. 84
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A 60 foot tall building casts a 20 foot. Shadow. Use the principles of similar triangles to determine the length of a shadow cast by a 5 foot 6 inch student
Answers
The length of the shadow cast by the 5 foot 6 inch student is approximately 1.83 feet.
To solve this problem, we'll set up a proportion using the principles of similar triangles. The two triangles in this case are the building and its shadow, and the student and their shadow.
Convert the height of the student to feet. 5 feet 6 inches is equal to 5.5 feet.
Set up the proportion. Let x represent the length of the shadow cast by the student. We have the following proportion:
(height of building) / (length of building's shadow) = (height of student) / (length of student's shadow)
60 / 20 = 5.5 / x
Cross-multiply and solve for x:
60 * x = 20 * 5.5
60x = 110
x = 110 / 60
x = 1.83 (rounded to two decimal places)
The length of the shadow cast by the 5 foot 6 inch student is approximately 1.83 feet.
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MarÃa is shopping for party supplies. She finds that paper plates come in packages of 8, napkins come in packages of 10, and paper cups come in packages of 12. What is the least number of packages of plates, napkins, and cups she has to buy so that she has the same number of each item for her party?
Answers
The least number of packages of plates, napkins, and cups Maria has to buy is 15 packages .
To find the least number of packages, we need to find the least common multiple (LCM) of the three package sizes: 8 (plates), 10 (napkins), and 12 (cups).
The prime factors of 8 are 2x2x2, of 10 are 2x5, and of 12 are 2x2x3. To find the LCM, we multiply the highest powers of each prime factor: 2³x3x5 = 120.
This means Maria needs 120 of each item. She will buy 120/8 = 15 packages of plates, 120/10 = 12 packages of napkins, and 120/12 = 10 packages of cups.
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If p and q are real numbers in the function f(x)=x4+5x3+px2+qx+30 and f(1)=0, which equation is true?
Answers
p + q + 36 = 0 is the equation that is true. From this equation, we can say that p + q = -36.
If we substitute x = 1 in the given function, we get:
f(1) = [tex](1)^4 + 5(1)^3 + p(1)^2 + q(1) + 30[/tex]
= 1 + 5 + p + q + 30
= p + q + 36
We are given that f(1) = 0. Therefore, we have:
p + q + 36 = 0
This is the equation that is true. From this equation, we can say that p + q = -36.
Now, let's see why this is the case. When we substitute x = 1 in the given function and get f(1) = 0, it means that (1, 0) is a point on the graph of the function. This point lies on the x-axis, which means that the function intersects the x-axis at x = 1. Since the x-axis is the line y = 0, this means that f(x) = 0 when x = 1.
Using this information, we can write an equation in terms of p and q. If we substitute x = 1 in the given function and get f(1) = 0, it means that:
f(x) = [tex](x - 1)(x^3 + 6x^2 + (6+p)x + (30-q))[/tex]
Therefore, we have:
[tex](x - 1)(x^3 + 6x^2 + (6+p)x + (30-q)) = 0[/tex]
Since (1,0) is a point on the graph of the function, we know that x = 1 is a root of this equation. Therefore, we have:
[tex](x - 1)(x^3 + 6x^2 + (6+p)x + (30-q)) = (x - 1)(x^2 + (7+p)x + (36-p-q))[/tex]
We know that (x - 1) is a factor of this equation, so we can use polynomial long division to divide the expression [tex](x^2 + (7+p)x + (36-p-q))[/tex] by (x - 1). The quotient will give us the other two roots of the equation. However, we do not need to find these roots to answer the question. All we need to know is that p + q = -36.
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Steve bought 10 gallons of gas at the gas station with the highest price. how much more than cole did he pay for gas?
please help, thank you.
Answers
Steve paid $10 more than Cole for gas, regardless of the actual prices of gas at the two gas stations.
To answer this question, we need to know the prices of gas at both gas stations. Let's assume that Cole bought 10 gallons of gas at the gas station with the lowest price, and that the price difference between the two gas stations is $x per gallon.
