MATHEMATICS HIGH SCHOOL

Identify the center and radius for the equation x ^ 2 + (y - 3) ^ 2 = 4

Answers

Answer 1

Answer:

Answer:

r = 2. The center is at (0, 3).

Step-by-step explanation:

Compare the given x ^ 2 + (y - 3) ^ 2 = 4 to the standard equation

(x - h)^2 + (y - k)^2 = r^2.

It becomes obvious that h = 0, k = 3 and r = 2. The center is at (0, 3).

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What is the oblique asymptote of the function f(x) = the quantity x squared plus 5x plus 6 over the quantity x plus 4?

Answers

Answer:

$x+1$

Step-by-step explanation:

A slant (oblique) asymptote occurs when the polynomial in the numerator is a higher degree than the polynomial in the denominator.

To find the slant asymptote you must divide the numerator by the denominator using either long division or synthetic division.

We are given a function:

$f(x)=(x^2+5x+6)/(x+4)$

Since in the given function the polynomial in the numerator is a higher degree than the polynomial in the denominator.

So, now to find oblique asymptote we will divide the numerator by the denominator

So, on dividing we get :

$f(x)=(x^2+5x+6)/(x+4)=x+1+\frac2{x+4}$ j

Now, As $x\to\pm\infty$ the remainder term disappears

So the oblique asymptote is the line $y=x+1$

Thus, the oblique asymptote of the function $f(x)=(x^2+5x+6)/(x+4)$ is $x+1$

$f(x)=(x^2+5x+6)/(x+4)=x+1+\frac2{x+4}$

As $x\to\pm\infty$ , the remainder term disappears, so the oblique asymptote is the line $y=x+1$ .

Factorise (x²+3x)²-3(x²+3x-4

Answers

Answer:x^4+6x^3+6x^2-9x+12

Step-by-step explanation:

What is the exact value of the trigonometric ratio of tan-240 degrees?

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Tan240=1.732050808
Tan^-1(240)=89.76126897

Write a variable expression that represents the word problem. Gisele gave d dimes and n nickles to her brother. Which expression represents the amount in dollars that Gisele gave to her brother?

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A variable expression is an equation made with variables, you are trying to find the total amount of money Gisele gave her brother. Let d be dimes, n be nickles, and y be the total dollar amount, y=n+b

The orginal price of a toy was $15 if the price is reduced by 20% what is the new price of the toy

Answers

It would be 20% off which is $3 so $12

Answer:

$12

Step-by-step explanation:

You have to find what is 20% of 15 which is 3, and then subtract 3 from from 15, which is 12. Real simple!

The speed of a body falling freely from rest in a vacuum varies directly with the length of the time it falls. If after 6 seconds, a body was falling 58.8 m/s, how fast was it falling 4 seconds later? (Round off your answer to the nearest meter per second.)

Answers

Answer:

The body is falling at 98 m/s after 4 seconds later.

Step-by-step explanation:

The magnitude of the speed of a body dropped from rest is:

$v = gt$

So, if the speed of a body dropped after 6 seconds is 58.8 m/s, after 4 seconds later is:

$v = gt = 9.81 m/s^(2)*(4s + 6s) = 98.1 m/s = 98 m/s$

Hence, the body is falling at 98 m/s after 4 seconds later.

I hope it helps you!

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