The formula in terms of x and y for dy/dx is -3y/x
The value of dy/dx at the point (81,16) is -0.5926
The question is incomplete, the full question is given below:
A manufacturer can produce 2970 cell phones when x dollars is spent on labor and y dollars is spent on capital. the equation that relates x and y is [tex]55x^{\frac{3}{4} } y^{\frac{1}{4} } =2970[/tex]
a. Find a formula in terms of x and y for [tex]\frac{dy}{dx}[/tex]
b. Find the value of dy/dx at the point (81,16). Round your answer to 4 decimal places
Part a
A formula in terms of x and y for [tex]\frac{dy}{dx}[/tex]
We differentiate equation that relates x and y with respect to x by implicit differentiation:
=[tex]\frac{d}{dx} (55x^{\frac{3}{4} } y^{\frac{1}{4} } )=\frac{d}{dx} (2970)[/tex]
=[tex]55(x^{\frac{3}{4} } \frac{d}{dx} (y^{\frac{1}{4} } )+y^{\frac{1}{4} } ((x^{\frac{3}{4} } ))=0[/tex]
=[tex]x^{\frac{3}{4} } y^{\frac{-3}{4} } \frac{dy}{dx} =3y^{\frac{1}{4} } x^{\frac{-1}{4} }[/tex]
= [tex]\frac{dy}{dx} =\frac{-3y^{0.5}x^{-0.5} }{x^{0.75}y^{-0.75} }[/tex]
[tex]=\frac{-3y}{x}[/tex]
=-3y/x
Part b
Value of dy/dx at the point (81,16)
dy/dx at (81,16), x=81, y=16
dy/dx=-3y/x
dy/dx=-3*16/81
dy/dx=-48/81
dy/dx=-16/27
=-0.5926
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Kim and jake are competing in the big race. jake starts at the starting line and rides at 2 meters per second. kim gets a 6 meter head start and rides at 3 meters every 2 seconds. write an equation for kim and jake
The equation obtained for Kim will be t = x/2
Equation obtained for Jake will be t = (x - 6)/1.5
As for the problem, Kim and Jake are competing in the big race. And the values of their speed are given below.
Kim moves at a 2-meter-per-second running pace.
Jake moves at a 1.5 meter per second running pace (3 meters per 2 seconds)
Jake gets 6 meters ahead of Kim.
To get equations for the same case to both persons we should get it as,
Let x be the complete race distance and t be either Kim's or Jake's total race time.
Time = Speed/Distance
Kim's time equation is t = x/ 2.
The time equation that Jake uses is t = (x - 6)/1.5.
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Please please please help me it's due at 10:00 P.M today
Answer: 20x
Step-by-step explanation:
Answer:
20x
Step-by-step explanation:
just trust me because you have to mulitply
Use the number line to add the fraction.
Drag and drop the answer into the box to match the sum
Answer:
the answer to the question is 1/8
Complete the square to transform the expression x2 + 4x + 2 into the form a(x − h)2 + k. (1 point) (x + 2)2 − 2 (x + 2)2 + 2 (x + 4)2 − 2 (x + 4)2 + 2
By completing squares we will rewrite the equation as:
(x + 2)^2 - 2
How to complete squares?
Here we have the quadratic equation:
x^2 + 4x + 2
And we want to complete squares, remember that the square trinomial is:
(a + b)^2 = a^2 + 2ab + b^2
We can rewrite the quadratic as:
x^2 + 2*2*x + 2
Now, adding and subtracting 2 we get:
x^2 + 2*2*x + 2 + 2 - 2
x^2 + 2*2*x + 4 - 2
(x^2 + 2*2*x + 2^2) - 2
(x + 2)^2 - 2
So the first option is the correct one.
