Achemical company makes two brands of antifreeze. the first brand is 45% pure antifreeze and the second brand is 70% pure antifreeze. in order to obtain 150 gallons of a mixture that contains 55% pure antifreeze, how many gallons of each brand of antifreeze must be used?

60 gallons of 70% antifreeze

Step-by-step explanation:

Let n be the amount of 70% antifreeze. And the second brand was 45% pure anti freeze Then:

According to the question

0.7 n+.45(150-n)=0.55(150)

 0.7 n+67.5-0.45 n=82.5

0.25×n=15

n=15/.25 = 60

You need 60 gallons of 70% antifreeze, and 90 gallons of 45% antifreeze for this mixture

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this

answer:

your answer is: c. 196 7/8 in^3.