a) The demand function is x = 16,000,000 / p^2 for x≥5 and p>0.
The demand function is x = k/p^2 where k is a constant of proportionality. Substituting x=16 and p=$1000, we get k=16*1000^2. Therefore, the demand function is x = 16,000,000 / p^2 for x≥5 and p>0.
b) The cost function is C(x) = 10,000 + 250x, where x is the number of units produced.
c) The profit function is P(x) = px - C(x) = xp - 10,000 - 250x. Substituting x = 16,000,000 / p^2, we get P(p) = (16,000,000/p) * p - 10,000 - 250(16,000,000/p^2) = 16,000p - 10,000 - 4,000,000/p.
To find the price that maximizes profit, we take the derivative of P(p) with respect to p and set it equal to zero: dP/dp = 16,000 + 4,000,000/p^2 = 0. Solving for p, we get p = √250.
Therefore, the price that maximizes profit is $500, and we should negotiate with our partner for this price. This is because the profit function is concave down, which means that increasing the price beyond $500 will result in decreasing profits, and decreasing the price below $500 will result in lower profits as well.
For more questions like Profit click the link below:
https://brainly.com/question/15699405
#SPJ11
Help and explain please
The function y = 0.4(1.06)^t represents exponential growth function and rate of change is 6%.
What is exponential growth function?A function called exponential growth depicts population growth that happens consistently over time. You can assume that data increases exponentially when populations double or triple in size.
Exponential decay, which occurs when data contracts rather than expands, is the opposite of exponential growth.
A function of the form [tex]y=a(1 - r)^t[/tex], where a > 0and 0 < r < 1, is an exponential decay function.
A function of the form [tex]y=a(1 +r)^t[/tex], where a > 0 and r > 0, is an exponential growth function.
As 1.06 > 1,
y = 0.4(1.06)^t is an exponential growth function and the
growth factor = 1 + r
= 1 + 0.06
Percent rate of change = 0.06
= 6/100 × 100%
= 6%
Thus, the function y = 0.4(1.06)^t represents exponential growth function and rate of change is 6%.
Learn more about exponential growth
https://brainly.com/question/12490064
#SPJ1
Do sides 5 cm 12cm and 13cm form a right angled triangle give reason?
Yes, the sides 5 cm, 12 cm, and 13 cm form a right-angled triangle.
This is because of the Pythagorean Theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, 13 cm is the hypotenuse, and 5 cm and 12 cm are the other two sides.
5^2 + 12^2 = 25 + 144 = 169
13^2 = 169
Since the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides, this means that the triangle is indeed a right-angled triangle.
To learn more about Pythagorean Theorem:
https://brainly.com/question/343682
#SPJ4
I need help on filling in the blanks for these shapes
The complete triangle congruence statement are:
a) ∠A ≅ ∠Y, ∠B ≅ ∠Z, ∠C ≅ ∠X
b) AB ≅ YZ, AC ≅ XY, BC ≅ XZ
c) ΔABC ≅ ΔXYZ.
What is the congruent triangle?
The triangles are congruent regardless of how they are rotated or flipped. The symbol “≅” is frequently used to express the congruence of two items. In the diagram given, ΔABC ≅ ΔXYZ.
The corresponding angles and the sides of the triangles are also congruent with each other.
We have given,
all the corresponding congruent angles and sides. Then the triangle congruence statement.
a)
∠A ≅ ∠Y
∠B ≅ ∠Z
∠C ≅ ∠X
b)
AB ≅ YZ
AC ≅ XY
BC ≅ XZ
c)
ΔABC ≅ ΔXYZ.
Therefore, the complete triangle congruence statement are:
a) ∠A ≅ ∠Y, ∠B ≅ ∠Z, ∠C ≅ ∠X
b) AB ≅ YZ, AC ≅ XY, BC ≅ XZ
c) ΔABC ≅ ΔXYZ.
To learn more about the congruent visit,
brainly.com/question/12413243
#SPJ1
A model rocket is launched 25 feet from you.When the rocket is at height h, the distance d between you and the rocket is given by d=\sqrt{625+h^2} where h and d are measured in feet. What is the rocket’s height when the dust between you and the rocket is 100 feet? around to the nearest hundredth.
The rocket’s height to the nearest hundredth when the distance between you and the rocket is 100 feet is equal to 96.83 feet.
