All categories

3 years ago

R=8cos(theta)-10sin(theta) to cartesian coordinates

1 answer:

dsp733 years ago

8 0

Convert polar equation (R, Ф):

(1) R= 8cos Ф - 10sin Ф into Cartesian (x , y)
We know that:
x = R.cos Ф → cos Ф = x/R , and
y = R.sin Ф → sin Ф = y/R
and that x² +y² = R²

Replace in
R= 8cos Ф - 10sin Ф , cos Ф and sin Ф by the related x and y:

R = 8(x/R) - 10(y/R)
Multiply both sides by R:

R² = 8R(x/R) - 10R(y/r) ↔ R² = 8x - 10y , but we have also R² = x² + y². hence: 8x -10y = x² + y²
OR x² + y² - 8x + 10y = 0
We can continue in completing th squares of (x² - 8x + ?) and (y² +10y + ?)

(x² - 8x + ?) = (x - 4)² - 16

and (y² +10y + ?) = (y +5)² - 25
Final Equation:
(x - 4)² - 16 + (y +5)² - 25 →→→(x - 4)² + (y +5)² = 41

You might be interested in

Question in the picture below. (30 points)

Elena L [17]

Answer:

there is no picture

3 0

3 years ago

When solving the equation such as 2/3x = 4/5 , why would you multiply both sides of the equation by the reciprocal of 2/3 ?

barxatty [35]

Answer: Well you’re solving for “x,” so you’ll need to isolate this variable. This means we need to “get rid of” the fraction 2/3 that is attached to it. The faction is attached by the operation multiplication, so to remove it we must divide it on both sides. And division with fractions requires the reciprocal. (Try watching an explanation if you’re confused on why division requires reciprocals).

7 0

3 years ago

Construct the confidence interval for the population mean mu. c = 0.90, x = 16.9, s = 9.0, and n = 45. A 90% confidence inte

Georgia [21]

Answer:

The 90% confidence interval for population mean is $14.7 < \mu < 19.1$

Step-by-step explanation:

From the question we are told that

The sample mean is $\= x = 16.9$

The confidence level is $C = 0.90$

The sample size is $n = 45$

The standard deviation

Now given that the confidence level is 0.90 the level of significance is mathematically evaluated as

$\alpha = 1-0.90$

$\alpha = 0.10$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the standardized normal distribution table. The values is $Z_{\frac{\alpha }{2} } = 1.645$

The reason we are obtaining critical values for $\frac{\alpha }{2}$ instead of that of $\alpha$ is because $\alpha$ represents the area under the normal curve where the confidence level 1 - $\alpha$ (90%) did not cover which include both the left and right tail while $\frac{\alpha }{2}$ is just considering the area of one tail which is what we required calculate the margin of error

Generally the margin of error is mathematically evaluated as

$MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

substituting values

$MOE = 1.645* \frac{ 9 }{\sqrt{45} }$

$MOE = 2.207$

The 90% confidence level interval is mathematically represented as

$\= x - MOE < \mu < \= x + MOE$

substituting values

$16.9 - 2.207 < \mu < 16.9 + 2.207$

$14.7 < \mu < 19.1$

3 0

3 years ago

Sue is thinking of buying some 2-liter sodas which are on sale for $1.25 each. The total cost, c, ofall the 2-liter sodas will b

4vir4ik [10]

Ways to get 2$ is easy just multiply

3 0

3 years ago

What is a complex number ?

ycow [4]

Answer:A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x² = −1. Because no real number satisfies this equation, i is called an imaginary number.

Step-by-step explanation:

5 0

3 years ago