The correct answer would be C: 1 2/5
Answer:
Step-by-step explanation:
step 1
Find the slope of the perpendicular line
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal
(the product of their slopes is equal to -1)
In this problem
we have
The equation of the given line is 
so
the slope of the perpendicular line to the given line is
step 2
Find the equation of the line in point slope form
we have
substitute
Convert to slope intercept form
Distribute right side
Draw and label a standard Oblique Triangle, as we’ve done in our previous lessons.
Determine the given congruence, either SAS or SSS, and pick the equation that helps you solve for either a missing side or angle.
Plug into your chosen equation and solve.
The "Law of Cosines" can be used to calculate one side of a triangle when the angle opposite and the other two sides are known. The "Law of Cosines" can be expressed as c2 = a2 + b2 - 2 a b cos C (1)
The cosine rule is an extension of this mathematic principal that makes it effective for non-right triangles and states that in regard to a certain angle, the square of the side of the triangle opposite that angle is equal to the squares of the other two sides added together, minus two times both..
Given plane Π : f(x,y,z) = 4x+3y-z = -1
Need to find point P on Π that is closest to the origin O=(0,0,0).
Solution:
First step: check if O is on the plane Π : f(0,0,0)=0 ≠ -1 => O is not on Π
Next:
We know that the required point must lie on the normal vector <4,3,-1> passing through the origin, i.e.
P=(0,0,0)+k<4,3,-1> = (4k,3k,-k)
For P to lie on plane Π , it must satisfy
4(4k)+3(3k)-(-k)=-1
Solving for k
k=-1/26
=>
Point P is (4k,3k,-k) = (-4/26, -3/26, 1/26) = (-2/13, -3/26, 1/26)
because P is on the normal vector originating from the origin, and it satisfies the equation of plane Π
Answer: P(-2/13, -3/26, 1/26) is the point on Π closest to the origin.
9514 1404 393
Answer:
20
Step-by-step explanation:
This triangle is your basic 3-4-5 triangle multiplied by 5 to become a 15-20-25 triangle. The missing leg is 20.
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More at brainly.com/question/23176381
