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3 years ago

Find the coordinates of the point P that lies

Mathematics

1 answer:

victus00 [196]3 years ago

5 0

The coordinates of point P are: (1/5 , -12/5)

Step-by-step explanation:

Here

R(-3,-4) = (x1,y1)

S(5,0) = (x2,y2)

The ratio is: 2:3

The coordinates of a point that divides the line in ratio m:n are given by:

Let P be the point then

$(x_P, y_P) = (\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

Putting values

$(x_P, y_P) = (\frac{(2)(5)+(3)(-3)}{2+3},\frac{(2)(0)+(3)(-4)}{2+3})\\= (\frac{10-9}{5},\frac{0-12}{5})\\=(\frac{1}{5},\frac{-12}{5})$

Hence,

The coordinates of point P are: (1/5 , -12/5)

Keywords: Coordinate geometry

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#LearnwithBrainly

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Simplify the expression below:<br> 4(n-3) - 2(-3 + x)

Margarita [4]

Answer:

4n-2x-6

Step-by-step explanation:

Let's simplify step-by-step.

4(n−3)−2(−3+x)

Distribute:

=(4)(n)+(4)(−3)+(−2)(−3)+(−2)(x)

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Combine Like Terms:

=4n+−12+6+−2x

=(4n)+(−2x)+(−12+6)

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Answer:

=4n−2x−6

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2 years ago

Which equation could represent a linear combination of the system?

Tems11 [23]

Answer:

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Step-by-step explanation:

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3 years ago

Find the slope of the line between the ordered pair (−1,4)and(4,−1) what is the answer??? please answer correctly

luda_lava [24]

9514 1404 393

Answer:

-1

Step-by-step explanation:

The slope formula works nicely for this.

m = (y2 -y1)/(x2 -x1)

m = (-1 -4)/(4 -(-1)) = -5/5 = -1

The slope of the line between the given points is -1.

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2 years ago

Lines m and p are perpendicular if the slope of line m is -3 what is the slope of line p

fenix001 [56]

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3 years ago

Please help with this Calculus questions

Triss [41]

Answer:

$\int_{0}^{1}\left( - \frac{3 u^{9}}{2} + \frac{2 u^{4}}{5} + 2 \right)du=\frac{193}{100}=1.93$ .

Step-by-step explanation:

To find $\int_{0}^{1}\left( - \frac{3 u^{9}}{2} + \frac{2 u^{4}}{5} + 2 \right)du$ .

First, calculate the corresponding indefinite integral:

Integrate term by term:

$\int{\left(- \frac{3 u^{9}}{2} + \frac{2 u^{4}}{5} + 2\right)d u}} =\int{2 d u} + \int{\frac{2 u^{4}}{5} d u} - \int{\frac{3 u^{9}}{2} d u}$

Apply the constant rule $\int c\, du = c u$

$\int{2 d u}} + \int{\frac{2 u^{4}}{5} d u} - \int{\frac{3 u^{9}}{2} d u} = {\left(2 u\right)} + \int{\frac{2 u^{4}}{5} d u} - \int{\frac{3 u^{9}}{2} d u}$

Apply the constant multiple rule $\int c f{\left(u \right)}\, du = c \int f{\left(u \right)}\, du$

$2 u - {\int{\frac{3 u^{9}}{2} d u}} + \int{\frac{2 u^{4}}{5} d u} = 2 u - {\left(\frac{3}{2} \int{u^{9} d u}\right)} + \left(\frac{2}{5} \int{u^{4} d u}\right)$

Apply the power rule $\int u^{n}\, du = \frac{u^{n + 1}}{n + 1}$

$2 u - \frac{3}{2} {\int{u^{9} d u}} + \frac{2}{5} {\int{u^{4} d u}}=2 u - \frac{3}{2} {\frac{u^{1 + 9}}{1 + 9}}+ \frac{2}{5}{\frac{u^{1 + 4}}{1 + 4}}$

Therefore,

$\int{\left(- \frac{3 u^{9}}{2} + \frac{2 u^{4}}{5} + 2\right)d u} = - \frac{3 u^{10}}{20} + \frac{2 u^{5}}{25} + 2 u = \frac{u}{100} \left(- 15 u^{9} + 8 u^{4} + 200\right)$

According to the Fundamental Theorem of Calculus, $\int_a^b F(x) dx=f(b)-f(a)$ , so just evaluate the integral at the endpoints, and that's the answer.

$\left(\frac{u}{100} \left(- 15 u^{9} + 8 u^{4} + 200\right)\right)|_{\left(u=1\right)}=\frac{193}{100}$

$\left(\frac{u}{100} \left(- 15 u^{9} + 8 u^{4} + 200\right)\right)|_{\left(u=0\right)}=0$

$\int_{0}^{1}\left( - \frac{3 u^{9}}{2} + \frac{2 u^{4}}{5} + 2 \right)du=\left(\frac{u}{100} \left(- 15 u^{9} + 8 u^{4} + 200\right)\right)|_{\left(u=1\right)}-\left(\frac{u}{100} \left(- 15 u^{9} + 8 u^{4} + 200\right)\right)|_{\left(u=0\right)}=\frac{193}{100}$

6 0

3 years ago