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3 years ago

Which of the following functions is graphed below?

Mathematics

1 answer:

Ghella [55]3 years ago

6 0

Selection A is appropriate.

_____
The black dot on the graph means that one of the regions of interest will be
x ≤ 1

The y-intercept for the left branch of the graph is -4, so we khow that
y = x³ -4, x ≤ 1
will be part of the function definition.

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Rewrite the statement in mathematical notation. (Let y be the distance from the top of the ladder to the floor, x be the distanc

In-s [12.5K]

Answer:

$\frac{dy}{dt}=\frac{6y}{x}\text{ ft per sec}$

Step-by-step explanation:

Let L be the length of the ladder,

Given,

x = the distance from the base of the ladder to the wall, and t be time.

y = distance from the base of the ladder to the wall,

So, by the Pythagoras theorem,

$L^2 = y^2 + x^2$

$\implies L = \sqrt{y^2 + x^2}$ ,

Differentiating with respect to time (t),

$\frac{dL}{dt}=\frac{d}{dt}(\sqrt{x^2 + y^2})$

$=\frac{1}{2\sqrt{x^2 + y^2}}\frac{d}{dt}(x^2 + y^2)$

$=\frac{1}{2\sqrt{x^2 + y^2}}(2x\frac{dx}{dt}+2y\frac{dy}{dt})$

$=\frac{1}{\sqrt{x^2 +y^2}}(x\frac{dx}{dt}+y\frac{dy}{dt})$

Here,

$\frac{dy}{dt}=-6\text{ ft per sec}$

Also, $\frac{dL}{dt} = 0$ ( Ladder length = constant ),

$\implies \frac{1}{\sqrt{x^2 +y^2}}(x(-6)+y\frac{dy}{dt})=0$

$-6x + y\frac{dy}{dt}=0$

$y\frac{dy}{dt}=6x$

$\implies \frac{dy}{dt}=\frac{6y}{x}\text{ ft per sec}$

Which is the required notation.

8 0

3 years ago

The diagram below shows a shaded parallelogram drawn inside a rectangle. Using Pythagoras, find the hypotenuse of triangle A and

Julli [10]

Answer: 5.9 cm for both triangles.

Step-by-step explanation:

Hi, since the situation forms 2 right triangles we have to apply the Pythagorean Theorem:

c^2 = a^2 + b^2

Where c is the hypotenuse of a triangle (the longest side of the triangle) and a and b are the other sides.

Replacing with the values given:

c^2 = 3^2 + 5^2

c^2 = 9+25

c^2 = 34

c = √34

c = 5.9 cm

Since both triangles are identical ( same side lengths) the hypotenuse is the same for both, 5.9 cm.

Feel free to ask for more if needed or if you did not understand something.

5 0

3 years ago

The elevation of driskill mountain Louisiana is 163 meters above sea level death Valley has an elevation of -86 meters right any

timama [110]

Answer:

$-86$

Step-by-step explanation:

We have been given that the elevation of driskill mountain Louisiana is 163 meters above sea level. The death Valley has an elevation of -86 meters.

We can represent this information in an inequality as: $-86$ . Our inequality means that the elevation of death valley is less than elevation of driskill mountain.

8 0

3 years ago

Read 2 more answers

(Set up and solve the system, then answer the associated question)

Dimas [21]

9514 1404 393

Answer:

red division: 6 teams
blue division: 5 teams

Step-by-step explanation:

We can let r and b represent the numbers of teams in the red and blue divisions, respectively. The total number of goals scored in each division will be the average for that division times the number of teams in that division.

r - b = 1 . . . . . . there is 1 more red team than blue

4.5r +4.2b = 48 . . . . . . total goals scored per week

Solving by substitution, we have ...

r = b +1

4.5(b +1) +4.2b = 48 . . . . substitute for r

8.7b +4.5 = 48 . . . . . . . . simplify

8.7b = 43.5 . . . . . . . . . . subtract 4.5

b = 43.5/8.7 = 5 . . . . . divide by 8.7

r = b +1 = 6 . . . . . . . . . find r

There are 6 red teams and 5 blue teams.

_____

<em>Additional comment</em>

The basic idea is that you make an equation for each relation given in the problem statement. For a problem like this, you do need to have an understanding of how the average number of goals would be calculated and how that relates to the total goals.

8 0

3 years ago

Is 3/5 mile closer than 1/2 mile

Romashka [77]

Yes to both, and for future help, if you find a common denominator(the bottom one) by multiplication and one is higher, boom you have your answer.

6 0

3 years ago