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3 years ago

Evaluate the following:

Mathematics

1 answer:

marusya05 [52]3 years ago

4 0

Answer:

csc∅ = 25/7

sec∅ = 25/24

cot∅ = 24/7

Step-by-step explanation:

Cosecant (csc) is 1/sin∅ or hypotenuse over opposite

Secant (sec) is 1/cos∅ or hypotenuse over adjacent

Cotangent (cot) is 1/tan∅ or adjacent over opposite

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A store has been selling 300 Blu-ray disc players a week at $600 each. A market survey indicates that for each $40 rebate offere

timurjin [86]

Answer:

75 $

Step-by-step explanation:

According to problem statement p(300) = 600

And we know that with a rebate of 40 $, numbers of units sold will increase by 80 then if x is number of units sold, the increase in units is

( x - 300 ) , and the price decrease

(1/80)*40 = 0,5

Then the demand function is:

D(x) = 600 - 0,5* ( x - 300 ) (1)

And revenue function is:

R(x) = x * (D(x) ⇒ R(x) = x* [ 600 - 0,5* ( x - 300 )]

R(x) = 600*x - 0,5*x * ( x - 300 )

R(x) = 600*x - 0,5*x² - 150*x

R(x) = 450*x - (1/2)*x²

Now taking derivatives on both sides of the equation we get

R´(x) = 450 - x

R´(x) = 0 ⇒ 450 - x = 0

x = 450 units

We can observe that for 0 < x < 450 R(x) > 0 then R(x) has a maximum for x = 450

Plugging this value in demand equation, we get the rebate for maximize revenue

D(450) = 600 - 0,5* ( x - 300 )

D(450) = 600 - 225 + 150

D(450) =

D(450) = 600 - 0,5*( 150)

D(450) = 600 - 75

D(450) = 525

And the rebate must be

600 - 525 = 75 $

5 0

3 years ago

Yo please help

Alex Ar [27]

Answer:

Options 1, 3 and 4 are true

Step-by-step explanation:

The legs EF and DF of the right triangle DEF have lengths of 24 units and 7 units, respectively. By the Pythagorean theorem,

$DE^2=EF^2+DF^2\\ \\DE^2=24^2+7^2\\ \\DE^2=576+49\\ \\DE^2=625\\ \\DE=25\ units$

Find trigonometric functions:

$\sin \angle D=\dfrac{\text{Opposite leg}}{\text{Hypotenuse}}=\dfrac{EF}{DE}=\dfrac{24}{25}$

$\cos \angle E=\dfrac{\text{Adjacent leg}}{\text{Hypotenuse}}=\dfrac{EF}{DE}=\dfrac{24}{25}$

$\tan \angle D=\dfrac{\text{Opposite leg}}{\text{Adjacent leg}}=\dfrac{EF}{DF}=\dfrac{24}{7}$

$\sin \angle E=\dfrac{\text{Opposite leg}}{\text{Hypotenuse}}=\dfrac{DF}{DE}=\dfrac{7}{25}$

Thus, options 1, 3 and 4 are true

5 0

3 years ago

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Epic math question that i cant solve

zvonat [6]

The area of the shaded region can be found by subtracting the area of the inside rectangle from the outside rectangle

area of outside: 6 X 10y —> 60y
area of inside: 3 X 5x —> 15x

so the area of the shaded region is 60y-15x

the GCF is 15, so the factored form is: 15(4y-x)

8 0

2 years ago

18/X=2.4/28 find X plz help

yulyashka [42]

Cross multiply

18 / X = 2.4 / 28
so
18 * 28 = X (2.4)
and that becomes
504 = X * 2.4
then divide by 2.4
X = 210

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3 years ago

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Margie's vegetable garden contains cucumbers, corn, potatoes, and tomatoes. About

Vitek1552 [10]

3/4 of the garden is not potatoes, or 75%

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2 years ago