How to calculate the amount of rocket’s height?Based on the information provided, the height h (in feet), of this rocket during its launching with respect to distance d between you and the rocket can be modeled by this quadratic function:
d(h) = √(625 + h²)
Substituting the given parameters into the quadratic function d(h), we have the following;
d(h) = √(625 + h²)
100 = √(625 + h²)
Taking the square of both sides of the quadratic function, we have the following:
100² = [√(625 + h²)]²
10,000 = 625 + h²
Rocket’s height, h² = 10,000 - 625
Rocket’s height, h² = 9,375
Rocket’s height, h = √9,375
Rocket’s height, h = 96.83 feet.
Read more on distance here: brainly.com/question/28353531
#SPJ1
When Han makes chocolate milk, he mixes 2 cups of milk with 3 tablespoons of chocolate syrup. Here is a table that shows how to make batches of different sizes. Use the information in the table to complete the statements. Some terms are used more than once.
Table with 2 columns and 4 rows of data.
The table shows a proportional relationship between ______________ and ______________.
The scale factor shown is ______________.
The constant of proportionality for this relationship is______________.
The units for the constant of proportionality are ______________ per ______________.
The table shows a proportional relationship between the cups of milk used and number of tablespoons of chocolate syrup used. The scale factor shown is 3/2. The constant of proportionality for this relationship is 3/2. The units for the constant of proportionality are teaspoons of chocolate syrup used per cups of milk used.
What is proportional relationship?When it comes to ratios and fractions, the concept of proportion is very connected. When two amounts with the same unit are compared, they form a ratio. When comparing two quantities, a ratio enables us to determine whether one is larger or smaller.
Two ratios or two fractions are equivalent when they are compared according to the proportional rule. To put it another way, two ratios are said to be proportional when they are equal. Performing arithmetic operations on both sides of the ratio taught us that a ratio can be expressed in a variety of ways.
Both the 3: 5 and 6: 10 are equivalent ratios. This indicates that these ratios are proportional. This proportionality can be expressed mathematically as follows:
[tex]$ \frac{3}{5} = \frac{6}{10}[/tex]
Learn more about proportionality
https://brainly.com/question/29126727
#SPJ1
Which of the following pairs of triangles can be proven similar through SSS similarity?
Answer:
C
Step-by-step explanation:
There are 3 pairs of corresponding sides with proportional lengths.
Solve for x.
8 = 2x+ 4
what does x=
Answer: x = 2
Step-by-step explanation:
8 = 2x + 4
2x = 8-4
= 4
x = 4 ÷ 2
= 2
x = 2
What it would look like if it was an actual equation :
8 = 2₂ + 4
Answer:
x = 2
Simple Algebraic EquationsTerminology
Variable: Any letter than stands for a value than can be solved and change value.
Coefficient: The number right before a variable (without being separated by an operator). It is a multiplication factor for a variable. Basically, it's just a way to express what you are multiplying a variable by,
If the coefficient is 1, it means [variable] * 1. 1[variable]
If the coefficient is 3, it means [variable] * x. 3[variable]
etc.
Constant: A fixed value (i.e. 3, 8, 1928). A variable is not a constant because if you were to add a coefficient (not including 0) to the start of a variable, the result would change depending on the value of the variable.
How to Solve
To solve, you must isolate the variable. It means moving the variable and it's coefficient to the other side of the equation with only the same variable on the same side with all the constants on the other side.
Do this with this rule that is extremely important in ALL of math beyond per-algebra and algebra.
Rule
If you multiply, divide, add, subtract, square root, exponent both sides of the equation by the same value, that end value stays the same. That is how you solve for it.
Q)Subtract 4 on both sides to isolate the variable.
8 - 4 = 2x + 4 - 4
Simplify by combining like terms.
4 = 2x
Divide 2 on both sides to solve for x as the coefficient is currently 2.
[tex]\frac{4}{2} =\frac{2x}{2}[/tex]
Simplify.
x = 2
please help
What are the steps for using a compass and straightedge to construct a square?
Drag the steps and drop them in order from start to finish.
The steps for using a compass and straightedge to construct a square are as follows :-
1. Use a straightedge to draw line a and label a point on the line as point P.
2. Construct a line perpendicular to line a through point P.
3. Label a point on this line as point R.
4. With the compass open to the desired side length of the square, place the compass point on point P and draw an arc on line a and an arc on PR←→.
5. Label the points of intersection as points S and T.
6. Keeping the same compass width, place the compass on point T and draw an arc in the interior of∠SPT to intersect the previously drawn arc.