If we denote the price per gallon of gas at the gas station where Cole bought gas as "c", then the total amount Cole paid for gas is:
10c
If we denote the price per gallon of gas at the gas station where Steve bought gas as "s", then the total amount Steve paid for gas is:
10s
The difference between the two amounts is:
10s - 10c
But we know that Steve bought gas at the gas station with the highest price, so we can assume that s = c + x.
Substituting this expression for s into the equation above, we get:
10s - 10c = 10(c + x) - 10c = 10x
So Steve paid $10 more than Cole for gas, regardless of the actual prices of gas at the two gas stations.
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CAN SOMEONE SHOW ME STEP BY STEP ON HOW TO DO THIS SOMEONE GAVE ME THE WRONG STEPS
A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
A polygon with a horizontal top side labeled 45 yards. The left vertical side is 20 yards. There is a dashed vertical line segment drawn from the right vertex of the top to the bottom right vertex. There is a dashed horizontal line from the bottom left vertex to the dashed vertical, leaving the length from that intersection to the bottom right vertex as 10 yards. There is another dashed horizontal line that comes from the vertex on the right that intersects the vertical dashed line, and it is labeled 12 yards.
What is the area of the playground?
900 square yards
855 square yards
1,710 square yards
1,305 square yards
Answers
The area of the playground include the following: 900 square yards.
How to calculate the area of a regular polygon?In Mathematics and Geometry, the area of a regular polygon can be calculated by using this formula:
Area = (n × s × a)/2
Where:
n is the number of sides.s is the side length.a is the apothem.In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:
Area of a parallelogram, A = base area × height
Area of playground, A = 45 × 20
Area of a playground, A = 900 square yards.
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Analyzing Solution Sets to Linear Equations with the Variable on Both Sides
2x + 5 = 3 + 2(x + 1)
Answers
Answer: it will need to be rewritten so that the variable is only on one side of the equation
Step-by-step explanation:f the equation contains fractions, you may elect to multiply both sides of the equation by the least common denominator
the measure of an angle is 156°. what is the measure of its supplementary angle
Answers
Answer:
24°
Step-by-step explanation:
Supplementary angles: 2 angles that add up to 180°.
We are given that one angle is 156°, so we can write an equation:
180=156+x
subtract both sides by 156
24=x
So, the measure of the supplementary angle is 24°.
Hope this helps!
A particle moves along the x-axis so that its position at time t>0 is given by
X(t) = (t^2 - 9)/(3t^2 + 8)
A) show that the velocity of the particle at time this given by v(t) = 70t/(3t^2 + 8)^2
B) is the particle moving toward the origin or away from the originator time t = 2? Give a reason for your answer.
C) The acceleration of the particle is given by £(t). Write an expression for £(t), and find the value of £(2).
D) What position does the particle approach as t approaches infinity?
Answers
The velocity of the particle at time t is given by [tex]v(t) = 70t/(3t^2 + 8)^2.[/tex]
The expression for the acceleration of the particle is a(t) [tex]= (210t^2 + 1120)/(3t^2+8)^3.[/tex]
A) To find the velocity of the particle, we need to take the derivative of its position with respect to time:
[tex]X(t) = (t^2 - 9)/(3t^2 + 8)[/tex]
[tex]v(t) = dX/dt = [(2t)(3t^2+8) - (t^2-9)(6t)]/(3t^2+8)^2[/tex]
[tex]v(t) = (6t^3 + 16t - 6t^3 + 54t)/(3t^2 + 8)^2[/tex]
[tex]v(t) = 70t/(3t^2 + 8)^2[/tex]
Therefore, the velocity of the particle at time t is given by[tex]v(t) = 70t/(3t^2 + 8)^2.[/tex]
B) To determine whether the particle is moving toward or away from the origin at time t = 2, we need to examine the sign of the velocity v(2). Plugging t = 2 into the expression for v(t), we get:
[tex]v(2) = 70(2)/((3(2)^2 + 8)^2) = 280/169[/tex]
Since v(2) is positive, the particle is moving away from the origin at time t = 2.
