All categories

3 years ago

Find the coordinats of P

Mathematics

1 answer:

Crazy boy [7]3 years ago

5 0

$\textit{internal division of a line segment using ratios} \\\\\\ A(8,6)\qquad B(-2,-9)\qquad \qquad \stackrel{\textit{ratio from A to B}}{3:2} \\\\\\ \cfrac{A\underline{P}}{\underline{P} B} = \cfrac{3}{2}\implies \cfrac{A}{B} = \cfrac{3}{2}\implies 2A=3B\implies 2(8,6)=3(-2,-9)$

$(\stackrel{x}{16}~~,~~ \stackrel{y}{12})=(\stackrel{x}{-6}~~,~~ \stackrel{y}{-27})\implies P=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{16-6}}{3+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{12-27}}{3+2} \right)} \\\\\\ P=\left( \cfrac{10}{5}~~,~~\cfrac{-15}{5} \right)\implies P=(2~~,~~-3)$

You might be interested in

What’s number 1? Please help

Viktor [21]

Answer:

Line XY is a line
Distance XY is the length between the two letters.

Step-by-step explanation:

When there's a line over two letters, that is a line.
When there's nothing above the two letters. it is the length between the two points on the line.

Be very careful with these two meanings.

6 0

3 years ago

Andy is building a model of a square pyramid for a class project. The side length of the square base is 11 inches and the slant

zvonat [6]

Answer:

The answer is 792.

Step-by-step explanation:

I got the answer by first imagining how the 3d shape looks ike. Since one of the sqaure base length is 11 I found the base surface area by doing 11 times 11.My answer was 132. The since one of the slant length of the pyramid's triangle is 15, I did 11 times 15, my answer was 165. There are four triangles in the pyramid so I did 165 times 4, my answer was 660.

All the triangle surface area is 660 plus the sqaure surface are which is 132, that gave me my answer 792.

4 0

4 years ago

Verify by direct substitution that the given power series is a solution of the indicated differential equation. [Hint: For a pow

shepuryov [24]

Answer:

The given power series $y =\sum^{\infty}_{n=0} {(-1)^n x^{2n}}$ is a solution of the differential equation (1+x^2)y' + 2xy = 0

Step-by-step explanation:

This is a very trivial exercise, follow the steps below for the solution:

Step 1: Since n = 0, 1, 2, 3, 4, ........, Substitute the values of n into equation (1) below.

$y =\sum^{\infty}_{n=0} {(-1)^n x^{2n}}$ .....................(1)

$y = 1 - x^2 + x^4 - x^6 + x^8.........$

Step 2: Find the derivative of y, i.e. y'

$y' = -2x + 4x^3 - 6x^5 + 8x^7 .............$

Step 3: Substitute y and y' into equation (2) below:

$(1+x^2)y' + 2xy = 0\\\\(1+x^2)(-2x + 4x^3 - 6x^5 + 8x^7......) + 2x(1 - x^2 + x^4 - x^6 + x^8.......) = 0\\\\-2x+ 4x^3 - 6x^5 + 8x^7........ - 2x^3 +4x^5 - 6x^7 + 8x^9 ......+ 2x - 2x^3 + 2x^5 - 2x^7 + 2x^9...... = 0\\\\0 = 0$

(Verified)

Since the LHS = RHS = 0, the given power series $y =\sum^{\infty}_{n=0} {(-1)^n x^{2n}}$ is a solution of the differential equation (1+x^2)y' + 2xy = 0

6 0

3 years ago

What 2v + 42.? What is the answer

seraphim [82]

Before 1901 Australia was ruled by the

5 0

3 years ago

What is the distance between (8,-3) and (4,-7)?

Scrat [10]

Answer:

4√ 2 ≈5.66 to 2 dec. places

Step-by-step explanation: