Answer:
A. 231.77 J
B. 5330.71 J
C. 46 donuts
Explanation:
A. To lift the barbell once, she will have to extend it the full length of her arm. The work done will then be:
W = F * d
Where the force is the weight of the barbell.
F = m * g
Hence, the work done in lifting the barbell is:
W = m * g * d
W = 43 * 9.8 * 0.55
W = 231.77 J
B. If she does 23 repetitions, the total energy she expend will be equal to the Potential energy when the barbell is lifted multiplied by 23:
E = 23 * m * g * d
E = 23 * 231.77
E = 5330.71 J
C. 1 Joule = 4.184 calories
5330.71 Joules = 5330.71 * 4.184 = 22303.69
If 1 donut contains 490 calories, the number of donuts she will need will be:
N = 22303.69/490 = 45.5 donuts or 46 donuts
Answer:
a) 
b) 
c) 
d) Displacement = 22 m
e) Average speed = 11 m/s
Explanation:
a)
Notice that the acceleration is the derivative of the velocity function, which in this case, being a straight line is constant everywhere, and which can be calculated as:

Therefore, acceleration is 
b) the functional expression for this line of slope 4 that passes through a y-intercept at (0, 3) is given by:

c) Since we know the general formula for the velocity, now we can estimate it at any value for 't", for example for the requested t = 1 second:

d) The displacement between times t = 1 sec, and t = 3 seconds is given by the area under the velocity curve between these two time values. Since we have a simple trapezoid, we can calculate it directly using geometry and evaluating V(3) (we already know V(1)):
Displacement = 
e) Recall that the average of a function between two values is the integral (area under the curve) divided by the length of the interval:
Average velocity = 
Answer:
g'(10) = 
Explanation:
Since g is the inverse of f ,
We can write
g(f(x)) = x <em> </em><em>(Identity)</em>
Differentiating both sides of the equation we get,
g'(f(x)).f'(x) = 1
g'(10) =
--equation[1] Where f(x) = 10
Now, we have to find x when f(x) = 10
Thus 10 =
+ 2
= 8
x = 
Since f(x) =
+ 2
f'(x) = -
f'(
) = -4 × 4 = -16
Putting it in equation 1, we get:
We get g'(10) = -