C) The acceleration of the particle is given by the derivative of its velocity with respect to time:
[tex]v(t) = 70t/(3t^2 + 8)^2[/tex]
[tex]a(t) = dv/dt = (70(3t^2+8)^2 - 2(70t)(2t)(3t^2+8))/(3t^2+8)^4[/tex]
[tex]a(t) = (210t^2 + 1120)/(3t^2+8)^3[/tex]
Therefore, the expression for the acceleration of the particle is [tex]a(t) = (210t^2 + 1120)/(3t^2+8)^3[/tex]. To find the value of a(2), we plug in [tex]t = 2:a(2) = (210(2)^2 + 1120)/(3(2)^2+8)^3 = 175/677[/tex]
D) To find the position that the particle approaches as t approaches infinity, we examine the behavior of X(t) as t gets very large. We can do this by looking at the leading term of the numerator and denominator of X(t) as t approaches infinity:
[tex]X(t) = (t^2 - 9)/(3t^2 + 8)[/tex]
As t approaches infinity, the numerator is dominated by the t^2 term, and the denominator is dominated by the 3t^2 term. Therefore, as t approaches infinity, X(t) approaches:
[tex]X(infinity) = t^2/3t^2 = 1/3[/tex]
So the particle approaches the point x = 1/3 as t approaches infinity.
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Find the perimeter of a square that has a side length of 4.3x + 2 inches.
Answers
The calculated perimeter of the square from the side length is 17.2x + 8
Finding the perimeter of a square from the side lengthFrom the question, we have the following parameters that can be used in our computation:
A square that has a side length of 4.3x + 2 inches.
Using the above as a guide, we have the following:
Perimeter = 4 * side length
Substitute the known values in the above equation, so, we have the following representation
Perimeter = 4 * (4.3x + 2)
When teh brackets are opened, we have
Perimeter = 17.2x + 8
Hence, the perimeter is 17.2x + 8
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Helpppppppppppppppppppppppp
Answers
Answer:
Point in the original figure: (5,4)
Point in the final figure: (0,-2)
Step-by-step explanation:
hope this works and helps! :)
Which of the data sets below have striking deviations? Select all that apply.
A) 65, 68, 61, 63, 71
B) 99, 95, 93, 97, 98
C) 22, 83, 85, 88, 91
D) 45, 47, 43, 45, 97
E) 72, 78, 71, 67, 35
Answers
The set of values for x that satisfies a quadratic inequality is x < -0.5 or x > 1.5
Write down a possible quadratic inequality. Please help - it’s a gcse maths question
Answers
Answer: x-0.5y=1.5
Step-by-step explanation:
Select the correct answer from each drop-down menu.
The three vertices of a triangle drawn on a complex plane are represented by 0 + 0i, 4 + 0i, and 0+ 3i.
The length of the hypotenuse is
units, and the area of the triangle is
square units. (Hint: Use the Pythagorean theorem.)
Answers
The area of the triangle is (a-6, b-12) square units 6 sq unit.
What is the triangle?A triangle is described as a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees.
This means that the sum of the interior angles of a triangle is equal to 180°
Now that we have the points they make a 3-4-5 triangle.
The two legs are 3 and 4, so the hypotenuse has to be 5.
We could also use the Pythagorean theorem a² + b² = c² 3² + 4² = c² 25 = c² c = 5
We then calculate the area
Area =1/2 b*h
Area = 1/2(3*4)
Area = 6 sq unit
The area of the triangle is (a-6, b-12) square units 6 sq unit.
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Can you guys help me on this algebra work? thankscompare b(x) = 6x^2 to f(x)compare m(x) = -1/3x^2 - 4
Answers
b(x) = 6x² and m(x) = -1/3x²- 4 have similarities and differences as quadratic functions with different coefficients and signs.
