The value of the limit of the expression Limit x tend to π 1-sinx/2(π-x) ² is infinity (∝)
How to evaluate the limit of the expressionGiven that
Limit x tend to π 1-sinx/2(π-x) ²
To solve this expression, we make use of
If limit of x to a+ of f(x) = limit of x to a- = L, then limit of x to a+ of f(x) = L
The interpretation is that we solve the expression by direct substitution
So, we have
Limit = 1 - sin(π)/2(π - π) ²
Evaluate the difference
Limit = 1 - sin(π)/2(0)²
Evaluate the exponent and the bracket
Limit = 1 - sin(π)/0
Divide
Limit = ∝
Hence, the limit of the expression is ∝
Read more about derivatives at
https://brainly.com/question/5313449
#SPJ1
2. Evaluate the logarithmic expression using properties of logs and the change of base formula
Expression
a. log5.625
b. log6.4 +log6.12
c. log3.9^4
(i put a period after a imaginary number)
The expressions can be written as :a. log5.625 ≈ 0.75.
b. log6.4 + log6.12 ≈ 1.67.
c. log3.9^{4} ≈ 2.47.
What is logarithm function?
A logarithm function is a mathematical function that determines the power to which a fixed number, called the base, must be raised to produce a given value and The logarithm function is the inverse of the exponential function. The most commonly used base for logarithmic functions is 10 (log base 10), but other bases such as 2 (log base 2) and the natural logarithm base e (ln) are also used.
a. Since there is no base specified, we assume the base to be 10 by default. Therefore, we can write:
log5.625 = log(5625/1000)
Using the property log(a/b) = log(a) - log(b), we can simplify this expression to:
log5.625 = log(5625) - log(1000)
Using the change of base formula, we can convert the logs to a common base, such as 2 or e:
log5.625 = log(5625)/log(10) - log(1000)/log(10)
Evaluating the logs using a calculator or by simplifying, we get:
log5.625 ≈ 0.75
Therefore, log5.625 ≈ 0.75.
b. Using the property log(a) + log(b) = log(ab), we can simplify the expression:
log6.4 + log6.12 = log(6.4 × 6.12)
Using the change of base formula, we can convert this to a common base:
log6.4 + log6.12 = log(6.4 × 6.12)/log(10)
Evaluating the log using a calculator or by multiplying 6.4 and 6.12 and simplifying, we get:
log6.4 + log6.12 ≈ 1.67
Therefore, log6.4 + log6.12 ≈ 1.67.
c. Using the property log(a^{n}) = n log(a), we can simplify the expression:
log3.9^{4} = 4 log3.9
Using the change of base formula, we can convert this to a common base:
log3.9^{4} = 4 log(3.9)/log(10)
Evaluating the log using a calculator or by simplifying, we get:
log3.9^{4} ≈ 2.47
Therefore, log3.9^{4} ≈ 2.47.
To learn more about logarithm function, visit the link:
https://brainly.com/question/13473114
#SPJ1
15 points! please help me out!
Answer: 260 ft^2
Step-by-step explanation:
Find the area of the triangle: 0.5*height*base = 0.5*10*20 = 100 ft^2
Find the area of the rectangle: 20*8 = 160 ft^2
Add them together: 160+100 = 260 ft^2
Katya is going on a 7-night trip. She is staying in a hotel that costs $129 per night and her airfare is $375. If she budged $2.000 for the trip, how much money will she have left for the trip?
A. $672
B. $686
C.$704
D.$722
Answer: D. $722
Step-by-step explanation:
$2,000 - $375 (initial airfare cost which will only be once)
= 1,625
7 x 129 = 903 (cost of the 7 nights in a hotel)
1,625 - 903 = 722
$722 left for the trip
Which of the following equation will produce the graph shown below
The quadratic equation in the given graph can be written in the vertex-form as:
y = -2(x - 1)² + 4
Which of the equations produce the given graph?We can see the graph of a quadratic equation. Remember that a quadratic equation with a vertex (h, k) and a leading coefficient a can be written as:
y = a*(x - h)² + k
in the graph we can see that the vertex is (1, 4), replacing that we will get:
y = a*(x - 1)² + 4
In the graph we also can see that the curve passes through the point (0, 2), replacing thesevalues in the equation we will get:
2 = a*(0 - 1)² + 4
2 = a + 4
-2 = a
Then the quadratic is:
y = -2(x - 1)² + 4
Learn more about quadratic equations at:
https://brainly.com/question/1214333
#SPJ1
11) m/EFG=132°, m/CFG=x+111,
and m/EFC=x+23. Find mLEFC.
