All categories

3 years ago

Find the distance between the points (-7, 5) and (4, 1).

Mathematics

2 answers:

Alla [95]3 years ago

8 0

2 because the square root is 12 and the distance is 12 units

anygoal [31]3 years ago

7 0

$\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ -7}}\quad ,&{{ 5}})\quad 
% (c,d)
&({{ 4}}\quad ,&{{ 1}})
\end{array}\qquad 
% distance value
d = \sqrt{({{ 4}}-{{ (-7)}})^2 + ({{ 1}}-{{ 5}})^2}
\\\\\\
d=\sqrt{(4+7)^2+(1-5)^2}$

You might be interested in

A box with a square base and open top must have a volume of 296352 c m 3 . We wish to find the dimensions of the box that minimi

mestny [16]

Answer:

Base Length of 84cm
Height of 42 cm.

Step-by-step explanation:

Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.

Step 1:

Let the side length of the base =x

Let the height of the box =h

Since the box has a square base

Volume, $V=x^2h=296352$

$h=\dfrac{296352}{x^2}$

Surface Area of the box = Base Area + Area of 4 sides

$A(x,h)=x^2+4xh\\$Substitute h=\dfrac{296352}{x^2}\\A(x)=x^2+4x\left(\dfrac{296352}{x^2}\right)\\A(x)=\dfrac{x^3+1185408}{x}$

Step 2: Find the derivative of A(x)

$If\:A(x)=\dfrac{x^3+1185408}{x}\\A'(x)=\dfrac{2x^3-1185408}{x^2}$

Step 3: Set A'(x)=0 and solve for x

$A'(x)=\dfrac{2x^3-1185408}{x^2}=0\\2x^3-1185408=0\\2x^3=1185408\\$Divide both sides by 2\\x^3=592704\\$Take the cube root of both sides\\x=\sqrt[3]{592704}\\x=84$

Step 4: Verify that x=84 is a minimum value

We use the second derivative test

$A''(x)=\dfrac{2x^3+2370816}{x^3}\\$When x=84$\\A''(x)=6$

Since the second derivative is positive at x=84, then it is a minimum point.

Recall:

$h=\dfrac{296352}{x^2}=\dfrac{296352}{84^2}=42$

Therefore, the dimensions that minimizes the box surface area are:

Base Length of 84cm
Height of 42 cm.

5 0

3 years ago

Al lives 30 mi. from Ann. At the same time, they start biking toward each other on the same road. Al’s constant rate is 12 mph.

dolphi86 [110]

C. 1.5 hours. divide 12 by 8, and you get 1.5.

4 0

3 years ago

Which element of variation would not be affected by adding the data value 15 to the data set {3, 5, 6, 8, 9, 10, 13, 14}

Andrei [34K]

It is 13,14 because it goes up two then one one then two again which will then mess up the rotation

8 0

3 years ago

What is the range of the function y = x 2?

garik1379 [7]

Answer:

The range of the function y = x2 is all real numbers, y, such that y ≥ 0. In the case of the function y = x2, the domain consists of all real numbers, because there is no number that, when plugged in for x into x2, would create an undefined expression.

Step-by-step explanation:

7 0

3 years ago

If he changed would you ever get back with him I think he truly means what he says he’s really hurt and always says he feels the

alukav5142 [94]

The answer is D. Angles 2 and 3

5 0

3 years ago