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Korolek [52]
3 years ago
13

Translate into an algebraic expression and simplify if possible. C It would take Maya x minutes to rake the leaves and Carla y m

inutes, what portion of the leaves do they rake in one minute if they work together?
Mathematics
1 answer:
lina2011 [118]3 years ago
8 0

Answer:

in one minute they rake \frac{y+x}{xy} leaves working together.

Step-by-step explanation:

If Maya rakes the leaves in x minutes, then, in one minute she rakes \frac{1}{x} leaves.

In the case of Carla, if she rakes the leaves in y minutes, in one minute she rakes \frac{1}{y} leaves.

Therefore, to know the portion of leaves they can rake in one minute working together, we need to sum up both of the portions each one of them rake in one minute, this gives us: \frac{1}{x}+ \frac{1}{y}

Now, to simplify this expression:

\frac{1}{x}+ \frac{1}{y}  =\frac{y+x}{xy}

Thus, in one minute they rake \frac{y+x}{xy} leaves.

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A television normally sells for $320 this week it’s on sale for 60% off the normal price what is the price of the sale
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Read 2 more answers
You need to construct an open-top rectangular box with a square base that must hold a volume of exactly 475 cm3. The material fo
zepelin [54]

Answer:

The dimensions of the box are:

x =  8,93 cm       and     h  =   5,95 cm

C(min) =  850,69 cents

Step-by-step explanation:

The volume of the box is:

V = x²*h          where    x is the side of the square base  and h the height

then    h  =  V/ x²  ⇒    h = 475 / x²

The total cost of box C is:

C  = C₁  +  4*C₂      Where C₁  and C₂  are the costs of the base and one lateral side respectevily

Then cost C =  8*x²   + 4* 6*h*x

The cost C as a function of x is

C(x)  =  8*x²  + (24* 475 /x² )*x

C(x)  =  8*x²  +  11400/x

Tacking derivatives on both sides of the equation

C´(x)  =  16*x -  11400/x²

C´(x)  =  0     ⇒    16*x  -  11400/x²  = 0

16*x³  =  11400     ⇒   x³  =  11400/16

x³ =  712,5

x  =  8,93  cm

and    h   =  475 / (8,93)²      ⇒      h  =  5,95  cm

C(min)  =  8*79,77  +  4* ( 8,93)*5,95

C(min)  =  638,16  +  212,53

C(min)  =  850,69 cents

To check if value x = 8,93 would make C(x) minimum we go to the second derivatives

C´´(x) =  16  +  22800/x³ > 0

Then we have a minimum of C at  x = 8,93

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3 years ago
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