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kicyunya [14]
3 years ago
14

Tony plans to run a 5,000-meter fun run at a constant rate of 250 meters per minute. He uses function f to model his distance fr

om the finish line x minutes after the start of the race.
x f(x)
0 5,000
1 4,750
2 4,500
3 4,250
4 4,000
5 3,750
6 3,500


A.
Tony's function is always decreasing.
B.
Tony's function is always negative.
C.
Tony's function is exponential.
D.
The domain of Tony's function is [0 , 5,000].

Mathematics
2 answers:
kramer3 years ago
8 0

Answer:

Option A.

Step-by-step explanation:

Based on the information provided on the question

the function used to model Tony's run is:

f(x) = -250*x  + 5000

This means that after x = 20 minutes, Tony will arrive to the finish line

f(20) = -250*(20)  + 5000 = -5000 + 5000 = 0

The function is always decreasing, because we are dealing with a line with negative slope.

Option A.

Elden [556K]3 years ago
5 0

Answer:

Step-by-step explanation:

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Sketch the region enclosed by y=3x and y=x^2 . Then find the area of the region.
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A=4.5u^2

Step-by-step explanation:

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\int\limits^3_0 {3x-x^2} \, dx =\left\frac{3x^2}{2}-\frac{x^3}{3}\right|^3_0=\frac{3(3)^2}{2}-\frac{(3)^3}{3}-\left(\frac{3(0)^2}{2}-\frac{(0)^3}{3}\right)\\\int\limits^3_0 {3x-x^2} \, dx =\frac{27}{2}-\frac{27}{3} =13.5-9=4.5u^2

6 0
3 years ago
Suppose a, b denotes of the quadratic polynomial x² + 20x - 2022 &amp; c, d are roots of x² - 20x + 2022 then the value of ac(a
Alja [10]
<h3><u>Correct Question :- </u></h3>

\sf\:a,b \: are \: the \: roots \: of \:  {x}^{2} + 20x - 2020 = 0 \: and \:  \\  \sf \: c,d \: are \: the \: roots \: of \:  {x}^{2}  -  20x  + 2020 = 0 \: then \:

\sf \: ac(a - c) + ad(a - d) + bc(b - c) + bd(b - d) =

(a) 0

(b) 8000

(c) 8080

(d) 16000

\large\underline{\sf{Solution-}}

Given that

\red{\rm :\longmapsto\:a,b \: are \: the \: roots \: of \:  {x}^{2} + 20x - 2020 = 0}

We know

\boxed{\red{\sf Product\ of\ the\ zeroes=\frac{Constant}{coefficient\ of\ x^{2}}}}

\rm \implies\:ab = \dfrac{ - 2020}{1}  =  - 2020

And

\boxed{\red{\sf Sum\ of\ the\ zeroes=\frac{-coefficient\ of\ x}{coefficient\ of\ x^{2}}}}

\rm \implies\:a + b = -  \dfrac{20}{1}  =  - 20

Also, given that

\red{\rm :\longmapsto\:c,d \: are \: the \: roots \: of \:  {x}^{2}  -  20x  + 2020 = 0}

\rm \implies\:c + d = -  \dfrac{( - 20)}{1}  =  20

and

\rm \implies\:cd = \dfrac{2020}{1}  = 2020

Now, Consider

\sf \: ac(a - c) + ad(a - d) + bc(b - c) + bd(b - d)

\sf \:  =  {ca}^{2} -  {ac}^{2} +  {da}^{2} -  {ad}^{2} +  {cb}^{2} -  {bc}^{2} +  {db}^{2} -  {bd}^{2}

\sf \:  =  {a}^{2}(c + d) +  {b}^{2}(c + d) -  {c}^{2}(a + b) -  {d}^{2}(a + b)

\sf \:  = (c + d)( {a}^{2} +  {b}^{2}) - (a + b)( {c}^{2} +  {d}^{2})

\sf \:  = 20( {a}^{2} +  {b}^{2}) + 20( {c}^{2} +  {d}^{2})

\sf \:  = 20\bigg[ {a}^{2} +  {b}^{2} + {c}^{2} +  {d}^{2}\bigg]

We know,

\boxed{\tt{  { \alpha }^{2}  +  { \beta }^{2}  =  {( \alpha   + \beta) }^{2}  - 2 \alpha  \beta  \: }}

So, using this, we get

\sf \:  = 20\bigg[ {(a + b)}^{2} - 2ab +  {(c + d)}^{2} - 2cd\bigg]

\sf \:  = 20\bigg[ {( - 20)}^{2} +  2(2020) +  {(20)}^{2} - 2(2020)\bigg]

\sf \:  = 20\bigg[ 400 + 400\bigg]

\sf \:  = 20\bigg[ 800\bigg]

\sf \:  = 16000

Hence,

\boxed{\tt{ \sf \: ac(a - c) + ad(a - d) + bc(b - c) + bd(b - d) = 16000}}

<em>So, option (d) is correct.</em>

4 0
2 years ago
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