solve completely(complementary function and particular integral) pdes

1 (1+D^2-D')z = -8siny

2 (D-D'-D'^2)z =132xy^10+504x^2y^6

3 (D^2-4DD' +4D'^2)z = x + y

4 (D^2-2DD'+ D'^2)z = e^2x-2y+x^2

Respond to the following in a minimum of 175 words: How will you graphically represent data in your future career? What types of graphs are typically used in that industry? What types of conclusions are drawn from the graphs?

Suppose A*B*A′ holds(B is between A and A')  and D ∈ Int(∠ABC). Prove that C ∈ Int(∠A′BD).

(a) Prove that C ∈ H(D,line A′B).

(b) Prove that C ∈ H (A′, line←→BD). Use point A.

(c) Deduce that C∈Int (∠A′BD).

14) To purchase studio space, on April 3, 2025 a pianist takes out a 30-year loan of $120,000 at an annual interest rate of 11%. The first monthly payment is to be made on May 3, 2025; the final payment is scheduled to be made April 3, 2055. The monthly payment is $1,142.79 . [Note: If you use the table you’ll get that the monthly payment is $1,142.40, but the table produces an approximation. $1,142.79 is the precise payment.]

a) Calculate the total interest charged over the course of the loan, assuming that nothing but the standard payment is made each month.

b) How much will she owe immediately after making the payment on June 3, 2025? (= the second payment) Round appropriately to the nearest penny.

c) Suppose that as part of that June 3, 2025 payment she pays an extra $300 as an overpayment. Calculate the dollar amount of interest which this saves in the future. Round your answer down to the nearest $10.

For each group in the following list find the order of each element in the group: Z₁₂, U(10) and U(12).

Find the real solutions of the following equation.

x^4 +7x^3+8x^2-7x+15=0

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

The solution set is { }

(Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed. Type each answer only once.)

B.

The solution set is

empty set∅.

1) Find the domain and range of the rational function y( x) = x^2-25 / 2x^2 + 13x+15

A) Factor the numerator and denominator

B) Determine the point of discontinuity if it exists.

Let Vector_1=[Column (1 &-2&1)],Vector_2=[Column(2&-1&1)],Vector_3=[Column(-2&... Let Vector_1=[Column (1 &-2&1)],Vector_2=[Column(2&-1&1)],Vector_3=[Column(-2&-2&0)],Vector_4=[Column(1&-2&-2)].

Show that S={Vector_1,Vector_2,Vector_3,Vector_4} is linearly dependent.

Show that Vector_3 can be written as a linear combination of Vector_1,Vector_2 and Vector_4.

Show that T={Vector_1,Vector_2,Vector_4} is linearly independent.

Show that the set of all linear combinations of vectors from S is the same as the set of all linear combinations of vectors from T.

Through the midpoint of each side of a triangle,a line is drawn parallel to the bisector of the opposite angle. Prove that these three lines are concurrent and that the point of concurrency is collinear with the centroid and the incenter of the triangel. (hint :use dilation)

Estimate the area A between the graph of the function f(x)= square root of x and the interval [0,49]. Use an approximation scheme with n=2,5, and 10 rectangles. Use the right endpoints.

Round your answers to three decimal places.

A2=

A5=

A10=

Land vs. Water Heating Differences. Refer to pgs. 114-115 of your text and notes from Unit 4 Lecture. In addition to the seasons, latitudinal differences, and altitude, a location’s proximity to a large water body may have a strong affect on temperature. We refer to this as the “marine” or “maritime” effect. In contrast, a large landmass with little marine influence has the opposite effect on temperature and is said to be “continental.”

1. List four reasons why water bodies do not heat up or cool down as much as continental areas of similar latitude. a. _____________________________________________ b. ______________________________________________ c. _______________________________________________ d. ________________________________________________

Daily Cycle of Temperature. Refer to pg. 95 of your text along with your notes from lecture 4.

2. At what time of day does maximum insolation normally occur?

3. The maximum daily temperature generally lags behind the time of maximum insolation. Why? Explain your answer in terms of net radiation.