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zhenek [66]
3 years ago
12

Bill and Mary went to the farmers market to buy fruit for their lunch at school next week. Bill bought 5 apples. Mary bought 2 a

pples and spent $1.86 for a container of blue berries. If they spent equal amount at the market, write and solve an equation that will determine the cost of one apple.
Mathematics
1 answer:
REY [17]3 years ago
3 0
2=1.86
5=x
----------------------
2x=17.29
divide both sides by 2
x=4.32 per apple
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Y=5x+3. because your y axis is moved
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Katen [24]

\green{\large\underline{\sf{Solution-}}}

<u>Given expression is </u>

\rm :\longmapsto\:\dfrac{5 \times  {25}^{n + 1}  - 25 \times  {5}^{2n} }{5 \times  {5}^{2n + 3}  -  {25}^{n + 1} }

can be rewritten as

\rm \:  =  \: \dfrac{5 \times  { {(5}^{2} )}^{n + 1}  -  {5}^{2}  \times  {5}^{2n} }{5 \times  {5}^{2n + 3}  -  {( {5}^{2} )}^{n + 1} }

We know,

\purple{\rm :\longmapsto\:\boxed{\tt{  {( {x}^{m} )}^{n}  \: = \:   {x}^{mn}}}} \\

And

\purple{\rm :\longmapsto\:\boxed{\tt{ \:  \:   {x}^{m} \times  {x}^{n} =  {x}^{m + n} \: }}} \\

So, using this identity, we

\rm \:  =  \: \dfrac{5 \times  {5}^{2n + 2}  - {5}^{2n + 2} }{{5}^{2n + 3 + 1}  -  {5}^{2n + 2} }

\rm \:  =  \: \dfrac{{5}^{2n + 2 + 1}  - {5}^{2n + 2} }{{5}^{2n + 4}  -  {5}^{2n + 2} }

can be further rewritten as

\rm \:  =  \: \dfrac{{5}^{2n + 2 + 1}  - {5}^{2n + 2} }{{5}^{2n + 2 + 2}  -  {5}^{2n + 2} }

\rm \:  =  \: \dfrac{ {5}^{2n + 2} (5 - 1)}{ {5}^{2n + 2} ( {5}^{2}  - 1)}

\rm \:  =  \: \dfrac{4}{25 - 1}

\rm \:  =  \: \dfrac{4}{24}

\rm \:  =  \: \dfrac{1}{6}

<u>Hence, </u>

\rm :\longmapsto\:\boxed{\tt{ \dfrac{5 \times  {25}^{n + 1}  - 25 \times  {5}^{2n} }{5 \times  {5}^{2n + 3}  -  {25}^{n + 1} }  =  \frac{1}{6} }}

4 0
3 years ago
Peter has 3200 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed a
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Answer:

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Expression for the rectangular area and perimeter are, respectively:

A (x,y) = x\cdot y

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After some algebraic manipulation, area expression can be reduce to an one-variable form:

y = 1600 -x

A (x) = x\cdot (1600-x)

The first derivative of the previous equation is:

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Let the expression be equalized to zero:

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The second derivative is:

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According to the Second Derivative Test, the critical value found in previous steps is a maximum. Then:

y = 800

The maximum area is:

A = (800\,yd)\cdot (800\,yd)

A = 640000\,yd^{2}

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Answer:

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Step-by-step explanation:

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