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according to the u.s. census bureau, the probability that a randomly selected worker primarily drives a car to work is 0.867. the probability that a randomly selected worker primarily takes public transportation to work is 0.048
The probability a randomly selected worker primarily drives a car or takes public transportation to work is 0.915
Here's the complete question:
According to the U.S. census bureau, the probability a randomly selected worker primarily drives a car to work is 0.76. the probability a randomly selected worker primarily takes public transportation to work is 0.05. what is the probability a randomly selected worker primarily drives a car or takes public transportation to work?
Given that according to the U.S. Census Bureau:
The probability that a randomly selected worker primarily drives a car to work is 0.867
The probability that a randomly selected worker primarily takes public transportation to work is 0.048
The probability that a randomly selected worker primarily drives a car or takes public transportation to work is
= 0.867 +0.048 = 0.915
(since these two are disjoint sets)
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help, i’ll give 20 points and thanks, and 5 stars
Answer: 8.75
Step-by-step explanation:
(0, 20) and (40, 370) any two coordinate points can be chosen
(370 - 20) / (40 - 0)
= 35/4 or 8.75
Find the slope of the line passing through each of the following pairs of points and draw the graph of the line. (-4, 3), (2,3)
Answer: The slope is 0.
Step-by-step explanation:
We will use the slope formula to find the slope of the line going through these two points.
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
[tex]\displaystyle \frac{3-3}{2--4}=\frac{0}{2+4} =0[/tex]
The slope of this line is 0.
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just help me please. it might be easy but I kinda forgot what goes into where. Please help me out tho!!
The matching of the mathematical terms to the equations, and expressions is as follows;
Area of a circle → π•r²
Percent equation → P = %dec × w
Percent proportion → [tex] \displaystyle{ \frac{p}{w} = \frac{\%}{100} }[/tex]
Circumference → π × d
Pi → π
Base equation → y = k•x
Constant of proportionality → [tex] \frac{y}{x} [/tex]
% increase → [tex] \frac{Amount \: increase}{Original \: amount} [/tex]
%decrease →[tex] \frac{Amount \: decrease}{Original \: amount} [/tex]
Interest Earned → P×r×t
What is an expression in mathematics?An expression in mathematics consists of mathematical symbols and variables joined together operators in the proper manner
Area of a circleThe area of a circle is π × r²
Where;
r = The radius of the circle
Percent equationA percent equation equation is one of the sides of the equation consists of a percentage
Percent proportion;A percent proportion express a proportion as a percentage
Circumference;The circumference of a circle is the distance round the circle, which is given by the product of Pi and the radius of the circle
Pi.The symbol Pi is π
Base EquationThe base equation is one written in simple form
Constant of proportionalityThe constant of is the constant ratio between variables that are proportional
%increaseThis is the ratio of the increase to the original amount expressed as a percentage
%decreaseThe ratio of the decrease to the original amount expressed as a percentage
Interest EarnedThis is the amount added to an investment sum or amount and it is given by the product of the principal, P, rate, r and time, t
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Anya earns $150 less than three times Rick's monthly salary. If Rick's salary is represented by x which expression represents Anya's salary
A x-3- $150
B 3(x+$150)
C 3(x-$150)
D 3x-$150
E 3x+$150
Answer:
d
Step-by-step explanation:
3 multiplied by ricks salary minus 150
Sorry guys one last question
a shipment of 22-inch pipes contains a pipe that is exactly 21.78 inches. What is the percent error, rounded to the nearest percent.
Please explain what you did step by the step. Thank you!
The percent error of the shipment pipes is 1.01%
Percent error:
Percent error is defined as a difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage.
It can be calculated using the formula,
PE = (|Estimated value-Actual value|/ Actual value) × 100
Given,
A shipment of 22-inch pipes contains a pipe that is exactly 21.78 inches.
Here we need to find the percent error of the shipment.
According to the percent error formula,
Here we have the values of the shipment are
Estimated value = 22
Actual value = 21.78
So, now we have to apply the values on the formula, then we get,
PE = (|22 - 21.78/21.78|) x 100
When we simplify it, then we get,
PE = 0.0101 x 100
PE = 1.01%
Therefore, the percent error in the shipment is 1.01%.
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he graph below shows the total cost for lunch, c, when Will and his friends buy a large salad to share and several slices of pizza, p.
A graph titled Lunch Cost. The x-axis shows the number of slices purchased, numbered 1 to 8, and the y-axis shows the cost in dollars, numbered 5 to 40. Blue diamonds appear at points (0, 7.5), (1, 10), (2, 12.5), (3, 15), (4, 17.5), (5, 20), (6, 22.5), (7, 25), (8, 27.5).
For each additional slice of pizza that is purchased, by how much does the total cost of lunch increase?
$1.50
$2.00
$2.50
$3.00
For each additional slice of pizza that is purchased, the amount by which the total cost of lunch increase is: C. $2.50.
What is a graph?A graph refers a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
In Mathematics, the graph of any proportional relationship is characterized by a straight line with the points passing through the origin (0, 0) because as the values on the x-axis increases or decreases, the values on the y-axis increases or decreases simultaneously.
Next, we would calculate the difference between the total cost when an additional slice of pizza is purchased:
Difference = 10 - 7.5 = 12.5 - 10 = 15 - 12.5 = $2.50
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what 5+5+5+7= what is it
Add 5 x 3 + 7
5 x 3 + 7
15 + 7
22
Answer:
Alternatively, you may use addition to solve
Step-by-step explanation:
5+5 = 10 and 5+7 = 12, and we know that 10+10 = 20
Just add the number 2 from the number 12 to 20, and you have the same answer
Solve the system of equations by elimination
From the equations we get 'x' as '-2' and 'y' as '-7'
What is an equation?
An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign. An equation consists of two expressions joined by an equals sign ("="). The expressions on each side of the equals sign are referred to as the equation's "left-hand side" and "right-hand side." The right-hand side of an equation is frequently considered to be zero.
4x - 2y = 6....................equation (1)
-2x + 4y = -24...............equation (2)
Multiply equation (1) by 2 and add with equation (2)
8x - 4y = 12
-2x + 4y = -24
----------------------
6x = -12
or, x = -12/6 = -2
from equation (1),
4x - 2y = 6
or, 4(-2) - 2y = 6
or, -2y = 6 + 8
or, y = 14/-2 = -7
Hence, from the equations we get 'x' as '-2' and 'y' as '-7'
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Matthew wants his run today to take no more than 90 minutes. He already has run 30 minutes at a pace of 10 minutes per mile. Part A) Write an inequality that Matt could solve to find out how many more miles he can run if he keeps his current pace. Show or explain the reasoning you used to determine your answer.
The inequality that Matt could solve to find out how many more miles he can run if he keeps his current pace is less than 6 miles.
How to express the inequality?It should be noted an inequality is used to show the expressions that are not equal.
In this case, Matthew wants his run today to take no more than 90 minutes and he already has run 30 minutes at a pace of 10 minutes per mile.
Therefore, the appropriate inequality will be;
Let miles = m
m <= 90/10 - 30/10
m <= 9 - 3
m <= 6
He has about 6 miles more.
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k(x) = 2x²-x-1 find the roots
Answer:
x = -1/2 , 1
Step-by-step explanation:
Caroline’s cell phone plan costs $32 per month. Create a table that shows the sum of the amounts that Caroline will pay for her cell phone plan over the next 4 months. Can y'all please help me
Answer:
Month:
1 = 32$
2 = 64$
3 = 96$
4 = 128$
Step-by-step explanation:
A total of 77 tornadoes have been documented in tuscaloosa county in the period beginning on january 1, 1950 and ending on december 31, 2020. What is the recurrence interval for tornadoes in tuscaloosa county?.
The Recurrence interval for tornadoes in tuscaloosa county is 0.909
What is recurrence interval ?