Applying the angle addition postulate, the value of x in the image given is calculated as: 49.
What is the Angle Addition Postulate?The Angle Addition Postulate states that for any angle, the sum of its adjacent angles is equal to the angle formed by combining them.
Therefore, we have:
x + 11 + x + 23 = 132
Combine like terms to find the value of x:
2x + 34 = 132
2x = 132 - 34
2x = 98
2x/2 = 98/2
x = 49
Learn more about the angle addition postulate on:
https://brainly.com/question/24746945
#SPJ1
The slope of a line is undefined, and the x-intercept is -7. What is the equation of the line?
Oy=-7
Ox=-7
Oy=-7x
Answer:
"Undefined slope"
Step-by-step explanation:
The line is vertical on the graph.
Every point on the line has the same x-coordinate.
If the line crosses the x-axis where x=-7, then the
x-coordinate of every point on the line is -7, and the
equation of the line is
x = -7 .
Hodgman Honest is evaluating a new project for her firm, Basket Wonders (BW). She has determined that the after-tax cash flows for the project will be $10,000; $12,000; $15,000; $10,000; and $7,000, respectively, for each of the Years I through 5. The initial cash outlay will be $40.000. For this project, assume that it is independent of any other potential projects that Basket Wonders may undertake. The management of Basket Wonders has set a maximum PBP of 3.5 years for projects of this type. Required: Evaluate this project using payback period technique and advise the management accordingly.
Answer:
To calculate the payback period (PBP) for this project, we need to determine how long it will take for the initial cash outlay of $40,000 to be recovered from the after-tax cash flows.
Year 1 cash flow = $10,000
Year 2 cash flow = $12,000
Year 3 cash flow = $15,000
Year 4 cash flow = $10,000
Year 5 cash flow = $7,000
Total cash inflows for year 1 and year 2 = $10,000 + $12,000 = $22,000
Total cash inflows for year 3 = $15,000
Total cash inflows for year 4 = $10,000
Total cash inflows for year 5 = $7,000
Cumulative cash inflows for year 1 and year 2 = $22,000
Cumulative cash inflows for year 3 = $37,000
Cumulative cash inflows for year 4 = $47,000
Cumulative cash inflows for year 5 = $54,000
It can be seen that the cumulative cash inflows reach the initial cash outlay of $40,000 after year 2, and therefore the payback period for this project is 2 years. Since the payback period is less than the maximum PBP of 3.5 years set by management, this project can be considered acceptable.
So, Hodgman Honest should recommend that Basket Wonders should accept this project as it has a payback period of only 2 years, which is less than the maximum PBP of 3.5 years set by management.
Question 2
(03.01 LC)
Which of the following is not created when a plane slices through a cone?
O Point
O Line
O Circle
O Square
A square is not created when a plane slices through a cone.
What is square?
A square is a geometrical shape that has four equal sides and four equal angles of 90 degrees.
What is cone?
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a pointed top or apex. It looks like a funnel or an ice cream cone.
According to given information:When a plane intersects or slices through a cone, it creates a variety of different shapes depending on the angle of the plane and the position of the cone.
If the plane intersects the cone at an angle perpendicular to its base, it will create a circle. If the plane intersects the cone at an angle that is not perpendicular to its base, it will create an ellipse.
If the plane intersects the cone at an angle that is parallel to one of its generators (the lines that can be drawn from the vertex of the cone to any point on its base), it will create a parabola. If the plane intersects the cone at an angle that is not parallel to one of its generators, it will create a hyperbola.
Therefore, a square is not created when a plane slices through a cone.
To learn more about cone visit:
https://brainly.com/question/1082469
#SPJ9
Represent the following sentence as an algebraic
expression, where "a number" is the letter x. You
do not need to simplify.
9 less than six times a number.
Algebraic expressions are useful for solving different and complex equations in mathematics, as well as for modelling real-life situations such as revenue, cost, inference, etc
The algebraic expression is: [tex]6x - 9[/tex].
