Answer:
(x^4-8)^45 /180 +c
Step-by-step explanation:
If u=x^4-8, then du=(4x^3-0)dx or du=4x^3 dx by power and constant rule.
If du=4x^3 dx, then du/4=x^3 dx. I just divided both sides by 4.
Now we are ready to make substitutions into our integral.
Int(x^3 (x^4-8)^44 dx)
Int(((x^4-8)^44 x^3 dx)
Int(u^44 du/4)
1/4 Int(u^44 dul
1/4 × (u^45 / 45 )+c
Put back in terms of x:
1/4 × (x^4-8)^45/45 +c
We could multiply those fractions
(x^4-8)^45 /180 +c
Answer:
10 gallons of the 1st brand and 30 gallons of the second brand.
Step-by-step explanation:
The equation I came up with is 0.6x+0.8y=0.75(x+y), with x and y representing the total amount of mixture of each brand. Meaning, 0.6x is the amount of pure antifreeze in the first brand, 0.8y is pure antifreeze in the second brand, and 0.75(x+y) is the amount of pure antifreeze there's supposed to be when you mix the two brands together.
Now, the question also says that the mixture is 40 gallons. The total mixture of the 2 brands is basically x+y = 40, then you can minus x from both sides and get y = 40-x, then you substitute it into the original equation: 0.6x+0.8(40-x)=0.75(x+40-x), x = 10, the amount of mixture from the first brand, which also means that 30 gallons is the amount of mixture from the second brand.
Answer:
17
Step-by-step explanation:
You have to multiply 2 and 9 first, so the product is 18. Now you have to subtract that from 1 itself and therefore, the final answer is 17.
Hope this helps you!?!
