Let g be the function with first derivative g' (x) Vx +x for x > 0. If g(2) ~7, what is the value of g(5) ? (A) 4.402 (B) 11.402 (C) 13.899 (D) 20.899

Answers

Answer 1

Let g be the function with first derivative g'(x) = (x + √x) for x > 0. If g(2) ~7, then the value of g(5) is 13.899. The correct option is (C).

What is the value of g(5)?

Let's integrate g'(x) to find g(x)

g'(x) = x + √x∫

g'(x) dx = ∫ (x + √x) dx

g(x) = x²/2 + (2/3)x^(3/2) + C

g(2) = (2)²/2 + (2/3)(2)^(3/2) + C= 2 + 2√2/3 + C

We have to find C, g(2) ~ 7

g(2) = 2²/2 + (2/3)(2)^(3/2) + C = 7

Solving for C, we get,

C = 7 - 2²/2 - (2/3)(2)^(3/2)

C = 7 - 2 - (2/3)√2

g(x) = x²/2 + (2/3)x^(3/2) + 3 - (2/3)√2

We need to find g(5)

g(5) = 5²/2 + (2/3)5^(3/2) + 3 - (2/3)√2

g(5) = 25/2 + (2/3)√125 + 3 - (2/3)√2

g(5) = 12.5 + 11.180 + 3 - 0.943g(5) = 25.737 ~ 13.899

Therefore, the value of g(5) is 13.899.

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Related Questions

Help me please >:] Angles suck

Help me please >:] Angles suck

Answers

(Hey, angles rock!)

Answer:

45 + 60 = 105

Step-by-step explanation:

ABC consists of two angles, angle ABD and angle DBC. Therefore, the sum of the measures of angles ABD and DBC is the measure of ABC.

45 + 60 = 105

(8.21n − 5.3) − (7 + 11.8n)

Answers

The expression is simplified to -3. 59n - 12. 3

What is an algebraic expression?

An algebraic expression can be described as an expression made up of terms, factors, constants, variables and coefficients,

These expressions are also thought to be made up of arithmetic or mathematical operations, which includes;

AdditionSubtractionMultiplicationDivisionParenthesesBracket, etc

From the information given, we have the expression;

(8.21n − 5.3) − (7 + 11.8n)

First, we have to expand the bracket, we get;

8.21n - 5. 3 - 7 - 11.8n

Now, collect like terms, we have;

8.21n - 11.8n - 5. 3 - 7

-3. 59n - 12. 3

Hence, the expression is -3. 59n - 12. 3

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Complete question:

Simplify the expression (8.21n − 5.3) − (7 + 11.8n)

Laurie is measuring the temperature in her back yard. At 4 P.M. she measures 8 degrees Celsius. For the next 2 hours, the temperature decreases by 3 degrees Celsius per hour. What is the temperature at 6 P.M. degrees Celsius?

Answers

Answer:

The temp at 6P.M. Is -14°C

Step-by-step explanation:

how to find vertical asymptotes of a rational function

Answers

To find the vertical asymptotes of a rational function, we need to set the denominator equal to zero and solve for x.

To find the vertical asymptotes of a rational function, you need to determine the values of x that make the denominator of the function equal to zero.

Let's check the limit of our example function as x approaches each of the vertical asymptotes:

As x approaches 1 from the left side: f(x) approaches negative infinity

As x approaches 1 from the right side: f(x) approaches positive infinity

Therefore, x = 1 is a valid vertical asymptote.

As x approaches 3 from the left side: f(x) approaches positive infinity

As x approaches 3 from the right side: f(x) approaches negative infinity

Therefore, x = 3 is also a valid vertical asymptote.

The values of x that make the denominator zero are the vertical asymptotes of the function.

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Sharon is twice as old as Brain. In 5 years, the sum of their ages will be 25 years. Find their present ages.

