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3 years ago

A home in small town in Texas is currently worth $344,000. It is expected to grow by 5% per year over the next several years.

Mathematics

1 answer:

Kitty [74]3 years ago

6 0

Answer:

Part A: The value of the house (y) after x years:

y = 344000 x (1 + 5/100)^x

Part B: Approximate value of the house after 10 years:

(Using the formula in part A)

V = 344000 x (1 + 5/100)^10 = 560339.8 $

Hope this helps!

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Consider the following. f(x) = x5 − x3 + 6, −1 ≤ x ≤ 1 (a) Use a graph to find the absolute maximum and minimum values of the fu

kykrilka [37]

ANSWER

See below

EXPLANATION

Part a)

The given function is

$f(x) = {x}^{5} - {x}^{3} + 6$

From the graph, we can observe that, the absolute maximum occurs at (-0.7746,6.1859) and the absolute minimum occurs at (0.7746,5.8141).

b) Using calculus, we find the first derivative of the given function.

$f'(x) = 5 {x}^{4} - 3 {x}^{2}$

At turning point f'(x)=0.

$5 {x}^{4} - 3 {x}^{2} = 0$

This implies that,

${x}^{2} (5 {x}^{2} - 3) = 0$

${x}^{2} = 0 \: or \: 5 {x}^{2} - 3 = 0$

$x = - \frac{ \sqrt{15} }{5} \: or \: x = 0 \: \: or \: x =\frac{ \sqrt{15} }{5}$

We plug this values into the original function to obtain the y-values of the turning points

$( - \frac{ \sqrt{15} }{5} , \frac{1}{125} ( 6 \sqrt{15} +750)) \:and \: (0, - 6) \: and\: ( \frac{ \sqrt{15} }{5} , \frac{1}{125} ( - 6 \sqrt{15} +750))$

We now use the second derivative test to determine the absolute maximum minimum on the interval [-1,1]

$f''(x) = 20 {x}^{3} - 6x$

$f''( - \frac{ \sqrt{15} }{5} ) \: < \: 0$

Hence

$( - \frac{ \sqrt{15} }{5} , \frac{1}{125} ( 6 \sqrt{15} + 750))$

is a maximum point.

$f''( \frac{ \sqrt{15} }{5} ) \: > \: 0$

Hence

$( \frac{ \sqrt{15} }{5} , \frac{1}{125} (- 6 \sqrt{15} + 750))$

is a minimum point.

$f''(0) \: =\: 0$

Hence (0,-6) is a point of inflexion

4 0

3 years ago

Molly spends 5 hours a week in art class. How many minutes does she spend in art class every week?

vampirchik [111]

Answer:

she spends 300 minutes in art class a week

Step-by-step explanation:

5 x 60 is 300

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3 years ago

Samantha and Jerrod were at the park, sitting on a park bench together. They decided to look at a fountain on their way home. Je

PilotLPTM [1.2K]

Answer:

Step-by-step explanation:

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3 years ago

I cannot find the answer to this question please help

Troyanec [42]

The answer would be 689

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3 years ago

A satellite is in orbit 600\ \mathrm{k}\mathrm{m}600 km above Earth's surface. Earth's radius is about 6370\ \mathrm{k}\mathrm{m

yKpoI14uk [10]

The distance from the satellite to the Earth's horizon is 6398 km

<h3>Pythagoras theorem</h3>

Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It is given by:

Hypotenuse side² = Adjacent side² + Opposite side²

Let x represent the distance from the satellite to the Earth's horizon

Hence:

x² = 6370² + 600²
x² = 40936900
x = 6398 km

The distance from the satellite to the Earth's horizon is 6398 km

Find out more on Pythagoras theorem at: brainly.com/question/343682

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2 years ago