Given figures along the curve of C are: 10, 20, 30, 40, 50
∫c Nabla f * dr ⇒ f(B)−f(A)= 50 − 10 = 40
Answer:
x=2 x=-4
Step-by-step explanation:
x^2 +2x-8=0
Factor
What numbers multiply to -8 and add to 2
-2*4 = -8
-2+4 =2
(x-2) (x+4) =0
Using the zero product property
x-2 =0 x+4 =0
x-2+2=0+2 x+4-4=0-4
x=2 x=-4
Answer:
Step-by-step explanation:
Let x represent the number of batches of soap that Lilth makes.
Let y represent the number of batches of lotion that Lilth makes.
It takes her 20 minutes(20/60 = 1/3 hours) to make a batch of soap and 35 minutes(35/60 = 7/12 hours) to make a batch of lotion. Lilth has 20 hours available to make soap and lotion. This means that
x/3 + 7y/12 = 20
4x + 7y = 240- - - - - - - - - - -1
The cost of producing each batch are $5 for the soap and $15 for the lotion. The materials to make the soap and lotion must cost at most $325. This means that
5x + 15y ≤ 325 - - - - - - - - -2
4x = 240 - 7y
x = (240 - 7y)/4
Substituting
5(240 - 7y)/4 + 15y ≤ 325
(1200 - 35y)/4 + 15y ≤ 325
1200 - 35y + 60y ≤ 1300
25y ≤ 1300 - 1200
25y ≤ 100
y ≤ 100/25
y ≤ 4
4x + 7 × 4 = 240
4x + 28 = 240
4x = 212
x = 212/4 = 53
Therefore, the solution (53, 4) means that she would make at most 53 batches of soap and at most 4 batches of lotion
The answer is 4.8. You have to subtract 98.6 from 103.4.
