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3 years ago

Given f(x) = 1/4 (5-x)^2 what is the value of f(11)

Mathematics

1 answer:

kupik [55]3 years ago

7 0

Answer:

Step-by-step explanation:

f(11) means that x = 11 (plug it in)

f(11) = 1/4(5-11)^2

= 9

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Let P and Q be polynomials with positive coefficients. Consider the limit below. lim x→[infinity] P(x) Q(x) (a) Find the limit i

jenyasd209 [6]

Answer:

If the limit that you want to find is $\lim_{x\to \infty}\dfrac{P(x)}{Q(x)}$ then you can use the following proof.

Step-by-step explanation:

Let $P(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{1}x+a_{0}$ and $Q(x)=b_{m}x^{m}+b_{m-1}x^{n-1}+\cdots+b_{1}x+b_{0}$ be the given polinomials. Then

$\dfrac{P(x)}{Q(x)}=\dfrac{x^{n}(a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)}+a_{0}x^{-n})}{x^{m}(b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m})}=x^{n-m}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)})+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}$

Observe that

$\lim_{x\to \infty}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)})+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}=\dfrac{a_{n}}{b_{m}}$

and

$\lim_{x\to \infty} x^{n-m}=\begin{cases}0& \text{if}\,\, nm\end{cases}$

Then

$\lim_{x\to \infty}=\lim_{x\to \infty}x^{n-m}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)}+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}=\begin{cases}0 & \text{if}\,\, nm \end{cases}$

3 0

3 years ago

N is an integer.<br>Write the values of n such that -15 < 3 < 6

Thepotemich [5.8K]

Answer:

Step-by-step explanation:

n could be : -14, -13, -12... -1, 0 , 1, 2, 3 ,4,5

3 0

3 years ago

∠CAT and ∠MUD are supplementary. If m∠CAT=11x+16 and m∠MUD=4x+14, find the measure of each angle.

Georgia [21]

Answers:

x = 10
angle CAT = 126 degrees
angle MUD = 54 degrees

=========================================================

Explanation:

∠CAT and ∠MUD are supplementary, which means the angle measures add to 180. They form a straight line.

( m∠CAT ) + ( m∠MUD ) = 180

( 11x+16 ) + ( 4x+14 ) = 180

11x+16 + 4x+14 = 180

(11x+4x) + (16+14) = 180

15x+30 = 180

15x = 180-30

15x = 150

x = 150/15

x = 10

Let's find each angle based on this x value

m∠CAT=11x+16 = 11*10+16 = 110+16 = 126 degrees
m∠MUD=4x+14 = 4*10+14 = 40+14 = 54 degrees

Those two angles add to 126+54 = 180 to confirm we do indeed have supplementary angles, and confirm the correct answers.

8 0

2 years ago

10|x+8| - 13 = -2|x+8|+11

PilotLPTM [1.2K]

Use the app Socratic

4 0

3 years ago

Solve for x. 7^8=7^8×7^x

denis-greek [22]

Answer:

x = 0

Step-by-step explanation:

Apply the exponent rule.

$7^8=7^{x+8} \\$

If $a^{f(x)} = a^{g(x)} then f(x) = g(x)$

8 = x + 8

x = 0

3 0

3 years ago