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AveGali [126]
3 years ago
13

The hypotenuse of a right triangle is 1m longer than twice one of the other two sides. The third side of the triangle is 15m. Fi

nd the lengths of the unknown side and the hypotenuse.
(this is within the unit of quadratic equations, so im not entirely sure how this would work)
Mathematics
2 answers:
Annette [7]3 years ago
6 0
X=8 remember length cannot be negative
Dimas [21]3 years ago
4 0

Let the length of unknown side be x

So, hypotenuse = 2x + 1

By pythagorean theorem ie , a² = b² + c²

(2x + 1)² = x² + 15²

4x² + 1 + 4x = x² + 225

3x² + 4x -224

(3x +28)(x-8)

x = -9.33 , 8

Since, length can't be negative

x = 8

∴Unknown side length = 8 m

Length of hypotenuse = 2 x 8 + 1 = 17 m

Hope it helps now.

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Answer:

2

Step-by-step explanation:

{16}^{ \frac{1}{4} }  \: can \: also \: be \: written \: as \: (  {{2}^{4})}^{ \frac{1}{4} }

because {2}^{4}  = 16

So,

{( {2}^{4} )}^{ \frac{1}{4} }  =  {(2)}^{4 \times  \frac{1}{4} }  = 2

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The Springer Dog Food Company makes dry dog food from two ingredients. The two ingredients (A and B) provide different amounts o
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Answer:

a) Objective function (minimize cost):

C=0.50A+0.20B

Restrictions

Proteins per pound: 16A+8B\leq 12

Vitamins per pound: 4A+8B\leq 6

Non-negative values: A,B\geq0

b) Attached

c) The optimum solution (minimum cost) is 0 pounds of ingredient A and 0.75 pounds of ingredient B. The cost is $0.15 per ration.

d) The optimum solution changes. The cost is now 0 pounds of ingredient A and 0.625 pounds of ingredient B. The cost is $0.125 per ration.

Step-by-step explanation:

a) The LP formulation for this problem is:

Objective function (minimize cost):

C=0.50A+0.20B

Restrictions

Proteins per pound: 16A+8B\leq 12

Vitamins per pound: 4A+8B\leq 6

Non-negative values: A,B\geq0

b) The feasible region is attached.

c) We have 3 corner points. In one of them lies the optimal solution.

Corner A=0 B=0.75

C=0.50*0+0.20*0.75=0.15

Corner A=0.5 B=0.5

C=0.50*0.5+0.20*0.5=0.35

Corner A=0.75 B=0

C=0.50*0.75+0.20*0=0.375

The optimum solution (minimum cost) is 0 pounds of ingredient A and 0.75 pounds of ingredient B. The cost is $0.15 per ration.

d) If the company requires only 5 units of vitamins per pound rather than 6, one of the restrictions change.

The feasible region changes two of its three corners:

Corner A=0 B=0.625

C=0.50*0+0.20*0.625=0.125

Corner A=0.583 B=0.333

C=0.50*0.583+0.20*0.333=0.358

Corner A=0.75 B=0

C=0.50*0.75+0.20*0=0.375

The optimum solution changes. The cost is now 0 pounds of ingredient A and 0.625 pounds of ingredient B. The cost is $0.125 per ration.

3 0
3 years ago
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