Question

EXERCISE 5.2
1. By what number should 2
power is
-3 be multiplied so that the product is 16?​

Answer 1

Answer:

the answer is

Step-by-step explanation:

◘ Given ◘

→ The equation of a line = (x/3) + (y/4) = 1 .

◘ To Find ◘

The points on x-axis whose distance from the line equation (x/3) + (y/4) = 1 is given as 4 units.

◘ Solution ◘

From given conditions,

The equation of a line = (x/3) + (y/4) = 1

It can be written as:

4x + 3y -12 = 0            …(i)

Compare the equation (1) with general line equation Ax + By + C = 0 we get :

A = 4

B = 3

C = -12

Let (a, 0) be the point on the x-axis whose distance from the given line is 4 units.

______________________

We know that,

The perpendicular distance (d) of a line Ax + By + C = 0 from a point (x₁, y₁) is given by D = |Ax₁ + By₁ + C| / √(A² + B²)

Substituting the values :-

\longrightarrow \sf{4=\dfrac{|4a+0+(-12)|}{\sqrt{4^2+3^2} } }⟶4=42+32∣4a+0+(−12)∣

\longrightarrow \sf{ 4=\dfrac{|4a-12|}{\sqrt{25}} }⟶4=25∣4a−12∣

\longrightarrow \sf{ 4=\dfrac{|4a-12|}{5} }⟶4=5∣4a−12∣

\longrightarrow \sf{ |4a-12|=20}⟶∣4a−12∣=20

\longrightarrow \sf{ \pm(4a-12)=20}⟶±(4a−12)=20

\longrightarrow \sf{ (4a-12)=20\:\:or\:\:-(4a-12)=20}⟶(4a−12)=20or−(4a−12)=20

______________________

(4a-12) = 20

\longrightarrow⟶ 4a = 20 + 12

\longrightarrow⟶ 4a = 32

\longrightarrow⟶ a = 8

______________________

-(4a - 12) = 20

\longrightarrow⟶ -4a + 12 = 20

\longrightarrow⟶ -4a = 20 - 12

\longrightarrow⟶ -4a = 8

\longrightarrow⟶ a= -2

______________________

Therefore,

a= 8 or -2

Hence, the required points on x axis are (-2, 0) and (8, 0).

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