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2 years ago

What is the radius of a circle whose equation is x2 + y2 + 8x - 6y + 21 = 0? units

Mathematics

1 answer:

pickupchik [31]2 years ago

6 0

Answer:r=2

Step-by-step explanation:

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What is the answer to 6x^2+17x+12=0 pls help me and I will help you back

Rina8888 [55]

Answer:

x=−4/3 or x=−3/2

Step-by-step explanation:

Let's solve your equation step-by-step.

6x2+17x+12=0

Step 1: Factor left side of equation.

(3x+4)(2x+3)=0

Step 2: Set factors equal to 0.

3x+4=0 or 2x+3=0

x=−4/3 or x=−3/2

4 0

3 years ago

2y+3x=90 what is x and y

yan [13]

If x=-6 then y=54.
If x=-4 then y=51.
If x=-2 then y=48.
If x=0 then y=45.
If x=2 then y=42.
If x=4 then y=39.
If x=6 then y=36.

There are an infinite variety of pairs of numbers for 'x' and 'y'
that can make that equation true.

You can use that equation to draw a line on a graph. Then
EVERY point on the line is a solution to the equation.

'x' and 'y' don't have single values unless you have TWO equations.

4 0

2 years ago

Find the Fourier series of f on the given interval. f(x) = 1, ?7 < x < 0 1 + x, 0 ? x < 7

Zolol [24]

$f(x)=\begin{cases}1&\text{for }-7$

The Fourier series expansion of $f(x)$ is given by

$\dfrac{a_0}2+\displaystyle\sum_{n\ge1}a_n\cos\frac{n\pi x}7+\sum_{n\ge1}b_n\sin\frac{n\pi x}7$

where we have

$a_0=\displaystyle\frac17\int_{-7}^7f(x)\,\mathrm dx$
$a_0=\displaystyle\frac17\left(\int_{-7}^0\mathrm dx+\int_0^7(1+x)\,\mathrm dx\right)$
$a_0=\dfrac{7+\frac{63}2}7=\dfrac{11}2$

The coefficients of the cosine series are

$a_n=\displaystyle\frac17\int_{-7}^7f(x)\cos\dfrac{n\pi x}7\,\mathrm dx$
$a_n=\displaystyle\frac17\left(\int_{-7}^0\cos\frac{n\pi x}7\,\mathrm dx+\int_0^7(1+x)\cos\frac{n\pi x}7\,\mathrm dx\right)$
$a_n=\dfrac{9\sin n\pi}{n\pi}+\dfrac{7\cos n\pi-7}{n^2\pi^2}$
$a_n=\dfrac{7(-1)^n-7}{n^2\pi^2}$

When $n$ is even, the numerator vanishes, so we consider odd $n$ , i.e. $n=2k-1$ for $k\in\mathbb N$ , leaving us with

$a_n=a_{2k-1}=\dfrac{7(-1)-7}{(2k-1)^2\pi^2}=-\dfrac{14}{(2k-1)^2\pi^2}$

Meanwhile, the coefficients of the sine series are given by

$b_n=\displaystyle\frac17\int_{-7}^7f(x)\sin\dfrac{n\pi x}7\,\mathrm dx$
$b_n=\displaystyle\frac17\left(\int_{-7}^0\sin\dfrac{n\pi x}7\,\mathrm dx+\int_0^7(1+x)\sin\dfrac{n\pi x}7\,\mathrm dx\right)$
$b_n=-\dfrac{7\cos n\pi}{n\pi}+\dfrac{7\sin n\pi}{n^2\pi^2}$
$b_n=\dfrac{7(-1)^{n+1}}{n\pi}$

So the Fourier series expansion for $f(x)$ is

$f(x)\sim\dfrac{11}4-\dfrac{14}{\pi^2}\displaystyle\sum_{n\ge1}\frac1{(2n-1)^2}\cos\frac{(2n-1)\pi x}7+\frac7\pi\sum_{n\ge1}\frac{(-1)^{n+1}}n\sin\frac{n\pi x}7$

3 0

2 years ago

A bottle of water contains 450ml. How many litres of water are there in 8 of these bottles

In-s [12.5K]

Answer:

3.6 litres

Step-by-step explanation:

1 bottle = 450ml

8 bottles = 450 × 8

= 3600ml

1000ml = 1 litre

3600ml = 3.6 litres (3600÷1000)

6 0

2 years ago

Read 2 more answers

Simplify the following fractions 8/24 8/32 6/30 12/24 9/21 5/20

Mademuasel [1]

Answer:

for 8/24 the answer will be 1/3.

and for 8/32 the answer will be 1/4.

and for 6/30 the answer will be 1/5.

and for 12/24 the answer will be 1/2.

and for 9/21 the answer will be 3/7.

and for 5/20 the answer will be 1/4

Step-by-step explanation:

4 0

2 years ago