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2 years ago

Prove the trigonometric identity! Please help!! 50 Points!

Mathematics

1 answer:

Rudiy272 years ago

3 0

Answer:

Step-by-step explanation:

For simplicity I will substitue $x$ for β.

$1-sin(2x)=(cosx-sinx)^2\\1-2sin(x)cos(x)=cos^2x-2sin(x)cos(x)+sin^2x\\1=cos^2(x)+sin^2(x)\\1=1$

In the first step I used the identity

$sin(2x)=2sin(x)cos(x)$

And I factored out $(cosx-sinx)^2$

Then it's just simple algebra to cancel till the 3rd step where we used another identity derived from the Pythagorean Theorem.

$cos^2(x)+sin^2(x)=1$

That's it!

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What is the probability of drawing five face cards?

anastassius [24]

Total number of cards = 52
Total number of face cards = 12

P( 5 face cards) = (12/52)(11/51)(10/50)(9/49)(8/48) = 33/108290

Answer: 33/108290

4 0

3 years ago

A can in the shape of a right circular cylinder is required to have a volume of 500 cubic centimeters. The top and bottom are ma

borishaifa [10]

Answer:

The answer to the question is

The total cost C of the material as a function of the radius r of the cylinder is

0.6912·r² + 800/r Dollars.

Step-by-step explanation:

To solve the question, we note that

The area of the top and bottom combined = 2·π·r²

The area of the sides = 2·π·r·h

and the volume = πr²h = 500 cm²

Therefore height = 500/(πr²)

Substituting the value of h into the area of the side we have

Area of the side = 2πr·500/(πr²) = 1000/r

Therefore total area of can = Area of top + Area of bottom + Area of side

Whereby the cost of the can = 0.11×Area of top +0.11×Area of bottom +0.8×Area of side

Which is equal to

0.11×2×π×r²+ 0.8×1000/r = 0.6912·r² + 800/r

The cost of the can is $(0.6912·r² + 800/r)

3 0

3 years ago

Plz Help me<br><br>3x + 5y = 13 <br>2x + y = 4

Finger [1]

Answer:

solve simultaneously

start by labeling them equation 1 and 2 then choose whether you want to make x or y the subject from knew of the equations

7 0

3 years ago

Please help ASAP thank you

vladimir1956 [14]

Answer:

Triangle.

Step-by-step explanation:

3 0

3 years ago

Swimming speed of salmon. The graph is showed below shows the influence of the temperature T on the maximum sustainable swimming

Doss [256]

Answer:

Here we have the relation between the speed of the salmon and the temperature.

a) the relation dS/dT tell us how the speed of the salmon changes as the temperature changes, and the units should be (if speed is m/s and temperature is in °C )

[dS/dT ] = [m/s*°C ].

b) I can not do a draw of the figure, but i can give a aproximation.

For T = 18°C, we can see that we are around the maximum of the curve, this means that around this point we will find the zero in the first derivate.

then S'(18) ≈ 0 m/s*°C

this means that around this point the changes are small.

for T = 10°C

Around this region, we can see almost a linear behavior.

so we can take a range of +-2°C

S(12°C) = 25m/s

S(8°C) = 20m/s

then the slope can be obtained using the relation:

S = (Y2 - Y1)/(X2 - X1) where this is the slope for the line that goes trough the pairs. (X1, Y1) and (X2, Y2)

S = (25 - 20)/(12 - 8) = 5/4

then we have that S´(10°C) ≈ 5/4 m/s*°C

Those two results are approximations, you may find better approximations by doing this with a ruler and drawing the tangents.

5 0

3 years ago