Are you sure you said the whole problem cuz that is impossible to answer
Answer:
2...........................
13.15 ounces of 72% acid and 71.85 ounces of 25% acid are needed
<u>Step-by-step explanation:</u>
Total mass of acid required= 85 ounces
Let the mass of 72% acid be 'a'
Let the mass of 25% acid be 'b'
a + b = 85
b = 85-a
85(40/100) = a(72/100) + b(25/100)
85(2/5) = a(72/100) +(85- a) (25/100)
34 = (72a/100) + (2125/100) - (25a/100)
34 - (2125/100) = (72a + 25a) /100
(3400-2125)/100 = 97a /100
97a = 1275
a = 13.15 ounces
b = 85 - 13.14
b = 71.85 ounces
13.15 ounces of 72% acid and 71.85 ounces of 25% acid are needed
Answer:
x=-11, -1, and 3
Step-by-step explanation:
x^3+9x^2-25x-33=0
There are formulas to solve cubics, but that probably is not the way you are expected to go. Here is a trial and error approach that works in this case.
Assume that the cubic can be factored and that the roots are r1, r2, and r3. Then the factored form is
(x-r1)(x-r2)(x-r3)=0
This shows that the constant must equal the product of the roots.
(r1)(r2)(r3)=-33
One possibility is that the roots are integers. In this case, a factor of 33 might work. Prime factorization of 33 gives 3 and 11. Try 3. Then (x-3) is a factor.
Divide the cubic by (x-3). It works. the result is
x^2+12x+11
This has factors of (x+11) and (x+1). Therefore, the roots are 3, -1, and -11
