I think it is 91 unless i am reading the problem wrong
Using 1st equation:
15 = 16/3 + b
(45-16)/3 = b
29/3 = b
Using last equation:
47 = 16*7/3 + b
(141-112)/3 = b
29/3 = b
Answer:
The volume of the solution with 20% acid is 27 gallons and the one with 10% acid is 18 gallons
Step-by-step explanation:
Myra needs to mix "x" gallons of the solution with 20% and "y" gallons of the solution with 10%. The volume of the final solution must be 45 gallons, therefore:
x + y = 45
The concentration of acid of the final solution is:
0.2*x + 0.1*y = 45*0.16
0.2*x + 0.1*y = 7.2
Therefore we have a system of equation:
x + y = 45
0.2*x + 0.1*y = 7.2
We need to multiply the first equation by -0.1:
-0.1*x -0.1*y = -4.5
0.2*x + 0.1*y = 7.2
We now sum both equation:
0.1*x = 2.7
x = 2.7/0.1 = 27 gallons
y = 45 - 27 = 18 gallons
The correct answer is:
x + 2y = −10
<span>3x − y = 12
</span>
Just did this test, and got that question correct.
Hope this helps!
Answer:
See below ~
Step-by-step explanation:
<u>Identities Needed</u>
- sec a = 1 / cos a
- cosec a = 1 / sin a
- cot a = 1 / tan a
<u />
<u>Proving</u>
- (sec²a)(cosec²a) = tan²a + cot²a + 2
<u>Taking the LHS</u>
- sec²a x cosec²a
- 1/cos²a x 1/sin²a
- 1/(sin²a)(cos²a) -(Equation 1)
<u>Taking the RHS</u>
- tan²a + cot²a + 2
- tan²a + cot²a + 2(tana)(cota)
- (tana + cota)²
- (sina/cosa + cosa/sina)²
- (sin²a + cos²a / sinacosa)²
- (1/sinacosa)²
- 1/(sin²a)(cos²a) -(Equation 2)
∴ Equation 1 = Equation 2
∴ <u>LHS = RHS</u>
Hence, proved.
