Ask question

Ask question

All categories

2 years ago

13

What is the length of the segment whose endpoints are A(4, –3) and B(10, 6)?

1 answer:

sineoko [7]2 years ago

7 0

$\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
A&({{ 4}}\quad ,&{{ -3}})\quad 
% (c,d)
B&({{ 10}}\quad ,&{{ 6}})
\end{array}\quad 
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
d=\sqrt{[10-4]^2+[6-(-3)]^2}\implies d=\sqrt{[10-4]^2+[6+3]^2}$

You might be interested in

A circular pizza that is 18 inches in diameter is cut into 7 equal slices. What is the area of a single slice?

KiRa [710]

Answer:

2.5 in

Step-by-step explanation:

6 0

1 year ago

Pam has 90 m of fencing to enclose an area in a petting zoo with two dividers to separate three types of young animals. The thre

andrew-mc [135]

Answer:

The area function is

$A=\frac{135}{2}x-\frac{9}{2}x^2$ .

The domain and range of A is $(0,15m)$ and $(0, 253.125 m^2]$ .

Step-by-step explanation:

The given length of fencing is $90 m$ .

Let the length and width of each pen be $x$ and $y$ respectively as shown in the figure.

As there are 3 pens, so, the total area,

$A= 3 xy \;\cdots (i)$

From the figure the total length of fencing is $6x+4y$ .

Here, for a significant area for the animals, $x>0$ as well as $y>0$ as $x$ and $y$ are the sides of ben.

From the given value:

$6x+4y=90\;\cdots (ii)$

$\Rightarrow y=\frac {45}{2}-\frac{3x}{2}$

Now, from equation (i)

$A=3x\left(\frac {45}{2}-\frac{3x}{2}\right)$

$\Rightarrow A=\frac{135}{2}x-\frac{9}{2}x^2\;\cdots (iii)$

This is the required area function in the terms of variable $x$ .

For the domain of area function, from equation (ii)

$x=15-\frac{2y}{3}$

$\Rightarrow x$ [as y>0]

So, the domain of area function is $(0,15m)$ .

For the range of area function:

As $x \rightarrow 0$ or $y\rightarrow 0$ , then $A\rightarrow 0$ [from equation (i)]

$\Rightarrow A>0$

Now, differentiate the area function with respect to $x$ .

$\frac {dA}{dx}=\frac{135}{2}-9x$

Equate $\frac {dA}{dx}$ to zero to get the extremum point.

$\frac {dA}{dx}=0$

$\Rightarrow \frac{135}{2}-9x=0$

$\Rightarrow x=\frac{15}{2}$

Check this point by double differentiation

$\frac {d^2A}{dx^2}=-9$

As, $\frac {d^2A}{dx^2}$ , so, point $x=\frac{15}{2}$ is corresponding to maxima.

Put this value back to equation (iii) to get the maximum value of area function. We have

$A=\frac{135}{2}\times \frac {15}{2}-\frac{9}{2}\times \left(\frac {15}{2}\right)^2$

$\Rightarrow A=253.125 m^2$

Hence, the range of area function is $(0, 253.125 m^2]$ .

4 0

2 years ago

How can you use a quick picture to find 3 times 2.7

snow_tiger [21]

3x2.7=8.1,,, im not sure this is what you were asking for but i hope it helps

XoXo

5 0

2 years ago

Read 2 more answers

Which of the following equations represents the graph shown?

Sonja [21]

Answer:

It's the first one. -x+2

Step-by-step explanation:

The slope is negative and the line intersects the y-intercept at positive 2.

5 0

2 years ago

Read 2 more answers

Triangle XY Z is similar to triangle ABC.

garri49 [273]

Answer:

13.5

Step-by-step explanation:

12/4=3

9/3=3

4.5x3=13.5

8 0

1 year ago

Read 2 more answers