05/12/23

Hi this is confusing me
Use the product rule to find the derivative of(2x^6-4x^10)(4e^x+9) You do not need to expand out your answer.
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05/12/23

Prove the identity. cos3x=4cos3x−3cosx
Prove the identity.cos3x=4cos3x−3cosx
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05/12/23

Derivative of a function
Suppose the derivative of a function f is f '(x) = (x + 1)4(x − 3)5(x − 6)6. On what interval is f increasing? (Enter your answer in interval notation.) 
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05/11/23

multivariate optimisation -

Given f(x,y) = x3+y3-10xy+25, S = {(x,y): 0 ≤ x ≤ 6, 0 ≤ y ≤ 6}match the point on the left with the classification on the right: (0,6)(10/3, 10/3)(Square root(20), 6)Global minimumNeitherGlobal max
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05/11/23

multivariate optimisation - Given f(x,y) = x^3 - 3x + xy + y^2,
the saddle point is ( , ) and the local minimum is ( , ). Round your answer to 4 decimal places. 
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05/11/23

Constrained optimisation problem / firm profit function
A firm uses two inputs x and y, and their profit function is P(x,y)=2xy+2x+3y. Input x costs $2 each and y costs $1 each and they are constrained to spend a total of $100 on inputs.If the firm... more
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05/11/23

Utility function
Given a consumer's utility function: U (x,y) = In(x - 3) + In(y)And their budget constraint: 3x + 2y = 100How much of good y should this consumer purchase? (Round to two decimal places only if... more
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05/11/23

constrained optimisation problem
What is the shadow price in the following constrained optimisation problem?Max y = 3x1x2 + x22s.t. 2x1 + x2 = 100
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05/11/23

Statistics: Confidence Intervals

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 70%. You would like to be 90% confident that your... more
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05/11/23

Use linear approximation to approximate sqrt(49.4) as follows.
Use linear approximation to approximate sqrt(49.4) as follows. Let 𝑓(𝑥)=√x. The equation of the tangent line to 𝑓(𝑥) at 𝑥=49 can be written in the form 𝑦=𝑚𝑥+𝑏.Compute 𝑚 and 𝑏.𝑚=𝑏=Using this find... more
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05/11/23

Let A be the area of a circle with radius r. If dr/dt=4, find dA/dt when r=5
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05/11/23

compute the volume of the solid obtained by rotating the region bounded by y=6x^2, 2x+y=8, and the y-axis about the line x=-1.

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05/10/23

So lost on finding the equation
A chemist has three different acid solutions. The first acid solution contains 15% acid, the second contains 25% and the third contains 65%. They want to use all three solutions to obtain a mixture... more
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05/10/23

find the taylor series of f(x) = 1/(x-1)^3 centered at a = 0
series written in summation form Σ n=0 to infinity
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05/10/23

the region between the graphs of y=x^2 and y=2x is rotated around the line x =2. what is the volume of the resulting solid?
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05/10/23

Find probability

A school newspaper reporter decides to randomly survey 14 students to see if they will attend Tet festivities this year. Based on past years, she knows that 23% of students attend Tet festivities.... more
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05/10/23

Given sin A = 5 / sqrt{89} ​and that angle A is in Quadrant I, find the exact value of cotA in simplest radical form using a rational denominator.
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05/09/23

A manufacturing company has a 2% defect rate. If 7 items are chosen at random, what is the probability that one will have a defect?
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05/09/23

first principals and derivatives

Let f(x) = sin x. Which of the following would you use to calculate f'(−π / 2) using the definition of derivative (i.e., first principles)?
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05/08/23

Probability Statistics
Among the 12 applicants for managerial positions at a chain of movie theaters, 8 are college graduates and 4 are high school graduates. If three of the applicants are randomly selected, a. Identify... more
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05/08/23

Differentiate the following
y= e^-2x cos6xy= -9(sin^2)x / cosx
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05/08/23

Differentiate the following

𝑦=sqrt 4+3𝑥
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05/08/23

Precalculus question
A can of soda at 39 °F is removed from a refrigerator and placed in a room where the air temperature is 68 °F. After 13 minutes, the temperature of the can has risen to 49 °F. How many minutes... more
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05/08/23

Precalculus question
The 1906 San Francisco earthquake had a magnitude of 7.9 on the MMS scale. Around the same time there was an earthquake in South America with magnitude 4.6 that caused only minor damage. How many... more
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05/08/23

Urgent! Expected Value, total variance
The number of winter storms in a good year is a Poisson random variable with mean 3, whereas the number in a bad year is a Poisson random variable with mean 5. If next year will be a good year with... more
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