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11111nata11111 [884]
2 years ago
9

Show that the following rectangular form x^2+y^2=2xy can be expressed as 1 = sin(2) in polar form.

Mathematics
1 answer:
lara [203]2 years ago
7 0

Answer:

Step-by-step explanation:

substitute x = r*cos(θ), y = r*sin(θ) ==> r²(cos²(θ) + sin²(θ)) = 2r²cos(θ)sin(θ). Cancel the r² on both sides. On the left, use pythagorean identity cos²(θ) + sin²(θ) = 1. On the right apply double angle identity sin(2θ) = 2cos(θ)sin(θ).

This yields 1=sin(2θ). (I assume you meant to type sin(2θ) on the right hand side of the equation).

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If a = and b = -1 what is the value of ab -b^2
svet-max [94.6K]

Answer:

-2

Step-by-step explanation:

To solve you need to replace the variables with their numbers.

3(-1) - (-1^2)

-1 x -1 = -1

3 x (-1) = -3

-3 - (-1) =

-2

8 0
3 years ago
HELP ME CANT FAIL!! Which parent function is represented by the graph?
frozen [14]
The answer is b

Explanation:
5 0
3 years ago
What are the approximate values of the minimum and maximum points of f(x) = x5 − 10x3 + 9x on [-3,3]?
nika2105 [10]

Answer:

Minimum : -37 at x=2.4 and

Maximum = 37 at x=-2.4.

Step-by-step explanation:

Given:

f(x)=x^5-10x^3+9x; [-3,3]

Explanation:

In order to find minimum/maximum of a function, we need to find the first derivative of the function and then set it equal to 0 to get critical points.

Therefore,

f'(x)=5x^4-30x^2+9

Setting derivative equal to 0, we get

5x^4-30x^2+9=0

On applying quadratic formula, we get

x=2.4, -2.4, -0.7, 0.7.

So, those are critical points of the given function.

Plugging the values x=2.4, -2.4, -0.7, 0.7, -3 and 3 in above function, we get

f(2.4)=(2.4)^5-10(2.4)^3+9(2.4)= -37.01376   : Minimum.

f(-2.4)=(-2.4)^5-10(-2.4)^3+9(-2.4)= 37.01376 : Maximum.

f(0.7)=(0.7)^5-10(0.7)^3+9(0.7) = 3.03807

f(-0.7)=(-0.7)^5-10(-0.7)^3+9(-0.7) = -3.03807

f(-3)=(-3)^5-10(-3)^3+9(-3) =0

f(3)=(3)^5-10(3)^3+9(3) =0

Therefore the approximate values of the minimum and maximum points of f(x) = x^5- 10x^3+ 9x on [-3,3] are:

Minimum : -37 at x=2.4 and

Maximum = 37 at x=-2.4.


7 0
3 years ago
An episode of a television show is 60 minutes long when it originally airs with commercials. On a DVD without commercials, the e
ryzh [129]
60-41 1/2=18 1/2 18 1/2 divided by 1/2=37/2*2 (cross cancel 2s)=37
8 0
3 years ago
Use the model to solve the equation 3/8 +2/8
torisob [31]
3+2=5
5/8. Hope that helps!
6 0
3 years ago
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