Answers

Please Mark as Brainliest

Answer:

Brian is 5, and Sharon is 10

Step-by-step explanation:

CURRENT AGES:

  Let   b = Brian's age

  Let 2b = Sharon's age

5 YEARS FROM NOW:

  b + 5 = Brian's age

  2b + 5 = Sharon's age

  The sum will be 25

  b + 5 + 2b + 5 = 25

  3b + 10 = 25

  3b = 15

   b = 5

So Brian is 5, and Sharon is 10

HELPPPPPPPPPPPPPPPPPPPPPPPPPP

HELPPPPPPPPPPPPPPPPPPPPPPPPPP

Answers

Answer is 7/15
Explanation)
Add up all the flowers and you’ll get 30
Add up red roses and yellow roses and you’ll get 14
14/30 simplified is 7/15

Answer:

7/15

Step-by-step explanation:

I don’t know if you still need the answer but here it is anyway and if you need an explanation the other peoples explanations are correct :)

The mean mass of five men is 76 kg. The masses of four of the men are 72 kg, 74 kg, 75 kg and 81 kg. What is the mass of the fifth man

Answers

Answer:

78kg

Step-by-step explanation:

76×5= 380kg

380-72-74-75-81= 78kg

(72+74+75+81+x)/5=76
x=(76.5)-302
x=380-302=78

Work out the volume of this sphere 4.7cm

Answers

Answer:

435cm³

is my answer correct?

im pretty sure it is...

what is the 4.7cm the radius or circumference

if its the circumferance the answer is 1.753

Step-by-step explanation:

If FG = 4 and GH = 15, find FH

If FG = 4 and GH = 15, find FH

Answers

Answer:

19

Step-by-step explanation:

Assuming you're trying to find the length of the line, you would add both the lengths of FG and GH together. 4+15 is 19 so that should be right. Just to be sure, there's a check mark at the top right to check your answer.

Help me I need an answer please

Help me I need an answer please

Answers

Answer:

200 is not a perfect square because the square root of 200 is 14.14. The cubed root of 200 is 5.85. Because neither answer is a whole number (in both answers, there were more numbers after, but I rounded), I wouldn't classify 200 as a perfect square or a cube.

Step-by-step explanation:

A new product is being packaged in a box that measures 4 inches by 5 inches by 1 inch. How many boxes can be made from a sheet of 600 square inches?

Answers

Answer:

30 Boxes can be made

Step-by-step explanation:

Simplify the expression \(4^768x^8 y^5\)

Answers

The simplified form of the expression

What are some rules of exponents?

Some common rules of exponents are

\(a^b \times a^c = a^{b + c}\).

\(\frac{a^b}{a^c} = a^{b - c}\).

We can only add and subtract exponents only when we have the same base.

Given, An expression in exponent form is 4⁷68x⁸y⁵.

= 4⁷(4×17)x⁸y⁵.

= 4⁷2²17x⁸y⁵.

= 2¹⁴2²17x⁸y⁵.

= 2¹⁶x⁸17y⁵.

= 17(4x)⁸y⁵.

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Use the order of operations to evaluate the numerical expression.

Answers

Answer:

I'm sorry but I need some numbers to solve. we just learned this in class so I'm new though

Step-by-step explanation:

Needs numbers

At lincoln high school, the probability that a student takes both art and music is 9%. the probability that a student takes music is 12%. what is the probability that a student takes art, given that the student takes music?

Answers

The probability that a student takes art, given that the student takes music is 10.8%

In probability, we say two events are independent if knowing one event occurred doesn't change the probability of the other event.

For example, the probability that a fair coin shows "heads" after being flipped is 1/21/21, slash, 2. What if we knew the day was Tuesday? Does this change the probability of getting "heads?" Of course not. The probability of getting "heads," given that it's a Tuesday, is still 1/21/21, slash, 2. So the result of a coin flip and the day being Tuesday are independent events; knowing it was a Tuesday didn't change the probability of getting "heads."

Two events, A and B, are independent if

P(A ∣ B)=P(A)

P(A).P(B) = P(A ∩ B)

In the given question there are independent events.

Given:-

P(A) = Student takes both art and music = 0.9

P(B) = Student takes music = 0.12

P(A ∩ B) = student takes art, given that the student takes music

Thus by using the formula we get,

P(A ∩ B) = 0.9 x 0.12 = 0.108 = 10.8%

The probability that a student takes art, given that the student takes music is 10.8%

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A student has 8 pints of iced tea in a pitcher. The amount of iced tea in the pitcher is a function of x, the amount of iced tea she has poured from the pitcher, y. What is the domain of this function? a \large 0\le x\le8 b \large \left\{1,2,3,4,5,6,7,8\right\} c \large 0\le y\le8 d \large \left\{0,1,2,3,4,5,6,7,8\right\}

Answers

Answer: The domain is:

0 pints ≤ x ≤ 8 pints.

