Suppose that the manufacturing cost of a particular item is approximated by M(x, y) 2x5 – æ?y2 + 4y3, where x is the cost of materials and y is the cost of labor. Find the following: Mz(x, y) My(x,
Answers
We have partial derivatives of the functions are:
\(Mx(x, y) = 10x^4\)
\(My(x, y) = -2y + 12y^2\)
What is function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
To find the partial derivatives of the function \(M(x, y) = 2x^5 - √y^2 + 4y^3\), we need to differentiate the function with respect to each variable separately.
The partial derivative of M with respect to x, denoted as Mx(x, y), is found by differentiating M(x, y) with respect to x while treating y as a constant:
\(Mx(x, y) = d/dx (2x^5 - √y^2 + 4y^3)\)
\(= 10x^4\)
The partial derivative of M with respect to y, denoted as My(x, y), is found by differentiating M(x, y) with respect to y while treating x as a constant:
\(My(x, y) = d/dy (2x^5 - √y^2 + 4y^3)\)
\(= -2y + 12y^2\)
Similarly, the partial derivative of M with respect to z, denoted as Mz(x, y), is found by differentiating M(x, y) with respect to z while treating x and y as constants. However, the given function M(x, y) does not contain a variable z, so the partial derivative Mz(x, y) is not applicable in this case.
Therefore, we have:
\(Mx(x, y) = 10x^4\)
\(My(x, y) = -2y + 12y^2\)
Note: It's worth mentioning that Mz(x, y) is not a valid partial derivative for the given function M(x, y) because there is no variable z involved in the expression.
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Related Questions
a business give 30% discount on everyting. If a radio costed 1610 Dollars how much did it cost before discount
Can someone help with the calculation of this.
Answers
Answer:
$2300
Step-by-step explanation:
$1610 is 7/10 the original cost. Multiplying by 10/7 reverses that, and we get the starting cost of $2300
Hope this helps!
Jake and Joshua go to different theme parks during two days. Jake must pay a fee of $30 for a ticket and additional 5$ for every food/beverage. Joshua has to pay 25$ for a ticket and additional 10$ for the food and drinks. How many beverages and food would it take for Joshua to have the same amount of pay as Jake? Graph the item.Write a system of equations, graph them, and type the solution.
Answers
Answer
Let's represent food/beverage f
Jake must pay a fee of $30 for a ticket and additional 5$ for every food
\(30+5f\)Joshua has to pay 25$ for a ticket and additional 10$ for the food and drinks.
\(25+10f\)Now
\(\begin{gathered} 30+5f=25+10f \\ \text{collect the like terms} \\ 30-25=10f-5f \\ 5=5f \\ \text{Divide both sides by 5} \\ \frac{5}{5}=\frac{5f}{5} \\ \\ f=1 \end{gathered}\)Factorise
a ) 21x+49=
b ) 3y^2-y=
c ) 8x^2+4x3=
d ) 24s^3t2+10s^2t4=
Can you answer these please :)
Answers
9514 1404 393
Answer:
a) 7(3x +7)
b) y(3y -1)
c) 4x^2(2 +x)
d) 2s^2t^2(12s +5t^2)
Step-by-step explanation:
These are factored by finding the greatest common factor of the given terms. Generally, that can be found by looking at the factors and finding the largest that is common to all terms.
__
a) 21 = 7·3; 49 = 7·7. The GCF is 7. Factoring that out gives ...
7(3x +7)
__
b) y is the only factor common to both terms.
y(3y -1)
__
c) 4 and x^2 are factors common to both terms, assuming the second term is 4x^3.
4x^2(2 +x)
__
d) 10 = 2·5; 24 = 2·12; the factors s^3 and s^2 share a factor of s^2; the terms t^2 and t^4 share a factor of t^2.
2s^2t^2(12s +5t^2)
there is one more answer it is d I will write it belowx. 2, 5, 8, 11.y -1, 0, 2, 5.
