The given equation is:
x y – 5000 = y
Rewrite this to create an explicit equation:
x y – y = 5000
y ( x – 1) = 5000
y = 5000 / (x – 1)
Derive to get dy / dx:
dy = - 5000 dx / (x – 1)^2
dy / dx = - 5000 / (x – 1)^2
So plugging in x = 6,
dy / dx = - 5000 / (6 – 1)^2
dy / dx = - 200
Answer:
[tex]\frac{dy}{dx}|_{x=6}= -200[/tex]
Step-by-step explanation:
Given : Demand equation [tex]xy − 5,000 = y[/tex]
To Find [tex]\frac{dy}{dx}|_{x=6}[/tex]
Solution :
[tex]xy- y= 5000[/tex]
[tex]y(x-1)= 5000[/tex]
[tex]y= \frac{5000}{x-1}[/tex]
Differentiating with respect to x
[tex]\frac{dy}{dx}= \frac{-5000}{(x-1)^2}[/tex]
Now substitute x = 6
[tex]\frac{dy}{dx}|_{x=6}= \frac{-5000}{(6-1)^2}[/tex]
[tex]\frac{dy}{dx}|_{x=6}= \frac{-5000}{5^2}[/tex]
[tex]\frac{dy}{dx}|_{x=6}= \frac{-5000}{25}[/tex]
[tex]\frac{dy}{dx}|_{x=6}= -200[/tex]
Hence [tex]\frac{dy}{dx}|_{x=6}= -200[/tex] =T-shirts per dollar
A like is drawn through (-4,3) and (4,3). which describes whether or not the line is represents a direct variation?
Calculate the length of the line segment. Round your answer to tje nearest tenth .
The required measure of the length of the given line is 8.6 units.
What is Distance?Distance is defined as the object traveling at a particular speed in time, from one point to another.
here,
Locate the end point of line in the graph,
end point of the line from the graph is given as (0, 8) and (7, 3)
Applying the distance formula,
D = √[[x₂ - x₁]² + [y₂ - y₁]²]
Substitute the point in the above equation,
D = √[[7]² + [3 - 8]²]
D = √49 + 25
D = √74
D = 8.6
Thus, the required measure of the length of the given line is 8.6 units.
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Celine's Cereal Company is launching a new brand of cereal and she is considering two different sizes for the base of the boxes. Box 1: The length is 3 times the width. Box 2: The length is 1 less than 4 times the width. The dimensions of the base of Box 1 are: width: x; length: 3 width: x; length: x + 3 width: x; length: x – 3 width: x; length: 3x
Answer:
D. Width = x and Length = 3x
Step-by-step explanation:
We are given that,
The length of Box 1 is 3 times the width of Box 1. ..................(1)
Let the width of Box 1 = x
So, from (1), we have,
Length of Box 1 = 3 × Width of Box 1
i.e. Length of Box 1 = 3x
Thus, the dimensions of Box 1 are : Width = x and Length = 3x
Hence, option D is correct.
In this exercise we have to identify which of the alternatives best represents the equation, like this:
Letter D
So we have that it is the area of a box, where we have:
The length of box is 3 times widthThe width of the box is XSo is the same as:
[tex]L= 3W\\W=X\\L=3X[/tex]
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f(x) = square root x - 5 find f^-1
A train travels 50 kilometers in 4 hours, and then 77 kilometers in 3 hours. What is its average speed?
The volume of a rectangular prism is given by the formula V = lwh, where l is the length of the prism, w is the width, and h is the height. Suppose a box in the shape of a rectangular prism has length (2a + 11), width (5a – 12), and height (a + 6). Which expression represents the volume of the box? v=(2a+11)(5a-12)(a+6) v=(10a^2-24a+55a-132)(a+6) v=(10a^3+60a^2-24a^2-144a+55a^2+330a-132a-792 v=10a^3+60a^2-24a^2+55a^2-144a+330a-132a-792 v=10^3+91a^2+54a-792
All of the given expressions for v are various stages in the process of "simplifying" the product of length, width, and height. Each and every one of them represents the volume of the box.