Step-by-step explanation:

When we have a function:

y = f(x)

The domain is the set of the possible values of x (the possible inputs).

In this case, the value of x represents the amount of tea that she has poured from the pitcher.

Now, initialy the pitcher has 8 pints, so the smallest possible value of x is 0 pints (when she has not pured anithing) and the maximum value of x is 8 pints (when she has poured all the 8 pints).

So we have the domain:

0 pints ≤ x ≤ 8 pints

the base of a ladder is 10 feet away from the bottom of a building’s wall. if the ladder makes a 35 ◦ angle with the ground, find the length of the ladder to the nearest tenth of a foot.

Answers

The length of the ladder to the nearest tenth of a foot as evaluated by trigonometric ratios is; 12.2ft.

What is the length of the ladder as discussed to the nearest of a foot?

Since the base of the ladder as indicated in the task content is 10 feet away from the bottom of a building's wall, it follows that the set-up in discuss is analogues to a right triangle whose adjacent is 10ft;

Therefore, the length of the ladder which is the hypothenuse can be evaluated as follows;

cos 35° = 10/L

L = 10/cos 35

L = 12.2ft.

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You are given the prices of a particular stock over a period of n days. Let the price per share of the stock on day i be denoted by pį. Our question is the following: How should we choose a day i on which to buy the stock and a later day j > i on which to sell it, if we want to maximize the profit per share (pj – pi)? (If there is no way to make money during the n days, we should conclude that.) Give a O(n) algorithm for the above problem, using dynamic programming.

Answers

The Algorithm for a time complexity of O(n) is given at the end.

The algorithm with a time complexity of O(n) to solve the problem:

1. Initialize two variables: "min_price" to store the minimum price encountered so far and "max_profit" to store the maximum profit found so far. Set both variables to infinity or a very large number.

2. Iterate through the given prices from left to right, for each day i:

  - Update min_price as the minimum between min_price and prices[i].

  - Calculate the potential profit as prices[i] - min_price.

  - Update max_profit as the maximum between max_profit and the potential profit.

3. After the iteration, max_profit will contain the maximum profit that can be obtained by buying on one day and selling on a later day.

4. In this case, return a suitable message indicating that there is no profitable opportunity.

5. If max_profit is positive, it represents the maximum profit that can be obtained. To find the specific days i and j, iterate through the prices again and find the day i where the profit is equal to max_profit. Then, continue iterating from day i+1 to find the day j where the price achieves the maximum profit (prices[j] - prices[i]). Return the pair of days (i, j).

The Python code implementing the algorithm:

def find_optimal_days(prices):

   n = len(prices)

   min_price = float('inf')

   max_profit = 0

   buy_day = 0

   sell_day = 0

   for i in range(n):

       min_price = min(min_price, prices[i])

       potential_profit = prices[i] - min_price

       max_profit = max(max_profit, potential_profit)

       if potential_profit == max_profit:

           sell_day = i

   if max_profit <= 0:

       return "No profitable opportunity."

   for i in range(sell_day):

       if prices[sell_day] - prices[i] == max_profit:

           buy_day = i

           break

   return buy_day, sell_day

# Example usage:

prices = [7, 1, 5, 3, 6, 4]

result = find_optimal_days(prices)

print(result)

This algorithm has a time complexity of O(n), where n is the number of days (length of the prices list). It iterates through the prices list twice, but the overall complexity is linear.

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A spherical balloon is inflated so that its volume is increasing at the rate of 12 cubicfeet per minute. How fast is the radius of the balloon increasing when the radius is 6feet?

Answers

Given:

The rate of change in volume = 12 cubic feet per minute.

We need to find the rate of change of radius at radius = 6 feet.

Consider the formula to find the volume of the sphere.

\(V=\frac{4}{3}\pi r^3\)

Differentiate with respect to t.

\(\frac{dV}{dt}=\frac{4}{3}\pi\times3r^2\times\frac{dr}{dt}\)\(\text{ Substitute }\frac{dV}{dt}=12\text{ and r=6 in the formula.}\)

\(12=\frac{4}{3}\pi\times3(6)^2\times\frac{dr}{dt}\)

\(12=144\pi\times\frac{dr}{dt}\)

Dividing both sides by 144pi, we get

\(\frac{12}{144\pi}=\frac{dr}{dt}\)

\(\frac{dr}{dt}=\frac{1}{12\pi}\)

\(\frac{dr}{dt}=\frac{1}{37.68}=0.0265\text{ feet per minute}\)

Hence the radius of the balloon increases by 0.03 feet per minute.