Answers
the table that represents a linear relatiponship is option C
Explanation:For the table to show linear relationship, the slope at any given two points should be equal.
slope = change iiny/change in x
\(m\text{ = }\frac{y_2-y_1}{x_2-x_1}\)Using the first two points for the x and y values in the table:
a) slope = (5-2)/(2-1) = (8-5)/(4-2)
slope = 3/1 = 3/2
slope = 3 = 3/2
The slopes are not equal for the points used
b) slope = (5-2)/(1-(-4)) = (8-5)/(2-1)
slope = 3/(1+4) = 3/1
slope = 3/5 = 3/1
The slopes are not equal for the points used
c) slope = (5-2)/(-2-(-4)) = (8-5)/(0-(-2))
slope = 3/(-2+4) = 3/(0+2)
slope = 3/2 = 3/2
The slopes are equal for the points used
d) slope = (5-2)/(0-(-1)) = (8-5)/(2-0)
slope = 3/(0+1) = 3/2
slope = 3/1 = 3/2
The slopes are not equal for the points used
Hence, the table that represents a linear relatiponship is option C
Which set of points includes all of the solutions for y = five halves times x plus three halves?
Answers
The set of points which includes all of the solutions for y in the given equation is the set of all real numbers.
What set of points includes all of the solutions for y?The equation given in the task content whose solution set is go be determined is;
y = (5/2)x + 3/2.
It therefore follows that the solution set for.tge equation includes all real numbers as the equation is linear.
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find all solutions of the equation in the interval , 02π. = 3sec2x320 write your answer in radians in terms of π.
Answers
The solutions in the interval 0 to 2π are x = cos⁻¹(√(3/320)) + 2πn, where n is an integer.
The equation we are given is 3sec²x - 320 = 0, and we are asked to find all solutions in the interval 0 to 2π. Here, sec²x means the square of the secant of x.
To solve this equation, we need to first isolate the variable, which in this case is x. To do this, we can begin by adding 320 to both sides of the equation, which gives us:
3sec²x = 320
Next, we can divide both sides of the equation by 3 to get:
sec²x = 320/3
Now, we need to take the square root of both sides of the equation. However, we must be careful because the square root of a number can have both positive and negative values. In this case, since secant is positive in the first and fourth quadrants of the unit circle, we only need to consider positive square roots. Therefore, we have:
secx = √(320/3)
Using the definition of the secant function, which is the reciprocal of cosine, we can rewrite this as:
cosx = √(3/320)
Now, we can take the inverse cosine of both sides of the equation to find the value(s) of x that satisfy the equation. Again, we must be careful to take the inverse cosine only of the positive value of the right-hand side. This gives us:
x = cos⁻¹(√(3/320))
This is the general solution of the equation. However, we need to find all solutions in the interval 0 to 2π. Since cosine is a periodic function with a period of 2π, we can find all solutions by adding integer multiples of 2π to the general solution.
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2x
3x
(x + 12)
(2x + 4)
Sum of angle measures: 360
Answers
Answer:
the value of x is 43....
all numbered streets run parallel to each other. Both 2nd and 4th streets are intersected by Marvin Ave. as shown:
Answers
A) the angle created by the driver turning is 60°
B) the driver who turned left into 2nd street created an angle of 120°
C) the driver who turned right onto 2nd street made an angle of 120°
What is the explanation for the above?a) The driver on 4th Street negotiated an angle that was opposite ∠60° shown above. Since opposite angles are equal in geometry, thence the agle created is 60°
b) The diver travelling southwest on Marvin Avenue created an 120° because the angle created is corresponding to the angle which is supplementary to 60°.
Since supplementary angles sum up to 180°
Hence 180-60 = 120°
c) The angle in this case is 120° because the angle created is opposite the one created in B above. recall that opposite angles are congruent.
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determine two pairs of polar coordinates for the point (4, -4) with
Answers
Answer:
(4√2cos 135, 4√2sin135)
Step-by-step explanation:
determine two pairs of polar coordinates for the point (4, -4) with
Given the rectangular coordintate
r = √4²+(-4)²
r = √16+16
r = √32
r = √16*2
r =4√2
Theta = arctan(-4/4)
theta = arctan(-1)
theta = -45
theta = 180 - 45
theta = 135 degrees
x = rcos theta
y = rsin theta
x = 4√2cos 135
y = 4√2sin135
Find the slope of the line. 10 point if you solve.
PLS HELP ME FAST
Answers
PLEASE HELP!!!!!!!!!!!!!!!
Answers
Answer:
27.6%
Step-by-step explanation:
See the attached worksheet. Find the total number of marbles (29) and then take the green marbles and divide by the total and multiply by 100%. (8/29)*(100%) = 27.6% to the nearest tenth.
What is the property of -10+3 = 3+(-10)
Answers
Answer: −7 = −7
Step-by-step explanation:
Answer:
Commutative Property of Addition
Step-by-step explanation:
Commutative Property of Addition states that A + B = B + A
someone help me please
Answers
Answer:
multiply vertically
Step-by-step explanation:
((will give brainliest)) What is the output of the function y = 12 + 3x if the input is 5.