Let w(s,t)=f(u(s,t),v(s,t)) where u(1,0)=−6,∂u∂s(1,0)=5,∂u∂1(1,0)=7 v(1,0)=−8,∂v∂s(1,0)=−8,∂v∂t(1,0)=6 ∂f∂u(−6,−8)=−1,∂f∂v(−6,−8)=2
What is the image of G for a dilation with center (0,0) and a scale factor of 1?
- 1/2 (-3/2x + 6x +1) -3
is c+3/5=15 an identity
Students were surveyed about their favorite colors one fourth of the students perfered red , one eighth of the students perferred blue, and three fifth of the remaining students perferred green . if 15 students perferred green , how many students were surveyed
Sin(x2 + y2) da r , where r is the region in the first quadrant between the circles with center the origin and radii 2 and 5
A double integral of Sin(x^2 + y^2) over a region between two circles with radii 2 and 5 is transformed into polar coordinates for simplification. The limits of the polar coordinates correspond to this region, and the integral becomes ∫ ∫ rSin(r^2) dr dθ, with r ranging from 2 to 5, and θ from 0 to π/2.
Explanation:The student asked about the calculation of a double integral over a region between two circles, presented in polar coordinates, where the function is Sin(x^2 + y^2). For simplification, we can change to polar coordinates. In polar coordinates, x = rcosθ and y = rsinθ. Thus, x^2 + y^2 becomes r^2, and the function becomes Sin(r^2).
For a region between two circles of radii 2 and 5 in the first quadrant, we can describe the limits of the polar coordinates. r will range from 2 to 5, and θ from 0 to π/2. Thus, the integral will be ∫(from 0 to π/2) ∫(from 2 to 5) rSin(r^2) dr dθ. Evaluation of the integral will require techniques of polar integration.
It's important to note that this is a theoretical discussion and the actual integration may have complex results depending on the function to integrate.
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We need solve the given integral, convert coordinates to polar form and integrate step by step. First we will solve the inner integral from 2 to 5 and then the outer integral from 0 to π/2
We need to evaluate the double integral of Sin(x² + y²) over the region between the circles with radii 2 and 5.
In polar coordinates, where x = r cos(θ) and y = r sin(θ), this integral becomes:
∫(from 0 to π/2) ∫(from 2 to 5) sin(r²) r dr dθ
Let's solve the inner integral first, with respect to r:
Firstly, set up the integral: ∫(from 2 to 5) sin(r²) r dr.
Then Use the substitution u = r², then du = 2r dr.
Now Rewriting the integral: (1/2) ∫(from 4 to 25) sin(u) du = (1/2) [-cos(u)] (from 4 to 25).
and evaluating this: (1/2) [-cos(25) + cos(4)].
Next, integrate the result with respect to θ:
Set up the outer integral: (1/2) ∫(from 0 to π/2) [-cos(25) + cos(4)] dθ.
Now since [-cos(25) + cos(4)] is constant, the integral is straightforward: (1/2) [-cos(25) + cos(4)] * (π/2).
Hence the final answer: (π/4) [-cos(25) + cos(4)].
Therefore, the integral evaluates to (π/4) [-cos(25) + cos(4)].
EDITED QUESTION
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Find the double integral Sin(x² + y²) over the region between the circles with radii 2 and 5.
7 • (–5) • (–3) • (–8)
A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t2 + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s. Which solution can be eliminated and why?
Answer:
Its -0.2 Because time cannot be a negative value.
Step-by-step explanation:
The correct value would be the 2.7 sec. one.
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
Here, Indicated when h(t) = 0, we are to find for the time where the football has reached a certain height.
⇒ - 16t² + 40t + 7 = 0
Then, the values of t would be -0.2 and 2.7.
Since, we are to look for the time, it is impossible for us to have an answer that has a negative value.
So based from our answer, the solution that we will eliminate is the -0.2 one. Since its value is negative.
Thus, the correct value would be the 2.7 sec. one.
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The length of a rectangle is 4 centimeters more than twice its width. If the perimeter of the rectangle is 86 centimeters , find the dimensions of the rectangle
In an American Sign Language (A.S.L) class of 26 students, 15 are hearing impaired. What fraction of the students are hearing impaired?
