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lawyer [7]
2 years ago
15

By , cos(θ) = StartFraction x Over r EndFraction, and by , sin(θ) = StartFraction y Over r EndFraction. Multiplying both sides o

f the above equations by r, we get that x = r cos(θ) and y = r sin(θ). The states that x2 + y2 = r2. By , we have [r cos(θ)]2 + [r sin(θ)]2 = r2. Applying the , the equation can be written as r2 cos2(θ) + r2 sin2(θ) = r2. Dividing both sides of the equation by r2 results in cos2(θ) + sin2(θ) = 1.
Mathematics
1 answer:
Marianna [84]2 years ago
8 0

Answer:

definition of cosine, definition of sine, pythagorean theorem, substitution, laws of exponents.

Step-by-step explanation:

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Tim has 39 pairs of headphones and 13 music players. Tim wants to sell all of the headphones and music players in identical pack
tiny-mole [99]

Answer:

he can make 4 packages hope this helps

8 0
2 years ago
Read 2 more answers
An isosceles triangle used to rack billiard balls has a base of 11.25 inches. The sides of the triangle meet at a 56° angle. To
lara [203]

Answer:

The measure of each sides of isosceles triangle is 16.67 inches , 16.67 inches , 11.25 inches

Step-by-step explanation:

Given as for a Isosceles triangle :

The base of Triangle = 11.25 inches

The sides of triangle meets at 56°

Let the unknown side measure = x inches

From <u>The property of isosceles triangle</u>

The angle opposite to the same side are equal

I.e \Theta _1 =  \Theta _2 = 56°

So, The third angle = 180° - ( \Theta _1 +  \Theta _2 )

Or, The third angle = 180° - ( 56° + 56° )

∴   The third angle = 180° - 112° = 68°

Now, From isosceles triangle

Tan 56° = \frac{perpendicular}{base}

Or, Tan 56° = \frac{x}{11.25}

∴   x = 11.25 × Tan 56°

Or, x = 11.25 × 1.482 = 16.672 inches

Hence The measure of each sides of isosceles triangle is 16.67 inches , 16.67 inches , 11.25 inches   Answer

6 0
2 years ago
Suppose that the weight of navel oranges is normally distributed with a mean µµ = 8 ounces, and a standard deviation σσ = 1.5 ou
monitta

Answer:

Hello some parts of your question is missing below is the missing part

c. If you randomly select a navel orange, what is the probability that it weighs between6.2 and 7 ounces

Answer: A) 0.0099

              B) 0.6796

              C) 0.13956

Step-by-step explanation:

weight of Navel oranges evenly distributed

mean ( u ) = 8 ounces

std ( б )= 1.5

navel oranges = X

A ) percentage of oranges weighing more than 11.5 ounces

P( x > 11.5 ) = P ( \frac{x - u}{ std} > \frac{11.5-8}{1.5} )

                   = P ( Z > 2.33 ) = 0.0099

                   = 0.9%

B) percentage of oranges weighing less than 8.7 ounces

  P( x < 8.7 ) = P ( \frac{x - u}{ std} > \frac{8.7-8}{1.5} )

                    = P ( Z < 0.4667 ) = 0.6796

                    = 67.96%

C ) probability of orange selected weighing between 6.2 and 7 ounces?

P ( 6.2 < X < 7 ) = P (\frac{6.2-8}{1.5} <  \frac{x - u}{ std} < \frac{7-8}{1.5} )

                          = P ( -1.2 < Z < -0.66 )

                          = Ф ( -0.66 ) - Ф(-1.2) = 0.13956

7 0
2 years ago
A sample of an unknown chemical element naturally loses its mass over time. The relationship between the elapsed time ttt, in mo
Naddik [55]

Answer:

Step-by-step explanation:

Given a sample M(t)

M(t) = 120 • ( 81 / 625)^t

When is the fraction of the mass decay to 3/5 of it's mass

Generally

M(t) = Mo•(k^t)

The original mass is 120

Mo = 120

So, we want to find time when it decay to 3/5 of it's original mas

M = 3/5 × 120

M = 72

Then,

M(t) = 120 • ( 81 / 625)^t

72 = 120 • ( 81 / 625)^t

72 / 120 = ( 81 / 625)^t

0.6 = ( 81 / 625)^t

Take natural logarithmic of both sides

In(0.6) = In(81/625)^t

In(0.6) = t•In(81/625)

t = In(0.6) / In(81/625)

t = In(0.6) / In(0.1296)

t = 0.25 monthly

t = ¼ monthly

6 0
2 years ago
Sadie runs a farm stand that sells blueberries and peaches. Each pound of blueberries sells for $3.25 and each pound of peaches
fiasKO [112]

Answer:

There were 14 pounds of blueberries sold and 42 pounds of peaches sold.

Step-by-step explanation:

Since Sadie sold 3 times as many pounds of peaches as pounds of blueberries, she sold more pounds of peaches, so if we multiply 3 by the number of pounds of blueberries sold, we will get the number of pounds of peaches sold, meaning pp equals 3b.

There were 14 pounds of blueberries sold and 42 pounds of peaches sold.

6 0
2 years ago
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