find the antiderivative of g(x)=−8ex 4−5x 7−5sec2(x 6). (do not include the constant c in your answer.)

The approximate radius of the cylinder  is 4.5m

The formula for calculating the surface area of cylinder is expressed as:

SA = 2πr(r+h)

where

r is the radius

h is the height

Given the following parameters

SA = 221.1 square meters

height = 7.8m

Substitute

221.1= 2(3.14)r(r+7.8)

221.1 = 6.28r^2 + 15.6r

Factorize to have

6.28r^2 + 15.6r - 221.6 = 0

On factoring, the value of the radius is 4.5 meters

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Answer:

the answer is A

Step-by-step explanation:

I hope it helps you

Answer:

A. 6

B. 48

Step-by-step explanation:

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Answer:

a. 6

b. 48

Step-by-step explanation:

For a, replace t with 1. 2^1 is 2, and 3 * 2 is 6.

For b, replace t with 4. 2^4 is 16, and 3 * 16 is 48.

Thank me later! 8)

The value that is added on the left-hand side to make the equation equal is -1/100.

In mathematics, an expression is a group of numbers and operations. The components of a mathematical expression that perform an operation are as follows: multiplication, division, addition, and subtraction.

Given [1/-2  - 3/4  of -8/15],

to add a number so the sum equals the product of -7/50 and 11/14

let the number be x

according to the question,

[1/-2  - 3/4  of -8/15] + x = -7/50*11/14

taking LHS

[1/-2  - 3/4  of -8/15] = -1/2 - (3(-8)/60)

[1/-2  - 3/4  of -8/15] = -1/2 + 24/60

[1/-2  - 3/4  of -8/15] = (-30 + 24)/60

[1/-2  - 3/4  of -8/15] =-6/60 = -1/10

RHS

-7/50*11/14 = -77/700 = -11/100

substitute the values

[1/-2  - 3/4  of -8/15] + x = -7/50*11/14

-1/10 + x = -11/100

x = -11/100 + 1/10

x = (-11 + 10)/100

x = -1/100

Hence -1/100 is added to make the equation equal.

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Answer:

2nd option

Step-by-step explanation:

Given

\(\frac{x}{5}\) = 5 ( multiply both sides by 5, the reciprocal of \(\frac{1}{5}\) to clear the fraction )

x = 25

Answer:

AB = 83

Step-by-step explanation:

The mid-point of any segment divides the segment into two equal parts

∵ B is the midpoint of segment AC

→ That means B divides AC into two equal segments AB and BC

∴ AB = BC

∵ AB = 12x + 11

∵ BC = 14x - 1

→ Equate them

∴ 14x - 1 = 12x + 11

→ Subtract 12x from both sides

∵ 14x - 12x - 1 = 12x - 12x + 11

∴ 2x - 1 = 11

→ Add 1 to both sides

∵ 2x - 1 + 1 = 11 + 1

∴ 2x = 12

→ Divide both sides by 2

∵ \(\frac{2x}{2}=\frac{12}{2}\)

∴ x = 6

→ To find AB substitute x by 6 in its expression

∵ ab = 12x + 11

∵ x = 6

∴ AB = 12(6) + 11

∴ AB = 72 + 11

∴ AB = 83

Can be cracked within eight hours by the average hacker.

With spaces included in the character count, 8 characters equals between 1 and 2 words. If spaces are excluded from the character count, 8 characters equals between 1 and 3 words.

There are 8-character passwords with capital letters, lowercase letters, and numerals that begin and end with the same symbol.A password of eight characters with just lowercase and capital letters offers 200 billion potential permutations.“1uppercase” is an example of an 8-character password. This password has one uppercase, one lowercase, one number, and one special character.

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To find the displacement and total distance traveled by the object from t=0 to t=6, we need to integrate the velocity function over the given time interval.

The displacement can be found by integrating the velocity function v(t) with respect to t over the interval [0, 6]. The integral of v(t) represents the net change in position of the object during this time interval.

The total distance traveled can be determined by considering the absolute value of the velocity function over the interval [0, 6]. This accounts for both the forward and backward movements of the object.

Now, let's calculate the displacement and total distance traveled using the given velocity function v(t) = t^2 - (1/t) - 12 over the interval [0, 6].

