Answer:
z=40 degrees
Step-by-step explanation:
a triangle is 180 degrees
<ACB=50 (180-130=50)
50+90=140
180-140=40
Answer:
4096b after 350 years, 4194304b after 700 years, and 4294967296b after 1050 years. 0.000433065 sq ft. per person after 1050 years making earth uninhabitable.
Answer:
Each shirt cost $12
Step-by-step explanation:
First, we have to interpret this question and turn each to an equation, letting shirts represent the letter s and ties represent the letter t.
6 shirts and 3 ties cost $79.50 would be interpreted to 6s+3t=79.5 ,and 3 shirts and 2 ties cost $41 would be interpreted to 3s+2t=41
Hence we have two equations, and we solve them simultaneously.
6s+3t=79.5 (Equation 1)
3s+2t=41 (Equation 2)
We can either use the substitution method or the elimination method but for the sake of this question, we use the Elimination method.
6s+3t=79.5 (Equation 1)
3s+2t=41 (Equation 2)
We multiply equation 1 by 2 and we multiply equation 2 by 3, I'm prefer to eliminate the
2(6s+3t=79.5)
12s+6t=159 Equation 3
3(3s+2t=41)
9s+6t=123 Equation 4
We subtract equation 4 from equation 3.
12s+6t=159
9s+6t=123
12s-9s=3s
6t-6t=0
159-123=36
We therefore have
3s=36
Divide both sides by 3
s=36/3
s=12
One shirt cost $12
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:
f(4) = -11
Step-by-step explanation:
Plug in 4 for x: Note that x = 4.
f(x) = -2x - 3
f(4) = -2(4) - 3
Remember to follow PEMDAS. First, solve the multiplication, then subtract:
f(4) = (-2 * 4) - 3
f(4) = (-8) - 3
f(4) = -11
f(4) = -11 is your answer.
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