Anthony is preparing to paint a large shipping container and needs to calculate the area of the container so he can buy the correct
amount of paint. The equation he uses to find the area, A, in square feet is A = 2(w + hw +1h) where / is the length, w is the width,
and h is the height of the container. The container is 8 feet wide, 12 feet high, and 24 feet long. What is the area of the container
in square feet?
Answers
Answer:
1152 square feetStep-by-step explanation:
The dimensions of the container:
w = 8 feet, h = 12 feet, l = 24 feetThe area of the container is:
A = 2(lw + hw + lh)A = 2(24*8 + 12*8 + 24*12) = 1152 square feetRelated Questions
PLEASEEE HELPPPPP!!!! у
Test Scores in Relation to Homework
2.
100
How would you characterize the relationship
between the hours spent on homework and
the test scores? Explain.
90
80
70
60
Test Scores
50
3. Draw a line of best fit on the graph.
40
4.
30
Based on your line, what is the likely test
score of a student who does not study for
the test?
20
10
0
1
2
3
8
9
4 5 6 7
Hours of Homework
Answers
Answer:
2. The more hours spent doing homework the better the test scores.
3. Just draw a line that runs through (1,50) (2,55) (3,60) (4,65)
4. Dunno
Step-by-step explanation:
Answer:
Number 4 would be 45%
Step-by-step explanation:
8 divided by 1 4/5 Arithmetic operation
Answers
Answer:
4.4
Step-by-step explanation:
13) mZFCD= x +41, mZBCF= x + 78,
and mZBCD=95°. Find x.
BO
C
D
Answers
Answer:
x = - 12
Step-by-step explanation:
∠ FCD + ∠ BCF = ∠ BCD , substitute values
x + 41 + x + 78 = 95 , that is
2x + 119 = 95 ( subtract 119 from both sides )
2x = - 24 ( divide both sides by 2 )
x = - 12
Each small square on the grid is 1 cm squared. Which estimate best describes the area of this figure?
O 15 cm2
O 20 cm2
O 25 cm 2
O 35 cm2
Answers
if z=13 which equation is true
Answers
Looking to receive help on this practice question thank you!The first part is vertex form.
Answers
We have the following equation
\(f(x)=x^2+8x+13\)Since
\(\begin{gathered} (x+4)^2=x^2+8x+16 \\ \text{then,} \\ x^2+8x=(x+4)^2-16 \end{gathered}\)So, we can rewrite our equation as
\(\begin{gathered} f(x)=(x+4)^2-16+13 \\ \text{which gives } \\ f(x)=(x+4)^2-3 \end{gathered}\)Then, the vertex form of our equation is:
\(f(x)=(x+4)^2-3\)The graph of this equation is:
The general vertex form of a quadratic equatio is:
\(\begin{gathered} y=a(x-h)^2+k \\ \text{with vertex (h,k)} \\ \end{gathered}\)By comparing this equation with our result, the vertex is:
\((x,f(x))=(-4,3)\)From the general vertex form, we know that the axis of symmtry is given by
\(\begin{gathered} x=h \\ \end{gathered}\)so, our axis of symmetry is x= -4.
The x-intercept ocurr at f(x)=0. Then, by subsituting this value into our function, we have
\(0=(x+4)^2-3\)which leads to
\(\begin{gathered} (x+4)^2=3 \\ x+4=\pm\sqrt[]{3} \\ x=-4\pm\sqrt[]{3} \end{gathered}\)which gives us two x-intercepts:
\(\begin{gathered} x\text{ - intercept (small value) :} \\ x=-4-\sqrt[]{3} \\ x\text{ - intercept (large value value) :} \\ x=-4+\sqrt[]{3} \end{gathered}\)
In the island nation of Autarka there are two amusement parks: Alfonso's Wonderland and Bernice's Wild Rides. The amusement parks are located at either end of the island, 1km apart.
Recently, a third rm, VendorCorp, has developed a new automation technology which promises to improve the eciency of amusement park rides. VendorCorp is o ering to sell the exclusive rights to this technology, and has asked the two parks to submit bids.
The new technology promises to reduce the marginal cost of operating rides for a customer by $6. However, experience in other countries has shown that, in about 30% of amusement parks, the technology encounters compatibility issues and only reduces the marginal cost by $3. Unfortunately, there is no way to know whether these issues will be encountered until the technology is installed.
In Autarka there are 9600 people who like to visit an amusement park. Each of these consumers wants to visit one park once. The consumers' homes are evenly spaced across the island, and they each su er a disutility of $24 for each kilometre they travel to reach an amusement park.