7. Label the point of intersection as point Q.
8. Without changing the compass width, place the compass point on point S and draw an arc in the interior of∠SPT .
9. Use the straightedge to draw QS ,QT,SR and RT.
What is a square?In geometry, a square is a plane figure with four equal sides and four right angles (90°). A square is a special kind of parallelogram as well as an equilateral rectangle.
A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles. It can also be explained as a rectangle with two adjacent sides that are of equal length.
Learn more about square on:
https://brainly.com/question/25092270
#SPJ1
7/9 + 5/6=???
I’m rushing to finish this I forgot to do it and I can’t figure it out!
Answer: 29/18 or 1 11/18
Step-by-step explanation: When adding fractions, you need the fractions to have a common denominator. In order to get the common denominator, find the lowest common number between 9 and 6. That number is 18.
7/9 times 18 = 14/18 5/6 times 18 = 15/18 14/18 + 15/18 = 29/18
Improper fraction: 29/18 Mixed number: 1 11/18
4) Write a system of equations to describe the situation below, solve using substitution, and
fill in the blanks.
◄)) Two classmates got together over the weekend to do their assigned History reading.
Olivia can read 3 pages per minute, while Donald can read 4 pages per minute. When they
met, Olivia had already read 22 pages, and Donald had already gotten through 12 pages.
After a while, they had both read the same number of pages. How long did that take? How
many pages had each one read?
◄) After _ minutes, Olivia and Donald had each read _
pages.
It took 19 minutes for each to read 115 pages.
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables , constants and exponents.
Let x be the number of minutes
And y be the number of pages.
y = 96 + x --equation1 (for danielle )
y=39+4x --equation2 (for lorenzo)
By substituting equation 1 in equation 2.
we get,
96+x = 39 + 4x
96-39+x = 39-39+4x
57+x = 4x
4x-x = 57
3x = 57
x = 57/3
x = 19 .
Substitute x = 19 in equation 1 we get y = 96 + 19 and y=115
in equation 2 we get , y = 39 + 4*19
y = 39+76
y = 115
Hence , it took 19 minutes for each to read 115 pages.
To learn more about Algebraic expression from the given link.
https://brainly.com/question/953809
#SPJ1
What is the distance between the graph of the equations x =- 4 and x =- 1?
The distance between the graph of the equations x =- 4 and x =- 1 is 3 units.
The equations x =- 4 and x =- 1 can be solved to be -4 and -1 respectively. The difference between these two numbers is 3, so the distance between the graphs of the equations is 3 units.
The distance between the graph of two equations can be found by subtracting the solutions of the two equations. For example, when subtracting the solution of x =- 4 and x =- 1, the difference between -4 and -1 is 3. Therefore, the distance between the graphs of the equations x =- 4 and x =- 1 is 3 units.
Learn more about distance here
https://brainly.com/question/28956738
#SPJ4
Is 3x² a polynomial?
Answer: Yes and no?
Step-by-step explanation: Yes, because since it is one single number, it would be considered a "linear" polynomial. But no, because since there is only one term, it wouldn't be considered a polynomial.
I only just learned about linear polynomials, so I think the safe answer would just be no, since there is only one term.
Which division expression shows 3/4
a. 43 div 34
b. 3 div 4
c. 4 div 3
d. 4 x 3
The division expression that shows 3/4 is b. 3 div 4
How to explain the expression?It is vital to note that in Mathematics, an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.
Un this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, division, etc.
In this case, 3/4 simply means 3 divided by 4. Therefore, the correct option to illustrate this is B.
Learn more about expressions on:
https://brainly.com/question/723406
#SPJ1
A triangular park with ide 115m, 81. 63m and 69. 27 m, ha to be fenced. Find the cot of fencing at the rate of ₹18. 50 per metre
The cost of fencing the triangular park at the rate of ₹18.50 per meter is ₹4903.65
To find the cost of fencing a triangular park with sides measuring 115m, 81.63m, and 69.27m, we first need to calculate the perimeter of the triangle. The perimeter of any two-dimensional figure is defined as the distance around the figure. We can calculate the perimeter of any closed shape just adding up the length of each of the sides.
Perimeter of triangle= Sum of the three sides
To do this, we add up the lengths of all three sides: 115m + 81.63m + 69.27m = 265.9m.
We can then multiply the perimeter by the cost per meter of fencing to find the total cost: 265.9m * ₹18.50/m = ₹4903.65.
