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2 years ago

9

If Eric Sanchez saves $60 a month by using coupons and doing comparison shopping, (a) what is the amount for a year? (b) What wo

uld be the future value of this annual amount over 10 years, assuming an interest rate of 3 percent?

1 answer:

svetoff [14.1K]2 years ago

4 0

A. Annual Savings = $60 * 12 = $720

b. $8384.48

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Which of the following points lies on the graph of y=x^2-5?

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(3, 4)

Step-by-step explanation:

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Help with this question, please!

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Answer:

Y Intercept: 0, 2.5

X Intercept: 3.5, 0

Explanation:

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Mr. Peterson sold a parcel of land and decided to share half of the amount he got among his three children Jane, Peter and marth

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ELEN [110]

Question:

Find the point (,) on the curve $y = \sqrt x$ that is closest to the point (3,0).

[To do this, first find the distance function between (,) and (3,0) and minimize it.]

Answer:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

Step-by-step explanation:

$y = \sqrt x$ can be represented as: $(x,y)$

Substitute $\sqrt x$ for $y$

$(x,y) = (x,\sqrt x)$

So, next:

Calculate the distance between $(x,\sqrt x)$ and $(3,0)$

Distance is calculated as:

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So:

$d = \sqrt{(x-3)^2 + (\sqrt x - 0)^2}$

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Evaluate all exponents

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Rewrite as:

$d = \sqrt{x^2 + x- 6x +9 }$

$d = \sqrt{x^2 - 5x +9 }$

Differentiate using chain rule:

Let

$u = x^2 - 5x +9$

$\frac{du}{dx} = 2x - 5$

So:

$d = \sqrt u$

$d = u^\frac{1}{2}$

$\frac{dd}{du} = \frac{1}{2}u^{-\frac{1}{2}}$

Chain Rule:

$d' = \frac{du}{dx} * \frac{dd}{du}$

$d' = (2x-5) * \frac{1}{2}u^{-\frac{1}{2}}$

$d' = (2x - 5) * \frac{1}{2u^{\frac{1}{2}}}$

$d' = \frac{2x - 5}{2\sqrt u}$

Substitute: $u = x^2 - 5x +9$

$d' = \frac{2x - 5}{2\sqrt{x^2 - 5x + 9}}$

Next, is to minimize (by equating d' to 0)

$\frac{2x - 5}{2\sqrt{x^2 - 5x + 9}} = 0$

Cross Multiply

$2x - 5 = 0$

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Split

$y = \frac{\sqrt 5}{\sqrt 2}$

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$y = \frac{\sqrt 5}{\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$y = \frac{\sqrt {10}}{\sqrt 4}$

$y = \frac{\sqrt {10}}{2}$

Hence:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

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3 years ago

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Nostrana [21]

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