Answer:
3 terms
Step-by-step explanation:
10x
-6+8+12 (constant)
r
In short, to convert two fractions to have the same denominator, we simply multiply one by the denominator of the other, so in this case, we'll multiply 1/3 by 5, top and bottom, and 1/5 by 3, top and bottom, thus
![\bf a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\ -------------------------------](https://tex.z-dn.net/?f=%5Cbf%20a%5E%7B%5Cfrac%7B%20n%7D%7B%20m%7D%7D%20%5Cimplies%20%20%5Csqrt%5B%20m%5D%7Ba%5E%20n%7D%20%0A%5Cqquad%20%5Cqquad%0A%5Csqrt%5B%20m%5D%7Ba%5E%20n%7D%5Cimplies%20a%5E%7B%5Cfrac%7B%20n%7D%7B%20m%7D%7D%5C%5C%5C%5C%0A-------------------------------)
![\bf \cfrac{15x^{\frac{1}{3}}}{y^{\frac{1}{5}}}\qquad \begin{cases} \frac{1}{3}=\frac{1\cdot 5}{3\cdot 5}\\ \qquad \frac{5}{15}\\\\ \frac{1}{5}=\frac{1\cdot 3}{5\cdot 3}\\ \qquad \frac{3}{15} \end{cases}\implies \cfrac{15x^{\frac{5}{15}}}{y^{\frac{3}{15}}}\implies 15\cdot \cfrac{x^{\frac{5}{15}}}{y^{\frac{3}{15}}}\implies 15\cdot \cfrac{\sqrt[15]{x^5}}{\sqrt[15]{y^3}} \\\\\\ 15\sqrt[15]{\frac{x^5}{y^3}}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B15x%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%7D%7By%5E%7B%5Cfrac%7B1%7D%7B5%7D%7D%7D%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0A%5Cfrac%7B1%7D%7B3%7D%3D%5Cfrac%7B1%5Ccdot%205%7D%7B3%5Ccdot%205%7D%5C%5C%0A%5Cqquad%20%5Cfrac%7B5%7D%7B15%7D%5C%5C%5C%5C%0A%5Cfrac%7B1%7D%7B5%7D%3D%5Cfrac%7B1%5Ccdot%203%7D%7B5%5Ccdot%203%7D%5C%5C%0A%5Cqquad%20%5Cfrac%7B3%7D%7B15%7D%0A%5Cend%7Bcases%7D%5Cimplies%20%5Ccfrac%7B15x%5E%7B%5Cfrac%7B5%7D%7B15%7D%7D%7D%7By%5E%7B%5Cfrac%7B3%7D%7B15%7D%7D%7D%5Cimplies%2015%5Ccdot%20%5Ccfrac%7Bx%5E%7B%5Cfrac%7B5%7D%7B15%7D%7D%7D%7By%5E%7B%5Cfrac%7B3%7D%7B15%7D%7D%7D%5Cimplies%2015%5Ccdot%20%5Ccfrac%7B%5Csqrt%5B15%5D%7Bx%5E5%7D%7D%7B%5Csqrt%5B15%5D%7By%5E3%7D%7D%0A%5C%5C%5C%5C%5C%5C%0A15%5Csqrt%5B15%5D%7B%5Cfrac%7Bx%5E5%7D%7By%5E3%7D%7D)
Answer: 1.5miles/hour
Step-by-step explanation:
About 55.8 (i suggest rounding up to 56) are packed in 480 seconds. just divide 480 by 8.6 to get the answer 55.8
9514 1404 393
Answer:
58.5 ft by 39 ft
Step-by-step explanation:
Let x represent the length of the two horizontal segments. Then the three vertical segments will be ...
(234 -2x)/3
The total enclosed area is the product of these dimensions:
A = (x)(234 -2x)/3
A = (2/3)(x)(117 -x)
This is the equation of a downward-opening parabola with zeros at x=0 and x=117. The maximum of the parabola will be on the line of symmetry, halfway between these zeros. The value of x there is ...
x = (0 +117)/2 = 58.5
The lengths of the vertical segments are ...
(2/3)(117 -58.5) = 2/3(58.5) = 39
The dimensions of the region enclosing the maximum area are 58.5 ft by 39 ft. The additional vertical segment is 39 ft.
_____
<em>Comment on maximum area problems</em>
You may have noticed that the total length of the fence allocated to the long sides (2×58.5 = 117) is half the total length of fence and is equal to the total length of fence allocated to the short sides (3×39 = 117).
This relationship is true in all rectangular fencing problems where the area is being maximized for a given total fence length. It doesn't matter how many partitions there are in either direction: <em>the total of horizontal lengths is equal to the total of vertical lengths</em>.