How do b(x) and m(x) compare?We can look at the similarities and differences to compare b(x) = 6x² and m(x) = -1/3x² - 4
Similarities:Both b(x) and m(x) are quadratic functions, which means they have an x² term.
They both have a constant term, with b(x) having a constant of 0 and m(x) having a constant of -4.
Differences:The coefficients of the x² term are different: b(x) has a coefficient of 6, while m(x) has a coefficient of -1/3.
The signs of the coefficients are different: b(x) has a positive coefficient, while m(x) has a negative coefficient.
Overall, b(x) and m(x) have some similarities in their form as quadratic functions, but their coefficients and signs are different, which means they will have different shapes and behaviors.
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Domain of the rational function.
(5x^2)/(1-x)
Answers
Answer:
(-∞, 1) ∪ (1, ∞)
Step-by-step explanation:
1 - x = 0
-x = -1
x = 1
In interval notation, the domain is (-∞, 1) U (1, ∞)
Find the slope from the data below
Answers
Answer:
m = -4
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (-3,12) (-2,8)
We see the y decrease by -4, and the x increase by 1, so the slope is
m = -4
So, the slope of the line representing by the data is -4.
Sentence:
7) Jenny bought a pair of boots priced at $85. If the boots were on gole for 15% off
regular price, how much did Jenny pay for the boots?
Let x =
(Remember to subtract sale
Answers
p - 0.15p = 0.85p
This means that the sale price is 85% of the original price. We know that Jenny bought the boots for $85, so we can set up the equation:
0.85p = 85
Solving for p, we get:
p = 100
Therefore, the original price of the boots was $100. To find out how much Jenny paid for the boots with the 15% discount, we can subtract the discount from the original price:
100 - 0.15(100) = 85
So Jenny paid $85 for the boots after the 15% discount.
For 50 points can you help me with this I really need help.
Answers
The coordinates of the points in the table indicates that the coordinates of the image following the reflections, can be presented on the coordinate plane as shown in the attached graph created with MS Excel.
What is a reflection transformation?A reflection transformation is one in which the mirror image of the preimage is created across a line of reflection.
The coordinate points of the image after the specified reflections can be presented as follows;
Original [tex]{}[/tex]Reflection across the x-axis Reflection across the y-axis y = -x
(0, 15) [tex]{}[/tex] (0, -15) (0, 15) (-15, 0)
(1, 15) [tex]{}[/tex] (1, -15) (-1, 15) (-15, -1)
(1, 13) [tex]{}[/tex] (1, -13) (-1, 13) (-13, -1)
(3, 15) [tex]{}[/tex] (3, -15) (-3, 15) (-15, -3)
(3, 12) [tex]{}[/tex] (3, -12) (-3, 12) (-12, -3)
(1, 10) [tex]{}[/tex] (1, -10) (-1, 10) (-10, -1)
(1, 8) [tex]{}[/tex] (1, -8) (-1, 8) (-8, -1)
(3, 10) [tex]{}[/tex](3, -10) (-3, 10) (-10, -3)
(3, 7) [tex]{}[/tex] (3, -7) (-3, 7) (-7, -3)
(1, 5) [tex]{}[/tex] (1, -5) (-1, 5) (-5, -1)
(1, 2) [tex]{}[/tex] (1, -2) (-1, 2) (-2, -1)
(4, 4) [tex]{}[/tex] (4, -4) (-4, 4) (-4, -4)
(5, 7) [tex]{}[/tex] (-5, 7) (5, -7) (-7, -5)
(7, 8) [tex]{}[/tex] (7, -8) (-7, 8) (-8, -7)
(6, 5) [tex]{}[/tex] (6, -5) (-6, 5) (-5, -6)
(8, 6) [tex]{}[/tex] (8, -6) (-8, 6) (-6, -8)
(9, 9) [tex]{}[/tex] (9, -9) (-9, 9) (-9, -9)
(11, 10) [tex]{}[/tex] (11, -10) (-11, 10) (-10, -11)
(10, 7) [tex]{}[/tex] (10, -7) (-10, 7) (-7, -10)