With their current technology, it costs an amusement park $12 for each customer they host. At present, the equilibrium price for an amusement park ticket is $36, and each rm has a pro t of $115,200.
This market is best modelled as Hotelling competition. You should neglect xed costs throughout your analysis.
Note: For the purp oses of this assignment you should treat this market as a one- shot game. Do not consider rep etition or asso ciated phenomena such as collusion or predatory pricing.
2.1 Your task
You have been hired by Alfonso's Wonderland to analyse the business case for purchasing the exclusive rights to the automation technology. You have been asked to determine:
The maximum price Alfonso's Wonderland should be willing to pay for the technology.
The price that Alfonso's Wonderland is likely to have to pay if it is successful.
The consequences for Alfonso's Wonderland if Bernice's Wild Rides purchases the exclusive rights instead of Alfonso's Wonderland.
In the analysis section you must complete each of the steps detailed below. When com-pleting the steps you must:
Step 1: Derive an expression for the location of the indi erent consumer. Use PA to represent the price of admission at Alfonso's Wonderland, and PBto represent the price of admission at Bernice's Wild Rides. (2 marks)
Step 2: Find the pro t function for Bernice's Wild Rides. You should assume that Ber- nice's marginal cost is $12. (4 marks)
Step 3: Find Bernice's best-response function. (4 marks)
Step 4: Find the pro t function for Alfonso's Wonderland for the case in which their marginal cost is $6. (4 marks)
Step 5: Find the best-response function for Alfonso's Wonderland for the case in which their marginal cost is $6. (4 marks)
Step 6: Find the equilibrium prices and pro ts for the case in which Alfonso's marginal cost is $6 and Bernice's marginal cost is $12. (7 marks)
Step 7: Find the pro t function for Alfonso's Wonderland for the case in which their marginal cost is $9. (4 marks)
Step 8: Find the best-response function for Alfonso's Wonderland for the case in which their marginal cost is $9. (4 marks)
Step 9: Find the equilibrium prices and pro ts for the case in which Alfonso's marginal cost is $9 and Bernice's marginal cost is $12. (7 marks)
Answers
The expression is x = (PA - PB) / (2 * (24 + 12)).Alfonso's marginal cost is $9 and Bernice's marginal cost is $12.Alfonso's best-response function can be determined by maximizing profit function with respect to PA.
The expression for the location of the indifferent consumer can be derived using the Hotelling model, where the consumer is equidistant between the two parks. Let x represent the distance from Alfonso's Wonderland. The expression is x = (PA - PB) / (2 * (24 + 12)).
The profit function for Bernice's Wild Rides can be found by subtracting the marginal cost of $12 from the revenue function, which is equal to the price PB multiplied by the number of customers.
Bernice's best-response function can be determined by maximizing their profit function with respect to PB.
The profit function for Alfonso's Wonderland, with a marginal cost of $6, can be found similarly by subtracting the marginal cost from the revenue function, which is equal to the price PA multiplied by the number of customers.
Alfonso's best-response function can be determined by maximizing their profit function with respect to PA.
The equilibrium prices and profits can be found by solving the simultaneous equations formed by the best-response functions of both parks.
Repeat steps 4 and 5 for the case where Alfonso's marginal cost is $9.
Repeat step 6 for the case where Alfonso's marginal cost is $9 and Bernice's marginal cost is $12.
By following these steps, we can determine the maximum price Alfonso's Wonderland should pay, the likely price they will have to pay, and the consequences of Bernice's Wild Rides acquiring the exclusive rights.
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at a sale, a sofa is being sold for of the regular price 33% the sale price is 184.80 what is the regular price?
Answers
The regular price is 275.82, according to given question.
What do you mean by regular price?
Regular price is the cost at which a provider continuously and actively sells goods or services to the general public over an extended period of time.
According to data in the given question,
We have the given information:
Sale discount 33% and the sale price 184.80.
Now, we will calculate the regular price:
Let Regular Price = x
33% Discount of x = 33/100 * x
33% Discount of x = 33x/100
Regular price - 33% Discount = Sale price
x-33x/100=184.80
(100x-33x)/100=184.80
67x/100=184.80
67x=18480
x=18480/67
x=275.82
Therefore, the regular price is 275.82.
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Part 1: Given cosine of theta is equal to radical 3 over 2 comma determine three possible angles θ on the domain [0,[infinity]). Part 2: Given θ = 495°, convert the value of θ to radians and find sec θ.
