Solve for X on both please:)

What is the ratio in which the point P(3/4,5/12) decides the line segment joining points A(1/2,3/2) and B(2,-5)

timama [110]

Given:

The point $P\left(\dfrac{3}{4},\dfrac{5}{12}\right)$ divides the line segment joining points $A\left(\dfrac{1}{2},\dfrac{3}{2}\right)$ and $B(2,-5)$ .

To find:

The ratio in which he point P divides the segment AB.

Solution:

Section formula: If a point divides a segment in m:n, then the coordinates of that point are,

$Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

Let point P divides the segment AB in m:n. Then by using the section formula, we get

$\left(\dfrac{3}{4},\dfrac{5}{12}\right)=\left(\dfrac{m(2)+n(\dfrac{1}{2})}{m+n},\dfrac{m(-5)+n(\dfrac{3}{2})}{m+n}\right)$

$\left(\dfrac{3}{4},\dfrac{5}{12}\right)=\left(\dfrac{2m+\dfrac{n}{2}}{m+n},\dfrac{-5m+\dfrac{3n}{2}}{m+n}\right)$

On comparing both sides, we get

$\dfrac{3}{4}=\dfrac{2m+\dfrac{n}{2}}{m+n}$

$\dfrac{3}{4}(m+n)=\dfrac{4m+n}{2}$

Multiply both sides by 4.

$3(m+n)=2(4m+n)$

$3m+3n=8m+2n$

$3n-2n=8m-3m$

$n=5m$

It can be written as

$\dfrac{1}{5}=\dfrac{m}{n}$

$1:5=m:n$

Therefore, the point P divides the line segment AB in 1:5.

6 0

3 years ago

*WILL GIVE BRAINLIEST*

tia_tia [17]

Answer:

c. is the answer

Step-by-step explanation:

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3 0

3 years ago

Suppose that a spherical droplet of liquid evaporates at a rate that is proportional to its surface area: where V = volume (mm3

Alex

Answer:

V = 20.2969 mm^3 @ t = 10

r = 1.692 mm @ t = 10

Step-by-step explanation:

The solution to the first order ordinary differential equation:

$\frac{dV}{dt} = -kA$

Using Euler's method

$\frac{dVi}{dt} = -k *4pi*r^2_{i} = -k *4pi*(\frac {3 V_{i} }{4pi})^(2/3)\\ V_{i+1} = V'_{i} *h + V_{i} \\$

Where initial droplet volume is:

$V(0) = \frac{4pi}{3} * r(0)^3 = \frac{4pi}{3} * 2.5^3 = 65.45 mm^3$

Hence, the iterative solution will be as next:

i = 1, ti = 0, Vi = 65.45

$V'_{i} = -k *4pi*(\frac{3*65.45}{4pi})^(2/3) = -6.283\\V_{i+1} = 65.45-6.283*0.25 = 63.88$

i = 2, ti = 0.5, Vi = 63.88

$V'_{i} = -k *4pi*(\frac{3*63.88}{4pi})^(2/3) = -6.182\\V_{i+1} = 63.88-6.182*0.25 = 62.33$

i = 3, ti = 1, Vi = 62.33

$V'_{i} = -k *4pi*(\frac{3*62.33}{4pi})^(2/3) = -6.082\\V_{i+1} = 62.33-6.082*0.25 = 60.813$

We compute the next iterations in MATLAB (see attachment)

Volume @ t = 10 is = 20.2969

The droplet radius at t=10 mins

$r(10) = (\frac{3*20.2969}{4pi})^(2/3) = 1.692 mm\\$

The average change of droplet radius with time is:

Δr/Δt = $\frac{r(10) - r(0)}{10-0} = \frac{1.692 - 2.5}{10} = -0.0808 mm/min$

The value of the evaporation rate is close the value of k = 0.08 mm/min

Hence, the results are accurate and consistent!

5 0

4 years ago

Brendan bought an iced tea that cost $4.06 plus 7% sales tax. If Brendan left an 18% tip on the $4.06, how much in total did he

ahrayia [7]

Answer:

Step-by-step explanation:

18% tip in $=18/100 * $4.06

$0.7308

7% sales tax in $= 7/100 * $4.06

$0.2842

Total amount he paid= $0.7308+$0.2842+$4.06

$5.07500

6 0

3 years ago

Read 2 more answers

Pls help me I'm taking a test and it's due in 30 mins idk this.

inessss [21]

Answer:

. y2 = 12x 40:12 :3 2. x² = -8y 408 3. (x + 2)2 = -4(y-1). \(-2,1) opens v. F-2,0) ... F (0:2). V(0,-2). F(4,2)

Step-by-step explanation:

4 0

4 years ago

Read 2 more answers