(12, 8) [tex]{}[/tex] (12, -8) (-12, 8) (-8, -12)
(13, 6) [tex]{}[/tex] (13, -6) (-13, 6) (-6, -13)
(11, 5) [tex]{}[/tex] (11, -5) (-11, 5) (-5, -11)
(14, 4) [tex]{}[/tex] (14, -4) [tex]{}[/tex] (-14, 4) (-4, -14)
(12, 3) [tex]{}[/tex] (12, -3) (-12, 3) (-3, -12)
(9, 4) [tex]{}[/tex] (9, -4) (-9, 4) (-4, -9)
(7, 3) [tex]{}[/tex] (7, -3) (-7, 3) (-3, -7)
(10, 2) [tex]{}[/tex] (10, -2) (-10, 2) (-2, -10)
(8, 1) [tex]{}[/tex] (8, -1) (-8, 1) (-1, -8)
(5, 2) [tex]{}[/tex] (5, -2) (-5, 2) (-2, -5)
(2, 0) [tex]{}[/tex] (2, 0) (-2, 0) (0, -2)
The above coordinate points can be used to plot the graphs showing the image of the points following the specified reflections across the x-, y-, and y = -x, axis.
Please find attached the required graph of the coordinate points following the reflection transformations, created with MS Excel.
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Can someone explain ._.
Answers
The mark-up value percentage is 25 %
Given data ,
The markup amount is the selling price minus the cost price, so:
Markup = $8630 - $6900 = $1730
The markup percentage is the markup amount divided by the cost price, expressed as a percentage:
Markup percentage = (Markup / Cost price) x 100%
Markup percentage = ($1730 / $6900) x 100%
Markup percentage = 0.25 x 100%
Markup percentage = 25%
Hence , the markup percentage is 25%
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The circumstances if the base of the cone is 12π cm. If the volume of the cone is 96π, what is the height
Answers
Answer:8
Step-by-step explanation:
n^2 - 5n + 6, n^2 - 4n+ 4 I need help, i know the answer may possibly be (n-3)(n-2)^2 factor it, an di need steps.
Answers
The simplified expression is (n - 3) / (n - 2).
What is the simplification of the expression?The expression is simplified as follows;
(n² - 5n + 6) / (n² - 4n + 4)
n² - 5n + 6 can be factored as (n - 2) (n - 3)
n² - 4n + 4 can be factored as (n - 2) (n - 2)
Therefore, the expression becomes:
[(n - 2) (n - 3)] / [(n - 2) (n - 2)]
We can cancel the (n - 2) factor in the numerator and denominator, leaving us with:
(n - 3) / (n - 2)
So the simplified expression is (n - 3) / (n - 2).
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!!I need help seriouslyyy!!
Answers
The average cost per day for the four service is $3.23 per day
What is average cost?Average cost refers to the per-unit cost of production, which is calculated by dividing the total cost of production by the total number of units produced.
Therefore average cost = total cost/ number of unit
total cost = $108
average cost for the three services = $108/3
= $36
total average cost = $36+$54.30
= $90.30
therefore average cost for a day will be average cost for a month over 28day i.e 7days ×4
= 90.30/28
= $3.23 per day
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A set of 9 books has 5,481 pages.
How many pages would be in each
book, if each book has the same
number of pages.
Answers
Answer:
609 pages
Hope this helps!
Step-by-step explanation:
9 books = 5481 pages
1 book = ? pages
9 books ÷ 9 = 1 book so 5481 pages ÷ 9 = 609 pages
1 book has 609 pages.
Please upload a picture of a piece of paper with the problem worked out, and draw the graph for extra points, there will be 6 of these, so go to my profile and find the rest, and do the same, for extra points. solve this one using the elimination method.
Answers
The solution to this system of equations are x = -5 and y = 8.