Answers
The required answer is sec θ = -√2.
Explanation:-
Part 1: Given cosine of theta is equal to radical 3 over 2 on the domain [0,[infinity]).
To determine three possible angles θ, the cosine inverse function which is a cos and since cosine function is positive in the first and second quadrant. Therefore conclude that, cosine function of θ = radical 3 over 2 implies that θ could be 30 degrees or 330 degrees or 390 degrees. So, θ = {30, 330, 390}.Part 2:To convert 495° to radians, multiply by π/180°.495° * π/180° = 11π/4To find sec θ, we use the reciprocal of the cosine function which is sec.
Therefore, sec θ = 1/cos θ.To find cos 11π/4, the reference angle, which is 3π/4. Cosine is negative in the third quadrant so the final result is sec θ = -√2.
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Calvin owns a toy store. He can spend at most $200 on restocking cars and dolls. A doll costs $6.50, and a car costs $8.00. Let x represent the number of cars, and let y represent the number of dolls. Identify an inequality for the number of toys he can buy. Then identify the number of dolls Calvin can buy if he buys 10 cars.
8x + 6.50y ≤ 200; no more than 19 dolls
8x + 6.50y ≤ 200; no more than 18 dolls
6.50x + 8y ≤ 200; no more than 19 dolls
6.50x + 8y ≤ 200; no more than 18 dolls
Answers
The required inequality expression is 8x + 6.50y ≤ 200
Maximum amount he can spend = $200
Cost of doll, = $6.50
Cost of car = $ 8.00
Mathematically, the maximum amount he can spend on restocking is cars and doll is :
(Cost of cars × number of cars) + (cost of doll × number of dolls) ≤ maximum amount
8x + 6.50y ≤ 200
Hence, the required inequality expression is : 8x + 6.50y ≤ 200
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Please help with an explanation of how you found the answer because I am really confused. I will mark brainliest for best answer!
Answers
Answer:
The answer is A
Step-by-step explanation:
The minimum is 52 and the maximum is 65 therefore B and C are false.
Data set total number is 13 D medium is 56
so A is the correct answer
What is the relationship between the two radios 10/24 and 5/12
Answers
Answer: These two ratios, 10/24 and 5/12 share a proportional relationship.
Step-by-step explanation:
Because when you divide the denominator and the numerator (10/24) by two they’ll equal the other ratio.
3 feet, 5 feets, 6 feets What is the area, in square feet, of the front side of the sign?
Answers
The area of triangle is 7.4833 ft².
What is Heron's Formula?Heron's formula used to calculate the areas of various triangles, including quadrilaterals and the equilateral, isosceles, and scalene triangles.
The Heron's Formula states that the area of a triangle is equal to √s(s-a)(s-b)(s-c), where s is the triangle's semi-perimeter and a, b, and c are its three side lengths.
s= (a+ b+ c)/2
Given:
sides: 3 feet, 5 feet and 6 feet.
semi- perimeter, s= 3+5+6/2 = 7
Now, Using Heron's Formula
= √s(s-a)(s-b)(s-c)
=√7(7-3)(7-5)(7-6)
=√7 x 4 x 2 x 1
=√56
= 7.4833 ft²
Hence, the area of triangle is 7.4833 ft².
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in this course, we will be doing lots of counting activities. suppose you have a set with k elements. set up a recurrence relation to count the number of subsets of the set (alternatively, the cardinality of its power set). don't forget your initial condition. hint: suppose sk is the cardinality of the power set of a set of size k. how does that cardinality change when you add one more element?
Answers
To count the number of subsets of a set with k elements, we use the recurrence relation sk+1 = 2sk with the initial condition s0 = 1.
For your initial condition, consider a set with 0 elements, which has only one subset - the empty set. Thus, S(0) = 1. Using the recurrence relation and initial condition, you can compute the cardinality of the power set for any set of size k.
To count the number of subsets of a set with k elements, we can set up a recurrence relation.
Let sk be the cardinality of the power set of a set with k elements. When we add one more element to the set, we have two options for each subset: either include the new element or don't include it.
This means that the number of subsets of the set with k+1 elements is twice the number of subsets of the set with k elements. Therefore, we have the recurrence relation: sk+1 = 2sk.
Our initial condition is the number of subsets of an empty set, which is 1 (since the empty set itself is a subset). So s0 = 1.
In this course, when working with counting activities and sets, you can set up a recurrence relation to count the number of subsets of a set with k elements. Let S(k) represent the cardinality of the power set of a set of size k.
