Write the equation in standard form for the circle with center (-5,8) and radius 4

Mathematics

2 answers:

Anon25 [30]2 years ago

8 0

Answer:

(x+5)^2+(y-8)^2=4^2

Step-by-step explanation:

I used a website called desmos.

Scilla [17]2 years ago

8 0

Answer:

(x + 5)² + (y - 8)² = 16

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

here (h, k ) = (- 5, 8 ) and r = 4 , then

(x - (- 5) )² + (y - 8)² = 4² , that is

(x + 5)² + (y - 8)² = 16

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The graph of a sinusoidal function has a minimum point at (0, - 10) and then has a maximum point at (2, - 4) Write the formula o

AleksAgata [21]

Answer: $\bold{y=3sin\bigg(\dfrac{\pi}{2}x-\dfrac{\pi}{2}\bigg)-7}$

Step-by-step explanation:

Minimum: (0, -10)

Maximum: (2, -4)

y = A sin (Bx - C) + D

Amplitude (A) = (Max - Min)/2
Period = 2π/B → B = 2π/Period
Phase Shift = C/B → C = B × Phase Shift
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$A=\dfrac{-4-(-10)}{2}\quad =\dfrac{-4+10}{2}\quad =\dfrac{6}{2}\quad =\large\boxed{3}$

$\text{x-value of Max minus x-value of Min}= \dfrac{1}{2}\text{Period}\\\\2 - 0 = \dfrac{1}{2}P\quad \rightarrow \quad P=4\\\\\\B=\dfrac{2\pi}{P}\quad =\dfrac{2\pi}{4}\quad =\large\boxed{\dfrac{\pi}{2}}\\$

$D = \dfrac{\text{Max + Min}}{2}\quad = \dfrac{-4+(-10)}{2}\quad =\dfrac{-14}{2}\quad =\large\boxed{-7}$

Sin usually starts at (0, 0). For this graph, the midline touches 0 when x = 1 so the Phase Shift = 1.

$C = B \times \text{Phase Shift}\quad = \dfrac{\pi}{2}\times 1\quad =\large\boxed{\dfrac{\pi}{2}}$

$A=3, \quad B=\dfrac{\pi}{2}, \quad C=\dfrac{\pi}{2},\quad D=-7\\\\\rightarrow \quad \large\boxed{y=3\sin \bigg(\dfrac{\pi}{2}x-\dfrac{\pi}{2}\bigg)-7}$