All categories

3 years ago

Can someone break this down for me?!

Mathematics

1 answer:

Anna [14]3 years ago

5 0

Answer:

The answers are in the question.

Step-by-step explanation:

The wording can be off-putting but the answers are mostly there for you. It says that when the wind was at the tail of the plane, the travel was hastened to 5 hours instead of six. Is the rate of speed with the wind in favor of the plane is r+21, then it stands to reason that traveling AGAINST the wind will cause the rate to drop to r-21. Taking the average of the two travel times (5 and 6 hours each), we get 5.5 hours. Since speed is distance divided by time, the speed of the plane in still air will be <em>d</em> / 5.5

Be sure to label the speed as mph.

You might be interested in

SOLVE THE QUESTION BELOW ASAP

qwelly [4]

Answer:

Part A) The graph in the attached figure (see the explanation)

Part B) 16 feet

Part C) see the explanation

Step-by-step explanation:

Part A) Graph the function

Let

h(t) ----> the height in feet of the ball above the ground

t -----> the time in seconds

we have

$h(t)=-16t^{2}+98$

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex is a maximum

To graph the parabola, find the vertex, the intercepts, and the axis of symmetry

<em>Find the vertex</em>

The function is written in vertex form

The vertex is the point (0,98)

Find the y-intercept

The y-intercept is the value of the function when the value of t is equal to zero

For t=0

$h(t)=-16(0)^{2}+98$

$h(0)=98$

The y-intercept is the point (0,98)

Find the t-intercepts

The t-intercepts are the values of t when the value of the function is equal to zero

For h(t)=0

$-16t^{2}+98=0$

$t^{2}=\frac{98}{16}$

square root both sides

$t=\pm\frac{\sqrt{98}}{4}$

$t=\pm7\frac{\sqrt{2}}{4}$

therefore

The t-intercepts are

$(-7\frac{\sqrt{2}}{4},0), (7\frac{\sqrt{2}}{4},0)$

$(-2.475,0), (2.475,0)$

Find the axis of symmetry

The equation of the axis of symmetry in a vertical parabola is equal to the x-coordinate of the vertex

$x=0$ ----> the y-axis

To graph the parabola, plot the given points and connect them

we have

The vertex is the point $(0,98)$

The y-intercept is the point $(0,98)$

The t-intercepts are $(-2.475,0), (2.475,0)$

The axis of symmetry is the y-axis

The graph in the attached figure

Part B) How far is the artifact fallen from the time t=0 to time t=1

we know that

For t=0

$h(t)=-16(0)^{2}+98$

$h(0)=98\ ft$

For t=1

$h(t)=-16(1)^{2}+98$

$h(1)=82\ ft$

Find the difference

$98\ ft-82\ ft=16\ ft$

Part C) Does the artifact fall the same distance from time t=1 to time t=2 as it does from the time t=0 to time t=1?

we know that

For t=1

$h(t)=-16(1)^{2}+98$

$h(1)=82\ ft$

For t=2

$h(t)=-16(2)^{2}+98$

$h(2)=34\ ft$

Find the difference

$82\ ft-34\ ft=48\ ft$

The artifact fall 48 feet from time t=1 to time t=2 and fall 16 feet from time t=0 to time t=1

therefore

The distance traveled from t=1 to t=2 is greater than the distance traveled from t=0 to t=1

8 0

3 years ago

How does the definition of the prefixes mono-,bi-, and tri- help when naming polynomials

Leviafan [203]

Answer:

They let you know the number of numbers there are/will be.

Step-by-step explanation:

Mono, being one, means there will only be one number is the equation.

Bi, being two, means there will be two numbers in the equation.

and tri, being three, means there are three numbers in the equation.

8 0

3 years ago

Read 2 more answers

A tennis racket at at sport city costs $180 and is discounted 15% the same model racket costs$200 at tennis world and is on sale

MaRussiya [10]

Mate, stop repeating questions, wait until your question has been answered.

15% of 180 is (180 * 0.15) = 27.

180 - 27 = $153 paid.

20% of 200 = (200 * 0.2) = 40.

200 - 40 = $160 paid.

Therefore Sport City offered the better deal.

4 0

3 years ago

Read 2 more answers

A cannon ball shoots out from a cannon that is 28 inches long at 2700 ft s. What is the

Reika [66]

Answer:

a = 1565217.39 ft / s ^ 2

t = 0.001725 seconds

Step-by-step explanation:

The first thing is to use the same system of units therefore we will pass the 28 inches to feet, like this:

28 in * (1 ft / 12 in) = 2.33 ft

Now yes, we can continue, we have the following data:

vi = 0

vf = 2700 ft / s

the equations in this case are as follows:

vf = vi + a * t

vf = a * t

rearranging for a

a = vf / t (1)

now with the position equation we know that:

x = vi * t + (a * t ^ 2) / 2

x = (a * t ^ 2) / 2 (2)

now replacing (1) in (2), we are left with:

x = (vf / t) * (t ^ 2) / 2

knowing that x would be 2.33 ft, which is when the cannonball exits the cannon.

2.33 = 2700 * t / 2

t = 2.33 * 2/2700 = 0.001725 seconds.

and now replace in (1)

a = vf / t = 2700 / 0.001725 = 1565217.39 ft / s ^ 2

3 0

3 years ago

There are four more girls than boys in Ms. Raub's class of 28 students. What is the ratio of number of girls to the number of bo

Alex73 [517]

16:12

Subtract 4 from 28 then divide by 2.

8 0

3 years ago