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3 months ago

Which of the following rational functions is graphed below?

Mathematics

2 answers:

Svet_ta [12.7K]3 months ago

6 0

Answer:

The rational function depicted on the graph is B.

zzz [12.3K]3 months ago

5 0

Answer:

The graphed rational function corresponds to:

Option: B

B. $F(x)=\dfrac{x}{(x-1)(x+1)}$

Detailed explanation:

Examining the graph indicates vertical asymptotes at x=1 and x= -1.

The vertical asymptotes occur where the denominator equals zero.

If the numerator’s degree is lower than the denominator’s, y=0 acts as the horizontal asymptote.

Only function B meets both criteria:

B. $F(x)=\dfrac{x}{(x-1)(x+1)}$

(For option A, denominator zeros are at x=0 and -1, so vertical asymptotes lie there.

Option C has vertical asymptotes at x=0 and 1.

Option D has a single vertical asymptote at x=0, which doesn’t match the graph.)

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Yuson must complete 210 min of community service. She does 30 min each day. Which linear equation represents the number of minut

PIT_PIT [12445]

Answer:

Comprehensive explanation: $y=-30x+210$

Let's denote

x -----> the number of days

and

y ----> the remaining minutes for Yuson

We know that

The linear equation in slope-intercept form can be represented as

$y=mx+b$

here

m indicates the slope

b represents the y-coordinate of the y-intercept (starting value)

In this scenario, we have

The slope is defined as

$m=-30\frac{min}{day}$ ----> negative, as it indicates a decreasing function

$b=210\ min$ ----> initial value

substituting the values

$y=-30x+210$

3 0

2 months ago

Find the dimensions of the closed rectangular box with maximum volume that can be inscribed in the unit sphere.

Inessa [12570]

Answer:

Wyjaśnienie krok po kroku:

Załóżmy, że prostokąt ma wierzchołki (x,y,z) w dodatnim oktancie. Prostokątny pudełko musi być symetryczne względem wszystkich trzech osi.

Wtedy jego boki to

$2x,2y,2z$

Objętość = $8xyz$

Maksymalizuj objętość przy założeniu

$x^2+y^2+z^2 =1$

tj. $g(x,y,z) = x^2+y^2+z^2 -1=0$

Użyj mnożników Lagrange'a, mamy

$∇f(x,y,z)=λ∇g(x,y,z)$ przy maksimum

$∇f(x,y,z)=λ∇g(x,y,z) =(8yz,8xz,8xy)\\∇g(x,y,z)=(2x,2y,2z)$

$8yz=2λx8xz=2λy8xy=2λz$

Dzieląc otrzymujemy

$\frac{y}{x} =\frac{x}{y} \\x^2=y^2$

Podobnie $y^2=z^2$

Zatem otrzymujemy $3x^2 =1\\x = \frac{1}{\sqrt{3} }$

Stąd wymiary to

(2x,2y,2z)

$\frac{2}{\sqrt{3} },\frac{2}{\sqrt{3} },\frac{2}{\sqrt{3} } )$

</pzatem>

3 0

3 months ago

Write the number 0.21212121.. as a fraction let x=

AnnZ [12381]

To work with the repeating decimals, note that since there are two digits repeating, you will be using a 1 followed by two zeros, which is 100. This factor will be important for subsequent calculations.

Let’s denote the repeating decimal as x.

Thus, you can write

x = 0.212121...

Now, if you multiply this equation by 100, you can write it on top of the previous equation.
This results in:

100x = 21.212121...
x = 0.212121...

Next, set up a subtraction by taking the second equation from the first:

100x = 21.212121...
x = 0.212121...
- ----------------------------
99x = 21

Solving for x involves dividing both sides by 3:

33x = 7

Then, divide both sides by 33:

x = 7/33

Thus, we conclude that the repeating decimal 0.212121... equates to the fraction 7/33.

Answer: the fraction is 7/33

7 0

3 months ago

A quarterback looks downfield at a receiver who is 14 yards away. The receiver is covered, so the quarterback turns 30° to his r

Zina [12379]

Your answer will be C.

8 0

2 months ago

Read 3 more answers