Answer: 1/10 or 0.1
Step-by-step explanation:
-(-7 - 4x) = -2(3x - 4)
7 + 4x = -6x + 8
* subtract 7 from both sides
4x = -6x + 1
* Add 6x to both sides
10 x = 1
* Divide both sides by 10
x = 1/10 or 0.10
Answer: 31
Step-by-step explanation:
add the 2 lengths of the given parts.
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.
Answer:
Factory A should be operated 6.11 days
Factory B should be operated 6.88 days
The minimum cost for factory A is $6,110
The minimum cost for factory B is $5,504
Step-by-step explanation:
Factory A
Daily production: 16 3-speed and 20 10-speed bikes
Total daily production = 16+20 = 36 speed bikes
Order: 80 3-speed and 140 10-speed bikes
Total order = 80+140 = 220 speed bikes
Number of days = 220/36 = 6.11 days
Cost per day = $1,000
Minimum cost for 6.11 days = $1000 × 6.11 = $6,110
Factory B
Daily production: 12 3-speed and 20 10-speed bikes
Total daily production = 12+20 = 32 speed bikes
Total order = 220 speed bikes
Number of days = 220/36 = 6.88 days
Cost per day = $800
Cost for 6.88 days = $800 × 6.88 = $5,504
