Answer:
Part A:
P(x)=15x^4+30x^3-50
Part B:
P(4)=$4270
Step-by-step explanation:
Part A:
In order to find the profit function P(x) we have to integrate the P'(x)
P'(x)=x(60x^2+90x)
P'(x)=60x^3+90x^2
P(x)=15x^4+30x^3+C
when x=0, C=-50
P(x)=15x^4+30x^3-50
Part B:
x=4
P(x)=15x^4+30x^3-50
P(4)=15*4^4+30*4^3-50
P(4)=$4270
Profit from selling 400 pounds is $4270
Answer:
-0.25, -1/5, -2.5, -5, -10
Step-by-step explanation:
1- Solution using graphs:Take a look at the attached images.
The red graph represents the first given function while the blue graph represents the second given function.
We can note that the two graphs are the same line (they overlap).
This means that any chosen point on one of them will satisfy the other.
This means that there are infinite number of solutions to these two equations.
2- Solution using substitution:The first given equation is:
y = -5x + 3 ...........> equation I
The second given equation is:
2y + 10x = 6 ...........> equation II
Substitute with I in II and solve as follows:
2(-5x+3) + 10x = 6
-10x + 6 + 10x = 6
0 = 0
This means that there are infinitely many solutions to the given system of equations.
Hope this helps :)
You can write this as a ratio to find the answer, but you first need to convert the gallon of white paint into ounces, which is 160 ounces. The ratio, red to blue to white, is 4:28:160, which you can simplify by dividing by 4 into 1:7:40. If 80 ounces of red tint are used, you need to multiply each value in the ratio by 80, which gives you 80:560:3200. This shows that you need 560 ounces of blue tint, which can also be written as 3.5 gallons. I hope this helps!
