The vector ab has a magnitude of 20 units and is parallel to the
vector 4i + 3j. Hence, The vector AB is 16i + 12j.
<h3>How to find the vector?</h3>
If we have given a vector v of initial point A and terminal point B
v = ai + bj
then the components form as;
AB = xi + yj
Here, xi and yj are the components of the vector.
Given;
The vector ab has a magnitude of 20 units and is parallel to the
vector 4i + 3j.
magnitude
Unit vector in direction of resultant = (4i + 3j) / 5
Vector of magnitude 20 unit in direction of the resultant
= 20 x (4i + 3j) / 5
= 4 x (4i + 3j)
= 16i + 12j
Hence, The vector AB is 16i + 12j.
Learn more about vectors;
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It's a y=mx+b equation, Carries' would be y=1/2 x - 125 (total profit is equal to the cupcake amount, each sold for 50 cents - the startup cost of 125). Juanita's would be y=2.25x-125. Comparing Carries' to Juanita's sales would mean that you would multiply x by 3 (no less than 3 times the ..). I may elaborate further on comparing in the comment section
Owner would lose out on $100
X = -6y - 12
4x + 5y =-39
4x + 5y = -39
-4(-6y - 12) + 5y = -39
-4(-6y) + 4(12) + 5y = -39
24y + 48 + 5y = -39
29y + 48 = -39
29y = -87
y = -3
x = -6y - 12
x = -6(-3) - 12
x = 28 - 12
x = 6
(x, y) = (6, -3)
Population are always modeled by exponential growth equation given by:
f(x)=a(1+b)^t
where:
a=original number
b=rate of growth
t=time
thus
f(x)=412(1.05)^t
the population after 9 months will be:
f(9)=412(1.05)^9=639.15=639
