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1 year ago

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Mathematics

1 answer:

tensa zangetsu [6.8K]1 year ago

8 0

Answer:

Step-by-step explanation:

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If f(x) = V7x + 31 , find f(0).

Arte-miy333 [17]

Answer:

f(0) = 31

Step-by-step explanation:

We are given the following function:

$f(x) = \sqrt{7x} + 31$

f(0).

This is the value of f when $x = 0$ . So

$f(0) = \sqrt{7*0} + 31 = \sqrt{0} + 31 = 0 + 31 = 31$

So f(0) = 31

3 0

3 years ago

Find out the number of combinations and the number of permutations for 8 objects taken 6 at a time. Express your answer in exact

umka2103 [35]

Solution:

The permutation formula is expressed as

$\begin{gathered} P^n_r=\frac{n!}{(n-r)!} \\ \end{gathered}$

The combination formula is expressed as

$\begin{gathered} C^n_r=\frac{n!}{(n-r)!r!} \\ \\ \end{gathered}$

where

$\begin{gathered} n\Rightarrow total\text{ number of objects} \\ r\Rightarrow number\text{ of object selected} \end{gathered}$

Given that 6 objects are taken at a time from 8, this implies that

$\begin{gathered} n=8 \\ r=6 \end{gathered}$

Thus,

Number of permuations:

$\begin{gathered} P^8_6=\frac{8!}{(8-6)!} \\ =\frac{8!}{2!}=\frac{8\times7\times6\times5\times4\times3\times2!}{2!} \\ 2!\text{ cancel out, thus we have} \\ \begin{equation*} 8\times7\times6\times5\times4\times3 \end{equation*} \\ \Rightarrow P_6^8=20160 \end{gathered}$

Number of combinations:

$\begin{gathered} C^8_6=\frac{8!}{(8-6)!6!} \\ =\frac{8!}{2!\times6!}=\frac{8\times7\times6!}{6!\times2\times1} \\ 6!\text{ cancel out, thus we have} \\ \frac{8\times7}{2} \\ \Rightarrow C_6^8=28 \end{gathered}$

Hence, there are 28 combinations and 20160 permutations.

7 0

1 year ago

What is your estimate for the number of airline flights in a year?

Firdavs [7]

The answer is between 45,000,000-65,000,000

8 0

3 years ago

Find the average rate of change of f(x)=2x^2-7x from x=2 to x=5

m_a_m_a [10]

Answer:

Step-by-step explanation:

The average rate of change of f(x) in the close interval [ a, b ] is

$\frac{f(b)-f(a)}{b-a}$

Here [ a, b ] = [2, 5 ]

f(b) = f(5) = 2(5)² - 7(5) = 50 - 35 = 15

f(a) = f(2) = 2(2)² - 7(2) = 8 - 14 = - 6, thus

average rate of change = $\frac{15-(-6)}{5-2}$ = $\frac{21}{3}$ = 7

3 0

3 years ago

Which of the following is a linear function?

Rama09 [41]

$\boxed{ \textbf{ \huge{Answer: A}}}$

A linear function has 1 as the highest power of the variable.

A. f(x) = 2 - 7x

here, the highest power of the variable x is 1.
Hence it is a LINEAR function.
___________

B. f(x) = 2 + x + x^2

here, the highest power of the variable x is 2.
Hence it is NOT a linear function.
_______________

$c.f(x) = \sqrt{2 + 7x}$
here, the highest power of the variable x is 1/2.
Hence it is NOT a linear function.
________________

6 0

2 years ago