When you add one more element to the set, you essentially double the number of possible subsets, as each existing subset can either include or exclude the new element.
Therefore, the recurrence relation can be expressed as:
S(k) = 2 * S(k-1)
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Sabia and arlan bougth 45 book for r 30 each old all ok them at the rote of 24 find the different the money pent and return
Answers
If Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, they can buy 34 books.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that, Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, how many books they can buy,
Rs 30 = 45 book
Rs 30 = 45
Rs 1 = 45 / 30
Rs 24 = 3/2 × 24
Rs 24 = 34 books
Thus, if Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, they can buy 34 books.
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Solve for b: 4b-3(2b-6)>3-(5b+9)
Answers
Answer:
b > -8
Step-by-step explanation:
Given inequality:
\(4b-3(2b-6) > 3-(5b+9)\)
To solve for b, begin by expanding the brackets on the left side of the inequality:
\(4b-3 \cdot 2b -3 \cdot (-6) > 3-(5b+9)\)
\(4b-6b +18 > 3-(5b+9)\)
Distribute the negative sign inside the parentheses on the right side:
\(4b-6b +18 > 3-5b-9\)
Combine like terms on both sides of the inequality:
\(-2b +18 > -5b-6\)
Add 5b to both sides:
\(-2b +18 +5b > -5b-6+5b\)
\(3b+18 > -6\)
Subtract 18 from both sides:
\(3b+18-18 > -6-18\)
\(3b > -24\)
Divide both sides by 3 to isolate b:
\(\dfrac{3b}{3} > \dfrac{-24}{3}\)
\(b > -8\)
Therefore, the solution to the given inequality is:
\(\large\boxed{\boxed{b > -8}}\)
Find the solution of the following initial value problem.g'(x)= 3x(x^2 -1/3) ; g(1) = 2
Answers
According to the question we have the solution of the given differential equation initial value problem is: g(x) = (3/4)x^4 - x + 9/4 .
To solve the given initial value problem, we need to integrate both sides of the differential equation. We have:
g'(x) = 3x(x^2 - 1/3)
Integrating both sides with respect to x, we get:
g(x) = ∫[3x(x^2 - 1/3)] dx
g(x) = ∫[3x^3 - 1] dx
g(x) = (3/4)x^4 - x + C
where C is the constant of integration.
To find the value of C, we use the initial condition g(1) = 2. Substituting x = 1 and g(x) = 2 in the above equation, we get:
2 = (3/4)1^4 - 1 + C
2 = 3/4 - 1 + C
C = 9/4
Therefore, the solution of the given initial value problem is:
g(x) = (3/4)x^4 - x + 9/4
In more than 100 words, we can say that the given initial value problem is a first-order differential equation, which can be solved by integrating both sides of the equation. The resulting function is a family of solutions that contain a constant of integration. To find the specific solution that satisfies the initial condition, we use the given value of g(1) = 2 to determine the constant of integration. The resulting solution is unique and satisfies the given differential equation as well as the initial condition.
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2+(G+5) Please help lol
Answers
Answer:
g + 7 Please mark me brainliest :)
Step-by-step explanation:
Eliminate redundant parentheses
2 + (g + 5)
2 + g + 5
Add the numbers
2 + g + 5
7 + g
Rearrange terms
7 + g
g + 7
Answer:
7+G
Step-by-step explanation:
2+(G+5)= 2+G+5= 7+G
calculate the rise and run to fine the slope of each line.
Answers
Answer:
All of them?
Step-by-step explanation:
The "Daisy Ad" for President Johnson's 1964 presidential campaign (credited as an important factor in Johnson's landslide victory over Batty Goldwater,) aired how many times?
Answers
The "Daisy Ad" for President Johnson's 1964 presidential campaign (credited as an important factor in Johnson's landslide victory over Batty Goldwater,) aired only once.
The "Daisy Ad" is a famous political advertisement that aired during the 1964 presidential campaign between President Lyndon B. Johnson and Senator Barry Goldwater. It is widely recognized as a highly impactful and influential advertisement. Despite its significant impact, the ad was actually broadcasted only once.
The ad featured a little girl counting the petals of a daisy before transitioning to a nuclear explosion, symbolizing the potential consequences of electing Goldwater as president. The ad aimed to evoke fear and concern about the possibility of nuclear war, ultimately contributing to Johnson's landslide victory in the election.
