Step One
Begin by drawing a line parallel to the x axis. Create it so it goes through (0,1)
This line you have drawn should hit points on the figure at (-5,1) (-2,1) and (3,1)
You now have a figure on the bottom that is a trapezoid. It has 2 small triangles on top of it. We'll talk about them later.
Step Two
Find the area of the trapezoid.
<em>Formula</em>
Area = (b1 + b2)*h/2
h = 1 - - 3 = 4
b1 = 3 - - 8 = 11
b2 = 3 - - 5 = 8
Area = (11 + 8)*4 / 2
Area = (19 ) * 2
Area = 38
Step Three
Find the area of the small triangle on the left.
The base goes from -5 to - 2 which is 3 units.
The height goes from 1 to 3 (using the y axis as a reference) which is 2
Area = 1/2 * b * h
Area = 1/2 *3 * 2
Area = 3
Step Four
Find the area of the small triangle on the right.
The base is 5 (see if you can get 5 as an answer)
The height is 1.
Area = 1/2 b * h
Area = 1/2 5 * 1
Area = 2.5
Step Five
Total Area is found by adding the three areas together.
Total Area = trapezoid + small triangle on the left + small triangle on the right
Total Area = 38 + 3 + 2.5 = 43.5
43.5 <<<< answer
3.866 microseconds? 7 x 522 nano seconds = 3.86600 ms
Answer:
27 ft
the maximum height of the arrow is 27 ft
Step-by-step explanation:
Given;
The height of the arrow is given by the function;
h(t) = -16t^2 + 32t + 11
Maximum height is at point when dh(t)/dt = 0.
Differentiating h(t), we have;
dh/dt = -32t + 32 = 0
Solving for t;
-32t = -32
t = -32/-32 = 1
t = 1 (time at maximum height is t = 1)
Substituting t=1 into h(t), to determine the value of maximum height;
h(max)= -16(1^2) + 32(1) + 11
h(max) = 27 ft
the maximum height of the arrow is 27 ft.
Answer:
Step-by-step explanation:
Given is a table showing the weights, in hundreds of pounds, for six selected cars. Also shown is the corresponding fuel efficiency, in miles per gallon (mpg), for the car in city driving.
Weight Fuel eff. x^2 xy y^2
X Y
28 20 784 560 400
3 22 9 66 484
35 19 1225 665 361
32 22 1024 704 484
30 23 900 690 529
29 21 841 609 441
Mean 26.16666667 21.16666667 797.1666667 549 449.8333333
Variance 112.4722222 1.805555556
Covariance -553.8611111
r -0.341120235
Correlaton coefficient =cov (xy)/S_x S_y
Covariance (x,y) = E(xy)-E(x)E(y)
The correlation coefficient between the weight of a car and the fuel efficiency is -0.341
