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3 years ago

Describe the end behavior of the following function:

Mathematics

1 answer:

Furkat [3]3 years ago

7 0

Answer:

C. The graph of the function starts high and ends low

Step-by-step explanation:

For $f(x)=-x^5+x^2-x$ , as $x$ approaches negative infinity, $f(x)$ approaches infinity, and as $x$ approaches infinity, $f(x)$ approaches negative infinity.

Thus, we have:

$\lim_{x\rightarrow -\infty}f(x)=\infty,\\\lim_{x\rightarrow \infty}f(x)=-\infty$

This corresponds with answer choice C. The graph of the function starts high and ends low.

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If the right side of the equation dy dx = f(x, y) can be expressed as a function of the ratio y/x only, then the equation is sai

melomori [17]

Answer:

y = x*sqrt(Cx - 1)

Step-by-step explanation:

Given:

dy / dx = (x^2 + 5y^2) / 2xy

Find:

Solve the given ODE by using appropriate substitution.

Solution:

- Rewrite the given ODE:

dy/dx = 0.5(x/y) + 2.5(y/x)

- use substitution y = x*v(x)

dy/dx = v + x*dv/dx

- Combine the two equations:

v + x*dv/dx = 0.5*(1/v) + 2.5*v

x*dv/dx = 0.5*(1/v) + 1.5*v

x*dv/dx = (v^2 + 1) / 2v

-Separate variables:

(2v.dv / (v^2 + 1) = dx / x

- Integrate both sides:

Ln (v^2 + 1) = Ln(x) + C

v^2 + 1 = Cx

v = sqrt(Cx - 1)

- Back substitution:

(y/x) = sqrt(Cx - 1)

y = x*sqrt(Cx - 1)

3 0

3 years ago

Round to the nearest Cent.

Westkost [7]

1. $.0999 = $.1

2. $2.0192 = $2.02

3. $21.5953 = $21.60

4. $35.6667 = $35.67

5. $1.3999 = $1.40

6. $25.3333 = $25.33

5 0

3 years ago

Read 2 more answers

Add the following quantities, 76.2 pm + 0.123fm

blondinia [14]

Answer:

1000

123f

381p

)

Step-by-step explanation:

i dont know if thats right that my compution

sorry

5 0

3 years ago

A corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial off

Yakvenalex [24]

Answer:

a) The officers can be appointed in 24024 different ways.

b) The committee can be appointed in 1001 different ways.

c) 1.1% probability of randomly selecting the committee members and getting the three youngest of the qualified candidates

Step-by-step explanation:

The order in which the officers are appointed is important(the first is the president, second the CEO and so on...). So the permutations formula will be used.

Otherwise, in the committee there are no roles, so the order is not important. So the combinations formula will be used.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

A. How many different ways can the officers be appointed?

4 from a set of 14, with roles. So a permutation.

$P_{(14,4)} = \frac{14!}{(14-4)!} = 24024$

The officers can be appointed in 24024 different ways.

B. How many different ways can the committee be appointed?

4 from a set of 14, without roles. So combination

$C_{14,4} = \frac{14!}{4!(14-4)!} = 1001$

The committee can be appointed in 1001 different ways.

C. What is the probability of randomly selecting the committee members and getting the three youngest of the qualified candidates?

A probability is the number of desired outcomes divided by the number of total outcomes.

Desired outcomes.

The three youngest(1 combination), and one of the other 14-3 = 11. So $D = 1*11 = 11$

Total outcomes:

From B., 1001, so $T = 1001$

Probability:

$p = \frac{D}{T} = \frac{11}{1001} = 0.011$

1.1% probability of randomly selecting the committee members and getting the three youngest of the qualified candidates

8 0

3 years ago

A tunnel is constructed with a semielliptical arch. The width of the tunnel is 60 feet, and the maximum height at the center of

rusak2 [61]

The height of the tunnel 5 feet from the edge is 13.82 feet option second 13.82 feet is correct.

<h3>What is an ellipse?</h3>

An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.

We have:

A tunnel is constructed with a semi-elliptical arch. The width of the tunnel is 60 feet, and the maximum height at the center of the tunnel is 25 feet.

2a = 60 (width of the tunnel is 60 feet)

a = 30

And the maximum height at the center of the tunnel is 25 feet

b = 25

Let's assume the center of the ellipse is at the origin.

So the equation of the ellipse:

$\rm \dfrac{x^2}{30^2}+\dfrac{y^2}{25^2}=1$