Answers
Answer:
y = 27
Step-by-step explanation:
The output is the value of y when x = 5
Substitute x = 5 into the function , that is
y = 12 + 3(5) = 12 + 15 = 27 ← output
to solve you plug in the input into x and rewrite the equation as y=12+3(5) then you add 12+15 and get y=27
1. A new pizza shop opened up and started out $6,378.60 in the hole. Their first month being open they
sold 56 pizzas ($6.63 profit each) and 91 sodas ($2.85 profit each). Their bills for the first month were
$1,547.76. How much money do they still need to make to break even?
Answers
Answer:
7212.53, i belive
Step-by-step explanation:
56 x 6.33 = 354.48
91 x 2.85 = 259.35
259.35 + 354.48 = 613.83
1547.76 - 613.83 = 933.93
6278.60 + 933.93 = 7212.53
2x−yz , where x=34 , y=−0.2 , and z = 6. Evaluate.
A) 0.3
B) 1.95
C) 2.7
Answers
x = 34, y = -0.2 and z = 6. We need to find 2x - y z. To find 2x - y z, we substitute x = 34, y = -0.2 and z = 6.2x - y z = 2(34) - (-0.2)(6)= 68 + 1.2= 69.2Therefore, 2x - y z = 69.2. ANSWER: 69.2. We are given x = 34, y = -0.2 and z = 6.
The correct option is : D
Now, we have to evaluate 2x - y z using these values. So, we will substitute the values of x, y, and z in the given expression: 2x - y z = 2(34) - (-0.2)(6) = 68 + 1.2 = 69.2Therefore, the value of the given expression 2x - y z is 69.2.Therefore,69.2 is the correct answer. To find the value of 2x - y z, we must substitute the values of x, y, and z into the given expression.
We know that x = 34, y = -0.2, and z = 6. Therefore,2x - y z = 2(34) - (-0.2)(6)= 68 + 1.2= 69.2This implies that the value of the given expression 2x - y z is 69.2. Hence, we can see that adding two odd numbers does not always result in an odd number. It can sometimes result in an even number. The statement "If two odd numbers are added, then the sum is also an odd number" is a false statement. This can be proved by finding a counterexample that shows that the statement is not true. A counterexample is an example that proves a general statement to be wrong or false. In this case, we need to find two odd numbers whose sum is an even number.
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Find the perimeter of a regular hexagon
with side 5cm.
Answers
Answer:
Step-by-step explanation:
Regular hexagon has six equal sides
Perimeter = 5 + 5 + 5 + 5 + 5 +5 or 6*5
= 30 cm
Problem 1 A car has an initial speed of vo= 25m/s to the east and a constant acceleration of a = 3m/s² when a water drop begins to fall from rest. After dropping a distance of h= 10m, the water drop strikes the hood of the car. Aerodynamic drag is not considered here. (1) Determine the speed of the drop and the speed of the car when the strike occurs. [16 pt.] (2) Determine the velocity and acceleration the drop appears to have with respect to a passenger in the car (direction and magnitude). [16 pt.]
Answers
The speed of the water drop when it strikes the hood is approximately 14.0 m/s downward, and the speed of the car at that moment is approximately 29.3 m/s to the east.
The drop appears to have a velocity of approximately 29.3 m/s to the west and 14.0 m/s downward with respect to the passenger in the car.
The drop appears to have an acceleration of approximately 3 m/s² to the west and 9.8 m/s² downward with respect to the passenger in the car.
Determining speed and velocity(To determine the speed of the water drop and the speed of the car when the drop strikes the hood,
use the kinematic equations of motion.
First, we can find the time it takes for the drop to fall 10m using the kinematic equation:
distance h = 10m,
\(h = 1/2 at^2\)
where
h is the vertical distance,
a is the acceleration due to gravity (9.8m/s²), and t is the time.
Substituting the values, we have;
\(10 = 1/2 (9.8) t^2 \\
t^2 = 20/9.8 \\
t ≈ 1.43 seconds\)
Next, find the final velocity of the drop using the kinematic equation:
\(v = vo + at\)
where v is the final velocity,
vo is the initial velocity (which is 0m/s for the drop),
a is the acceleration due to gravity, and
t is the time we just calculated.
