Determine which value best approximates the length of the arc represented by the integral ∫_0^1 √1 + [d/dx(4/x+1)]² dx.
(Make your selection on the basis of a sketch of the arc and not
by performing any calculations.)
(a) 10
(b) -5
(c) 2
(d) 4
(e) 1

Answer:

Step-by-step explanation:

a1=5

d=2-5=-3

[tex]a_{n}=5+(n-1)(3)\\a_{n}=5+3n-3\\a_{n}=3n+2[/tex]

Answer:

s = 22.5 m

Step-by-step explanation:

the equation for the speed change of a coach moving along a straight section of the road and starting braking at a speed of 20 m / s has the form v (t) = 25-5t. Using integral calculus, determine the coach's braking distance.

v (t) = 25 - 5 t

at t = 0 , v = 20 m/s

Let the distance is s.

[tex]s =\int v(t) dt\\\\s =\int (25 - 5t)dt\\\\s= 25 t - 2.5 t^2 \\[/tex]

Let at t = t, the v = 20

So,

20 = 25 - 5 t

t = 1 s

So, s = 25 x 1 - 2.5 x 1 = 22.5 m

Answer:

[tex] { \boxed{ \blue{ \tt{last \: term : l = a + (n - 1)d}}}} \\ \\ { \boxed{ \green{ \tt{sum : s = \frac{n}{2} (2a + (n - 1)d}}}} \\ or\\ { \boxed{ \tt{ \red{sum : s = \frac{n}{2} (a + l)}}}} \\ { \bf{s \: is \: sum }} \\ { \bf{ l \: is \: last \: term}} \\{ \bf{ n \: is \: number \: of \: terms}} \\{ \bf{ d \: is \: common \: difference}} \\ \\ { \underline{ \blue{ \tt{becker \: jnr}}}}[/tex]

Answer:

53

Step-by-step explanation:

By taking the number "41" and minus it with "35" and you'll get 12. Take the number "12" and plus with "41" and you'll get the answer.

the population variance is 144 and the population standard deviation is 12.

To find the population variance and standard deviation for the given data set, follow these steps:

Step 1: Find the mean (average) of the data set.

Step 2: Subtract the mean from each data point to find the differences.

Step 3: Square each difference.

Step 4: Calculate the sum of the squared differences.

Step 5: Divide the sum of squared differences by the total number of data points to find the variance.

Step 6: Take the square root of the variance to find the standard deviation.

Given data set: 8, 17, 29, 35, 41

Step 1: Find the mean (average):

Mean = (8 + 17 + 29 + 35 + 41) / 5

Mean = 130 / 5

Mean = 26

Step 2: Find the differences from the mean:

Differences: (8 - 26) = -18, (17 - 26) = -9, (29 - 26) = 3, (35 - 26) = 9, (41 - 26) = 15

Step 3: Square each difference:

Squared differences: [tex](-18)^2 = 324, (-9)^2 = 81, 3^2 = 9, 9^2 = 81, 15^2 = 225[/tex]

Step 4: Calculate the sum of squared differences:

Sum of squared differences = 324 + 81 + 9 + 81 + 225 = 720

Step 5: Calculate the variance:

Variance = Sum of squared differences / Number of data points

Variance = 720 / 5

Variance = 144

Step 6: Calculate the standard deviation:

Standard deviation = √Variance

Standard deviation = √144

Standard deviation = 12

So, the population variance is 144 and the population standard deviation is 12.

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Answer:

a.5years=300 rabbits

b. 50 years(multiply 50 by 300)

Step-by-step explanation:

hope this is helpful

Answer:

No real solutions.

