How much of a 50% Alcohol solution should we mix with 10 gallons of 35% solution to get 40% solution

Solution:

Let "x" is the gallons of 50 % alcohol solution

Then, 10 gallons is 35 % solution

The, 10 + x is the gallons of 40 % solution

Then, according to question,

"x" gallons of 50 % solution is mixed with 10 gallons of 35 % solution to get 10 + x gallons of 40 % solution

Therefore,

Thus 5 gallons of 50 % alcohol solution is used

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: