Answer:
10 feet
Step-by-step explanation:
Given
Dimension = 2 feet by 3 feet
Required
Determine the length of the short side if the longer side is scaled to 15 feet
Represent the before and after enlargement as a ratio:
Before Enlargement
Ratio = 2 ft : 3ft
After Enlargement
Ratio = x : 15 ft
Where x represents the length of the shorter side
Since they're both proportional, their ratio must be equal.
So, we have:
2 : 3 = x : 15
Convert ratio to fraction
⅔ = x/15
Multiply both sides by 15
15 * ⅔ = 15 * x/15
15 * ⅔ = x
30/3 = x
10 = x
x = 10
Hence, the length of the shorter side must be 10 feet
Let p(x) be a polynomial, and suppose that a is any real
number. Prove that
lim x→a p(x) = p(a) .
Solution. Notice that
2(−1)4 − 3(−1)3 − 4(−1)2 − (−1) − 1 = 1 .
So x − (−1) must divide 2x^4 − 3x^3 − 4x^2 − x − 2. Do polynomial
long division to get 2x^4 − 3x^3 − 4x^2 – x – 2 / (x − (−1)) = 2x^3 − 5x^2 + x –
2.
Let ε > 0. Set δ = min{ ε/40 , 1}. Let x be a real number
such that 0 < |x−(−1)| < δ. Then |x + 1| < ε/40 . Also, |x + 1| <
1, so −2 < x < 0. In particular |x| < 2. So
|2x^3 − 5x^2 + x − 2| ≤ |2x^3 | + | − 5x^2 | + |x| + | − 2|
= 2|x|^3 + 5|x|^2 + |x| + 2
< 2(2)^3 + 5(2)^2 + (2) + 2
= 40
Thus, |2x^4 − 3x^3 − 4x^2 − x − 2| = |x + 1| · |2x^3 − 5x^2
+ x − 2| < ε/40 · 40 = ε.
Answer:The nail would be at the same height since trees grow at their tops.
Step-by-step explanation:
Answer:
If you are multiplying both 2 1/2% * 13.7 the answer is = 0.3425
Step-by-step explanation:
