Vectors p1 = [10 2] and p2 = [2 15] are represented in o₁x₁y₁ coordinate frame. Translate o₁x₁y₁ by t = [30 1]^T and rotate by 45^◦ to obtain o₂x₂y₂. Is the dot product of p₁ and p₂ same in o₁x₁y₁ and o₂x₂y₂?

I believe o₁x₁y₁ and o₂x₂y₂ are the pair of vectors before and after the translation and rotation

How many ways can a gardener plant five different species of shrubs in a circle? What is the answer if two of the shrubs are the same? What is the answer if all the shrubs are identical?

Use separation of variables to solve uxx+2uy+uyy=0, u(x, 0) = f(x), u(x, 1) = 0, u(0, y) = 0, u(1, y) = 0.

Each short-answer question below can be answered with a few sentences.

2. A colleague of yours is faced with testing a relationship at the .05 level or significance or the .01 level of significance. What is your advice to your colleague? Why?

3. A colleague of yours has made a decision to decrease the sample size because of limited funding. What should they expect to happen to the probability of uncovering statistically significant findings in their research? Why?

4. What information is provided by calculations of the “chi-square” test statistic?

5. What information is provided by calculations of the “t” test statistic?

A study conducted by the Metro Housing Agency in a midwestern city revealed the following information concerning the age distribution of renters within the city. (Round your answers to four decimal places.)

(a) What is the probability that an adult selected at random from this population is a renter?


(b) If a renter is selected at random, what is the probability that he or she is in the 21-44 age bracket?


(c) If a renter is selected at random, what is the probability that he or she is 45 years old or older?

Solve the following differentioal equation by undetermined coefficients:

1- yⁿ - 4y = (x² - 3 ) sin 2x

2- y⁴ - yⁿ = 4x + 2xe^-x

3- yⁿ + 3y = -48x²e^3x

6.3

. The DVM has a 200 kHz clock, and the integrator control waveform frequency is 45 Hz. Calculate the number of clock pulses that occur during tl and determine a suitable time duration for t2 when the input is 1V. Recalculate t1, t2 and the measured voltage if the clock frequency drifts by -5%.

Initial Value Problem. Use Laplace transform.

m''(t) - m'(t) - 6*m(t) = e^(4t)

where m(0) = 1 and m'(0) = 1

Let f left parenthesis x comma y right parenthesis equals cos left parenthesis pi space x right parenthesis plus 3 y squared minus 6 y. Which of the following are TRUE? Select ALL that apply. a. f has a saddle point at left parenthesis k comma 1 right parenthesis whenever k is an odd integer b. f has a saddle point at left parenthesis k comma 1 right parenthesis whenever k is an even integer c. f has a local minimum at left parenthesis k comma 1 right parenthesis whenever k is an odd integer d. f has a local maximum at left parenthesis k comma 1 right parenthesis whenever k is an even integer

An invasive species from maize crops comes into contact with a population. It has been measured that 200,000 plants remain on the second day and 90,000 plants remain on the fifth day.

a) What was the number of plants when the invasive species entered?

b) Crop insurance will pay for total losses when only 5% of the amount of plants remains. How long should it take for farmers to claim their insurance?

Give an isomorphism that proves the two vector spaces M3,2 and P5 are isometric to each other.

plz solve in detail

Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated value. First use

h = 0.1

and then use

h = 0.05

y' = y − y², y(0) = 0.8;    y(0.5)

A company manufactures and sells scientific calculators. The function P=7.87.8x2plus+59705970xminus−290 comma 000290,000​, x≤​150, gives the profit if x thousand calculators are manufactured and sold. Use the table feature of a graphing calculator or use a spreadsheet to make a table of values for the profit function with x=​0, 5, 10,​ ..., 150. Use the table to answer the following question.

Approximately how many calculators must be sold in order for the company to make a​ profit?