Now you have
<u />
<u>(.15)0.5 lb peanuts</u> = <u>0.075 lb peanuts</u>
0.5 lb nuts 0.5 lb nuts
for every pound of 75% mixed nuts you add, you get .75 lb peanuts, how many pounds, x, do you need to add to get the ratio 50 to 100?
<u>0.075 lb peanuts + 0.75x lb peanuts</u><em> = <u /></em><u> 50 </u><u>
</u>0.5 lb nuts + x lb nuts 100
cross multiply
(0.075 + .75x) 100 = (0.5 + x) 50
7.5 + 75x = 25 + 50x
25x = 17.5
x = 0.7 lb of 75% peanuts
Answer:
D. dA/dt = 4h dh/dt in²/sec
Step-by-step explanation:
Given:
A = wh
w = 2h
Substitute:
A = 2h²
Take derivative with respect to time:
dA/dt = 4h dh/dt
dA/dt has units of in²/sec.
Answer: G(x) = 3|x + 2| - 8
<u>Step-by-step explanation:</u>
"a" represents the vertical stretch <em>(or shrink)</em>
"h" represents the x-coordinate of the vertex
- x-axis goes left and right
"k" represents the y-coordinate of the vertex
F(x) = 3|x - 2| - 5
G(x) = 3(x - 2 + 4| - 5 - 3
= 3|x + 2| - 8
Slope: 7 given point: (1,8)
y = 7x + b step 1 - plug in the slope in the formula
8 = 7(1) + b step 2 - plug in the given point
8 = 7 + b step 3 - simplify the expression
b = 1 step 4 - solve for b
y = 7x + 1 step 5 - plug in b
formula: y = 7x + 1
Answer:
Step-by-step explanation:
Recall that the notion of the derivative of a function is the rate of change of it. So it kind of tells us how much the value of functioin changes as the independt variable increases or decreases. If it is positive, this means that the function will increase as the indepent variable increases, and if it is negative, that means that the function will decrease as the indepent variable increases.
a) Since f(x) is the number of units you can make out of x units of raw material, it is natural to think that the more material you have, the more units you can make, so we expect f'(x) to be positive.
b) The company buys each unit of raw material at the price w. So the product wx represents the total cost of the raw material used to produce f(x) units. Since each produced unit is sell at the price of p, then the product pf(x) represents the total income for selling all f(x) units.Recall that the profit is the difference between the total income and the total cost of production. Hence, the profit in this case is represented by the formula pf(x)-wx.
c) Recall that a function h(x) that is differentiable attains it's maximum when it's derivative is 0 and it's second derivative is negative.
In this case, we know that the derivative of the profit function, evaluated at x* must be 0, since it is a maximum. So, using the rules of derivation, we know that the derivative of the profit function is pf'(x)-w. Hence,
pf'(x*)-w =0. From where we know that f'(x*)=w/p.
