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2 years ago

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The value of a gold coin picturing the head of the Roman Emperor Vespasian is increasing at the rate of 5% per year. If the coin

is worth $105 now, what will it be worth in 11 years?

2 answers:

valkas [14]2 years ago

7 0

Answer:

$179.59

Step-by-step explanation:

Step 1 Write the exponential growth function for this situation.

y = a(1 + r)t Write the formula.

= 105(1 + 0.05)t Substitute 105 for a and 0.05 for r.

= 105(1.05)t Simplify.

Step 2 Find the value in 11 years.

y = 105(1.05)t Write the formula.

= 105(1.05)11 Substitute 11 for t.

≈ 179.59 Use a calculator and round to the nearest hundredth.

bazaltina [42]2 years ago

6 0

Answer:

255.75

Step-by-step explanation:

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Two cars got an oil change at the same auto shop. The shop charges customers for each quart of oil plus a flat fee for labor. Th

amm1812

(5,22.45),(7,25.45)
slope = (25.45 - 22.45) / (7 - 5) = 3/2 or 1.5

y = mx + b
slope(m) = 1.5
use either of ur points...(5,22.45)...x = 5 and y = 22.45
now sub and find b
22.45 = 1.5(5) + b
22.45 = 7.5 + b
22.45 - 7.5 = b
14.95 = b

so ur equation is : y = 1.5x + 14.95.......this means that each quart of oil costs $ 1.50 and the labor fee costs $ 14.95

3 0

3 years ago

Find the point (,) on the curve =8 that is closest to the point (3,0). [To do this, first find the distance function between (,)

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:

$d = \sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}$

So:

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

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

Evaluate all exponents

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

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

$2x - 5 = 0$

Solve for x

$2x =5$

$x = \frac{5}{2}$

Substitute $x = \frac{5}{2}$ in $y = \sqrt x$

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

Split

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

Rationalize

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

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

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

Hence:

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

3 0

3 years ago

PLEASE ANSWER FAST

Lina20 [59]

The square root of 16 is 4

7 0

3 years ago

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Will the sum of 2x3 + x2 - 4 and -5x² - 6x? be a polynomial?<br> yes<br> no

Eva8 [605]

Answer:

Yes

Step-by-step explanation:

Since we are adding two polynomials

The sum will also be polynomial

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3 years ago

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Phoenix [80]

Answer:

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Step-by-step explanation:

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