Which of the following functions has an initial value of 3/2 and a rate of change of -2/3?

We are given the Indefinite integral ;

[tex]{:\implies \quad \displaystyle \sf \int \dfrac{dx}{x-x^{3}}}[/tex]

Take x common from denominator ;

[tex]{:\implies \quad \displaystyle \sf \int \dfrac{dx}{x(1-x^{2})}}[/tex]

Now , Put ;

[tex]{:\implies \quad \displaystyle \sf x^{2}=u}[/tex]

So that ;

[tex]{:\implies \quad \displaystyle \sf dx=\dfrac{du}{2\sqrt{u}}\quad and\quad x=\sqrt{u}}[/tex]

Now , putting the values ;

[tex]{:\implies \quad \displaystyle \sf \int \dfrac{1}{\sqrt{u}(1-u)}\times \dfrac{1}{2}\times \dfrac{du}{\sqrt{u}}}[/tex]

Now , as constant can be taken out of the integrand, so now ;

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}\int \dfrac{du}{u(1-u)}}[/tex]

Using partial fraction decomposition, Rewrite the integral as ;

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}\int \left(\dfrac{1}{u}+\dfrac{1}{1-u}\right)du}[/tex]

As Integrals follow distributive property, so breaking the integral into two integrals, and continuing the integration

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}\left(\int \dfrac{1}{u}du+\int \dfrac{1}{1-u}du\right)}[/tex]

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}\bigg\{log|u|+\dfrac{log|1-u|}{(-1)}\bigg\}+C}[/tex]

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}(log|u|-log|1-u|)+C}[/tex]

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}log\bigg|\dfrac{u}{1-u}\bigg| +C}[/tex]

Putting value of u ;

[tex]{:\implies \quad \therefore \quad \underline{\underline{\displaystyle \bf \int \dfrac{dx}{x-x^{3}}=\dfrac{1}{2}log\bigg|\dfrac{x^2}{1-x^{2}}\bigg| +C}}}[/tex]

This is the required answer

We are given that the circumference of a circle is 77 units and we need to find it's diameter . But let's recall that for any Circle with radius r , the circumference is given by 2πr . And diameter is double of radius i.e d = 2r , so we can write the circumference as 2r(π) i.e dπ . So , now here

[tex]{:\implies \quad \sf d\pi =77}[/tex]

[tex]{:\implies \quad \sf d\times \dfrac{22}{7}=77}[/tex]

[tex]{:\implies \quad \sf d=\dfrac{77\times 7}{22}}[/tex]

[tex]{:\implies \quad \sf d=\dfrac{\cancel{11}\times 7\times 7}{\cancel{11}\times 2}}[/tex]

[tex]{:\implies \quad \sf d=\dfrac{49}{2}}[/tex]

[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{Diameter=24.5\:\: units}}}[/tex]

Answer:

87

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

Are f(x)=x2 and g(x) =4/5x2 correctly written?

This answer assumes they are supposed to be:

f(x)=x^2 and g(x) = (4/5)x^2

If these revisions are correct, g(x) would produce values that are (4/5) of f(x).

See attached graph.

I don't see any of the options for "best statement."

Answer:

$7.00

Step-by-step explanation:

Each pound cost $2 and we have 3 pounds which means that's $6:

3 • 2= 6

But then we have half a pound (1/2), well whats half of 2? the answer is 1 which means we add another dollar making that $7.00! :)

Answer:

sometimes, if their average angle is over 45 degrees

never are 2 obtuse angles summing to 180 degrees

always.  two 90 degree angles always sum to 180 which is a straight line

Answer:

×=7 or ×= ⅓ or ×=¼

Step-by-step explanation:

12׳ - 91ײ + 50× -7=0

(× -7)(3×- 1)(4×-1)=0

×-7=0 or 3× -1 =0 or 4× -1 = 0

×=7 or × =⅓ or ×=¼

Answer:

False

Step-by-step explanation:

3+2=5

3+2=55-1=4

3+2=55-1=44x4=16

3+2=55-1=44x4=16Hence, the equation is true.

Considering the situation described, we have that:

a) The Poisson distribution is used because we only have the mean.

b) There is a 0.0907 = 9.07% probability that there will be no defects.

c) There is a 0.2177 = 21.77% probability that there will be one defect.

d) There is a 0.3084 = 30.84% probability that there will be fewer than two defects.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

Item a:

The Poisson distribution is used because we only have the mean.

We have 0.8 defects per m² and 3 m², hence the mean is given by:

[tex]\mu = 3 \times 0.8 = 2.4[/tex]

Item b:

The probability is P(X = 0), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-2.4}(2.4)^{0}}{(0)!} = 0.0907[/tex]

There is a 0.0907 = 9.07% probability that there will be no defects.

Item c:

The probability is P(X = 1), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 1) = \frac{e^{-2.4}(2.4)^{1}}{(1)!} = 0.2177[/tex]

There is a 0.2177 = 21.77% probability that there will be one defect.

Item d:

The probability is P(X < 2), hence:

P(X < 2) = P(X = 0) + P(X = 1) = 0.0907 + 0.2177 = 0.3084.

There is a 0.3084 = 30.84% probability that there will be fewer than two defects.

More can be learned about the Poisson distribution at https://brainly.com/question/13971530

Answer:

Lines RS and TV are parallel.

Line TV has a slope of 0.

Line SW has an undefined slope.

