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3 years ago

Find the coordinates of the point P that divides the directed line segment from A to B in the given ratio.

Mathematics

1 answer:

VladimirAG [237]3 years ago

7 0

Answer:

P ( -1, -3)

Step-by-step explanation:

Given ratio is AP : PB = 3 : 2 = m : n and points A(5,6) B(-5,-9)

We will calculate coordinates of the point P which divides line segment AB

in the following way:

xp = (n · xa + m · xb) / (m+n) = (2 · 5 + 3 · (-5)) / (3+2) = (10-15) / 5 = -5/5 = -1

xp = -1

yp = (n · ya + m · yb) / (m+n) = (2 · 6 + 3 · (-9)) / (3+2) = (12-27) / 5 = -15/5 = -3

yp = -3

Point P( -1, -3)

God with you!!!

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2 years ago

Let f(x)=x+a/x+b such that f(f(1)=0 & f(2)=-3 then a&b resctivily are.

Yuliya22 [10]

Answer:

The value of a = - 1 , And b = $\frac{ - 7 }{3}$

Step-by-step explanation:

Given as :

Function f(x) = $\frac{(x + a)}{(x + b)}$

And f(f(1)) = 0 And f(2) = - 3

Now For , x = 2 , y = - 3

I.e f(2) = $\frac{(2 + a)}{(2 + b)}$

or, - 3 = $\frac{(2 + a)}{(2 + b)}$

I.e 2 + a = - 6 - 3b

Or, a + 3b = - 8 ....... 1

Again f(f(1)) = 0

So, $\frac{(1 + a)}{(1 + b)}$ = 0

Or, 1 + a = 0

∴ a = - 1

So , put htis value of a i n eq 1 , we get value of b

So , - 1 + 3b = - 8

Or, 3b = - 7

∴ b = $\frac{ - 7 }{3}$

Hence The value of a = - 1 , And b = $\frac{ - 7 }{3}$ Answer

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2 years ago

Piper deposited $734.62 in a savings account that earns 2.6% simple interest. What is Piper’s account balance after seven years?

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3 years ago

Read 2 more answers

a rectangle has a perimeter of 3o inches and a width of 6 inches what are the dimensions of a similar rectangle with a perimeter

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2 years ago

Find sin theta if theta is an angle in standard position and the point with coordinates (3, -4) lies on the terminal side of an

alisha [4.7K]

Answer:

$\sin \theta=-\frac{4}{5}$

Step-by-step explanation:

Given:

Angle is in standard position which means the starting ray is at the origin. The terminal side has coordinates (3, -4).

So, the 'x' value is 3 and 'y' value id -4.

Using Pythagoras Theorem, we find the hypotenuse.

Hypotenuse = $\sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5$

Now, using the sine ratio for the angle, we have

$\sin \theta=\frac{Opposite}{Hypotenuse}\\\sin \theta=\frac{-4}{5}\\\sin \theta=-\frac{4}{5}$

Therefore, the value of $\sin \theta$ is $-\frac{4}{5}$ .

The value is negative as the point (3, -4) lies in the fourth quadrant and sine ratio is negative in the fourth quadrant,

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2 years ago