Percent change = [(45 - 60) / 60] x 100 = -25 % (decrease)
The total front footage of all three lots is 370.
Water that weighs 325 lbs will fill 5.2 cubic feet.
Step-by-step explanation:
This is a simple question of cross multiplication
<u>DATA:</u>
<em>1. The weight of water for 1 cubic feet is 62.5</em>
<em>2. The weight of water for 'X' cubic feet is 325 </em>
<em>3. To find x, form an equation:</em>
Cubic feet : Weight of water
1 : 62.5
X : 325
<em>4. Cross multiply</em>
X x 62.5 = 1 x 325
62.5X = 325
<em>5. Make X the subject</em>
X = ![\frac{325}{62.5}](https://tex.z-dn.net/?f=%5Cfrac%7B325%7D%7B62.5%7D)
<em>6. Solve to find X</em>
X = 5.2 cubic feet
Therefore, water that weighs 325 lbs will fill 5.2 cubic feet.
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If you're just starting calculus, perhaps you're asking about using the definition of the derivative to differentiate
.
We have
![\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x+h)^4 - x^4}h](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7D%20x%5E4%20%3D%20%5Cdisplaystyle%20%5Clim_%7Bh%5Cto0%7D%20%5Cfrac%7B%28x%2Bh%29%5E4%20-%20x%5E4%7Dh)
Expand the numerator using the binomial theorem, then simplify and compute the limit.
![\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x^4+4hx^3 + 6h^2x^2 + 4h^3x + h^4) - x^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} \frac{4hx^3 + 6h^2x^2 + 4h^3x + h^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} (4x^3 + 6hx^2 + 4h^2x + h^3) = \boxed{4x^3}](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7D%20x%5E4%20%3D%20%5Cdisplaystyle%20%5Clim_%7Bh%5Cto0%7D%20%5Cfrac%7B%28x%5E4%2B4hx%5E3%20%2B%206h%5E2x%5E2%20%2B%204h%5E3x%20%2B%20h%5E4%29%20-%20x%5E4%7Dh%20%5C%5C%5C%5C%20~~~~~~~~%20%3D%20%5Clim_%7Bh%5Cto0%7D%20%5Cfrac%7B4hx%5E3%20%2B%206h%5E2x%5E2%20%2B%204h%5E3x%20%2B%20h%5E4%7Dh%20%5C%5C%5C%5C%20~~~~~~~~%20%3D%20%5Clim_%7Bh%5Cto0%7D%20%284x%5E3%20%2B%206hx%5E2%20%2B%204h%5E2x%20%2B%20h%5E3%29%20%3D%20%5Cboxed%7B4x%5E3%7D)
In general, the derivative of a power function
is
. (This is the aptly-named "power rule" for differentiation.)
The perimeter is the distance all the way around. So it's the sum of the lengths of all 4 sides.
From the picture, you can clearly see the lengths of all 4 sides.
Writum down and adum up !