Substituting the values, we have
v = 0 + (9.8)(1.43)
v ≈ 14.0 m/s downward
Finally, find the speed of the car when the drop strikes the hood using the kinematic equation:
\(v = vo + at\)
v = 25 + (3)(1.43)
v ≈ 29.3 m/s to the east
Therefore, the speed of the water drop when it strikes the hood is approximately 14.0 m/s downward, and the speed of the car at that moment is approximately 29.3 m/s to the east.
To determine the velocity and acceleration
The velocity of the water drop with respect to the passenger in the car is simply the vector difference between the velocity of the water drop and the velocity of the car:
v_drop,p = v_drop - v_car
where v_drop is the velocity of the water drop (14.0 m/s downward) and
v_car is the velocity of the car (29.3 m/s to the east).
Substituting the values, we get:
v_drop,p = (0, -14.0, 0) - (29.3, 0, 0)
v_drop,p = (-29.3, -14.0, 0) m/s
Thus, the drop appears to have a velocity of approximately 29.3 m/s to the west and 14.0 m/s downward with respect to the passenger in the car.
The acceleration of the water drop with respect to the passenger in the car is simply the vector difference between the acceleration of the water drop and the acceleration of the car:
a_drop,p = a_drop - a_car
where a_drop is the acceleration due to gravity (9.8 m/s² downward) and
a_car is the acceleration of the car (3 m/s² to the east).
Substituting the values, we have,
a_drop,p = (0, -9.8, 0) - (3, 0, 0)
a_drop,p = (-3, -9.8, 0) m/s²
Therefore, the drop appears to have an acceleration of approximately 3 m/s² to the west and 9.8 m/s² downward with respect to the passenger in the car.
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: Identify the equation as homogeneous, Bernoulli, linear coefficients, or of the form y' = G(ax + by). cos (7x + y) dy = sin (7x + y) dx A. the form y' = G(ax + by) B. homogeneous C. Bernoulli D. linear coefficients
Answers
The correct option is C. "Bernoulli". because it can be written in the form dy/dx + P(x)y = Q(x)yⁿ, where n is a constant.
The given equation, cos(7x + y)dy = sin(7x + y)dx, can be identified as a Bernoulli equation.
A Bernoulli equation is a type of first-order ordinary differential equation that can be written in the form:
dy/dx + P(x)y = Q(x)yⁿ
In this equation, we have cos(7x + y)dy = sin(7x + y)dx. To identify it as a Bernoulli equation, we need to rewrite it in the standard form. Let's start by dividing both sides by dx:
(1/cos(7x + y))dy/dx = sin(7x + y)
Now, let u = 7x + y. Differentiating both sides with respect to x gives:
du/dx = 7 + dy/dx
Substituting these values back into the equation, we have:
(1/cos(u)) * (du/dx - 7) = sin(u)
Simplifying further, we get:
du/dx - 7cos(u) = sin(u)cos(u)
This equation matches the form of a Bernoulli equation, with P(x) = -7cos(u) and Q(x) = sin(u)cos(u).
The power of y in the equation is 1, which is why it is classified as a Bernoulli equation.
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How can you find 50% of any number? Select all that apply.
Divide by 50
Find 1/2 of the number.
Divide the number by 2.
Divide by 100.
Answers
In ΔGHI, the measure of ∠I=90°, GH = 8.5 feet, and IG = 4.7 feet. Find the measure of ∠G to the nearest tenth of a degree
Answers
Answer:
56.4
Step-by-step explanation:
The student council wanted to know students’ opinions about the music at school dances. They asked all the girls in a dance class to fill out a survey. Was the survey collected in a biased manner? Explain how you decided.
Answers
Answer:
Yes
Step-by-step explanation:
The student council only asked a specific group of people for their opinion on the music. They will only have the dance class' opinions and not an accurate representation of the whole student population.
Answer:
Step-by-step explanation:
The student council only asked a specific group of people for their opinion on the music. They will only have the dance class' opinions and not an accurate representation of the whole student population.
Valentino wants to estimate the product (5.2)(9.9). Which expression shows each factor rounded to the nearest whole
number?
(5)(9)
(6)(10)
(6)(9)
(5)(10)
Answers
Answer:(5)(10)
Step-by-step explanation:
Answer:
(5)(10)
Step-by-step explanation:
Solve the following systems of equations using Gaussian Elimination. 2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13
Find the inner product of two vectors A = (2, -3,0) and B = = (-1,0,5)
Answers
The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).
