evaluate the following integral in cylindrical coordinates. 2 ∫−2 4−x2 ∫0 1 ∫0 1 1 x2 y2dz dy dx 1 2 2 −2 question content area bottom part 1 2 ∫−2 4−x2 ∫0 1 ∫0 1 1 x2 y2dz dy dx

The value of a(t) is -1 and b(t) is 55 + \(e^t\)

No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + \(e^t\)

Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)

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Answer:

5000

Step-by-step explanation:

in order to find how many revolutions, you need to find the circumference of the circle which is  2pi r.

thus, you will get this working out:

circum= 2 times 22/7 times 14

= 88cm

4.4 km = 440000cm

Then, 440000cm divide 88 cm =5000.

Thus, 5000 revolutions.

Step-by-step explanation:

hope it's helpful

thanks

Answer:

find the value of 'c' sach that the point (1.5) 2,-3) and(C,7) are colliner?

Answer:

ASA

Step-by-step explanation:

Hope this helps:)

A brownie recipe calls sugar for 1 time = 1 cup

A brownie recipe calls sugar for 12 times = 1*12

= 12

Answer:

2(x + 5)

twice — 2

the sum of an unknown number and 5 — x + 5

Answer:

5/1

Step-by-step explanation:

Answer:

5/1

Step-by-step explanation:

The distance between two lines measured along a perpendicular line to the line is always the same is called as equidistant .

Given :

The distance between two lines measured along a perpendicular line to the line is always the same.

What is Equidistant ?

Distances between two points from a common points are equal then it is called as equidistant .

Formulas :

Midpoint = ( x1 + x2 / 2 , y1 + y2 / 2 )

Distance = \(\sqrt{(x2 - x1 )^2 - (y2 - y1)^2 }\)

These are two main formulas are used to find whether equidistant or not.

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Answer:

Step-by-step explanation:

law of sines is :   Sin(A) / a = Sin(C) / c

where A=35

a = BC

C=50

c=20

Sin(35) / a = Sin(50) /  20

0.5735764 / a = 0.76604444 / 20

0.5735764 / a = 0.03830222

0.5735764 / 0.03830222 = a

14.975 = a

BC = 15.0

1) (a) The transformations that occur from the parent function are horizontal translation of 2 units to the left and vertical translation of 4 units to the down.

(b) (-2, -4)

(c) Graph is given below.

1) Given a function,

g(x) = (x + 2)² - 4

(a) Given a parent function p(x) = x².

We can write g(x) as,

g(x) = p(x + 2) - 4

So the transformation is horizontal translation of 2 units to the left and vertical translation of 4 units to the down.

(b) Vertex formula of a parabola is,

y = a (x - h)² + k, where (h, k) is the vertex.

Comparing the given function with vertex form,

Vertex of the parabola = (-2, -4)

(c) Graph of g(x) will be a parabola with vertex at (-2, -4).

It is given below.

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Answer:

D

Step-by-step explanation:

P prime of t indicates a rate of change

The required expression that gives the rate of the population of the city will be changing at time t=5 is D) P'5. Option D is correct.

Given that,
A city planner developed the function P to model the population of a city over the next 25 years, where P(t) is the projected population of the city t years from now.

Rate of change is defined as the change in value with rest to the time is called rate of change.

Here,
The rate of the population expression at t = 5 is given by the differentiation of the expression at t = 5 because differentiation represents the rate for the given equation of population. i.e.
P'5

Thus, the required expression that gives the rate of the population of the city will be changing at time t=5 is D) P'5. Option D is correct.

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Answer:

Step-bThe FitnessGram™ Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it continues.

The 20 meter pacer test will begin in 30 seconds. Line up at the start.

The running speed starts slowly, but gets faster each minute after you hear this signal.

A single lap should be completed each time you hear this sound.

Remember to run in a straight line, and run as long as possible.

The second time you fail to complete a lap before the sound, your test is over.

The test will begin on the word start.

On your mark, get ready, start.

[Level 1]

Feel it

One

Two

Three

Four

Five

Six

Seven; end of level one

[Level 2]

Eight

Feel it

Nine

Ten

Eleven

Twelve

Thirteen

Fourteen

Fifteen; end of level two

y-step explanation:

Answer:

.5 or 1/2

Step-by-step explanation:

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Peace

The value of v is 63 degrees.

There are two angles given, adding them we get

38°+25° = 63°

Since v is an opposite angle, we can deduce that v = 63

Also if we want to go a long way, we can see that angle 1 and angle 2 are forming a straight line with ∠3 whose sum is 180 degrees.

Subtracting their sum, we get:

180-63=117

Now,

angle v is forming a straight line with angle 3, on simplifying we get:

180-∠ 3 = v

180-117=63

Therefore v is 63°.

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Answer:

A.    Bank B

Step-by-step explanation:

First the formulae necessary to calculate compound and simple interest

P = principal = amount deposited

r = interest rate as a decimal (i%  interest => r = i/100)

t = number of years

n = number of times compounded

\(\text{Compound Interest }= P\left(1 + \dfrac{r}{n}\right)^{nt} - P\)

In this case, we have P = 800
r = 8/100 = 0.08
n = 12 since the interest is compounded monthly
t = 2 years

So compound interest

\(CI = 800\left(1 + \dfrac{0.08}{12}\right)^{12 \times 2} - 800\\\\CI = 800(1.00667)^{24} - 800\\\\\\CI = 938.31 - 800\\\\CI = $138.31\)

For Bank B, the interest is calculated at 9% annually and the interest is given by the formula
SI = P x r x t
SI = 800 x 0.09 x 2    (r = 9%/100 = 0.09)

SI =  $144.00

So depositing in bank B is preferred

Answer:

the answer is a because it's the best one you could pick

Answer:

B

Step-by-step explanation:

The sqaure root of 140 is 11.8321595662 and you would round to the nearest tenth and get 11.8

The real number √21 is an example of an irrational number. (Correct choice: C)

According to number theory, real numbers are formed by the following sets:

Then, by direct inspection we get the following conclusions:

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The probability that the mean of a sample of 55 families will be between 17 and 18 pounds is approximately 71.55%.

σ_sample = σ / sqrt(n)

σ_sample = 2.5 / sqrt(55)

σ_sample ≈ 0.336

Now, we can standardize the values of 17 and 18 pounds using the Z-score formula. This will tell us how many standard deviations away from the population mean these values are:

Z = (X - μ) / σ_sample

Z_17 = (17 - 17.2) / 0.336 ≈ -0.595

Z_18 = (18 - 17.2) / 0.336 ≈ 2.381

Now we will use the standard normal distribution (Z-distribution) to find the probabilities corresponding to these Z-scores. You can use a Z-table, statistical software, or an online calculator to find these probabilities.

P(Z < -0.595) = 0.2760

P(Z < 2.381) = 0.9915

To find the probability that the mean of a sample of 55 families will be between 17 and 18 pounds, we will find the difference between the probabilities corresponding to the two Z-scores:

P(17 < X < 18) = P(Z < 2.381) - P(Z < -0.595)

P(17 < X < 18) = 0.9915 - 0.2760

P(17 < X < 18) ≈ 0.7155

So, the probability that the mean of a sample of 55 families will be between 17 and 18 pounds is approximately 71.55%.

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By solving a quadratic equation, it can be calculated that-

x = 2 or x = \(\frac{1}{2}\) and y = -3

What is a quadratic equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.

A two degree equation is known as quadratic equation.

Here, a quadratic equation needs to be solved

The graph of the curve y=2x²-5x -1 and a straight line PQ where drawn, to solve the equation 2x²-5x+2=0

2x²-5x -1 - y =  2x²-5x+2

-1-y = 2

y = -1-2

y = -3

Now, the quadratic equation is

2x²-5x+2 = 0

2x²-4x-x+2 = 0

2x(x - 2) - 1(x - 2) = 0

(x - 2)(2x - 1) = 0

x - 2 = 0 or 2x - 1 = 0

x = 2 or x = \(\frac{1}{2}\)

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(a) The probability that X is less than 3, P(X < 3), is 0.

(b) The mean of X, denoted as E(X), is 71/24, which is approximately 2.9583 when rounded off to four decimal places.

(c) Given Y = e^X, the mean of Y, denoted as E(Y), is approximately 15.75 when rounded off to two decimal places.

(a) It is required to compute P(X<3). Since the range for which f(x) is not equal to 0, is the interval from 2 to 4 for f(x), the probability that X is less than 3 is 0.

Similarly, for X > 4, P(X > 4) = 0.

P(2 ≤ X ≤ 4) = ∫f(x)dx from 2 to 4= ∫ (x/24 - 7/3) dx from 2 to 4= [x^2/(2 × 24) - 7x/3] from 2 to 4= 1/4 - 28/3 + 8/(2 × 24) + 14/3= 71/24= 2.9583(rounded off to four decimal places)

(b) The mean of X can be computed as follows:

E(X) = ∫xf(x)dx from -∞ to ∞= ∫ (x/24 - 7/3) dx from 2 to 4= [x^2/(2 × 24) - 7x/3] from 2 to 4= 1/4 - 28/3 + 8/(2 × 24) + 14/3= 71/24= 2.9583(rounded off to four decimal places)

(c) Y = e^X

The mean of Y can be computed as follows:

E(Y) = E(e^X)= ∫ e^x f(x) dx from -∞ to ∞= ∫ e^x (x/24 - 7/3) dx from 2 to 4= [e^x (x - 31)/(24)] from 2 to 4= (e^4/6 - 31e^4/24 - e^2/6 + 31e^2/24) ≈ 15.75(rounded off to two decimal places).

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Answer:

To solve the equation, you have to to isolate the variable. So, first you subtract both sides by 7.

x +7 - 7 = -2 - 7

When you simplify further,

x = -9.

Hope this helps! :)

Answer:

7.6 cm

Step-by-step explanation

gucci gang

Answer:

B) 7.6cm

Step-by-step explanation:

edge 2021

Answer:

x° = 99°

Step-by-step explanation:

The polygon is a hexagon and the sum of its internal angles is:

\(180(n-2)=180(6-2)=180(4)=720^{0}\)

subtract the 5 known angles:

\(x^{0} =720-145-164-59-132-121=99^{0}\)

Hope this helps

Answer:

A. 3x+6

Step-by-step explanation:

To answer this problem you would want to replace the g(x) equation with for the x in the f equation and solve/simplify.

f(x)=x+2, g(x)=3x+4

(3x+4)+2

3x+6

The Empirical Rule states that approximately 68% of the observations in a bell-shaped frequency distribution are within one standard deviation of the mean.

Hence option C is correct.

The Empirical Rule, also known as the 68-95-99.7

Rule applies to bell-shaped frequency distributions.

It states that approximately 68% of the observations will fall within one standard deviation of the mean.

Specifically, this means that if you have a dataset with a bell-shaped distribution, about 68% of the data points will be within one standard deviation above or below the mean.

This rule is a useful tool for understanding the spread and distribution of data.

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Answer:

pretty sure x=34

Step-by-step explanation:

straight line equals 180 degrees. 34+12= 46. 46+34= 80. 100+80=180

Answer:

Shown below.

Step-by-step explanation:

Test Marks          Tally          Frequency          Percentage

1                                                    8                   8/60 = 0.133

2                                                   6                   6/60 = 0.100

3                                                   5                   5/60 = 0.083

4                                                   5                   5/60 = 0.083

5                                                   5                   5/60 = 0.083

6                                                   8                   8/60 = 0.133

7                                                   6                   6/60 = 0.100

8                                                   7                   7/60 = 0.116

9                                                   4                   4/60 = 0.066

10                                                 5                   5/60 = 0.083

Total                                            59                 59/60 = 0.983

For the Tally section, I believe you just fill in tally marks corresponding to the frequency. One of the observations in the table is 0, which is not a column in the frequency table.