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3 years ago

Write the equation in graphing form and the graph the shape. NO LINKS/ASSESSMENT!!

Mathematics

1 answer:

charle [14.2K]3 years ago

4 0

Answer:

see explanation

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

Given

16 + x² + y² - 8x - 6y = 0 ( subtract 16 from both sides )

x² + y² - 8x - 6y = - 16 ( collect x and y terms together )

x² - 8x + y² - 6y = - 16

Use the method of completing the square

add ( half the coefficient of the x/y terms)² to both sides

x² + 2(- 4)x + 16 + y² + 2(- 3)y + 9 = - 16 + 16 + 9

(x - 4)² + (y - 3)² = 9 ← in standard form

with centre (4, 3 ) and r = $\sqrt{9}$ = 3

This is a circle with centre (4, 3 ) and radius 3

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Show that cos2x=cosx

PSYCHO15rus [73]

cos (2x) = cos x

2 cos^2 x -1 = cos x using the double angle formula

2 cos ^2 x -cos x -1 =0

factor

(2 cos x+1) ( cos x -1) = 0

using the zero product property

2 cos x+1 =0 cos x -1 =0

2 cos x = -1 cos x =1

cos x = -1/2 cos x=1

taking the arccos of each side

arccos cos x = arccos (-1/2) arccos cos x = arccos 1

x = 120 degrees x=-120 degrees x=0

remember you get 2 values ( 2nd and 3rd quadrant)

these are the principal values

now we need to add 360

x = 120+ 360n x=-120+ 360n x = 0 + 360n where n is an integer

3 0

4 years ago

The total resistance in a circuit with two parallel resistors is 2 ohms and R1 is 6 ohms. Using the equation for R2, in terms of

ivanzaharov [21]

<h2>Answer:</h2>

$R_2$ is 3 ohms

<h2>Step-by-step explanation:</h2>

In a circuit containing two resistors $R_1$ and $R_2$ connected together in parallel, the total resistance $R_T$ is given by;

$\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2}$ ---------(i)

<em>Make </em> $R_2$ <em> subject of the formula;</em>

=> $\frac{1}{R_2} = \frac{1}{R_T} - \frac{1}{R_1}$

=> $\frac{1}{R_2} = \frac{R_1 - R_T}{R_TR_1}$

=> ${R_2} = \frac{R_TR_1}{R_1 - R_T}$ ---------------(ii)

From the question,

$R_1$ = 6Ω

$R_T$ = 2Ω

Substitute these values into equation (ii) as follows;

=> ${R_2} = \frac{2*6}{6 - 2}$

${R_2} = \frac{12}{4}$

$R_2$ = 3Ω

Therefore, the value of $R_2$ = 3 ohms or $R_2$ = 3Ω

3 0

3 years ago

Please answer this question with any of the 4 choices i have been struggling with this

kotegsom [21]

Answer:

Choice A. $\frac{2}{3}$

Step-by-step explanation:

Turn the mixed numbers into improper fractions:

$\frac{14}{9} /\frac{7}{3}$

Flip the second term and multiply:

$\frac{14}{9} /\frac{3}{7}$
$\frac{42}{63}$

Simplify:

$\frac{2}{3}$

7 0

3 years ago

Read 2 more answers

angelo rode his bike around a bike trail that was 1/4 of a mile long.he rode his bike around thetrail 8 times.Angelo says he rod

forsale [732]

Hi there!

From this problem we can pull out some key information and remove any excess.

- The trail is 1/4 of a mile long.
- Angelo rode around the trail 8 times.
- Angelo claims he rode 8/4 miles.
- Teresa claims he rode 2 miles.

From that we know that if Angelo rode around the trail 8 times and the trail is 1/4 a mile, he in total rode 8/4 of a mile.

However, Teresa claims he rode 2 miles!

And the answer is... they're both correct!

Angelo did indeed ride 8/4 miles however that is equivalent to 2 miles so they are both in the right.

7 0

4 years ago

What is the value of this expression when a= - 3 and b=-2?<br> (3a^-2b^6/2a^-1b^5)^2

lisabon 2012 [21]

Answer:

so lets just rewrite it with A=-3 amd B=-2

(-9^4^-9^2^5)^2

which is equal to... 1!

Hope This Helps!!!

7 0

3 years ago