So the cost of fencing the triangular park at the rate of ₹18.50 per meter is ₹4903.65
To learn more about triangle visit-
brainly.com/question/2773823
#SPJ4
5 Andrew saves the same amount of money each week. The table shows the amount he saves in different numbers of weeks. How much money does Andrew save in 40 weeks? Show your work. Week 7 9 11
Answer:
hw could make 200 dollars in 4 weeks
is this ordered pair a (-1,3) a solution to the inequality
Yes, The ordered pair (-1,- 3) is a solution to the inequality y > -5x⁴ + 7x³ + 8.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
We have to given that;
The inequality is,
⇒ y > -5x⁴ + 7x³ + 8.
And, The point is (- 1, - 3).
Now, We can substitute the value of (x, y) = (- 1, - 3) in given inequality and check as;
⇒ y > -5x⁴ + 7x³ + 8.
⇒ -3 > -5(-1)⁴ + 7(-1)³ + 8
⇒ -3 > -5 + 7 × - 1 + 8
⇒ - 3 > - 5 - 7 + 8
⇒ - 3 > - 4
This is true.
Thus, The ordered pair (-1,- 3) is a solution to the inequality
y > -5x⁴ + 7x³+ 8.
Learn more about the inequality visit:
https://brainly.com/question/25944814
#SPJ1
The complete question is this,
The ordered pair (-1,- 3) is a solution to the inequality y >-5x⁴ + 7x³ + 8.
1) True
2) False
A florit ha 55 flower he want to put the ame number of flower in each vae without a leftover. Hould he put 2,3 or 5 flower in each vae?
As per the combination method, if we take 5 vases, then we can put 11 flowers on each of them then we have the given combinations.
Here we have given that the florist has 55 flower and then he want to put the them in the same number of flower in each vase without a leftover.
Here we need to find the number of ways to put them as 2,3 or 5 flower in each vase.
If we take 2 vase, then here we have total number of 55 flower, then it can be separated as,
Here we have to take 25 flowers on first vase and then we have to put the remaining 30 flowers on the second vase because here we have taken one 2 vase.
Then the partition can be written as
=> 25 + 30
If we take 3 vase, then we get the following combination on it.
In the similar way here we have take the 3 vases, and then we have to divide the flowers in the following manner,
=> 25 + 15 + 15
Similarly, if we take 5 vases, then we can put 11 flowers on each of them then we have the given combinations.
Then if we take the 5 vases then we have to put the flowers in the following manners,
=> 11 + 11 + 11 + 11 + 11
To know more about Combination here.
https://brainly.com/question/28998705
#SPJ4
Find measurement of V.
The measurement of V can be calculated by adding the two equations: 10x-27 + 2x+29 = V. This simplifies to 12x+2 = V, so V = 12x+2.
Find measurement of V?In order to find the measurement of V, we must first find the value of X.We can do this by solving the equations for Y and W simultaneously.To do this, we must first subtract the equation for W from the equation for Y.This will give us 10x - 2x = 29 - 27, or 8x = 2.We can then divide both sides by 8 to get x = 1/4. Now that we have the value of X, we can substitute it into either of the original equations to find the value of V.If we substitute 1/4 into the equation for Y, we get V = (10 x 1/4) - 27 = 10/4 - 27 = -17/4.Therefore, the measurement of V is -17/4.V is the difference between the two expressions: Y and W. Therefore, V can be found by subtracting W from Y.Y=(10x-27)
W=(2x+29)
V=Y+W
V= 10x-27 + 2x+29
V= 12x+2.
To learn more about algebraic addition refer to:
https://brainly.com/question/24536701
#SPJ1
For your chemitry experiment, you are trying to keep the water temperature at 35 degree Celiu, For the experiment to work properly, the actual temperature can vary by a much a 1%. Write and olve an abolute value inequality to find the acceptable temperature of the water
An absolute value inequality for 35 degrees C with the temperature able to vary as much as 1% is 34.65 ≤ x ≤ 35.35
The term inequality is defined as a relationship between two expressions or values that are not equal to each other
Here we have given that in your chemistry experiment, you are trying to keep the water temperature at 35°C.
And in the experiment to work properly, here the actual temperature can vary as much as 1%.
Here let us consider that x refers the actual temperature
Then it can be written as,
=> 1% of 35
When we simplify this one then we get,
=> 0.01(35) = 0.35
Here let us consider that the value is less that the simplified version, then it can be written as,
=> l x - 35 l ≤ 0.35
Therefore, it can be rewritten as,
=> -0.35 ≤ x - 35 ≤ 0.35
When we simplify this by add the value 35, then we get the resulting inequality as,
=> 34.65 ≤ x ≤ 35.35
To know more about inequality here.
https://brainly.com/question/28823603
#SPJ4
What is the difference between real and imaginary numbers?