To find the displacement, we integrate the velocity function as follows:

Displacement = ∫[0,6] (t^2 - (1/t) - 12) dt.

To find the total distance traveled, we integrate the absolute value of the velocity function as follows:

Total distance = ∫[0,6] |t^2 - (1/t) - 12| dt.

By evaluating these integrals, we can determine the displacement and total distance traveled by the object from t=0 to t=6.

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Hicksian demand functions are:x1** = 2P₁x₂ ; x₂** = P₂²

Utility function: u(x1+x2) = .5ln(x1) + .25ln(x₂) .The Marshallian demand functions are: x1* = - and x₂* = P₂.

The indirect utility function is found by substituting Marshallian demand functions into the utility function and solving for v(P₁, P₂, Y).u(x1*,x2*) = v(P₁,P₂,Y) ⇒ u(-, P₂) = v(P₁,P₂,Y) ⇒ .5ln(-) + .25ln(P₂) = v(P₁,P₂,Y) ⇒ v(P₁,P₂,Y) = - ∞ (as ln(-) is not defined)

Thus the indirect utility function is undefined.

Minimum expenditure function can be derived from the Marshallian demand function and prices of goods:

Exp = P₁x1* + P₂x2* = P₁(-) + P₂P₂ = -P₁ + P₂²

Minimum expenditure function is thus:

Exp = P₁(-) + P₂²

Hicksian demand functions can be derived from the utility function and prices of goods:

H1(x1, P1, P2, U) = x1*H2(x2, P1, P2, U) = x2*

Hicksian demand functions are:

x1** = 2P₁x₂

x₂** = P₂²

If there are no restrictions on the amount of money the consumer can spend, the Hicksian demand functions for x1 and x2 coincide with Marshallian demand functions.

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The variables "era" and "number of wins" are both quantitative variables.

This matters because quantitative variables have numerical values that can be compared and analyzed, while categorical variables are descriptive and non-numerical.

Quantitative variables, such as era and number of wins, have numerical values that can be subjected to mathematical operations and statistical analysis. This distinction is important because it determines the appropriate methods and techniques for data analysis.

For example, with quantitative variables, you can calculate the mean, median, or mode, as well as perform regression analysis or correlation tests. In contrast, categorical variables are analyzed using different methods, such as frequency tables or chi-square tests.

Understanding the difference between quantitative and categorical variables is essential for correctly interpreting data and making informed decisions based on the results of the analysis.

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Answer:

92 mph

Step-by-step explanation:

Let the speed of the van travelling south  

=

v

mph  

The distance travelled by the car travelling north is

d

1

=

10

⋅

2.5

=

25

The distance travelled by the car travelling south is

d

2

=

v

⋅

2.5

=

2.5

v

The distance between the cars after  

2.5

h

is

d

1

+

d

2

=

255

25

+

2.5

v

=

255

2.5

v

=

255

−

25

=

230

v

=

230

2.5

=

92

mph

The speed is  

=

92

mph

Answer:

C. The quotient of two times some number and four

Step-by-step explanation:

Given the expression 2x÷4

The x be the unknown number.

2x can be written as:

Product of some number and 2 OR two times an unknown number

2x÷4 will then be written as:

The quotient of two times a number and 4

The correct option to describe the equation is "The quotient of two times some number and four"

A 94.6 L gasoline with a density of 0.680 g/cm^3 has a mass of 64328 g.

Density is defined as the ratio between the mass of a substance and the volume it occupies. Denoted by ρ, density is mass per unit volume and the formula is given below:

ρ =  mass / volume

Converting first the volume from L to cm^3.

1 L = 1000 cm^3

94.6 L = 94.6(1000 cm^3)

94.6 L = 94,600 cm^3

Given the density of the gasoline and its volume, solve for the mass of the gasoline using the formula for the density.

ρ =  mass / volume

0.680 g/cm^3 = mass / 94,600 cm^3

mass = 0.680 g/cm^3 (94,600 cm^3)

mass = 64328 g

mass = 64.328 kg

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The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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Answer:

13.2 g

Step-by-step explanation:

let x = grams sugar in a 200 ml glass

16.5 g sugar / 250 ml = x g sugar / 200 ml

x(250) = (16.5)(200)

x =  (16.5)(200) / (250) = 3300 / 250 = 13.2

Answer:  there are 13.2 g sugar in a 200 ml glass of juice

The value of m is -26.6. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

In mathematics, "arithmetic operations" refer to the four basic operations that can be used to express any real number. Division, multiplication, addition, and subtraction are the four operations which yields quotient, product, sum and difference respectively.

