Question

CALCULUS HELP ASAP

Electricity is consumed between the hours of midnight (t = 0) and 6 a.m. (t = 6). Selected values of the rate of consumption are shown in the table below, with t measured in hours past midnight, and R(t) measured in KW per hour. Use 4 trapezoids to estimate the total amount of electricity to the nearest KW consumed between midnight and 6 a.m. (10 points)

t (hours) 0 1 2 5 6
R(t) KW/hr 400 200 350 200 150


Thank you very much!

Answer 1

Answer: 1575 KW

Diagram is shown below.

==============================================

Step-by-step explanation:

Refer to the graph shown below. I've plotted the given data such that

x = t = number of hours

y = R(t) = rate of electricity consumed in KW per hour

The area under the curve is what we want. Unfortunately we don't know the function for R(t), but we can estimate it using trapezoids as shown in the diagram.

I've labeled the four trapezoids P, Q, R, and S

The area of a trapezoid formula is

A = h*(b1+b2)/2

where h is the height and b1,b2 are the parallel bases. Each trapezoid shown in the diagram has the height running horizontal.

----------

Let's calculate the area of each trapezoid

area = height*(base1+base2)/2

P = 1*(400+200)/2

P = 300

Q = 1*(200+350)/2

Q = 275

R = 3*(350+200)/2

R = 825

S = 1*(200+150)/2

S = 175

Side note: Trapezoid R is the only trapezoid to have a height that isn't 1.

----------

To recap we found these trapezoidal areas

• P = 300
• Q = 275
• R = 825
• S = 175

To get the final answer we add up those subtotals

P+Q+R+S = 300+275+825+175 = 1575

We estimate that 1575 KW of electricity was consumed.