All categories

3 years ago

According to the graph, what is the value of the constant in the equation

Mathematics

1 answer:

love history [14]3 years ago

7 0

Answer:

The value of the constant is 3

Step-by-step explanation:

Let

y ----> the height

x ----> the width

we have

$y=kx$

This is the equation of a linear direct variation

The equation of the line passes through the origin

we have the points

(0.5,1.5), (2,6) and (3,9)

see the attached figure to better understand the problem

Find the value of the constant of proportionality k

$k=\frac{y}{x}$

For (0.5,1.5) ----> $k=\frac{1.5}{0.5}=3$

For (2,6) ----> $k=\frac{6}{2}=3$

For (3,9) ----> $k=\frac{9}{3}=3$

therefore

The value of k is equal to 3

The linear equation is

$y=3x$

$Height=3Width$

You might be interested in

What role do animals have in the carbon cycle?

dangina [55]

I believe it is use sugar and and release carbon. We breath in oxygen so you know it can’t be anything where we release oxygen. And I don’t know how we could release nitrogen so I would go with the second one

4 0

2 years ago

Read 2 more answers

A student finished 72 of her homework problems in class. If the ratio of problems she finished to problems she still had left wa

kramer

Finished:Left

8:1

8/1 = 72/x

Cross Multiply

8x=72

divide each side by 8

x=9

She already finished 72 and has 9 remaining

Total = Finished + Remaining = 72 + 9 = 81

4 0

2 years ago

Question 5: prove that it’s =0

mamaluj [8]

Answer:

Proof in explanation.

Step-by-step explanation:

I'm going to attempt this by squeeze theorem.

We know that $\cos(\frac{2}{x})$ is a variable number between -1 and 1 (inclusive).

This means that $-1 \le \cos(\frac{2}{x}) \le 1$ .

$x^4 \ge 0$ for all value $x$ . So if we multiply all sides of our inequality by this, it will not effect the direction of the inequalities.

$-x^4 \le x^4 \cos(\frac{2}{x}) \le x^4$

By squeeze theorem, if $-x^4 \le x^4 \cos(\frac{2}{x}) \le x^4$

and $\lim_{x \rightarrow 0}-x^4=\lim_{x \rightarrow 0}x^4=L$ , then we can also conclude that $\im_{x \rightarrow} x^4\cos(\frac{2}{x})=L$ .

So we can actually evaluate the "if" limits pretty easily since both are continuous and exist at $x=0$ .

$\lim_{x \rightarrow 0}x^4=0^4=0$

$\lim_{x \rightarrow 0}-x^4=-0^4=-0=0$ .

We can finally conclude that $\lim_{\rightarrow 0}x^4\cos(\frac{2}{x})=0$ by squeeze theorem.

Some people call this sandwich theorem.

6 0

3 years ago

The mean length of 5 childrens' index finger is 5.6cm.

Brilliant_brown [7]

The mean length (rounded to 2 DP) of these 8 people's index finger is 5.83

<h3>What is the mean length (rounded to 2 DP) of these 8 people's index finger?</h3>

The given parameters are:

<u>Children</u>

Mean = 5.6 cm

Frequency = 5

<u>Adult</u>

Mean = 6.2 cm

Frequency = 3

The mean length of these 8 people's index finger is calculated as:

$\bar x = \frac{\sum fx}{\sum f}$

So, we have

Mean = (5.6 * 5 + 6.2 * 3)/(5 + 3)

Evaluate

Mean = 5.83

Hence, the mean length (rounded to 2 DP) of these 8 people's index finger is 5.83