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4 years ago

9

Christopher drove 360 miles this week. last week he drove 480 mile. what is the percent decrease in the number of miles christop

her drove this week compared to last week

1 answer:

Harlamova29_29 [7]4 years ago

8 0

Last week, Christopher drove 480 miles
This week, Christopher drove 360 miles

The difference in miles this week compared to last week = 480 - 360 = 120 miles.

The percentage of decrease in miles compared to last week's = (Difference in miles ÷ Total miles last week) multiplied by 100 = (120 ÷ 480) x 100 = 0.25 x 100 = 25%

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The spread of a virus is modeled by V (t) = −t 3 + t 2 + 12t,

VashaNatasha [74]

Functions can be used to model real life scenarios

The reasonable domain is $\mathbf{[0,\infty)}$ .
The average rate of change from t = 0 to 2 is 20 persons per week
The instantaneous rate of change is $\mathbf{V'(t) = -3t^2 + 2t + 12}$ .
The slope of the tangent line at point (2,V(20) is 10
The rate of infection at the maximum point is 8.79 people per week

The function is given as:

$\mathbf{V(t) = -t^3 + t^2 + 12t}$

<u>(a) Sketch V(t)</u>

See attachment for the graph of $\mathbf{V(t) = -t^3 + t^2 + 12t}$

<u />

<u>(b) The reasonable domain</u>

t represents the number of weeks.

This means that: <em>t cannot be negative.</em>

So, the reasonable domain is: $\mathbf{[0,\infty)}$

<u />

<u>(c) Average rate of change from t = 0 to 2</u>

This is calculated as:

$\mathbf{m = \frac{V(a) - V(b)}{a - b}}$

So, we have:

$\mathbf{m = \frac{V(2) - V(0)}{2 - 0}}$

$\mathbf{m = \frac{V(2) - V(0)}{2}}$

Calculate <em>V(2) and V(0)</em>

$\mathbf{V(2) = (-2)^3 + (2)^2 + 12 \times 2 = 20}$

$\mathbf{V(0) = (0)^3 + (0)^2 + 12 \times 0 = 0}$

So, we have:

$\mathbf{m = \frac{20 - 0}{2}}$

$\mathbf{m = \frac{20}{2}}$

$\mathbf{m = 10}$

Hence, the average rate of change from t = 0 to 2 is 20

<u>(d) The instantaneous rate of change using limits</u>

$\mathbf{V(t) = -t^3 + t^2 + 12t}$

The instantaneous rate of change is calculated as:

$\mathbf{V'(t) = \lim_{h \to \infty} \frac{V(t + h) - V(t)}{h}}$

So, we have:

$\mathbf{V(t + h) = (-(t + h))^3 + (t + h)^2 + 12(t + h)}$

$\mathbf{V(t + h) = (-t - h)^3 + (t + h)^2 + 12(t + h)}$

Expand

$\mathbf{V(t + h) = (-t)^3 +3(-t)^2(-h) +3(-t)(-h)^2 + (-h)^3 + t^2 + 2th+ h^2 + 12t + 12h}$ $\mathbf{V(t + h) = -t^3 -3t^2h -3th^2 - h^3 + t^2 + 2th+ h^2 + 12t + 12h}$

Subtract V(t) from both sides

$\mathbf{V(t + h) - V(t)= -t^3 -3t^2h -3th^2 - h^3 + t^2 + 2th+ h^2 + 12t + 12h - V(t)}$

Substitute $\mathbf{V(t) = -t^3 + t^2 + 12t}$

$\mathbf{V(t + h) - V(t)= -t^3 -3t^2h -3th^2 - h^3 + t^2 + 2th+ h^2 + 12t + 12h +t^3 - t^2 - 12t}$

Cancel out common terms

$\mathbf{V(t + h) - V(t)= -3t^2h -3th^2 - h^3 + 2th+ h^2 + 12h}$

$\mathbf{V'(t) = \lim_{h \to \infty} \frac{V(t + h) - V(t)}{h}}$ becomes

$\mathbf{V'(t) = \lim_{h \to \infty} \frac{ -3t^2h -3th^2 - h^3 + 2th+ h^2 + 12h}{h}}$

