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2 years ago

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What happens to the value of the expression \dfrac{10}{d} d 10 start fraction, 10, divided by, d, end fraction as ddd increase

s from a small positive number to a large positive number?

1 answer:

pishuonlain [190]2 years ago

8 0

Answer:

The quotient decreases

Step-by-step explanation:

Give the expression :

10 / d

What happens to the expression as d increases. from small positive to large positive ;

d in the expression is the denominator ;the value obtained by dividing the numerator by the denominator is the quotient.

Since the value of the numerator is constant ;

As the value of d increases, the quotient obtained becomes smaller `

For instance,

Let

d = 2;

10 /2 = 5

d = 3

10 / 3 = 3.333

d = 4

10 / 4 = 2.5

And the trend continues

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F(x)=3x 2 +9f, left parenthesis, x, right parenthesis, equals, 3, x, squared, plus, 9 and g(x)=\dfrac{1}{3}x^2-9g(x)= 3 1 x 2

34kurt

Answer:

$f(g(x)) = \frac{1}{3}x^4 - 18x^2 + 252$

$g(f(x)) = 3x^4 + 18x^2 + 18$

<em>f(x) and g(x) and not inverse functions</em>

Step-by-step explanation:

Given

$f(x) = 3x^2 + 9$

$g(x) = \dfrac{1}{3}x^2 - 9$

Required

Determine f(g(x))

Determine g(f(x))

Determine if both functions are inverse:

Calculating f(g(x))

$f(x) = 3x^2 + 9$

$f(g(x)) = 3(\frac{1}{3}x^2 - 9)^2 + 9$

$f(g(x)) = 3(\frac{1}{3}x^2 - 9)(\frac{1}{3}x^2 - 9) + 9$

Expand Brackets

$f(g(x)) = (x^2 - 27)(\frac{1}{3}x^2 - 9) + 9$

$f(g(x)) = x^2(\frac{1}{3}x^2 - 9) - 27(\frac{1}{3}x^2 - 9) + 9$

$f(g(x)) = \frac{1}{3}x^4 - 9x^2 - 9x^2 + 243 + 9$

$f(g(x)) = \frac{1}{3}x^4 - 18x^2 + 252$

Calculating g(f(x))

$g(x) = \dfrac{1}{3}x^2 - 9$

$g(f(x)) = \frac{1}{3}(3x^2 + 9)^2 - 9$

$g(f(x)) = \frac{1}{3}(3x^2 + 9)(3x^2 + 9) - 9$

$g(f(x)) = (x^2 + 3)(3x^2 + 9) - 9$

Expand Brackets

$g(f(x)) = x^2(3x^2 + 9) + 3(3x^2 + 9) - 9$

$g(f(x)) = 3x^4 + 9x^2 + 9x^2 + 27 - 9$

$g(f(x)) = 3x^4 + 18x^2 + 18$

Checking for inverse functions

$f(x) = 3x^2 + 9$

Represent f(x) with y

$y = 3x^2 + 9$

Swap positions of x and y

$x = 3y^2 + 9$

Subtract 9 from both sides

$x - 9 = 3y^2 + 9 - 9$

$x - 9 = 3y^2$

$3y^2 = x - 9$

Divide through by 3

$\frac{3y^2}{3} = \frac{x}{3} - \frac{9}{3}$

$y^2 = \frac{x}{3} - 3$

Take square root of both sides

$\sqrt{y^2} = \sqrt{\frac{x}{3} - 3}$

$y = \sqrt{\frac{x}{3} - 3}$

Represent y with g(x)

$g(x) = \sqrt{\frac{x}{3} - 3}$

Note that the resulting value of g(x) is not the same as $g(x) = \dfrac{1}{3}x^2 - 9$

<em>Hence, f(x) and g(x) and not inverse functions</em>

4 0

2 years ago

Here is the histogram of a data distribution. All class widths are 1. What is the median of this distribution?

Bingel [31]

Answer:

The median is 4.

Step-by-step explanation

if you layout all the number, you get

1,2,2,3,3,3,4,5,5,5,6,6,7

So, to find the median you find the number(s) right in the middle.

(Ex. 3,4,5; 4 is the median)

(Ex. 3,4,5,7; 4.5 is the answer)

The middle number of

1,2,2,3,3,3,4,5,5,5,6,6,7

is 4, so 4 is the median.

hope this helps. :)

6 0

2 years ago

A track and field coach wants to analyze the effect of sports drinks on the performance of his athletes. He decides to test thre

balu736 [363]

Answer:

Different timings for drinking before the run can decrease the accuracy of the outcome.

But different drinks for different people before a single run can ruin the experiment causing usless result. Effect of different sports drink on athletes can not be measured accurately.

6 0

2 years ago

An up-and-coming artist has 85 followers on Twitter and this number doubles every week. In what week will the artist first reach

Alik [6]

Answer:

5.8 , which approximately is 6 weeks.

Step-by-step explanation:

the first method is the short one since u just have to double the 85 then divide to 1000.

1000 ÷ ( 85 × 2)

1000 ÷ 170 = 5.882,,,,,. round off to whole number to get 6.

the second method is the addition method.

we start by 85 then keep doubling 85 for every week........inshort.......we add 170 to each weeks number to get the number of followers for the following week.

85 ⇒ 170 ⇒ 340 ⇒ 510 ⇒ 680 ⇒ 850 ⇒ 1020.

1st 2nd 3rd 4th 5th 6th week.

u notice that we add (85×2), 170, to get the following week's number of followers..

in 5 weeks..... the number of followers is yet to get to 1000.

when u divide, u get 5.8.....,and it is not logic to say 5.8823....weeks

since she reaches 1000 followers in the 6th week.......though there is an addition,,,, it is the most appropriate answer.

3 0

2 years ago

For the function f(t) = Pe^rt, if P= 6 and r = 0.06, then what is the value of f(6) to the nearest tenth? A. 219.6 B. 8.6 C. 0.1

Ann [662]

<span>B. 8.6 Let's substitute the given values into the function and calculate the result. So: f(t) = Pe^rt f(t) = 6e^0.06t f(6) = 6e^(0.06*6) f(6) = 6e^(0.36) f(6) = 6*1.433329415 f(6) = 8.599976487 Rounding to the nearest tenth, gives: 8.6 So the answer is "B. 8.6"</span>

7 0

2 years ago