The time period in which a new occurrence of something that happened or appeared before : a repeated occurrence or The time frame in which a previously occurring event or appearance first occurs: a recurring occurrence
Given that,
Total number of tornadoes is 77
Total time for Recurrence is 70 years
Using these data,
Recurrence = Total time for recurrence / Total number of tornadoes
Substituting we get,
Recurrence interval = 70/77
= (70/77)
= (0.909)
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consider the function rpresented by 9x + 3y = 12 with x as the independant variable. How can this function be writte using function notation? f(y) = - 1/3y + 4/3, f(x) = -3x + 4, f(x) = - 1/3 x + 4/3 f(y), = - 3y + 4
The slope-intercept form of a function f(x) = mx + c therefore,f(x) = -3x + 4 is the correct notation of the function 9x + 3y = 12 so option (B) is correct.
What is a function?The function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
As per the given function,
9x + 3y = 12
Subtract 9x both sides,
9x - 9x + 3y = 12 - 9x
3y = 12 - 9x
Divide by 3 into both sides,
y = 12/3 - 9x/3
y = -3x + 4
Since,y = f(x)
f(x) = -3x + 4 .Here -3 is the slope while 4 is the y-intercept.
Hence "The slope-intercept form of a function f(x) = mx + c therefore,f(x) = -3x + 4 is the correct notation of the function 9x + 3y = 12".
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Question 1 (2 points)
(02.04)
For the function f(x) = -2(x + 3)2 - 1, identify the vertex, domain, and range.
Answer:
Vertex: (-3,-1)
Domain : (negative inf. , inf.)
Range: (negative inf. , 1]
Please help me !! due tonight
Answer:
y=-2x+5
Step-by-step explanation:
This is my last one for today hahaha. Good luck on the rest.
A baseball Dimond is a square with sides of 90 feet. What is the shortest distance, to the nearest tenth of a foot, between first base and third base?
Using the pythagorean theorem we get that:
[tex]\begin{gathered} d^2=(90ft)^2+(90ft)^2=2(90ft)^2 \\ d=\sqrt[]{2}(90ft)=127.3ft \end{gathered}[/tex]Note: the shortest distance between two points in a plane is a stright line, that is why we calculated d.
What is the answer to
k + 4n+ 8=
Answer:
answer is 2 since k =1 and 4n will be 2 ×2 so 8 will be equivalent to 4 which will be 2
solutions to 2-variable equations 4x-1=3y+5
A solar panel covers the hood of a truck. The area is 0.8 the width of the panel is 1.6 meters, what is the length of the panel
The length of the panel is 0.5 meter.
What is the area of rectangle?To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
Given that,
Area of the panel = 0.8 [tex]m^{2}[/tex]
width of the panel = 1.6 meter
Here, solar panel is in the form of rectangle.
Area of rectangle = length× width
0.8 = 1.6 × length
length = [tex]\frac{0.8}{1.6}[/tex]
length = 0.5 meter
Hence, The length of the panel is 0.5 meter.
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Jaclyn says 7 5 has the same answer as 3/7 + 2/7 is she correct explain why or why not
3/7 + 2/ 7 = (3+2)/7 = 5/7
Then Jaclyn is WRONG
Because 5/7 is the inverse of 7/5
find the slope 35 points
When we want to find the slope of a line,
We find two points and connect them to form a right triangle.
We then divide the increase in the [tex]y[/tex]-axis by the increase in the [tex]x[/tex]-axis to find the slope.
Since the line is tilted to the right, the slope is positive.
The answer must be 3.exapnd and simplify (3x+4)(2x+3)
please help asap
this is an assignment due today please help real quick
Answer:
A (3; 4)
B (5; 2)
C (4; 0)
D (-6; -2)
E (-2; -5)
I hope this helps!
Suppose you want to convert kilometers to miles. Which unit should be in the
numerator of the conversion factor? Which unit should be in the denominator?
Explain your reasoning.
Answer:
see below
Step-by-step explanation:
km * miles/km
see how the 'km' then 'cancels out' and you are left with 'miles' the underlined shows the units of the conversion factor