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Misha Larkins [42]
3 years ago
15

If I had a 2% solution, added 2 ounces to a gallon (128 ounces) What is the final concentration of the solution.

Mathematics
1 answer:
Ne4ueva [31]3 years ago
6 0
<span>A 2% solution of chlorohexidine added to 126 oz of water. The total oz 128.

Solute: chlorohexidine, 2%=0.02
solvent: water (0%)

Concentration, C, volume V
CV=c1v1+c2v1
128C=0.02*2 + 0.00*126 = 0.04

Concentration
C=0.04/128 = 0.0003125 = 0.03125%</span>
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160- 12.6
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The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is nine
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Nellie made 734 quarts of soup that she put into 14-quart containers. She filled each container completely before starting to fi
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Amount of soup Nellie made = 734 quarts

Amount of soup each container contains = 14 quarts

So, the number of containers Nellie filled = \frac{734}{14} = 52.42

So, Nellie filled 52 containers completely.

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3 years ago
A catapult launches a boulder with an upward velocity of 112 ft/s. The height of the boulder, h, in feet after t seconds is give
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h = -16t² + 112t + 30
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The maximum height is reached when t = 3.5 sec 

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This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the ex
olga nikolaevna [1]

Answer:

maximum value , f max = 169 (taking the most out of the 4th power)

minimum value , f min = 169/3 (taking the least out of the 4th power)

Step-by-step explanation:

A) Since both function and restriction are symmetrical with respect to x,y and z, there is no reason for one to be more important than the others and therefore one solution would be x=y=z=λ and thus

x2 + y2 + z2 = 13  → 3λ² = 13 →λ² = 13/3

and f would be

f (x, y, z) = x4 + y4 + z4 = 3λ⁴ = 3*(13/3)²=13²/3=169/3

since x⁴ increases faster than 3*x² , f(x,y,z) would be a minimum

and the maximum value would be obtained taking the most out of x⁴, thus doing 2 coordinates =0 ( can be x=0 and y=0) and

z²= 13

f (x, y, z) = x4 + y4 + z4 = 13² = 169

B) strictly, using Lagrange multipliers

f (x, y, z) = x4 + y4 + z4

g (x, y, z) = x2 + y2 + z2 - 13

F(x,y,z) = f (x, y, z) -λ*g (x, y, z)

such that

Fx (x,y,z)=  fx(x, y, z) -λ*gx (x, y, z) = 0 → 4*x³ - λ*2*x = 0 → 2*x*(2*x² -λ) = 0

thus x=0 or x²= λ/2

Fy (x,y,z)=  fy(x, y, z) -λ*gy (x, y, z)= 0 → 4*y³ - λ*2*y = 0 → 2*y*(2*y² - λ) = 0

thus y=0 or y²= λ/2

Fz (x,y,z)=  fz(x, y, z) -λ*gz (x, y, z)= 0 → 4*z³ - λ*2*z = 0→ 2*z*(2*z² - λ) = 0

thus z=0 or z²= λ/2

g (x, y, z) = 0  → x2 + y2 + z2 = 13 → 3*(λ/2) = 13 → λ=13*2/3

thus  x²=y²=z²= λ/2 =13/3

f min = f (x, y, z) = x4 + y4 + z4 = 3*(13/3)²=169/3

for the x=0 , y=0 → z²= 13

f max = f (x, y, z) = x4 + y4 + z4 = 13² = 169

3 0
3 years ago
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