Answer:
The solution is:
Step-by-step explanation:
Given the expression

Solving


so



∵ 
Therefore, the solution is:

Answer:
Step-by-step explanation:
Given that L is a line parametrized by

The plane perpendicular to the line will have normal as this line and hence direction ratios of normal would be coefficient of t in x,y,z
i.e. (2,3,-1)
So equation of the plane would be of the form

Use the fact that the plane passes through (2,0,-1) and hence this point will satisfy this equation.

So equation is

b) Substitute general point of L in the plane to find the intersecting point

i.e. same point given.
Answer:
12 boys
Step-by-step explanation:
From the above question:
Number of boys = 3
Number of girls = 2
Boys: Girls
3:2
Let :
a = boys
b = girls
Hence, a : b = 3 : 2
a/b = 3/2
Cross Multiply
2a = 3b .......... Equation 1
a = 3b/2
If four more girls join the class, there will be the same number of boys and girls
Hence,
a: b + 4 = 3 : 3
a/b + 4 = 3/3
Cross Multiply
3a = 3(b + 4)
3a = 3b + 12 ........ Equation (2)
From Equation 1: a = 3b/2
Substitute 3b/2 for a in Equation 2 we have:
3a = 3b + 12 .........Equation 2
3(3b/2) = 3b + 12
9b/2 = 3b + 12
Cross Multiply
9b = 2(3b + 12)
9b= 6b + 24
9b - 6b = 24
3b = 24
b = 8
Substitute 8 for b in Equation 1
a = 3b/2
a = 3 × 8/2
a = 24/2
a = 12
Therefore, the number of boys in the class is 12
Answer:
1 
Step-by-step explanation:
- First convert this mix number into a improper number
13/3-5/2
- Then find the LCM of the denominator
26/6-15/6
11/6
1 
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