Step-by-step explanation:

We want to solve the equation:

[tex]\ln(x-2)+\ln (x+2)=4[/tex]

Recall that:

[tex]\displaystyle \ln a-\ln b=\ln\left(\frac{a}{b}\right)[/tex]

Therefore:

[tex]\displaystyle \ln\left(\frac{x-2}{x+2}\right)=4[/tex]

By Definition:

[tex]\displaystyle e^4=\frac{x-2}{x+2}[/tex]

Cross-multiply:

[tex]e^4(x+2)=x-2[/tex]

Distribute:

[tex]xe^4+2e^4=x-2[/tex]

Isolate the x:

[tex]xe^4-x=-2-2e^4[/tex]

Factor:

[tex]\displaystyle x(e^4-1)=-2-2e^4[/tex]

Divide. Therefore:

[tex]\displaystyle x=\frac{-2-2e^4}{e^4-1}=\frac{2+2e^4}{1-e^4}\approx-2.07[/tex]

However, note that logs cannot be negative and must be nonzero. According to the first logarithm, x > 2 and according to the second, x > -2. Since the answer is not greater than two, there are no real solutions.

9514 1404 393

Answer:

  arc SU ≈ 2.62 . . . units

Step-by-step explanation:

The arc length is given by ...

  s = rθ

where r is the radius, and θ is the central angle in radians.

  arc SU = ST·STU = 3·(50°·π/180°) = 5π/6

  arc SU ≈ 2.62 . . . units

Answer:

y = 658.3 ft

Step-by-step explanation:

Alternate angles are equal. Therefore,

Reference angle (θ) = 28°

Length of side Opposite to reference angle = 350 ft

Adjacent side = y

Apply TOA, which is:

Tan θ = Opp,/Adj

Substitute

Tan 28 = 350/y

y*tan 28 = 350

y = 350/tan 28

y = 658.3 ft (nearest tenth)

Answer:

False

Step-by-step explanation:

3a + bc = 16.

Let a=4 b=6 c=3

3(4) + 6*3 = 16

Multiply

12+18 =16

30 = 16

False

Answer:

False!

Step-by-step explanation:

There is no a variable that is given, though I'm going to assume you mean that x=4 is supposed to be a=4. If I'm mistaken, there isn't much to say about whether the statement is true or false, because there's no false statement as it'd give you a=? and you can't prove or disprove this information without more information.

If my assumption is correct, we'll first start solving this problem by substituting in the variables, which would give us: 3(4)+(6)(3)=16

Then, we'll evaluate 3(4) first, because of order of operations, which gives us 12. To reiterate the problem, we now have: 12+(6)(3)=16 From here, we can already tell this is going to be a false statement, as there is no way 6 times anything but zero will give a sum less than 6, but if you didn't catch that, we can continue with our next step.

Evaluate (6)(3) in order to get 18, in order to get: 12+18=16

And finally, we'll add. 12+18 is 30, which as we know, is not equal to 16, so that makes this statement false. 30≠16

Answer:

[tex]g(x) = -\frac{1}{2}\tan{x}[/tex]

Step-by-step explanation:

Tangent function:

The tangent function is:

[tex]f(x) = \tan{x}[/tex]

Horizontally compressed by a factor of 1/2

Horizontally compressing by a factor of 1/2 is multiplying by 1/2. So

[tex]g(x) = \frac{1}{2}\tan{x}[/tex]

Reflected over the x-axis.

Reflecting a function over the x-axis is the same as multiplying it by -1. Then g is given by:

[tex]g(x) = -\frac{1}{2}\tan{x}[/tex]

Answer:

its for sure C

Step-by-step explanation:

Answer:

tanx=30/27

tanx=10/9

x=48

Answer:

1/2

If you divide both numbers by 5, you would get 1/2

Answer:

20

Step-by-step explanation:

Answer:

o ye}x+3 and 3x –y> 2 system of linear inequalities is represented by the graph.

PLEASE LET ME KNOW IF ¡ AM WRONG!

The system of linear inequalities represented by the graph is

y ≥ (1/3)x + 3 and 3x - y  > 2

Option A is the correct answer.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =≤

Greater than and equal = ≥

We have,

We see that,

When we graph,

y ≥ (1/3)x + 3 and 3x - y  > 2 we get the graph shown.

y ≥ (1/3)x + 3

This inequality is positive on the y-axis.

3x - y  > 2

3x > 2 + y

This inequality is positive on the x-axis.