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The menu at an ice cream store is shown below
ice cream menu
Size Flavor Topping
small vanilla dip
medium chocolate sprinkles
large strawberry Crunch Coat
How many different choices of one size, one flavor, and one topping can be made from the menu?
a. 3
b. 9
c. 18
d. 27
Answers
3 (options for size) x 3 (options for flavor) x 3 (options for topping) = 27
Therefore, there are 27 different choices of one size, one flavor, and one topping that can be made from the menu.
The answer is (d) 27.
The total number of ways an ice-cream can be selected is 27.
What is combination?A combination is "an arrangement of objects where the order of the constituents is immaterial," according to the definition. In situations where the order of the elements is immaterial, combining these two terms means "Selection of things." Combinations are a subset of permutations in which the order of the choices is ignored.
As per the given data:
A table is given, in which information regarding the ice cream menu is shown.
We have to find the total number of different choices of ice cream that can be made.
Number of sizes = 3
Number of flavors = 3
Number of toppings = 3
ways for selecting one ice cream = \(^3C_{1} \times ^3C_{1} \times ^3C_{1}\) = 3 × 3 × 3 = 27
The total number of ways an ice-cream can be selected is 27.
Hence, The total number of ways an ice-cream can be selected is 27.
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A ___ data table has input values that are listed either as column-oriented or row-oriented
Answers
The correct statement is: 'A one-variable data table has input values that are listed either down a column (column-oriented) or across a row (row-oriented). '
The correct answer is an option (a)
We know that a one-variable data table contain its input values either in a single column (column-oriented), or across a row (row-oriented).
And any formula in this data table must refer to only one input cell.
Whereas we se a two-variable data table to see how different values of two variables in one formula will change the formula results.
Custom data tables are used for: Building data-driven services that can easily be updated without modifying it and storing the results.
And the pre-formatted data tables stored as building blocks in galleries that can be accessed any time and be reused any number of times you want.
Therefore, the correct answer is an option (a)
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The complete question is:
A ________ data table has input values that are listed either as column-oriented or roworiented.
A) one-variable
B) two-variable
C) custom
D) pre-formatted
edge lengths are given in units. Find the surface area of each prism in square units
Answers
To find the surface area of a prism, we need to add up the areas of all the faces. For a rectangular prism, we have two congruent rectangular faces and four congruent rectangular faces. The area of each rectangular face is simply length times width, so for a rectangular prism with edge lengths a, b, and c, the surface area is 2ab + 2bc + 2ac.
This formula gives the total surface area of the prism in square units. Make sure to substitute the given edge lengths into the formula and simplify the expression to get your final answer in square units. To find the surface area of a prism with given edge lengths in units, you need to first identify the type of prism (e.g., rectangular, triangular, etc.).
Then, determine the areas of each face by multiplying the edge lengths corresponding to each face. Finally, add the areas of all the faces together to find the total surface area in square units. Remember, the surface area will be expressed in square units.
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the ratio of boys to girls in Mr.Cunningham's class is 2 to 3. there is 18 girls in the class. how many boys are in the class
Answers
Step-by-step explanation:
If the ratio of boys to girls in the class is 2 to 3, this means that for every 2 boys, there are 3 girls.
Let's use the variable "x" to represent the number of boys in the class.
If the ratio of boys to girls is 2 to 3, then the ratio of boys to the total number of students in the class is 2 to 5
We know that there are 18 girls in the class, so the total number of students is:
18 girls + x boys = 18 + x students
And we also know that the ratio of boys to the total number of students is 2 to 5.
So we can set up the following proportion:
2/5 = x/(18 + x)
Cross-multiplying gives:
2(18 + x) = 5x
Expanding the left side gives:
36 + 2x = 5x
Subtracting 2x from both sides gives:
36 = 3x
Dividing both sides by 3 gives:
x = 12
Therefore, there are 12 boys in Mr. Cunningham's class.
If B is the midpoint of AC and AC = 40, what is the measure of BC?
BC =
Answers
Answer:
BC = 20
Step-by-step explanation:
Since B is the midpoint of AC , then
AB = BC = \(\frac{1}{2}\) AC = \(\frac{1}{2}\) × 40 = 20
each lower section is a total of two inches wider than the section above it. if the yellow top of the upper section has an area of 12.56 square inches, what is the approximate area of the green visible portion of the bottom section which he will need to cover with icing?
Answers
The approximate area of the green visible portion of the bottom section is around 33.51 square inches.
Let x be the width of the green visible portion of the bottom section in inches. Then, the width of the yellow top of the bottom section is x + 2, and the width of the yellow top of the upper section is (x + 2) + 2 = x + 4.
