Ask question

Ask question

All categories

3 years ago

9

The function s(t) represents the position of an object at time t moving along a line. Suppose s(2)=150 and s(5)=237. Find the a

verage velocity of the object over the interval of time [1, 3].

1 answer:

trapecia [35]3 years ago

5 0

Answer:

29 is answer.

Step-by-step explanation:

Given that the function s(t) represents the position of an object at time t moving along a line. Suppose s(2)=150 and s(5)=237.

To find average velocity of the object over the interval of time [1,3]

We know that derivative of s is velocity and antiderivative of velocity is position vector .

Since moving along a line equation of s is

use two point formula

$\frac{s-150}{237-150} =\frac{t-2}{5-2} \\s=29t-58+150\\s=29t+92$ gives the position at time t.

Average velocity in interval (1,3)

= $\frac{1}{3-1} (s(3)-s(1))\\=\frac{1}{2} [87+58-29-58]\\=29$

You might be interested in

Find the volume of the pyramid below.<br> 7.2 in<br> 9.7 in

kumpel [21]

Answer:

23.28 inches (im not sure if this is correct because you need length, height, and width.)

Step-by-step explanation:

<u>lwh</u>

3

4 0

2 years ago

The amount of time Ricardo spends brushing his teeth follows a Normal distribution with unknown mean and standard deviation. Ric

Papessa [141]

Let $X$ denote the number of minutes spent brushing his teeth, and let $\mu$ be the mean and $\sigma$ the standard deviation for this distribution.

$\mathbb P(X$

The z-score corresponding to this probability is approximately $z=-0.2533$ , which means

$\dfrac{1-\mu}\sigma=-0.2533\iff\mu-0.2533\sigma=1$

Next, (note the sign change)

$\mathbb P(X>2)=0.02\implies\mathbb P(X\le2)=\mathbb P\left(\dfrac{X-\mu}\sigma\le\dfrac{2-\mu}\sigma\right)=0.98$

The corresponding z-score is approximately $z=2.0538$ , so you have

$\dfrac{2-\mu}\sigma=2.0538\iff\mu+2.0538\sigma=2$

Solving the two equations for $\mu$ and $\sigma$ , you'll find that the mean is approximately $\mu=1.1098$ and the standard deviation is approximately $\sigma=0.4334$ .

7 0

3 years ago

I REALLY NEED HELP WORTH 10 POINTS URGENT!!!!!

polet [3.4K]

Answer:

$(f\circ g)(4)=31$

Step-by-step explanation:

<u>Composite Function</u>

Given f(x) and g(x) real functions, the composite function named fog(x) is defined as:

$(f\circ g)(x)=f(g(x))$

For practical purposes, it can be found by substituting g into f.

We have:

$f(x)=3x+1$

$g(x)=x^2-6$

Computing the composite function:

$(f\circ g)(x)=f(g(x))=3(x^2-6)+1$

Operating:

$(f\circ g)(x)=3x^2-18+1$

Operating:

$(f\circ g)(x)=3x^2-17$

Now evaluate for x=4

$(f\circ g)(4)=3(4)^2-17=48-17$

$\boxed{(f\circ g)(4)=31}$

8 0

3 years ago

Greg swam 4 kilometers against the current in the same amount of time it took him to swim 16 kilometers with the current. The ra

ad-work [718]

Answer:

5 kmph

Step-by-step explanation:

Given: Greg swam 4 kilometers against the current.

Greg swam 16 kilometers with the current.

Rate of the current was 3kmph.

Lets assume the speed of greg swimming with no current be "x".

∴ Speed of swimming against current= $(x-3)\ kmph$

Speed of swimming with current= $(x+3)\ kmph$

As given, it took same amount of time to swim both with current and against current.

∴ Forming an equation to find the value of x, which is speed of greg swimming with no current.

We know, $Time= \frac{Distance}{Speed}$

⇒ $\frac{4}{(x-3)} = \frac{16}{(x+3)}$

Multiplying both side by (x+3) and (x-3)

⇒ $4\times (x+3)= 16\times (x-3)$

Using distributive property of multiplication.

⇒ $4x+12= 16x-48$

Subtracting both side by 4x and adding by 48.

⇒ $60= 12x$

Dividing both side by 12

⇒ $x= \frac{60}{12} = 5\ kmph$

Hence, Greg can swim at the rate of 5kmph with no current.

7 0

3 years ago

1. A certain ceiling is made up of tiles. Every square meter of ceiling requires 10.75 tiles. Fill in the table with the missing

dybincka [34]

Given:

Consider the below table attached with this question.

Every square meter of ceiling requires 10.75 tiles.

To find:

The missing values in the table.

Solution:

We have,

1 square meter of ceiling = 10.75 tiles. ...(i)

Therefore, the number of tiles corresponding to 1 square meter of ceiling is 10.75.

Multiply both sides by 10.

10×1 square meter of ceiling = 10×10.75 tiles.

10 square meter of ceiling = 107.5 tiles.

Therefore, the number of tiles corresponding to 10 square meter of ceiling is 107.5.

Divide both sides by 10.75 in (i).

$\dfrac{1}{10.75}$ square meter of ceiling = 1 tile.

Multiply both sides by 100.

$\dfrac{100}{10.75}$ square meter of ceiling = 100 tiles.

On approximating the value, we get

9.3 square meter of ceiling = 100 tiles.

Therefore, the square meters of ceiling corresponding to 100 tiles is about 9.3.

Multiply both sides by a in (i).

a×1 square meter of ceiling = a×10.75 tiles.

a square meter of ceiling = 10.75a tiles.

Therefore, the number of tiles corresponding to a square meter of ceiling is 10.75a.

8 0

3 years ago

Read 2 more answers