Step-by-step explanation:

Lines RS and TV are parallel as we know they will never meet because they are straight lines.

Line TC has a slope of 0 because it is horizontal.

Line RS can't be the slope of 6, because a slope greater or less than 0 will be diagonal.

Line SW has an undefined slope because it is vertical.

Line SW is perpendicular to both as it forms a 90-degree angle for both, so the 5th term is wrong.

The statements A, B, and D are true about the given lines for the shown figure.

Parallel lines are two or more lines in a plane that are equidistant from each other at all points. This means that they never meet or cross each other, no matter how far they are extended.

As per the shown graph, we have:

Lines RS and TV are parallel since we know they will never intersect due to their straightness.

Because line TC is horizontal, it has no slope.

Line RS cannot have a slope of 6, since any slope higher or less than 0 is diagonal.

Since Line SW is vertical, it has an undefined slope.

Since line SW creates a 90-degree angle with both, the fifth statement is incorrect.

Therefore, statements A, B, and D are true about the given lines for the shown figure.

Learn more about the Lines here:

brainly.com/question/14511992

#SPJ7

Answer:

5/8 ft more

Step-by-step explanation:

3/4-1/8=5/8

6/8-1/8=5/8

Answer:

A=1/2b*h

Step-by-step explanation:

A=1/2b*h

a rectangle is b*h, and a right triangle is half a rectangle.

Answer

There is no Question??

Answer:

2*3

Step-by-step explanation:

first name last sw do

Stefany Tolesteros and LOLOftes thanks me later

Answer:

$84

Step-by-step explanation:

$80 * .05=4.00

$80 +4=$84.00

sure I will help in what you need help

Answer:

sure but what's the question???

Answer:

False

Step-by-step explanation:

2x6=12

2x6=1212-3=9

Hence, the equation is false.

Answer:

$18 = 6 pounds

Step-by-step explanation:

Answer:

AE = ED/////  A MIDPOINT DIVIDES A SEGMENT INTO TWO CONGRUENT SEGMENTS

AB = DC ///// OPPOSITE SIDES OF A RECTANGLE ARE CONGRUENT

<A IS A RIGHT ANGLE ///// THE INTERIOR ANGLES OF A RECTANGLE ARE RIGHT ANGLES

<D IS A RIGHT ANGLE ///// THE INTERIOR ANGLES OF A RECTANGLE ARE RIGHT ANGLES

<A = <D ///// ALL RIGHT ANGLES ARE CONGRUENT

TRIANGLES ABE = DCE ///// SAS

Hope this might help you.

Step-by-step explanation:

Answer:

y=11 * (18/5)

Step-by-step explanation:

y = kx

Where k is constant of proportionality

18 = k(5)

Hence k = (18/5)

For x = 11, y is....

Y = kx

Y= (18/5) * 11

Answer:

C.$20.00

Because it has to be lower than $400 and higher than $10

Answer:

60/7

Step-by-step explanation:

8x7=56

56+4=60

Answer:

[tex]=\frac{60}{7}[/tex]

Step-by-step explanation:

Given the following question:

[tex]8\frac{4}{7}[/tex]

In order to convert the mixed number into an improper fraction multiply the denominator by the whole number and then add the numerator. While of course keeping the denominator the same.

[tex]8\frac{4}{7}[/tex]
[tex]8\frac{4}{7}=7\times8=56+4=60=\frac{60}{7}[/tex]
[tex]=\frac{60}{7}[/tex]

Your answer is indeed "60/7."

Hope this helps.

Answer:

Let A(9, 9) & B(1, 4) are two point through which Line e passes.

Equation of e is given by

y - y1 = y2 - y1/ x2 - x1(x - x1)

or, y - 9 = 4-9/1-9 (x - 9)

or, -8y + 72 = -5x + 45

or, 5x - 8y + 27 = 0...........1.

Again,

consider C (1, 5) & D (9, 10) are other two points through with Line f pass through.

Also, eqn of f is,

y- 5 = 10-5/9-1 (x - 1)

or, 8y - 5 = 5x - 5

or, 5x - 8y =0 ...........2.

Let m1 and m2 are slopes between the lines.

Now, slope of 1. = - coef. of x/ coef. of y

= -5/-8 = 5/8 =m1

& slope of 2. = -5/-8 = 5/8 = m2

Since slopes of lines i. e. m1 = m2, so the lines are parallel to each other.

pi is 22 divide by seven. we can also say that

pi is a constant number. More than how did it form I think it's more important that why did it formed. It formed to calculate many matters about circle. Like we know that value of gravity is 9.8 it is a constant for circle

Already answered here: https://brainly.com/question/26860297

Step-by-step explanation:

[tex]2 log(x) - log(x - 2) = 2 log(3) [/tex]

[tex] log(x {}^{2} ) - log(x - 2) = log(9) [/tex]

[tex] log( \frac{ {x}^{2} }{x - 2} ) = log(9) [/tex]

[tex] \frac{ {x}^{2} }{x - 2} = 9[/tex]

[tex] {x}^{2} = 9x - 18[/tex]

[tex] {x}^{2} - 9x + 18 = 0[/tex]

[tex](x - 3)(x - 6) = 0[/tex]

[tex]x = 3[/tex]

and

[tex]x = 6[/tex]

yes

yes

Step-by-step explanation:

I am in the blooket

Answer:

ok

Step-by-step explanation: