My late response (haha): First, you would write a proportion.
Step 1: 2496 over 48 = x over 31
(x represents the area of the land that is not fenced).
Step 2: Cross multiply
2496 times 31 and x times 48
Step 3: Calculate
77376 = 48x
Step 4: Divide both sides by 48
77376/48 = 1612
48x/48 = x
Step 5: Write it as a sentence
The area of the land that is not fenced is 1612 squared meters.
Hope that helped! Good luck! :]
Answer:
⅔ √(x + 1) (x − 2) + C
Step-by-step explanation:
∫ x / √(x + 1) dx
Add and subtract 1 to the numerator.
∫ (x + 1 − 1) / √(x + 1) dx
Split the fraction.
∫ [ (x + 1) / √(x + 1) − 1 / √(x + 1) ] dx
∫ [ √(x + 1) − 1 / √(x + 1) ] dx
Rewrite with exponents.
∫ [ (x + 1)^½ − (x + 1)^-½ ] dx
Use u-substitution.
u = x + 1, du = dx
∫ (u^½ − u^-½) du
Integrate using power rule.
⅔ u^(3/2) − 2 u^½ + C
Factor.
u^½ (⅔ u − 2) + C
⅓ u^½ (2 u − 6) + C
Substitute back.
⅓ (x + 1)^½ (2 (x + 1) − 6) + C
Simplify.
⅓ √(x + 1) (2x + 2 − 6) + C
⅓ √(x + 1) (2x − 4) + C
⅔ √(x + 1) (x − 2) + C
Answer:
60°
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
Here n = 5 ( pentagon ), thus
sum = 180° × 3 = 540°
let x be the size of the equal angles
Sum the interior angles and equate to 540
(3 × 140 ) + 2x = 540
420 + 2x = 540 ( subtract 240 from both sides )
2x = 120 ( divide both sides by 2 )
x = 60
Thus the size of 1 of the 2 equal angles = 60°
So.. if the width is say "w", twice the width will then be 2*w or 2w
and 4 greater than that, => 2w + 4
thus
![\bf \qquad \qquad \textit{volume of a rectangular prism}\\\\ V=l\cdot w\cdot h\qquad \begin{cases} l=length\\ w=width\\ h=height\\ -------\\ h=17\\ l=2w+4\\ V=2,720 \end{cases}\implies 2720=(2w+4)(w)(17)](https://tex.z-dn.net/?f=%5Cbf%20%5Cqquad%20%5Cqquad%20%5Ctextit%7Bvolume%20of%20a%20rectangular%20prism%7D%5C%5C%5C%5C%0AV%3Dl%5Ccdot%20w%5Ccdot%20h%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0Al%3Dlength%5C%5C%0Aw%3Dwidth%5C%5C%0Ah%3Dheight%5C%5C%0A-------%5C%5C%0Ah%3D17%5C%5C%0Al%3D2w%2B4%5C%5C%0AV%3D2%2C720%0A%5Cend%7Bcases%7D%5Cimplies%202720%3D%282w%2B4%29%28w%29%2817%29)
solve for "w"
A function in which the dependent variable decreases by the same factor over each unit of time