The 15/26 fraction of the students is hearing impaired if in an American Sign Language (A.S.L) class of 26 students, 15 are hearing impaired.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
In an American Sign Language (A.S.L) class of 26 students, 15 are hearing impaired.
The fraction:
= 15/26
We can convert the above value in the percentage as follows:
The best method for obtaining this answer is to divide 15 by 26 to obtain the number 0.5769, multiply that number by 100 to obtain the number 57.69; and then round it to the closest full number if necessary.
15/26 in percentage will be 57.69
Thus, the 15/26 fraction of the students is hearing impaired if in an American Sign Language (A.S.L) class of 26 students, 15 are hearing impaired.
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can you show me the work to get this answer write two expressions that have a gcf of 8xy
how do you know that the sum of (-2 3/4) and 5/9 is rational?
A.The sum is a terminating and repeating decimal
B.The sum is a non-terminating and a non-repeating decimal.
C.The sum is a fraction
D.The sum is an integer
Answer:
c
Step-by-step explanation:
Answer:
The sum is fraction therefore rational
Step-by-step explanation:
Given two numbers
[tex]-2\frac{3}{4}\text{ and }\frac{5}{9}[/tex]
we have to tell that how their sum is rational.
we add the above two number
[tex]-2\frac{3}{4}+\frac{5}{9}[/tex]
[tex]\frac{-11}{4}+\frac{5}{9}[/tex]
[tex]\frac{-99+20}{36}=\frac{-79}{36}=-2.194444...[/tex]
Hence, the sum is we can say fraction or non-terminating but repeating which is the definition of a rational number.
∴ from the given options answer C is correct.
The sum is fraction therefore rational.
Sections of pre-fabricated fencing are each 4 1/3feet long how long are 6 1/2 sections placed end to end
Solve for x. 3/4+x=1/2
Given that the points (-1, 10), (2, 10), (2, -2), and (-1, -2) are vertices of a rectangle, what is the ratio of the rectangle's length to its width?
Eight members of a chess club are having a tournament. In the first round every player will play a chess game against every other player. How many games will be in the first tournament
A cubic yard of topsoil weighs 4,128 pounds.About how many 50-pound bags can you fill with one cubic yard of topsoil?
Answer:
Approximately 83 bags each carrying 50 pounds of soil will carry 1 cubic yard of soil or 4,128 pounds of soil.
Step-by-step explanation:
We are given the following information in the question:
1 cubic yards is equal to 4128 pounds that is
[tex]1~yard^3 = 4,128~pounds[/tex]
Amount of soil 1 bag can hold = 50 pounds
Number of bags to hold 1 cubic yard of soil or 4,128 pounds of soil:
Formula:
[tex]\text{Number of bags} = \displaystyle\frac{\text{Total amount of soil}}{\text{Amount of soil 1 bag can hold}}[/tex]
[tex]= \displaystyle\frac{4128}{50} = 82.56[/tex]
Thus, approximately 83 bags each carrying 50 pounds of soil will carry 1 cubic yard of soil or 4,128 pounds of soil.
About 11/12 of a golf course is in the fairways, 1/11 in the greens, and the rest in the trees. What part of the golf course is in the trees?
[tex]\frac{1}{132}[/tex] part of the golf course is in the trees.
To find out what part of the golf course is in the trees, we need to add the fractions of the golf course that are in the fairways and the greens, and then subtract that sum from 1 (which represents the whole golf course).
First, we add the fractions of the golf course that are in the fairways and greens:
Fairways: [tex]\frac{11}{12}[/tex]Greens: [tex]\frac{1}{11}[/tex]To add these fractions, we must first find a common denominator. The denominators are 12 and 11, so the common denominator is 12 x 11 = 132.
