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2 years ago

Determine the equation of a circle with the center (8,10) and radius 6

Mathematics

1 answer:

lyudmila [28]2 years ago

8 0

Answer:

(x - 8)² + (y - 10)² = 36

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Coordinates (x, y)

Pre-Calculus

Circle Center Formula: (x - h)² + (y - k)² = r²

(h, k) is center
r is radius

Step-by-step explanation:

Step 1: Define

Identify

(h, k) = (8, 10)

r = 6

Step 2: Find Equation

Substitute in variables [Center Circle Formula]: (x - 8)² + (y - 10)² = 6²
Evaluate exponents: (x - 8)² + (y - 10)² = 36

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A cruise left port A and traveled towards port B 225 km away. After 1.5 hours of travel, the cruise was stopped for a half an ho

Softa [21]

Answer:

Step-by-step explanation:

v = the original speed of the cruise

d = 225 km the distance passed

t = d/v = 225/v the total time of the travel

v*1.5 + (v + 10)(d/v - 1.5 - 0.5) = d (using the formula distance = speed*time)

1.5v + (v + 10)(225/v - 2) = 225

Look at the images to see the solved equation

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2 years ago

A rocket is launched from the top of a 99-foot cliff with an initial velocity of 122 ft/s.

Harman [31]

Remember that c is the initial height. Since we the rocket is in a 99-foot cliff, c=99. Also, we know that the velocity of the rocket is 122 ft/s; therefore v=122
Lets replace the values into the the vertical motion formula to get:
$0=-16 t^{2} +122t+99$
Notice that the rocket hits the ground at the bottom of the cliff, which means that the final height is 99-foot bellow its original position; therefore, our final height will be h=-99
Lets replace this into our equation to get:
$-99=-16 t^{2} +122t+99$
$-16 t^{2} +122+198=0$

Now we can apply the quadratic formula $t= \frac{-b+or- \sqrt{ b^{2} -4ac} }{2a}$ where a=-16, b=122, and c=198
$t= \frac{-122+or- \sqrt{ 122^{2}-(4)(-16)(198) } }{(2)(-16)}$
$t= \frac{-122+ \sqrt{27556} }{-32}$ or $t= \frac{-122- \sqrt{27556} }{-32}$
$t= \frac{-122+166}{-32}$ or $t= \frac{-122-166}{-32}$
$t= \frac{-11}{8}$ or $t=9$

Since the time can't be negative, we can conclude that the rocket hits the ground after 9 seconds.

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3 years ago

Read 2 more answers

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nikitadnepr [17]

Answer:

A man borrows * 8000

He agrees to repay with a total interest of 1360 in 12 monthly instalments.

Each instalment being less than the preceding one by * 40

= $\frac{12}{1360}$ x 40