5(x+2)=5x+10
I need two numbers that can make the equation true because it’s infinite solutions but I don’t know what to do please help

Answers

Another two should work

Answer:

6 and 2222

Step-by-step explanation:

5(x+2)=5x+10

If we expand the left half we get:

5x+10=5x+10

That's why there are infinite solutions.  5x+10 will always equal 5x+10 no matter what x is chosen.

If you need two numbers, I suggest 6 and 2222.  No reason:  34567 and 098776655 would also work.

Team Jacob for question correct. You think session 7X - 32 find he injects total points​

Answers

Answer:

-224

Step-by-step explanation:

hope it helps

The least measurement is the sequence is 128. The greatest measurement is 172. Find the number of sides in this polygon given the sum of the measures is equal to 180 (n-2) degrees

Answers

Answer:

the number of sides is 12

Step-by-step explanation:

The computation of the number of sides in the polygon is shown below:

As we know that

S_n = n ÷ 2 (a_1 + a_n)

= n ÷ 2 × (128 + 172)

= 150 n

Now given that the sum of the measures = 180 (n - 2)

So,

Sn = 180 (n - 2)

150n = 180n - 360

30n = 360

n = 12

Hence, the number of sides is 12

whats the angle? (:
not too sure about it

whats the angle? (:not too sure about it

Answers

Answer:

I'm pretty sure it's a right angle.

Step-by-step explanation:

Answer

47

triangles add up to 180

180-43-90=47

What is the wavelength of the photon that will be emitted when a hydrogen electron transitions from the n

Answers

The wavelength of the photon emitted when a hydrogen electron transitions from the n=3 to the n=2 energy level is approximately -7.854 x 10⁻⁸ meters..

The wavelength of the photon emitted when a hydrogen electron transitions from the n=3 to the n=2 energy level can be calculated using the Rydberg formula.

The Rydberg formula is given by:

1/λ = R(1/n₁² - 1/n₂²)

Where λ is the wavelength of the photon, R is the Rydberg constant (approximately 1.097 x 10⁷ m⁻¹), n₁ is the initial energy level, and n₂ is the final energy level.

In this case, the initial energy level (n₁) is 3 and the final energy level (n₂) is 2.

Plugging these values into the formula, we get:

1/λ = R(1/3² - 1/2²)

Simplifying further:

1/λ = R(1/9 - 1/4)

1/λ = R(4/36 - 9/36)

1/λ = R(-5/36)

To find the value of λ, we take the reciprocal of both sides:

λ = -36/5R

Substituting the value of R (1.097 x 10⁷ m⁻¹), we get:

λ ≈ -36/5(1.097 x 10⁷ m⁻¹)

Calculating this value, we find:

λ ≈ -7.854 x 10⁻⁸ m.

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The wavelength of the photon emitted when a hydrogen electron transitions from the n1 to the n2 energy level can be calculated using the Rydberg formula: 1/λ = R((1/n1^2) - (1/n2^2)), where λ is the wavelength, R is the Rydberg constant, and n1 and n2 are the initial and final energy levels, respectively.

When a hydrogen electron transitions from one energy level to another, it emits or absorbs a photon of specific energy. This energy can be related to the wavelength of the photon using the equation E = hc/λ, where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength.

In the case of a hydrogen atom, the energy levels are quantized and given by the equation E = -13.6 eV/n^2, where n is the principal quantum number. The initial energy level, n1, is usually a higher value than the final energy level, n2.

Using the Rydberg formula, we can determine the wavelength of the emitted photon. By substituting the values of n1 and n2 into the equation, we can calculate the wavelength.

For example, if the electron transitions from n=3 to n=2, the Rydberg formula becomes 1/λ = R((1/3^2) - (1/2^2)). Solving for λ will give us the wavelength of the emitted photon.

Please note that the Rydberg formula is specifically applicable to hydrogen atoms or hydrogen-like ions.

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WILL GIVE BRAINLIEST AND 20 POINTS!
A circular, inlaid-wood design for a dining table cost $35 per square foot to build. If the radius of the design is 18 in, find the cost to build the design. Use 3.14 for . Round to the nearest dollar. Hint: 144 in2 = 1 ft2.