Thus,

The system of linear inequalities represented by the graph is

y ≥ (1/3)x + 3 and 3x - y  > 2

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Step-by-step explanation:

(7-11)+(-3+51)

(-4)+(48)

44 ans

Answer:

44

Step-by-step explanation:

7-11= -4

-3+51=48

-4+48=44

what are the suggestions?

Answer:

what are the options

Step-by-step explanation:

Answer:

what is the following

Step-by-step explanation:

Answer:

$180

Step-by-step explanation:

$600/$100 = 6

$600 es 6 veces $100.

Por vender $600 gana 6 veces mas que por vender $100.

6 * $30 = $180

Respuesta: $180

9514 1404 393

Answer:

  A

Step-by-step explanation:

The square root of any integer that is not a perfect square will be irrational.

  √5 is irrational

__

Any decimal number that terminates or repeats is a rational number, regardless of sign. All of the decimal numbers shown are rational. (All terminate after a finite number of digits.)

Of course, any ratio of integers is a rational number. That's what the word "rational" means.

Answer:

$325.50, mentioned methods below.

Step-by-step explanation:

55% means it increases by 55%.  an increase of 50% is basically taking half of the original amount .  So a 50% increase of 4 would be 4 + .5*4 = 4+2 = 6

So for 210 that's 210 + .55*210 = 325.50

You could also factor to make it a little simpler.

210 + .55*210 = 325.50

210(1 + .55) = 325.50

210*1.55 = 325.50

.55 = 55/100 = 11/20

Answer:

I think the answer is C

Step-by-step explanation:

Answer:

-14c

Step-by-step explanation:

I’m using the actual values 1F = -17C so just times that by 5.4

Answer:

750 ft²

Step-by-step explanation:

.Given :

Charge per ft² = 50¢ = $0.5

Total cost = ((charge per ft² * number of ft²) + cost of paint)

Given that :

Paint cost = $100

Total cost = $475

Number of ft² = x

Plugging values into the equation :

475 = (( 0.5 * x) + 100)

475 = 0.5x + 100

475 - 100 = 0.5x

375 = 0.5x

x = 375 / 0.5

x = 750 ft²

Normal good

There are 3 basic types of commodities or goods;

i. The normal good

ii. The luxury good

iii. The inferior good

Relative to income and demand, when an increase in income causes an increase in the demand for a good, then the good is a normal good. For a normal good, the measure of the responsiveness of demand to a change in income (known as income elasticity of demand) is always greater than 0. In other words, it is positive.

If instead, an increase in income causes a decrease in the demand for a good, then the good is an inferior good. The income elasticity of demand for an inferior good is less than 0. In other words, it is negative.

When the increase in income causes a larger percentage in the demand for a good, then the good is a luxury good. Luxury goods are a special type of normal goods. The income elasticity of demand for a luxury good is greater than 1 since their is a larger percentage increase in the demand.

Income elasticity of demand is calculated by finding the ratio of the percentage increase in the demand to the percentage increase in income.

In the illustration given, the consumer's income increases by 50% causing the demand for good Y to increase by 25%. This is an example of a normal group. i.e increase in income causes an increase in the demand for good Y.

The income elasticity of demand for good Y is given as the ratio of the percentage increase in demand (25%) to the percentage increase in income (50%). Therefore, the income elasticity of demand for good Y is;

25% / 50% = 0.5

Since the income of elasticity of demand for good Y is 0.5 which is greater than 0, good Y is a normal good.

Answer:

27

Step-by-step explanation:

specific probability = number of specific possibilities divided by number of total possibilities.

the number of total possibilities is 72 (we can pull one out of 72).

the probability of pulling a red back is 3/8.

so, to find the actual number of specific possibilities (actual number of red balls in the overall sample size of 72) we need to bring this ratio of 3/8 to an expression of x/72.

what is the factor to turn 8 into 72 ? 9.

8×f = 72

f = 72/8 = 9

to keep the ratio unchanged in its dimension, we need to apply the same factor to 3 to get x.

3/8 × f/f = x/72

3/8 × 9/9 = x/72

3×9 / 72 = x/72

3×9 = x = 27

so, the probability ratio based on actual possibilities (number of balls available) is 27/72

=>

there are 27 red balls in the bag of total 72 balls.