We are given -5(m + 30) = -17

On solving the equation using the arithmetic operations, we get

⇒-5(m + 30) = -17

⇒-5m - 150 = -17           (On multiplying the bracket by -5)

⇒-5m = 133                   (On adding 150 on both the sides)

⇒m = -26.6                   (On dividing both the sides by -5)

Hence, we obtained the value of m as -26.6.

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Answer:

Equation : x + 40° + 91° + 53° = 180°

All angles in a triangle add up to 180°

The value of x is -4.

Now,

x + 40 + 91° + 53° = 180° ( ▼ Sum of three

angle of triangle is 180°)

x + 184 = 180

x = 180 - 184

▲ x = - 4

This is a Right answer....

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By considering the planet's diameter as the distance from its center, we can determine the gravitational acceleration at that altitude. At an altitude equal to the planet's diameter, the gravitational acceleration would be 3.825 m/s² on this hypothetical planet.

The inverse square law of gravity states that the gravitational force decreases as the square of the distance from the center of mass increases.

Since the diameter of the planet is equal to twice the radius, the altitude equal to the planet's diameter is equivalent to being at a distance twice the radius away from the center of mass.

Let's denote the planet's surface gravitational acceleration as "g" and the radius as "R".

Using the inverse square law, we can calculate the gravitational acceleration at an altitude equal to the planet's diameter as follows:

g_altitude = g * (R / (2R))²

= g * (1/4)

= g/4

= 15.3 m/s² / 4

= 3.825 m/s²

Therefore, at an altitude equal to the planet's diameter, the gravitational acceleration would be 3.825 m/s² on this hypothetical planet.

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The mass of the ball of radius R with the given mass density function is proportional to R^5.

To find the mass of the ball of radius R, we need to use the given mass density function. Let's assume that the center of the ball is at the origin and that the equatorial plane is the xy-plane.

We can use spherical coordinates to express the mass density function in terms of the radial distance, θ and φ. Since the density is proportional to the product of the radial distance and the distance to the equatorial plane, we have:

ρ(r,θ,φ) = kr^2cos(θ)

where k is a constant of proportionality.

The volume element in spherical coordinates is given by:

dV = r^2sin(θ)drdθdφ

To find the mass of the ball, we need to integrate the mass density over the volume of the ball:

M = ∫∫∫ ρ(r,θ,φ) dV

M = ∫∫∫ kr^2cos(θ) r^2sin(θ)drdθdφ

The limits of integration for r are 0 to R, for θ are 0 to π, and for φ are 0 to 2π.

M = k ∫∫∫ r^4cos(θ)sin(θ)drdθdφ from 0 to R, 0 to π, 0 to 2π

This integral can be evaluated using standard techniques. The final answer is:

M = (4/15)πkR^5

The mass of the ball of radius R with the given mass density function is proportional to R^5.

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Answer:

so you cant turn that into a mixed number i dont think

Step-by-step explanation:

Answer:

740

Step-by-step explanation:

37 times 20

Answer:

740 miles

Step-by-step explanation:

37 miles in 1 day

So we need to multiply 37*20 to find the number of miles for 20 days

So, he travels 740 miles

Answer:

88 inches

Step-by-step explanation:

Divide the shape into 2 shapes and add all side lengths.

20+8+8+16+12+24=88

Answer:

12 x 8 divided by 2 = 48cm

Step-by-step explanation:

The indefinite integral is (1÷4)√(4x² + 49) + C.

we will use substitution and include the constant of integration (C) in the final answer.

Substitute back the original expression for u.
Finally, substitute u = 4x^2 + 49 back into the expression: (1/4)√(4x² + 49) + C

So, the indefinite integral of (1/(x√(4x^2 + 49))) dx is (1/4)√(4x^2 + 49) + C. Absolute values were not necessary in this case, as the function remains positive for all x values.

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Answer:

620

Explanation:

When the sample is given, the number of elk are likely to be infected is to be considered as the 620.

Calculation of the number of elk:

Since the population is 7,750.

The random sample is 50.

So here be like

= 620

hence, When the sample is given, the number of elk are likely to be infected is to be considered as the 620.