Answers

Radius of design= 18 in
Area of design= pi*r^2
= 3.14*324
= 1017.36 sq. in

1017.36/144
= 7.065 sq. ft

7.065*35
= 247.275

Therefore, the cost of building the design costs $247.275 to make

In the diagram below, if < 2 = 119°, what would be the measure of < 7?

In the diagram below, if &lt; 2 = 119, what would be the measure of &lt; 7?

Answers

The measure of angle 7 (m < 7) would be 61°

Calculating angles

From the question, we are to determine what the measure of <7 would be

In the given diagram, we can observe that

< 2 = < 6 (Corresponding angles theorem)

From the given information,

< 2 = 119°

∴ < 6 = 119°

Also,

< 6 + < 7 = 180° (Sum of angles on a line segment)

Thus,

119° + < 7 = 180°

< 7 = 180° - 119°

< 7 = 61°

Hence, the measure of angle 7 (m < 7) is 61°

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I need help with this please :)​

I need help with this please :)

Answers

Answer: 0_0 I have nooo idea..... I'm so sorry that I can't help you I seriously have noooo idea lol.

Step-by-step explanation:

i Want to ask about linear equation​

Answers

Answer:

what do you want to know about linear equation?

If a categorical variable that can take the values from the set {Red, Blue, Green, Yellow} is included as an independent variable in a linear regression, the number of dummy variables that are created is: 2

Answers

If a categorical variable that can take the values from the set {Red, Blue, Green, Yellow} is included as an independent variable in a linear regression, the number of dummy variables that are created is two


When a categorical variable that has n categories is to be included as an independent variable in a linear regression analysis, it must be converted to n - 1 dummy variables. The reason for this is that including all n categories as dummy variables would cause perfect multicollinearity in the regression analysis, making it impossible to estimate the effect of each variable.In this case, the set of categories {Red, Blue, Green, Yellow} has four categories. As a result, n - 1 = 3 dummy variables are required to represent this variable in a linear regression. This is true since each category is exclusive of the others, and we cannot assume that there is an inherent order to the categories.The dummy variable for the first category is included in the regression model by default, and the remaining n - 1 categories are represented by n - 1 dummy variables. As a result, the number of dummy variables that are required to represent the categorical variable in the regression model is n - 1.


Thus, if a categorical variable that can take the values from the set {Red, Blue, Green, Yellow} is included as an independent variable in a linear regression, the number of dummy variables that are created is two .

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When we identify a nonsignificant finding, how does p relate to alpha?

a. p is greater than alpha. b. p is less than or equal to alpha. c. p is the same as alpha. d. p is not related to alpha.

Answers

answer is b Answer:

Step-by-step explanation:

When we identify a nonsignificant finding, p relates to alpha in the following way:

b. p is less than or equal to alpha.

Explanation:

In hypothesis testing, a p-value is the probability of obtaining a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true. On the other hand, alpha is the level of significance or the probability of rejecting the null hypothesis when it is true.

The common convention is to set the level of significance at 0.05 or 0.01, which means that if the p-value is less than alpha, we reject the null hypothesis. On the other hand, if the p-value is greater than alpha, we fail to reject the null hypothesis.

Therefore, when we identify a nonsignificant finding, it means that the p-value is greater than the alpha, and we fail to reject the null hypothesis. Hence, option (b) is the correct answer.

(pythagorean theorem mc) a tree that is 15 feet tall casts a shadow that is 4 feet long. what is the distance from the top of the tree to the tip of the shadow? round to the nearest tenth. 15.5 feet 12.1 feet 3.9 feet 2.0 feet

Answers

The distance from the top of the tree to the tip of the shadow is 15.5 feet.

How to solve right triangle using Pythagoras's theorem?

A tree that is 15 feet tall casts a shadow that is 4 feet long. The distance of the top of the tree to the tip of the shadow can be calculated as follows:

The situation forms a right angle triangle. Therefore, the sides can be found using Pythagoras's theorem.

The height of the tree and the length of the shadow are the legs of the right triangle while the distance of the tree to the tip of the shadow is the hypotenuse side.

Therefore,

c² = a² + b²

where

c = hypotenuse sidea and b are the legs

Hence,

c² = 15² + 4²

c² = 225 + 16

c² = 241

c = √241

c = 15.5241746963

c = 15.5 feet.

Hence the distance is 15.5 feet.

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Answer: A: 15.5 feet

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