Answer to Question #213467 in Calculus for ellea

Question

Performance Task: Beyond Walls

The Congressman of your town will visit your school for the inauguration of the newly constructed building. You are a painter who is famous for designing regions bounded by curves, that is why you are asked to present your geometric pattern design and computations for the cost of paint which will be used by the Principal. Your output will be subject for approval based on the criteria:

1. illustration of design (5 points)

2. accuracy (5 points)

3. exactness of solutions (5 points)

4. overall presentation (5 points)

Perform the following:

1. State your proposed function and graph

2. Solve the area of the regions bounded by the two functions

3. Use this ratio to estimate the paint needed and to compute the cost of paint 1 square unit = 10 sq. ft. 1 liter of paint (cost P200) can cover 12 sq. ft.

Answer 1

1. Square of 2 side $\intop_0^h\intop_0^ldxdy$

Where h- height of the side, l - length of the side.

So Square is $\sum_{i=1}^N\intop_0^{h_i}\intop_0^{l_i}dxdy$

Where N is a number of the sides in school.

2. Also we have doors and windows in school. Their square we can write as

$\sum_{i=1}^W\intop_0^{H_i}\intop_0^{L_i}dxdy$

Where W- number of windows in school, H - height of window, L - length of window.

$\sum_{i=1}^D\intop_0^{k_i}\intop_0^{p_i}dxdy$

Where D- number of doors in school, k - height of door, p - length of door.

So we can write a function as

$S=\sum_{i=1}^N\intop_0^{h_i}\intop_0^{l_i}dxdy -\sum_{i=1}^W\intop_0^{H_i}\intop_0^{L_i}dxdy-\sum_{i=1}^D\intop_0^{k_i}\intop_0^{p_i}dxdy$

3. A cost of paint is

$Q=200S/12=16,67(\sum_{i=1}^N\intop_0^{h_i}\intop_0^{l_i}dxdy -\sum_{i=1}^W\intop_0^{H_i}\intop_0^{L_i}dxdy-\sum_{i=1}^D\intop_0^{k_i}\intop_0^{p_i}dxdy)$