The table gives the values of a function obtained from an experiment. use them to estimate 9 f(x) dx 3 using three equal subintervals with right endpoints, left endpoints, and midpoints. x 3 4 5 6 7 8 9 f(x) −3.4 −2.2 −0.6 0.2 0.8 1.5 1.7

With right endpoints: -6.4

With left endpoints: 3.8

With midpoints: -1

Step-by-step explanation:

Given

x     3     4       5      6     7    8   9  

f(x) −3.4 −2.2 −0.6 0.2 0.8 1.5 1.7

We are asked to estimate the integral 3 to 9 f(x) dx.  

Using the intervals 3 to 5, 5 to 7 and 7 to 9, the length of the intervals is Δx = 2

With right endpoints the integral is:

f(3)*Δx + f(5)*Δx + f(7)*Δx  = (-3.4)*2 + (-0.6)*2 + 0.8*2 = -6.4

With left endpoints the integral is:  

f(5)*Δx + f(7)*Δx + f(9)*Δx  =  (-0.6)*2 + 0.8*2 + 1.7*2 = 3.8

With midpoint s the integral is:

f(4)*Δx + f(6)*Δx + f(8)*Δx = (-2.2)*2 + 0.2*2 + 1.5*2 = -1

the sum of all the angles in a triangle are equal to 180

so you can add   the 3 given angles together to equal 180:

5y + 2y + 2y = 180

or since all three angles have the same letter, combine the 3 angles to equal 180:

9y = 180