Real numbers and imaginary numbers are distinguished because real numbers have real square roots whereas imaginary numbers do not.
Why do you use the terms "real" and "imaginary"?A real number in mathematics is the sum of all whole, natural, and integer numbers, both rational and irrational. A number line cannot show an imaginary number since it is not a real number.In mathematics, real numbers and imaginary numbers are distinguished because real numbers have real square roots whereas imaginary numbers do not. A number is multiplied by itself when it is squared. The same reasoning that is used to build zero is also used to construct this.Real numbers are all decimal, fractional, and both negative and positive integers that do not contain imaginary numbers.To learn more about imaginary numbers refer to:
https://brainly.com/question/5564133
#SPJ4
You have 8 marbles: 5 purple, 2 orange and 1 blue. You select a marble without looking at it then put it back. If you do this 48 times, what is the best prediction possible for the number of times you will pick an orange or blue marble?
Write a proportion to solve this problem.
The number of times we will pick an orange or blue marbles = 1/768
What is probability?The term probability refers to the possibility of happening an event. It is the ratio of favorable outcome to the total possible outcome.
What is the probability of picking an orange or blue marble?Available marbles = 8
purple marbles = 5
orange marble = 2
blue marble = 1
probability of picking an orange marble = 2/48 = 1/16
as the marble is put back each time after picking up so
the probability of picking a blue marble = 1/48
Now we multiply the probabilities of each individual events = 1/16 × 1/48
the proportion = 1/768
To learn more about probability visit:
https://brainly.com/question/30034780
#SPJ1
please help i need to get this done i asked everyone i could
Please Help me!!!! Sorry for the small picture!!
Answer:
Please see attached.
Step-by-step explanation:
What kind of a triangle it is if the lengths of the sides are 6cm 10cm and 13cm respectively?
one of the angles measures greater than 90 degrees (110.01 degrees), this is an obtuse triangle.
An obtuse triangle is a triangle that has one angle which measures greater than 90 degrees. In order to determine if a triangle is an obtuse triangle, we need to calculate its angles.
To calculate the angles of the triangle, we can use the following formula:
Angle 1 = arccos ( (b2 + c2 - a2) / 2bc )
Angle 2 = arccos ( (a2 + c2 - b2) / 2ac )
Angle 3 = arccos ( (a2 + b2 - c2) / 2ab )
In this case, a = 6cm, b = 10cm, and c = 13cm. Substituting these values into the formula, we get:
Angle 1 = arccos ( (102 + 132 - 62) / 2 x 10 x 13 ) = 89.99 degrees
Angle 2 = arccos ( (62 + 132 - 102) / 2 x 6 x 13 ) = 110.01 degrees
Angle 3 = arccos ( (62 + 102 - 132) / 2 x 6 x 10 ) = 89.99 degrees
Since one of the angles measures greater than 90 degrees (110.01 degrees), this is an obtuse triangle.
Learn more about angle here
https://brainly.com/question/28451077
#SPJ4
Which equation correctly shows that (x^2)^4=x^8
Number 4 is the correct answer
Solution:
Using law of exponent:
x^2*x^2*x^2*x^2 is the same as x^(2+2+2+2)= x^8
Is there a triangle whose sides are of length 2cm 3cm and 5cm?
Yes, there is possibility to construct a triangle whose sides are 2 cm, 3 cm and 5 cm.
According to the SSS or side-side-side rule of triangle, the sum of any two sides of triangle should be greater than third side of triangle. Assuming the side a to be 2 cm, side b to be 3 cm and side c to be 5 cm.
Side a + side b > side c
2 + 3 > 5
Performing addition on Left Hand Side of the equation
5 = 5
Side b + side c > side a
3 + 5 > 2
Performing addition on Left Hand Side of the equation
8 > 2
side c + side a > side b
5 + 2 > 3
Performing addition on Left Hand Side of the equation
7 > 3
Thus, we see the sum to be greater in two situations. Hence, the triangle is possible.
Learn more about triangle -
https://brainly.com/question/25215131
#SPJ4
QUICK WILL MARK BRAINLIEST !!! 50 POINTSS!! please solve this porblem i need to know tge range and ordered pair
The range:{-8, 4, 10} and the function as set of ordered pair is {(-2, -8),(2, 4),(4, 10)}
What is ordered pair?A pair of numbers in a certain order is called an ordered pair. Ordered pairs include, for instance, (1, 2) and (-4, 12). The two numbers' relative placement is crucial: (2) is not equal to (1, 1) (2, 1) — (1, 2)≠(2, 1). (2, 1).
