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xenn [34]
3 years ago
8

Find an equation equivalent to r = 10sin ø in rectangular coordinates.

Mathematics
1 answer:
kherson [118]3 years ago
4 0

Answer: x^2 + y^2 -10y = 0

Step-by-step explanation:

Cartesian coordinates, also called the Rectangular coordinates, isdefined in terms of x and y. So, for the problem θ has to be eliminated or converted using basic foundations that are described by the unit circle and the right triangle trigonometry.

r= 10sin(θ)

Remember that:

x= r × cos(θ)

y= r × sin(θ)

r^2= x^2 + y^2

Multiply both sides of the equation by r. This will give:

r × r = 10r × sin(θ)

r^2 = 10r × sin(θ)

x^2 + y^2= 10r × sin(θ)

Because y= r × sin(θ), we can make a substitution. This will be:

x^2 + y^2= 10y

x^2 + y^2 -10y = 0

The above equation is the Rectangular coordinate equivalent to the given equation.

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Interger for 6(-7) + (-8).
timama [110]

6 multiplied by negative 7 would be negative 42. Negative 42 added by negative 8 would be negative 34.

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3 years ago
It took 35 seconds for 5 songs to download to Rebecca’s computer. The next day, it took 42 seconds for 6 songs to download. Writ
sleet_krkn [62]

The equation in point-slope form to represent the time y it took to download x songs is; (y - 35) = 7(x - 5)

  • Since it took 35 seconds for 5 songs to download

  • and it took 42 seconds for 6 songs to download

In essence, we can represent the information as;

  • (5, 35) and (6,42)

To find the slope of the equation; we have;

  • Slope, m = (42-35)/(6-5)

  • m = 7

In essence, the equation in point-slope form to represent the time y it took to download x songs is;

  • (y - 35) = 7(x - 5)

Read more:

brainly.com/question/6497976

3 0
2 years ago
On any given day, mail gets delivered by either Alice or Bob. If Alice delivers it, which happens with probability 1/4 , she doe
Troyanec [42]

Answer:

(a) The value of fₓ (9.5) is 0.125.

(b) The value of fₓ (10.5) is 0.50.

Step-by-step explanation:

Let <em>X</em> denote delivery time of the mail delivered by Alice and <em>Y</em> denote delivery time of the mail delivered by Bob.

It i provided that:

X\sim U(9, 11)\\Y\sim U(10, 12)

The probability that Alice delivers the mail is, <em>p</em> = 1/4.

The probability that Bob delivers the mail is, <em>q</em> = 3/4.

The probability density function of a Uniform distribution with parameters [<em>a</em>, <em>b</em>] is:

f(x)=\left \{ {{\frac{1}{b-a};\ a, b>0} \atop {0;\ otherwise}} \right.

The probability density function of the delivery time of Alice is:

f(X_{A})=\left \{ {{\frac{1}{b-a}=\frac{1}{2};\ [a, b]=[9, 11]} \atop {0;\ otherwise}} \right.

The probability density function of the delivery time of Bob is:

f(X_{B})=\left \{ {{\frac{1}{b-a}=\frac{1}{2};\ [a, b]=[10, 12]} \atop {0;\ otherwise}} \right.

(a)

Compute the value of fₓ (9.5) as follows:

For delivery time 9.5, only Alice can do the delivery because Bob delivers the mail in the time interval 10 to 12.

The value of fₓ (9.5) is:

f_{X}(9.5)=p.f(X_{A})+q.f(X_B})\\=(\frac{1}{4}\times \frac{1}{2})+(\frac{3}{4}\times0)\\=\frac{1}{8}\\=0.125

Thus, the value of fₓ (9.5) is 0.125.

(b)

Compute the value of fₓ (10.5) as follows:

For delivery time 10.5, both Alice and Bob can do the delivery because Alice's delivery time is in the interval 9 to 11 and that of Bob's is in the time interval 10 to 12.

The value of fₓ (10.5) is:

f_{X}(10.5)=p.f(X_{A})+q.f(X_B})\\=(\frac{1}{4}\times \frac{1}{2})+(\frac{3}{4}\times\frac{1}{2})\\=\frac{1}{8}+\frac{3}{8}\\=0.50

Thus, the value of fₓ (10.5) is 0.50.

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Please help with my math problem. What's 3+2? 10 points.
zhuklara [117]

Answer:

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Step-by-step explanation:

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Use a system of equations:

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