how are the knowledge of lines shapes and forms useful in art appreciation and creation?

In 1950, Brian's dad recieved $20 for his tenth birthday. His mother deposited it into a bank account for him. Everyone forgot about the money and made no further deposits or withdrawls. The table shows the account balance for several years.

5A) Enter the info on your calculator. Look at the scatterplot. What type of function represents this curve?

5B)what is the equation of best fit? Round all values to the nearest hundreth

5C)Use your equation to estimate the balance in the account when Brian's dad turn 70

Please show work will rate if done all questions

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x, y) = 7y cos(x),    0 ≤ x ≤ 2π

Given the differential equation y’’ +5y’+6y=te^t with start value y(0) = 0 and y’(0). Let Y(s) be the Laplace transformed of y(t).

a) Find an expression for Y(s)

b) Find the solution to the equation by using inverse Laplace transform.

1)Select all that applies to the Fourth-order Runge-Kutta (RK4) method K subscript

1 equals f left parenthesis t subscript k comma y subscript k right parenthesis K subscript

2 equals f left parenthesis t subscript k plus h over 2 comma space y subscript k plus h over 2 space K subscript 1 right parenthesis K subscript

3 equals f left parenthesis t subscript k plus h over 2 comma space y subscript k plus h over 2 space K subscript 2 right parenthesis K subscript

4 equals f left parenthesis t subscript k plus h comma space y subscript k plus h space K subscript 3 right parenthesis

2) y subscript k plus 1 end subscript equals ? Select one or more:

A. - It has four function evaluations - and y subscript k plus 1 end subscript equals y subscript k plus space left parenthesis 1 third space K subscript 1 plus 2 over 3 space K subscript 2 plus 2 over 3 space K subscript 3 plus 1 third space K subscript 4 right parenthesis space h over 2

B. - It is a fourth-order accurate method - and it has seven function evaluations

C. All of the above.

D. K subscript 1 comma space K subscript 2 comma space K subscript 3 space a n d space K subscript 4 are also called slopes of the solution curve or integral curve.

E. The method is named after two German Mathematicians Runge and Kutta.

Find the coordinates of the other endpoint of the​ segment, given its midpoint and one endpoint.​ (Hint: Let​ (x,y) be the unknown endpoint. Apply the midpoint​ formula, and solve the two equations for x and​ y.) midpoint ​(6​,-13​), endpoint ​(14​,-10​)

Given the function u(p,q,r)=((p-q)/(q-r)), with p=x+y+z,q=x-y+z, and r=x+y-z, find the partial derivatives au/ax=, au/ay=, au/az=

I need to know the inflection and to be able to explain how I got the answer please

How are the column space and the row space of a matrix A related
to the column space and row space of its reduced row echelon form?
How does this prove the column rank of A equals the row rank?

A fisherman can row upstream at 4mph and downstream at 6mph. He started rowing upstream until he got tired and then rowed downstream to his starting point. How far did the fisherman row if the entire trip too 6 hours?

The distance the fisherman rowed in ----- miles
     (Type an integer or a decimal)

Let f(x) be differentiable on the interval [a,b]. Select all of the following statements which must be true.

1. f(x) must attain its maximum value on the interval [a,b]

2. There is some number c in the interval (a,b) such that f′(c)= (f(b)−f(a))/ (b−a)

3. f(x) is integrable on [a,b].

4. f(x) is continuous on (a,b).

5. f(x) is a polynomial.

6. f(x) is an increasing function.