What is the equation of the function:(-1,3),(0,4),(2,6)<br> A) f(x)= x^2 +x -4

A body moves s metres in a time t seconds so that s = t3 – 3t2 + 8. Find:

Lady bird [3.3K]

Using derivatives, it is found that:

i) $v(t) = 3t^2 - 6t$

ii) 9 m/s.

iii) $a(t) = 6t - 6$

iv) 6 m/s².

v) 1 second.

<h3>What is the role of derivatives in the relation between acceleration, velocity and position?</h3>

The velocity is the derivative of the position.

The acceleration is the derivative of the velocity.

In this problem, the position is:

$s(t) = t^3 - 3t^2 + 8$

item i:

Velocity is the <u>derivative of the position</u>, hence:

$v(t) = 3t^2 - 6t$

Item ii:

$v(3) = 3(3)^2 - 6(3) = 27 - 18 = 9$

The speed is of 9 m/s.

Item iii:

Derivative of the velocity, hence:

$a(t) = 6t - 6$

Item iv:

$a(2) = 6(2) - 6 = 6$

The acceleration is of 6 m/s².

Item v:

t for which a(t) = 0, hence:

$6t - 6 = 0$

$6t = 6$

$t = \frac{6}{6}$

$t = 1$

Hence 1 second.

You can learn more about derivatives at brainly.com/question/14800626

7 0

2 years ago

The equation h(t) = -16t² + 80t + 64 represented the height, in feet, of a potato t seconds after it has been launched.

Lyrx [107]

Answer:

Part A) The potato hit the ground at t=5.70 seconds (see the explanation)

Part B) The potato is 40 feet off the ground at the time t=5.28 seconds (see the explanation)

Step-by-step explanation:

we have

$h(t)=-16t^2+80t+64$

where

h(t) is the height of a potato in feet

t is the time in seconds

Part A) Write an equation that can be solved to find when the potato hits the ground. Then solve the equation

we know that

When the potato hit the ground, the value of h(t) must be equal to zero

so

For h(t)=0

$-16t^2+80t+64=0$

Solve the quadratic equation

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-16t^2+80t+64=0$

so

$a=-16\\b=80\\c=64$

substitute in the formula

$t=\frac{-80\pm\sqrt{80^{2}-4(-16)(64)}} {2(-16)}$

$t=\frac{-80\pm\sqrt{10,496}} {-32}$

$t=\frac{-80+\sqrt{10,496}} {-32}=-0.70$

$t=\frac{-80-\sqrt{10,496}} {-32}=5.70$

therefore

The potato hit the ground at t=5.70 seconds

Part B) Write an equation that can be solved to find when the potato is 40 feet off the ground. Then solve the equation

For h(t)=40 ft

substitute in the quadratic equation

$-16t^2+80t+64=40$

$-16t^2+80t+24=0$

Solve the quadratic equation

we have

$a=-16\\b=80\\c=24$

substitute in the formula

$t=\frac{-80\pm\sqrt{80^{2}-4(-16)(24)}} {2(-16)}$

$t=\frac{-80\pm\sqrt{7,936}} {-32}$

$t=\frac{-80+\sqrt{7,936}} {-32}=-0.28$

$t=\frac{-80-\sqrt{7,936}} {-32}=5.28$

therefore

The potato is 40 feet off the ground at the time t=5.28 seconds

3 0

3 years ago

When given a raw score, explain how to use the normal curve to compare that

stepladder [879]

First of all, you need to come to an understanding of what you mean by "compare that score to the population." Often, that will mean determining the percentile rank of the score.

To determine the percentile rank of a raw score, you first nomalize it by determining the number of standard deviations it lies from the mean. That is, you subtract the population mean and divide that difference by the population standard deviation. Now, you have what is referred to as a "z-score".

Using a table of standard normal probability functions (or an equivalent calculator or app), you look up the cumulative distribution value corresponding to the z-score you have. This number between 0 and 1 (0% and 100%) will be the percentile rank of the score, the fraction of the population that has raw scores below the raw score you started with.

7 0

3 years ago

That is weird but here it is again

borishaifa [10]

Answer: 3.6 feet per year

Pick any column and divide the feet over the years

eg: 7.2/2 = 3.6 (column 1)

You can think of it as the ratio

7.2 feet: 2 years

and then divide both sides by 2 to get "1 year" on the right side

7.2 feet: 2 years

7.2/2 feet: 2/2 years

3.6 feet: 1 year

3 0

3 years ago

Read 2 more answers

Is the following relation a function?

Stels [109]

No, if you do the vertical line test( draw a vertical line on each graph line that hits the circle) if the lline touches more than one point AT ANY TIME it is not a function. So in this case it is not a function

3 0

3 years ago

Read 2 more answers

What is the equation of the function:(-1,3),(0,4),(2,6) A) f(x)= x^2 +x -4