Solving the given system of equations using Gaussian elimination:
2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13
Matrix form of the system is
[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13
Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1
Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4
Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5
Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5
Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6
The solution is (x,y,z) = (6,-5,5)
Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).
The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by
A·B = |A||B|cosθ
Given,A = (2, -3,0) and B = (-1,0,5)
Magnitude of A is |A| = √(2²+(-3)²+0²) = √13
Magnitude of B is |B| = √((-1)²+0²+5²) = √26
Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2
Cosine of the angle between A and B is
cosθ = A·B / (|A||B|)
cosθ = -2 / (√13×√26)
cosθ = -2 / √(13×26)
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Find a vector equation with parameter t for the line of intersection of the planes x y z=2 and x z=0.
Answers
The vector equation with parameter t for the line of intersection of the planes x + y + z = 2 and x + z = 0 is r(t) = <0, 2, 0> - t<1, -1, 0>.
To find a vector equation with parameter t for the line of intersection of the planes x + y + z = 2 and x + z = 0, we can solve the system of equations formed by the planes.
First, let's solve for y in terms of x and z from the equation x + y + z = 2. Rearranging the equation, we have y = 2 - x - z.
Now, substitute this expression for y in the equation x + z = 0. We have x + (2 - x - z) + z = 2, which simplifies to 2 - z = 2.
Solving for z, we find z = 0.
Substituting z = 0 into the equation x + z = 0, we have x = 0.
Now that we have the values of x, y, and z, we can form a vector equation for the line of intersection as follows:
r(t) = = <0, 2 - x - z, 0> = <0, 2, 0> - t<1, -1, 0>.
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12 bars of soap for $10.00 or 5 bars of soap for $4.00.
Answers
Answer:
12 bars for $10.00
Step-by-step explanation:
WORD PROBLEM! Sally has 15 apples. She gives some of her apples to three friends. They each get the same amount. Sally now has 9 apples. How many did each friend get?
Answers
Answer:
Each friend got 2 apples
Step-by-step explanation:
[original amount of apples]-[Apples Sally has after distribution] = [friends] x [number of apples]
Filling in the brackets, you get this equation.
15-9=3 x apples per friend
6=3 x apples per friend
2 = apples per friend
Answer:
6
Step-by-step explanation:
15 ÷ 3= 2
friend 1
2 Friend 2
2 friend 3
2
Add up each one to get 6.
15 - 6 = 9
Hope this helps.
Solve the equation. 3/2x -5 = -11
Answers
Reasoning: To get rid of a fraction you need to multiply it by its inverse
Researchers would like to compare exercise and meditation to see which is more effective in reducing stress. One hundred people who suffer from high stress volunteer to participate in a study for ten weeks. These volunteers will either participate in a 10-week exercise program or a 10-week meditation program. The researchers must decide whether to randomly assign the volunteers to the two programs, or allow them to choose which program to be in. Which one of the following is the main advantage of randomly assigning participants to the two programs rather than allowing them to choose?
A. In order for the results of an experiment to be deemed "statistically significant," random assignment must be used.
B. The participants are more likely to stick with the program for the full 10 weeks if random assignment is used.
C. Random assignment will ensure that the results of an experiment are double- blind
D. Lurking variables, such as experience with exercise or past practice of meditation, should be approximately equal for the two groups if random assignment is used.
E. If random assignment is not used, the researchers will end up with something called a placebo effect.
Answers
Lurking variables, such as experience with exercise or past practice of meditation, should be approximately equal for the two groups if random assignment is used. Option D
What is random assignment in research?
Randomization ensures that the groups being compared are comparable in terms of any potential confounding factors or hidden variables that can affect the study's conclusion. The researchers can evenly divide these characteristics throughout the groups by randomly allocating people to the programs, which lessens the possibility of skewed outcomes.
As a result, it is possible to compare the benefits of exercise and meditation on stress reduction with more accuracy because any differences between the groups may be more reliably assigned to the intervention itself rather than to unrelated factors.
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hey can someone help me pls *ANSWER ASAP*
Answers
This is a translation of 2 units to the left and 5 units up, so the correct option is the first one.,
Which is the translation applied?Remember that a vertical translation of N units is:
g(x) = f(x) + N
if N < 0 the translation is down.
if N > 0 the translation is up.
And a horizontal translation of N units is:
g(x) = f(x + N)
If N > 0 the translation is to the right.
if N < 0 the translation is to the left.
Here we have the transformation:
f(x) = x²
g(x) = (x + 2)² + 5
So this is a translation of 2 units to the left and 5 units up.
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