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2 years ago

Find the solutions. Show steps please!

Mathematics

1 answer:

san4es73 [151]2 years ago

6 0

Answer:

x = 0, π/4, π, 7π/4

Step-by-step explanation:

sin(2x) = √2 sin x

Use double angle formula.

2 sin x cos x = √2 sin x

Move everything to one side.

2 sin x cos x − √2 sin x = 0

Factor.

sin x (2 cos x − √2) = 0

Solve.

sin x = 0, cos x = ½√2

x = 0, π/4, π, 7π/4

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-16m = 7 + 9

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1 year ago

Joely's Tea Shop, a store that specializes in tea blends, has available 45 pounds of A grade tea and 70 pounds of B grade tea. T

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Answer:

Hence, (75,40) is the maximum point and maximum profit is $192.5

Step-by-step explanation:

Let the breakfast be x

And let the lunch or afternoon be y

Inequalities will become

$\frac{1}{3}x+\frac{1}{2}y\leq 45$

$\frac{2}{3}x+\frac{1}{2}y\leq 70$

And objective function will be

Z=1.5x+2.0y

You can see the graph in the attachement

ABCD is the feasible region

Points of feasible region is (0,90) ,(0,0) ,(75,40) and(105,0)

We have to find Z by substituting the points of feasible region

At (0,90) we get

Z=1.5(0)+2(90)

Z=180

At (0,0)

Z=1.5(0)+2(0)

Z=0

At (75,40)

Z=1.5(75)+2(40)

Z=192.5

At (105,0)

Z=1.5(105)+2(0)

Z=157.5

The maximum number we are getting is 192.5 which is at (75,40)

Hence, (75,40) is the point of maximum

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3 years ago