How many ft and in are in 10 ft?
1 answer:
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Answer:
Step-by-step explanation:
A direct variation equation has the form:
Where <em>k</em> is a constant.
By definition, we know that the perimeter of the square is the sum of the lengths of its sides or, as all the sides are equal, you can multiply the lenght of any side by 4.
Then, knowing that <em>y</em> is the dependent value and <em>x</em> the independent value and the constant <em>k=4, </em> you can write the following direct variation equation that represents the situation.
For E to be the midpoint of DF, it needs to divide DF in 2 equal segments, DE and EF. If E is the midpoint of DF, then DE and EF are equal, so the reason is that the expressions for DE and EF are equal. The reason is:
Answer: y = (5832/25)*(5/18)^x
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Explanation:
Any general exponential function is of the form
y = a*b^x
Plug in (x,y) = (3,5) and we get
y = a*b^x
5 = a*b^3
If you plug in (x,y) = (2,18), then we'll get this other equation
18 = a*b^2
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So we have this system of equations
From here, we divide the two equations straight down. The left hand sides divide to 5/18. The right hand sides divide to (ab^3)/(ab^2) which simplifies to b. The 'a' terms cancel and we subtract the exponents for the b terms.
Overall, we end up with b = 5/18
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Use that value of b to find 'a'
18 = a*b^2
18 = a*(5/18)^2
18 = a*(25/324)
18*(324/25) = a
a = 5832/25
You could use the other equation as well to find 'a'
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Therefore, the equation in y = a*b^x form is y = (5832/25)*(5/18)^x
To verify this, plugging in x = 3 should lead to y = 5. Similarly, plugging in x = 2 should lead to y = 18.