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3 years ago

Which parametric equations represent (x + 1)2 + (y – 3)2 = 16

Mathematics

2 answers:

valentina_108 [34]3 years ago

4 0

Answer:

see image below

Step-by-step explanation:

max2010maxim [7]3 years ago

3 0

Answer:

x = 4cos(t) – 1 and y = 4sin(t) + 3

Step-by-step explanation:

Equation of a circle:

The equation of a circle has the following format:

$(x - x_0)^2 + (y - y_0)^2 = r^2$

In which:

The centre is is $(x_0,y_0)$ and r is the radius. The parametric equations are given by:

$x(t) = r\cos{(t)} + x_0$

$y(t) = r\sin{(t)} + y_0$

In this question:

$(x + 1)^2 + (y - 3)^2 = 4^2$

This means that the centre is $(-1,3)$ and the radius is 4. So, the answer is:

x = 4cos(t) – 1 and y = 4sin(t) + 3

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3 years ago

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3 years ago

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3 years ago

Let f(x)=x^2f ( x ) = x 2. Find the Riemann sum for ff on the interval [0,2][ 0 , 2 ], using 4 subintervals of equal width and t

sladkih [1.3K]

Answer:

$A_L=1.75$

Step-by-step explanation:

We are given:

$f(x)=x^2$

$interval = [a,b] = [0,2]$

Since $n = 4$ ⇒ $\Delta x = \frac{b-a}{n} = \frac{2-0}{4}=\frac{1}{2}$

Riemann sum is area under the function given. And it is asked to find Riemann sum for the left endpoint.

$A_L= \sum\limits^{n}_{i=1}\Delta xf(x_i) = \frac{1}{2}(0^2+(\frac{1}{2})^2+1^2+(\frac{3}{2})^2)=\frac{7}{4}=1.75$

Note:

If it will be asked to find right endpoint too,

$A_R=\sum\limits^{n}_{i=1}\Delta xf(x_i) =\frac{1}{2}((\frac{1}{2})^2+1^2+(\frac{3}{2})^2+2^2)=\frac{15}{4}=3.75$

The average of left and right endpoint Riemann sums will give approximate result of the area under $f(x)=x^2$ and it can be compared with the result of integral of the same function in the interval given.

So, $(A_R+A_L)/2 = (1.75+3.75)/2=2.25$

$\int^2_0x^2dx=x^3/3|^2_0=8/3=2.67$

Result are close but not same, since one is approximate and one is exact; however, by increasing sample rates (subintervals), closer result to the exact value can be found.

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3 years ago