The depth of the water is changing at a rate of approximately 0.39 m/s when the radius of the top of the water is 10 meters.

To find the rate at which the depth of the water is changing, we can use related rates.

Given:
Height of the cone (h) = 8 meters
Base radius (r) = 26 meters
Rate of filling (dV/dt) = 12 m³/s
Radius of the top of the water (x) = 10 meters

First, we establish the relationship between the height and radius of the cone using similar triangles. The ratio of the height to the radius is constant, so we have h/r = 8/26.

Next, we differentiate both sides of the equation with respect to time (t) to find dh/dt in terms of dx/dt. This gives us (dh/dt)/(dr/dt) = 0.3077.

We can then substitute the given values into the equation: (dh/dt)/(dx/dt) = 0.3077. Rearranging the equation, we find that dx/dt = (dh/dt) / 0.3077.

To find the value of dh/dt, we can substitute the given rate of filling, dV/dt = 12 m³/s, into the equation. Solving for dh/dt, we get dh/dt = 3.693 m/s.

Finally, we substitute the values of dh/dt and 0.3077 into the equation to find dx/dt. This gives us dx/dt ≈ 0.39 m/s.

Therefore, the depth of the water is changing at a rate of approximately 0.39 m/s when the radius of the top of the water is 10 meters.

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The sample size of each study is often used as the weight in pooling the effects to calculate a weighted average of the population effect size.

When conducting a meta-analysis or pooling effects from individual studies, researchers typically assign weights to each study based on certain criteria. The most common weight used is the sample size of each study. The rationale behind using sample size as the weight is that studies with larger sample sizes are considered to provide more precise estimates of the population effect size.

By assigning higher weights to studies with larger sample sizes, the meta-analysis gives more importance to those studies in calculating the overall effect size. This approach accounts for the fact that larger studies tend to have more statistical power and provide more reliable estimates of the true population effect.

The weighted average is calculated by multiplying the effect size of each study by its corresponding weight (usually the sample size), summing up these weighted effects across studies, and dividing by the total weight. This yields an estimate of the population effect size that takes into account the relative contribution of each study based on its sample size.

The weight often used in pooling effects from individual studies to calculate a weighted average of the population effect size is the sample size of each study. Larger sample sizes are assigned higher weights, as they are considered to provide more precise estimates of the true population effect.

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The fewest number of posts required to fence an area of 36 meters by 60 meters is 12 posts.

According the information given by the statement, the number of posts (\(n\)) is determined by the following formula:

\(n = 1 + \frac{2\cdot x_{1}+x_{2}}{d} \) (1)

Where:

The fewest number of posts is represented by the minimum \(n\) associated to a combination of \(x_{1}\) and \(x_{2}\).

\(n = 1 + \frac{2\cdot (36\,m)+60\,m}{12\,m} \)

\(n = 12\)

\(n = 1 + \frac{2\cdot (60\,m)+36\,m}{12\,m} \)

\(n = 14\)

Hence, the fewest number of posts required to fence an area of 36 meters by 60 meters is 12 posts. \(\blacksquare\)

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The required number of years at which the account balances will be equal is 4.1 years (to the nearest tenth).

The first bank account has a principal of $1000 earning 13% compounded quarterly.

The second bank account has a principal of $8000 earning 5% compounded annually.

To determine the number of years to the nearest tenth at which the account balances will be equal,We can start by using the compound interest formula,

A = P(1 + r/n)^(nt)

where A = final amount

P = principal (initial amount)

R = rate of interest

N = number of times interest is compounded per year

T = time in years.

Now we have to find the time t when the balance in both accounts is equal.

Thus, we can write:

For the first bank account, A1 = P(1 + r/n)^(nt)

where P = 1000 , r = 13% = 0.13 , n = 4 times compounded per year,

so n = 4t = time

For the second bank account, A2 = P(1 + r/n)^(nt)

where P = 8000 , r = 5% = 0.05 , n = 1 time compounded per year,

so n = 1t = time

At the time when the balances will be equal,  A1 = A2,  then,

1000(1 + 0.13/4)^(4t)

= 8000(1 + 0.05/1)^(1t)

Solving the above equation for t, we get,

t = 4.1 years.

Hence, the required number of years is 4.1 years (to the nearest tenth).

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