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2 years ago

Hello can you please help me with it I don't really understand this question

Mathematics

1 answer:

9966 [12]2 years ago

8 0

Answer:

see explanation

Step-by-step explanation:

solving the inequality

$\frac{x}{5}$ ≥ 8 ( multiply both sides by 5 to clear the fraction )

x ≥ 40

Then from the values given

39 → No

40 → Yes

41 → Yes

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Evaluate the expression 9P1

garri49 [273]

Answer :

Explanation :

The expression above signifies the Permutation expression

Permutation expression is given as nPr

The Permutation expression is calculated as:

nPr = P(n, r) = n! / (n - r)!

It the above question, we were asked to evaluate the expression 9P1

From the above question, we can see that:

n = 9 and r = 1

Therefore, the expression

9P1 = 9! / ( 9 - 1) !

9P1 = 9! / 8!

= 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 / 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 362880 /40320

= 9

Therefore, the evaluation of the expression 9P1 = 9

4 0

3 years ago

As the value of x increases, which of the following functions would eventually exceed to the other three?

MariettaO [177]

$x\ \ \ \ \ \ \ \ |\ \ \ \ \ 0\ \ \ \ |\ \ \ \ \ 1\ \ \ \ \ \ |\ \ \ \ \ 10 \ \ \ \ \ |\ \ \ \ \ \ 100\ \ \ \ \ \ |\\-----------------------\\1000x\ \ |\ \ \ \ 0\ \ \ \ \ |\ \ \ 1000\ \ \ | \ \ \ 10000 \ \ \ |\ \ \ \ 100000\ \ \ \ |\\-----------------------\\100x^2\ \ |\ \ \ \ 0\ \ \ \ \ |\ \ \ \ 100\ \ \ \ | \ \ \ 10000 \ \ \ |\ \ 1000000\ \ \ \ |\\-----------------------\\50x^3\ \ \ |\ \ \ \ 0\ \ \ \ \ |\ \ \ \ \ 50\ \ \ \ \ | \ \ \ 50000 \ \ \ |\ \ 50000000\ \ \ |\\-----------------------$
$2^x\ \ \ \ \ \ |\ \ \ \ 1\ \ \ \ \ |\ \ \ \ \ \ 2\ \ \ \ \ \ | \ \ \ \ 1024 \ \ \ |\ \ \ \ 1024^{10}\ \ \ \ \ |\\$

$if\ x\ \rightarrow\ +\infty\ \ \ then$

$f_1(x)\$

6 0

4 years ago

The diameter of each wheel of a bicycle is 26 inches. If you traveling at a speed of 35 miles per hour on this bicycle, through

krek1111 [17]

Answer:

452.49 rev/min

Step-by-step explanation:

The circumference of the wheel is pi times the diameter. The rest is units conversion.

$35\dfrac{mi}{h}=\dfrac{35\,mi}{1\,h}\cdot\dfrac{1\,h}{60\,min}\cdot\dfrac{5280\,ft}{1\,mi}\cdot\dfrac{12\,in}{1\,ft}\cdot\dfrac{1\,rev}{26\pi\,in}\\\\=\dfrac{35\cdot 5280\cdot 12}{60\cdot 26\pi}\cdot\dfrac{rev}{min}\approx\dfrac{452.49\,rev}{min}$

7 0

3 years ago

What is the slope of the line that passes through the points (3,8) and (8,13) write the answer in simplest form

qwelly [4]

Answer: y=5

X=5

5/5 or 1

Step-by-step explanation:

4 0

3 years ago

How to do question 1?Had no idea how to do both parts

givi [52]

$y=\dfrac{\ln x}{3x-6}$

Differentiate both sides with respect to $x$ :

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{3x-6}x-3\ln x}{(3x-6)^2}$

When $x=1$ , you have

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{3-6}1-3\ln1}{(3-6)^2}=\dfrac{-3}9=-\dfrac13$

For part (b), we now assume that $x$ and $y$ are functions of an independent variable, which we'll call $t$ (for time). Now differentiating both sides with respect to $t$ , we have

$\dfrac{\mathrm dy}{\mathrm dt}=\dfrac{\frac{3x-6}x-3\ln x}{(3x-6)^2}\dfrac{\mathrm dx}{\mathrm dt}$

where the chain rule is used on the right side. We're told that $y$ is decreasing at a constant rate of 0.1 units/second, which translates to $\dfrac{\mathrm dy}{\mathrm dt}=-0.1$ . So when $x=1$ , you have

$-0.1=\dfrac{\frac{3-6}1-3\ln1}{(3-6)^2}\dfrac{\mathrm dx}{\mathrm dt}$
$-0.1=-\dfrac13\dfrac{\mathrm dx}{\mathrm dt}$
$\dfrac{\mathrm dx}{\mathrm dt}=0.3$

where the unit is again units/second.

6 0

3 years ago