$\mathbf{V'(t) = \lim_{h \to \infty} -3t^2 -3th - h^2 + 2t+ h + 12}$

Limit h to 0

$\mathbf{V'(t) = -3t^2 -3t\times 0 - 0^2 + 2t+ 0 + 12}$

$\mathbf{V'(t) = -3t^2 + 2t + 12}$

<u>(e) V(2) and V'(2)</u>

Substitute 2 for t in V(t) and V'(t)

So, we have:

$\mathbf{V(2) = (-2)^3 + (2)^2 + 12 \times 2 = 20}$

$\mathbf{V'(2) = -3 \times 2^2 + 2 \times 2 + 12 = 4}$

<em>Interpretation</em>

V(2) means that, 20 people were infected after 2 weeks of the virus spread

V'(2) means that, the rate of infection of the virus after 2 weeks is 4 people per week

<u>(f) Sketch the tangent line at (2,V(2))</u>

See attachment for the tangent line

The slope of this line is:

$\mathbf{m = \frac{V(2)}{2}}$

$\mathbf{m = \frac{20}{2}}$

$\mathbf{m = 10}$

The slope of the tangent line is 10

<u>(g) Estimate V(2.1)</u>

The <em>value of 2.1 </em>is

$\mathbf{V(2.1) = (-2.1)^3 + (2.1)^2 + 12 \times 2.1}$

$\mathbf{V(2.1) = 20.35}$

<u />

<u>(h) The maximum number of people infected at the same time</u>

Using the graph, the maximum point on the graph is:

$\mathbf{(t,V(t) = (2.361,20.745)}$

This means that:

The maximum number of people infected at the same time is approximately 21.

The rate of infection at this point is:

$\mathbf{m = \frac{V(t)}{t}}$

$\mathbf{m = \frac{20.745}{2.361}}$

$\mathbf{m = 8.79}$

The rate of infection is <em>8.79 people per week</em>

Read more about graphs and functions at:

brainly.com/question/18806107

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3 years ago

45.36482 rounds to the neatest thousandths

Pani-rosa [81]

Answer:

45.365

Step-by-step explanation:

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4 years ago

Will someone please answer? I will mark brainliest!

Karo-lina-s [1.5K]

Answer:

Option 4

Step-by-step explanation:

Functions must pass the Vertical Line Test (VLT). Every input has to have exactly one output.

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3 years ago

Mrs. Bogaczyk got bored and decided to go on an Amazon spending spree! She bought 3 pairs of flip flops for $14.95 each, a sundr

Dovator [93]

Step-by-step explanation:

3 pairs of flip flops = 14.95 x 3 = 44.85

Total amount spent = 44.85 + 21.50 + 9.99 + 15. 44 = 91.78

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Mrs B spent 99.12 altogether

Budget = 100

Then money left = 100 - 99.12 = 0.88

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3 years ago

Let f(x) = 12x5 − 36x4 − 6x3 and g(x) = 3x2. Find f of x over g of x.

allsm [11]

Answer:

$4x^3-12x^2-2x$

Step-by-step explanation:

Given:

$f(x)= 12x^5-36x^4-6x^3$

$g(x)=3x^2$

We need to find $\frac{f(x)}{g(x)}$ .

Solution:

We have attached the division for your reference.

Step 1:

Now here Dividend is $12x^5-36x^4-6x^3$ and Divisor is $3x^2$ so we will multiply the Divisor with $4x^3$ we will get the answer as $12x^5$ so from dividend $12x^5$ will get subtracted and the remainder will be $-36x^4-6x^3$ and the Quotient will be $4x^3$ .

Step 2:

Now the Dividend is $-36x^4-6x^3$ and Divisor is $3x^2$ so we will multiply the Divisor with $-12x^2$ we will get the answer as $-36x^2$ so from dividend $-36x^2$ will get subtracted and the remainder will be $-6x^3$ and the Quotient will be $4x^3-12x^2$

Step 3:

Now the Dividend is $-6x^3$ and Divisor is $3x^2$ so we will multiply the Divisor with $-2x$ we will get the answer as so $-6x^3$ from dividend $-36x^2$ will get subtracted and the remainder will be 0 and the Quotient will be $4x^3-12x^2-2x$

Hence $\frac{f(x)}{g(x)} =4x^3-12x^2-2x$ .

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