How to solve these system of linear equations?In order to determine the solution to a system of two linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method.
Given the following system of linear equations:
x + y = 3 .........equation 1.
x - 3y = -29 .........equation 2.
By subtracting equation 2 from equation 1, we have:
(x - x) + (y - (-3y) = 3 - (-29)
y + 3y = 3 + 29
4y = 32
y = 32/4 = 8
x = 3 - y
x = 3 - 8
x = -5
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Which function is increasing and has a domain of (1,infiniti)?
A. F(x) = log(x - 1) + 2
B. F(x) = -log(x - 2) + 1
C. F(x) = -log(x - 1) + 2
D. F(x) = log(x - 2) + 1
Answers
The function that is increasing and has a domain of (1, infinity) is A. F(x) = log(x - 1) + 2.
To determine the increasing function with the specified domain, let's analyze each option:
A. F(x) = log(x - 1) + 2
This function is increasing because the logarithm of a positive number is always increasing. The domain is (1, infinity), which matches the requirement.
B. F(x) = -log(x - 2) + 1
This function is decreasing because the negative sign in front of the logarithm inverts the increase. The domain is (2, infinity), which does not match the requirement.
C. F(x) = -log(x - 1) + 2
This function is also decreasing because of the negative sign in front of the logarithm. The domain is (1, infinity), which matches the requirement, but the function is not increasing.
D. F(x) = log(x - 2) + 1
This function is increasing because the logarithm of a positive number is always increasing. However, the domain is (2, infinity), which does not match the requirement.
The function that is increasing and has a domain of (1, infinity) is A. F(x) = log(x - 1) + 2.
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The weekly demand for wireless mice manufactured by Insignia Consumer Electronic
Products group is given by
p(x) = -0.005x + 60, where p denotes the unit price in dollars and x denotes the quantity demanded. The weekly cost
function associated with producing these wireless mice is given by
C(x) = -0.001x^2 + 18x + 4000
Where C(x) denotes the total cost in dollars incurred in pressing x wireless mice (a) Find the production level that will yield a maximum revenue for the manufacturer. What will
be maximum revenue? What price the company needs to charge at that level? (b) Find the production level that will yield a maximum profit for the manufacturer. What will be
maximum profit? What price the company needs to charge at that level?
Answers
The production level that will yield maximum revenue is 6000 units, the maximum revenue is $180,000, and the price the company needs to charge at that level is $30. The production level that will yield maximum profit is 5250 units, the maximum profit is $59,250, and the price the company needs to charge at that level is $37.25.
To find the production level that will yield maximum revenue, we need to determine the quantity demanded that maximizes the revenue. The revenue function is given by
R(x) = xp(x) = x(-0.005x + 60) = -0.005x^2 + 60x
To find the maximum value of R(x), we need to take the derivative of R(x) and set it equal to zero
R'(x) = -0.01x + 60 = 0
x = 6000
So the production level that will yield maximum revenue is 6000 units.
To find the maximum revenue, we can plug this value into the revenue function
R(6000) = -0.005(6000)^2 + 60(6000) = $180,000
To find the price the company needs to charge at that level, we can plug the production level into the demand function
p(6000) = -0.005(6000) + 60 = $30
To find the production level that will yield maximum profit, we need to determine the quantity that maximizes the profit function. The profit function is given by
P(x) = R(x) - C(x) = -0.005x^2 + 60x - (-0.001x^2 + 18x + 4000) = -0.004x^2 + 42x - 4000
To find the maximum value of P(x), we need to take the derivative of P(x) and set it equal to zero
P'(x) = -0.008x + 42 = 0
x = 5250
So the production level that will yield maximum profit is 5250 units.
To find the maximum profit, we can plug this value into the profit function
P(5250) = -0.004(5250)^2 + 42(5250) - 4000 = $59,250
To find the price the company needs to charge at that level, we can plug the production level into the demand function
p(5250) = -0.005(5250) + 60 = $37.25
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