Convert each fraction to have this common denominator:
[tex]\frac{11}{12}[/tex] = [tex]\frac{121}{132}[/tex][tex]\frac{1}{11}[/tex] = [tex]\frac{12}{132}[/tex]Now, add these converted fractions together:
[tex]\frac{121}{132}[/tex] + [tex]\frac{12}{132}[/tex] = [tex]\frac{133}{132}[/tex]
Since the sum [tex]\frac{133}{132}[/tex] is greater than 1, we convert it to a whole number plus a fraction. [tex]\frac{133}{132}[/tex] = 1 + [tex]\frac{1}{132}[/tex].
Now, to find the part of the golf course in the trees, subtract this sum from the whole golf course:
1 - 1 + [tex]\frac{1}{132}[/tex] = [tex]\frac{1}{132}[/tex]
So, [tex]\frac{1}{132}[/tex] of the golf course is in the trees.
Complete question:
About [tex]\frac{11}{12}[/tex] of a golf course is in the fairways, [tex]\frac{1}{11}[/tex] in the greens, and the rest in the trees. What part of the golf course is in the trees?
A machine produces 268 bolts in 28 minutes. At the same rate, how many bolts would be produced in 21 minutes?
Using simple mathematical operations, we know that 201 bolts are produced in 21 minutes.
What exactly are mathematical operations?A mathematical function known as an operation converts zero or more input values into a precisely defined output value.The quantity of operands affects the operation's arity.We can recall the PEMDAS steps in the following order: parentheses, exponents, multiplication, division (from Left to right), addition, and subtraction (from left to right).So, the bolts produced in 21 minutes are:
Bolts produce is 28 min: 268In 21 minutes: xCalculate as follows:
268/28 = x/21 (Cross-multiply)28x = 21(268)28x = 5,628x = 5,628/28x = 201Therefore, using simple mathematical operations, we know that 201 bolts are produced in 21 minutes.
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Final answer:
To find the number of bolts produced in 21 minutes, set up a proportion using the given information: 268 bolts / 28 minutes = x bolts / 21 minutes. Simplifying, we find that x = 201 bolts.
Explanation:
To find the number of bolts produced in 21 minutes, we can set up a proportion using the given information. We know that the machine produces 268 bolts in 28 minutes. Let x be the number of bolts produced in 21 minutes.
Using the proportion:
268 bolts / 28 minutes = x bolts / 21 minutes
Multiplying both sides by 21, we get:
(268 bolts / 28 minutes) * 21 minutes = x bolts
Simplifying, we find that x = 201 bolts.
Each side of a square is lengthened by 2 inches. the area of the new, larger square is 121 square inches. find the length of a side of the original square.
The length of the original square is 9 inches
What is a square?A square is defined as a polygon that has four sides and is a closed, two-dimensional (2D) object. A square has equal and parallel sides on all four sides.
Area of square = x * x
where x is the side of the square
According to the question,
The area of the new square is 121 square inches.
Let the side of the original square is = x inches
Then the side of the new square is = x + 2 inches
Area of the new square = ( x + 2 )²
121 = ( x + 2 )²
11 = x + 2
x = 9 inches
Therefore, The length of the original square is 9 inches.
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Tom is afraid of heights above 9 feet. He is asked to repair a slide of a high deck. The bottom of a laddar must be placed 6 feet from a deck. The laddar is 10 feet long. How far above the ground does the laddar touch the deck? Is Tom afraid of the hieght?
the temperature on the earth's surface is about 5500 degrees Celsius .scientist believe that the temperature of the center of the sun is 270 times hotter. what is the temperature oof the center of the Sun?
16 lbs of brand M cinnamon costing $17/lb was made by combining Indonesian cinnamon which costs $19/lb with Thai cinnamon which costs $11/lb. Find out how much of each type of cinnamon was used to make the Brand M blend. (Need it done algebraically)
Which number does the 6 have a value that is one-tenth the value of 6 in 34,761?
The number in which the 6 has a value that is one-tenth the value of the 6 in 34,761 is 3,476.1
In the number 34,761, the digit 6 is in the tens place, giving it a value of 60. To find a number where the value of 6 is one-tenth of 60, we look for a place value that is one position to the right.
In 3,476.1, the 6 is in the ones place, making its value 6, which is one-tenth of 60. This shift from the tens place to the ones place decreases the value by a factor of ten.