Answer:
Step-by-step explanation:
step 1
Find the circumference of the circle
The circumference is equal to
we have
substitute the values
step 2
Remember that
360 degrees subtends the arc of length 
(circumference)
so
by proportion
Find the measure of θ by an arc of length 5 m
assume 
Answer: The number is 10.
Step-by-step explanation:
Let x be the required number.
Given: 11 is multiplied to the number then 24 is subtracted from that and the result is 86.
The mathematical statement for the given situation,
11x -24 = 86
To solve the equation, Add 24 on both sides , we get
11x - 24 +24 = 86+24
⇒ 11x = 110
Divide both sides by 11, we get
x = 10
hence, the number is 10.
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.
0.5
+0.3
---------
0.8
The answer is 8 tenths
Answer:
c. -70
Step-by-step explanation:
subtract 50 from 120 you get 70, and since we are below sea level it is negative
