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3 years ago

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Simon is buying a sofa for $995. If he makes a down payment of 15% of the selling price, the furniture store will allow him to p

ay off the rest in monthly payments. If he wants to make monthly payments, how much of a down payment does Simon have to make?
:)

1 answer:

SVEN [57.7K]3 years ago

6 0

Answer: 15% of 995 is 149.25, rounded up he should be paying 149 monthly

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2 years ago

Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Spr

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First, we determine the length of the cable.

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Distance between point (x,0) and Shelvyfield(0,-7) is:

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To find the critical point, we set the derivative of L(x)=0

$L^{'}(x)=-1+\frac{2x}{\sqrt{\left( 49 - x^{2}\right) }}$

$\frac{-\sqrt{\left( 49 - x^{2}\right)}+2x}{\sqrt{\left( 49 - x^{2}\right)}}=0\\-\sqrt{\left( 49 - x^{2}\right)}+2x=0\\\sqrt{\left( 49 - x^{2}\right)}=2x\\(\sqrt{\left( 49 - x^{2}\right)})^2=(2x)^2\\49 - x^{2}=4x^2\\49=5x^2\\x^2=\frac{49}{5}\\x= 3.1305$

To verify that L(x) has a minimum at this critical number we compute the second derivative L″(x) and find its value at the critical number.

$L^{''}(x)=\frac{\left( 98\right) \,\sqrt{\left( 49 - x^{2}\right) }}{{\left( 7 - x\right) }^{2}\,{\left( 7+x\right) }^{2}}\\At \:x=3.1305, L^{''}=0.3993$

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Next, we find the minimum length by substituting z=3.1305 into L(x)

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Minimum Length, L=20.2057

The minimum length of the cable is 20.2057 Units.

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