When displaying two variables, ordered pairs are frequently used. By writing (x, y) = (7, - 2), we indicate that x = 7 and y = -2. The terms "x-coordinate" and "y-coordinate" refer to the number that relates to the value of x and the value of y, respectively.
The, function is given as y = 3x - 2
Lets put this in graph
Domain: {-2, 2, 4}
put the x values in function
y = 3(-2) - 2
y = −8
y = 3(2) - 2
y = 4
y = 3(4) - 2
y = 10
Range: {-8, 4, 10}
The function as set of ordered pair is {(-2, -8),(2, 4),(4, 10)}
Thus, the range:{-8, 4, 10} and the function as set of ordered pair is {(-2, -8),(2, 4),(4, 10)}
Learn more about function
https://brainly.com/question/12431044
#SPJ1
A square has an area of 100square meters. What is the perimeter of the square?
The perimeter of a square with an area of 100 square meters is calculated to be 40 m
How to find the perimeter of the squareThe perimeter of a square is calculated using the formula 4 * length
Some necessary properties of a square
A square is a four sided polygon otherwise known as quadrilateral
All the sides are equal hence Length = width or breadth
The angles at which each side intersect is at 90 degrees
The area of a square is Length² hence
Length² = 100
Length = √100
Length = 10
plugging in Length = 10 to the perimeter
P = 4 * length
P = 4 *10
P = 40 m
Learn more about area of square at:
https://brainly.com/question/11444061
#SPJ1
How early can cervix dilate?
For weeks before labor starts, the cervix can dilate to 1 centimeter. The cervix is only beginning to prepare for labor at this stage of dilatation.
Every woman experiences a different amount of time between dilation to 1 cm and delivery. While another woman maybe 1-2 cm dilated for days or weeks, one woman may move from having a closed cervix to giving birth in a matter of hours.
Some women don't start dilating until they start laboring actively. This indicates that the cervix is initially fully closed, but as labor goes on, it opens to a diameter of 10 cm. First pregnancies are where it occurs most frequently. Other women, particularly those who have already given birth, may begin dilating days or weeks before the commencement of labor.
To learn more about cervix dilation, visit the link below:
brainly.com/question/28147754
#SPJ4
evaluate the integral (3 to 0) ( x2 + 9)^0.5 dx
The value of the expression: [tex]\int\limits^0_3 {( x^2 + 9)^{0.5}} \, dx[/tex] will be: [tex]\frac{1}{1.5} [18^{1.5}\times 36][/tex]
We have to determine the value of the expression: [tex]\int\limits^0_3 {( x^2 + 9)^{0.5}} \, dx[/tex]
First solving the expression without using the values of Limits:
As we can write the above as:
[tex]\int {( x^2 + 9)^{0.5}} \, dx \\\frac{1}{0.5+1}[( x^2 + 9)^{0.5+1}] \times \frac{x^3}{3} +9x[/tex]
As we know, [tex]\int{x^n} \, dx =\frac{1}{n+1}x^{n+1}[/tex], where, n is any number.
So we can write the above as:
[tex]\\\frac{1}{1.5}[( x^2 + 9)^{1.5} \times \frac{x^3}{3} +9x][/tex]
Now we will put the value of limits in the above expression:
First putting the lower limit, i.e. the value of x = 3
We will get it as:
[tex]\frac{1}{1.5}[( 3^2 + 9)^{1.5} \times (\frac{3^3}{3} +9\times 3)]\\\frac{1}{1.5} [18^{1.5}\times (9+27)]\\\frac{1}{1.5} [18^{1.5}\times 36][/tex]
Now putting the value of lower limit, i.e the value of x = 3,
We will get it as:
[tex]\frac{1}{1.5}[( 0^2 + 9)^{1.5} \times ({\frac{0^3}{3} +9\times 0)}]\\\frac{1}{1.5} [9^{1.5}\times ({0+0})]\\\frac{1}{1.5} [9^{1.5}\times 0]=0[/tex]
Now, for detemining the value of the expression,
We will subtract the value of lower limit from upper limit
We will get it as; [tex]\frac{1}{1.5} [18^{1.5}\times 36][/tex]
For more questions on Integrals
https://brainly.com/question/24171063
#SPJ4