Since the area of a circle is given by A = πr^2, and the yellow top of the upper section has an area of 12.56 square inches, we can set up the equation:
12.56 = π((x+4)/2)^2
Simplifying and solving for x, we get:
x ≈ 4.02
Therefore, the width of the green visible portion of the bottom section is approximately 4.02 inches, and its area is:
A ≈ (π/4)(x+2)^2 - 12.56 ≈ 33.51 square inches.
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Take the first 4 digits of your student number as the first number and the last 3 digits as the second number. Write the matlab code to find the greatest common divisor of these numbers using the Euclidean algorithm.
Answers
The required Matlab code to find the greatest common divisor of a number using the Euclidean algorithm is shown.
To find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm in MATLAB, you can use the following code:
% Replace '12345678' with your actual student number
studentNumber = '12345678';
% Extract the first 4 digits as the first number
firstNumber = str2double(studentNumber(1:4));
% Extract the last 3 digits as the second number
secondNumber = str2double(studentNumber(end-2:end));
% Find the GCD using the Euclidean algorithm
gcdValue = gcd(firstNumber, secondNumber);
% Display the result
disp(['The GCD of ' num2str(firstNumber) ' and ' num2str(secondNumber) ' is ' num2str(gcdValue) '.']);
Make sure to replace '12345678' with your actual student number. The code extracts the first 4 digits as the first number and the last 3 digits as the second number using string indexing. Then, the gcd function in MATLAB is used to calculate the GCD of the two numbers. Finally, the result is displayed using the disp function.
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Expressions for consecutive triangular numbers are
0. 5n(n + 1) and 0. 5(n+1)(n+2)
Prove that the sum of two consecutive triangular numbers
is always a square number.
Answers
Consecutive triangular numbers can be represented as n and n + 1.
Using the expressions for consecutive triangular numbers,
0. 5n(n + 1) and 0. 5(n+1)(n+2), the sum of two consecutive triangular numbers can be calculated as follows:0. 5n(n + 1) + 0. 5(n+1)(n+2)0.5n(n+1) + 0.5(n+1)(n+2)0.5 [n(n+1) + (n+1)(n+2)]0.5 [n2 + n + n2 + 3n + 2]0.5 [2n2 + 4n + 2] = 0.5 × 2(n2 + 2n + 1) = (n + 1).
The sum of two consecutive triangular numbers is always a square number which is (n + 1)2.Hence, the given statement has been proved. Now, combine the above equation to get the sum of two consecutive triangular numbers.
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What is the equation of the line that passes through the point (8, 1) and has a slope of -3/4?
Answers
Answer:
y-1= -(3/4)(x-8)
Step-by-step explanation:
y -1 =(-3/4)(x-8)
Distribute
y -1= (-3/4)x+6
Get rid of -1 by adding 1 to both sides
y=(-3/4)x+7
Hope this helps :)
1)Evaluate the following limits.
(a) lim x→[infinity]3/ex+9=
(b) lim x→−[infinity]3/ex+9=
Answers
After evaluating, value of the limits are :
(a) lim x→∞ 3/(eˣ + 9) = 0,
(b) lim x→−∞ 3/(eˣ + 9) = 1/3.
Part (a) lim x→∞ 3/(eˣ + 9)
As x approaches infinity, the exponential term eˣ grows much faster than the constant term 9. So, we can approximate the limit by considering only the exponential term:
lim x→∞ 3/(eˣ + 9) ≈ lim x→∞ 3/eˣ
Since the denominator eˣ approaches infinity as x approaches infinity, the fraction 3/eˣ approaches zero:
So, lim x→∞ 3/(eˣ + 9) ≈ 0
Part (b) lim x→−∞ 3/(eˣ + 9)
As x approaches negative infinity, the exponential term eˣ approaches zero, and the constant term 9 remains the same. So, we can approximate the limit by considering only the constant term:
lim x→−∞ 3/(eˣ + 9) ≈ lim x→−∞ 3/9
Since the denominator 9 remains constant as x approaches negative infinity, the fraction 3/9 simplifies to 1/3:
lim x→−∞ 3/(eˣ + 9) ≈ 1/3
Therefore, the limit as x approaches negative infinity is 1/3.
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The given question is incomplete, the complete question is
Evaluate the following limits.
(a) lim x→∞ 3/(eˣ + 9) =
(b) lim x→−∞ 3/(eˣ + 9) =