All categories

3 years ago

Given line segment AB, the coordinates of A are (3,-5) and the coordinates midpoint are (5,-1), what are the coordinates for B?

Mathematics

1 answer:

dsp733 years ago

6 0

Answer:

Step-by-step explanation:

Point P(5, -1) being the midpoint of AB means that $x_P-x_A=x_B-x_P$

$5-3=x_B-5\\\\2+5=x_B\\\\x_B=7$

and $y_P-y_A=y_B-y_P$

$-1-(-5)=y_B-(-1)\\\\-1+5=y_B+1\\\\y_B=3$

You might be interested in

Use the general slicing method to find the volume of the following solids. The solid whose base is the region bounded by the cur

Y_Kistochka [10]

Answer:

The volume is $V=\frac{64}{15}$

Step-by-step explanation:

The General Slicing Method is given by

<em>Suppose a solid object extends from x = a to x = b and the cross section of the solid perpendicular to the x-axis has an area given by a function A that is integrable on [a, b]. The volume of the solid is</em>

$V=\int\limits^b_a {A(x)} \, dx$

Because a typical cross section perpendicular to the x-axis is a square disk (according with the graph below), the area of a cross section is

The key observation is that the width is the distance between the upper bounding curve $y = 2 - x^2$ and the lower bounding curve $y = x^2$

The width of each square is given by

$w=(2-x^2)-x^2=2-2x^2$

This means that the area of the square cross section at the point x is

$A(x)=(2-2x^2)^2$

The intersection points of the two bounding curves satisfy $2 - x^2=x^2$ , which has solutions x = ±1.

$2-x^2=x^2\\-2x^2=-2\\\frac{-2x^2}{-2}=\frac{-2}{-2}\\x^2=1\\\\x=\sqrt{1},\:x=-\sqrt{1}$

Therefore, the cross sections lie between x = -1 and x = 1. Integrating the cross-sectional areas, the volume of the solid is

$V=\int\limits^{1}_{-1} {(2-2x^2)^2} \, dx\\\\V=\int _{-1}^14-8x^2+4x^4dx\\\\V=\int _{-1}^14dx-\int _{-1}^18x^2dx+\int _{-1}^14x^4dx\\\\V=\left[4x\right]^1_{-1}-8\left[\frac{x^3}{3}\right]^1_{-1}+4\left[\frac{x^5}{5}\right]^1_{-1}\\\\V=8-\frac{16}{3}+\frac{8}{5}\\\\V=\frac{64}{15}$

5 0

3 years ago

Use the functions f(x) = 4x − 5 and g(x) = 3x + 9 to complete the function operations listed below.

vlada-n [284]

A. (f + g)(x) = f(x) + g(x) = 4x - 5 + 3x + 9 = 7x + 4

B. f.g (x) = f(x) * g(x) = (4x - 5)*(3x + 9) = 12x^2 + 36x - 15x - 45
= 12x^2 + 21x - 45

C Replace the x in f(x) by g(x):-
= 4(3x + 9) - 5
= 12x + 36 - 5
= 12x + 31

8 0

3 years ago

2. What's the position of 9 in the number 932,805?

Sergio039 [100]

It is 900,000 it is in the hundreds thousandths place.

4 0

3 years ago

Read 2 more answers

Please help thank you

worty [1.4K]

Answer:

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.

7 0

3 years ago

Manny made 4 pizzas to share among himself and 6 friends How much pizza will each person get? Well reread the question and ask y

Assoli18 [71]

....... shouldn't that be a question instead of an answer? Well, I guess it is what it is, and I understand it thx anyways. (=^\/^=)

6 0

3 years ago

Read 2 more answers