Hello :
let A(0,3,2) and (Δ) this line , v vector parallel to (<span>Δ).
M</span>∈ (Δ) : vector (AM) = t v..... t ∈ R
1 ) (Δ) parallel to the plane x + y + z = 5 : let : n an vector <span>perpendicular
to the plane : n </span>⊥ v .... n(1,1,1) so : n.v =0 means : n.vector (AM) = 0
(1)(x)+(1)(y-3)+(1)(z -2) =0 ( vector (AM) = ( x, y -3 , z-2 )
x+y+z - 5=0 ...(1)
2) (Δ) perpendicular to the line (Δ') : x = 1+t , y = 3 - t , z = 2t :
vector (u) ⊥ v .... vector(u) parallel to (Δ') and vector(u) = (1 , -1 ,1)
vector (u) ⊥ vector (AM) means :
(1)(x)+(-1)(y-3)+(2)(z -2) =0
x - y+2z - 1 = 0 ...(2)
so the system :
x+y+z - 5=0 ...(1)
x - y+2z - 1 = 0 ...(2)
(1)+(2) : 2x+3z - 6 =0
x = 3 - (3/2)z
subsct in (1) : 3 - (3/2)z +y +z - 5 =0
y = 1/2z +2
let : z=t
an parametric equations for the line (Δ) is : x = 3 - (3/2)t
y = (1/2)t +2
z=t
verifiy :
1) (Δ) parallel to the plane x + y + z = 5 :
(-3/2 , 1/2 ,1) <span>perpendicular to (1,1,1)
</span>because : (1)(-3/2)+(1)(1/2)+(1)(1) = -1 +1 = 0
2) (Δ) perpendicular to the line (Δ') :
(-3/2 , 1/2 ,1) perpendicular to (1,-1,2)
because : (1)(-3/2)+(-1)(1/2)+(1)(2) = -2 +2 = 0
A(0, 3, 2)∈(Δ) :
0 = 3-(3/2)t
3 = (1/2)t+2
2 =t
same : t = 2
-11-8-13(-10)
First, multiply since multiplication goes before subtraction according to the order of operations.
-11-8+130
Then add and subtract from left to right.
-11-8= -19
-19+130=111
Final answer: 111
Answer:
You'll get an A and you can celebrate.
Step-by-step explanation:
The hypothesis for the first conditional is met, so we can assume the conclusion is true: you'll get an A.
That conclusion satisfies the hypothesis of the second conditional, so we can assume its conclusion is true: you can celebrate.
Taken together, we can assume ...
You'll get an A and you can celebrate.
Answer:
6. D
7. F
8.A
9. B
10 C
13.Question- Write an expression using division and subtraction with a difference of 3.
answer- (12 divide 3) -1
Twelve divided by three is four. Four minus 1 is three.
12. Question- Write an expression using multiplication and addition with a sum of 16.
answer- There are many answers for this and this is one of them:
Y=4(3+1)
Y=16
or
Y=2(6+2)
Y=16
11. Question- Sam bought two CDs for $13 each. Sales tax for both CDs was $3. Write an expression to show how much Sam paid in all.
answer- Expression- (13*2)(3*2)=$32
This is the answer because Sam bought two CD's for 13, 13*2, and the sales tax was $ 3, so 3*2=6
Answer:
the room dimensions that result in a minimum cost for the paint is;
x = 11 ft
y = 11 ft
z = 8.25 ft
Step-by-step explanation:
Shown in the attachment;
