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3 years ago

Classify the limaçon represented by the equation r=(1/2)-(1/2)sin(theta)

Mathematics

1 answer:

babunello [35]3 years ago

4 0

We know that

Limacons are in the form
r=a(+-)b*sin (theta) or r=a(+-)b*cos (theta)

in this problem
r=a(+-)b*sin (theta)
so
is symmetric to y axis
a=1/2
b=1/2
a/b=1---------> Cardioid (hearth shaped)

see the attached figure

the answer is the option
<span>A. Cardioid </span>

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Find the area bounded by the graphs of the indicated equations over the given interval.

NeX [460]

Answer:

Step-by-step explanation:

$y = 0$

is basically the horizontal axis.

First, find the integral of x^2-25.

Remember that

integral of a constant is that constant times x.

Also that

to take the integral of a power function, add 1 to the degree and divide by that same degree.

$y = {x}^{2} - 25$

We then get

$\frac{ {x}^{3} }{3} - 25x$

Evaluate at -3

$\frac{ - 3 {}^{3} }{3} - 25( - 3)$

$- 27 + 75 = 48$

Then we evaluate at 0

$\frac{0 {}^{3} }{3} - 25(0) = 0$

Next, we subtract the the answer then we get

$48 - 0 = 48$

8 0

2 years ago

Part A: The area of a square is (9x2 − 12x + 4) square units. Determine the length of each side of the square by factoring the a

Sladkaya [172]

Answer:

Part A: The length of each side is $3x-2$ units long.

Part B: The dimensions are 5x-4 and 5x+4 units long.

Step-by-step explanation:

Part A:

--> $9x^2-12x+4$

--> Multiply 9 times 4 to see the factors of that product

--> 9 times4 = 36

Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36

Use the factor 6 and make it negative so -6

add another -6

Keep in mind that it is -6x

--> 9x^2-6x-6x+4

Separate the four terms into two different binomials

--> 9x^2-6x and -6x+4

Factor the binomials

With 9x^2-6x you can factor a 3x

So it will 3x(3x-2)

Do the same thing with -6x+4

You can factor out a -2

-2(3x-2)

The reason you factor out a -2 and not 2 is because it has to be same so in this case it is (3x-2)

Take the two numbers that you factored and put them to make an expression so (3x-2)

--> (3x-2)(3x-2) or (3x-2)^2

3x-2 is the length of each side so it is 3x-2 units long

Part B:

-->25x^2-16y^2

Use the difference of squares

take the square root of 25x^2

that is 5x

take the square root of 16y^2

that is 4y

write it in this way (5x+4y)(5x-4y)

These are the dimensions of the rectangle

3 0

2 years ago

Please help me!!!!!!!! Factor z2 – 3z – 18

Vladimir [108]

First, the factor pairs for 18 are:
1, 18
2, 9
3, 6

Since the middle term is -3, the two factors must be 3 apart. The only pair that is 3 values apart is 3, 6.
Since the middle value is negative, the larger number is negative. This means that the 6 is negative.
z = -6
z = 3

Set each equal to 0;
z = -6
z + 6 = 0

z = 3
z - 3 =0
So your factors are (z+6) and (z-3), or answer B.

4 0

3 years ago

Given the triangle below, find the value of x

Nataliya [291]

Answer:

I think it is b I’m not quite sure though. Sorry if wrong…

Step-by-step explanation:

6 0

2 years ago

Work out 60 × 2/3 (2 over 3)

Taya2010 [7]

Solution:
60 x 2/3
60/1 x 2/3
120/3
40
Answer:
40

hope this helps!

3 0

3 years ago