What is the use of algebraic expression?To represent the sentence as an algebraic expression, we can follow these steps: Identify the variable. In this case, “a number” is x. Identify the operation. In this case, “less than” means subtraction and “times” means multiplication.
An algebraic expression is an expression that contains variables, constants and mathematical operations. Algebraic expressions are useful because they can help us solve different and complex equations.
For example, if you want to calculate the area of a rectangle with length x and width y, you can use the algebraic expression xy to represent the area.
Write the expression using the order of operations. In this case, we need to multiply six by x first, then subtract nine from the result.
Therefore, The algebraic expression is: [tex]6x - 9[/tex]
Learn more about expression here:
https://brainly.com/question/953809
#SPJ1
A brick of mass 2 kg falls through water with an acceleration of 2 ms 2. The total force of the resistance is N.
The calculated value of the force of the resistance is 15.62 N
Calculate the force of the resistanceWe can use Newton's Second Law of Motion to solve this problem. The formula is:
F = m*a
where F is the net force, m is the mass of the object, and a is the acceleration.
In this case, the brick is falling through water, so there are two forces acting on it:
gravity (pulling it down) water resistance (slowing it down).The net force is the difference between these two forces:
F_net = F_gravity - F_resistance
The weight of the object is:
F_gravity = m*g
So, we have
F_gravity = 2 kg * 9.81 m/s^2 = 19.62 N
Now we can use the formula for net force to find the force of water resistance:
F_net = F_gravity - F_resistance
F_resistance = F_gravity - F_net
F_resistance = 19.62 N - m*a
This gives
F_resistance = 19.62 N - 2 kg * 2 m/s^2 = 15.62 N
Therefore, the force of water resistance is 15.62 N.
Read more about force at
https://brainly.com/question/13370981
#SPJ1
Find what percentage of $6500 is $4250
Step-by-step explanation:
To find the percentage that $4250 represents of $6500, we can use the following formula:
percentage = (part / whole) x 100%
where "part" is $4250 and "whole" is $6500.
Substituting these values into the formula, we get:
percentage = (4250 / 6500) x 100%
percentage = 0.6538 x 100%
percentage = 65.38%
Therefore, $4250 represents 65.38% of $6500.
Answer: It is approximately 65%
Step-by-step explanation: Divide $4,250 by $6,500 and your answer without rounding is 65.3846%
I need this work sheet done in 10 minutes or less!!
Answer:
3. 216 cm^3
4a. A = 5 ft, B = 4 ft.
4b. 88 ft^3
Step-by-step explanation:
3. Separate into two rectangular prisms:
Volume of first one: 4cm*2cm*3cm = 24cm^3
Volume of second one: 4cm*12cm*4cm = 192cm^3
Add them together: 24 + 192 = 216cm^3
4a.
Length A = 8-3 = 5ft.
Width B = 8-4 = 4ft.
4b. Separate into two rectangular prisms:
Volume of first one: 2ft*3ft*4ft = 24ft^3
Volume of second one: 8ft*4ft*2ft = 64ft^3
Add them together: 24 + 64 = 88ft^3
Ricardo took out a single payment loan for $2500 at 7.8% ordinary interest to pay his federal income tax bill. Find the maturity value of the loan if he had to pay it back after 180 days.
Answer:
Therefore, the maturity value of the loan is $2568.75.
Step-by-step explanation:
To calculate the maturity value of the loan, we need to add the interest to the principal.
First, we need to find out how much interest Ricardo will owe for the 180-day period.
The formula for calculating ordinary interest is:
Interest = Principal x Rate x Time
where:
Principal = $2500
Rate = 7.8% = 0.078 (expressed as a decimal)
Time = 180/360 (since the interest is for a 180-day period and the rate is an annual rate)
Time is expressed as a fraction of a year because the rate is an annual rate. In this case, the time is 180/360 because the loan is for 180 days, which is half of a year.
Using the formula above, we can calculate the interest as follows:
Interest = $2500 x 0.078 x 180/360 = $68.75
Therefore, Ricardo will owe $68.75 in interest for the 180-day period.
To find the maturity value of the loan, we add the interest to the principal:
Maturity Value = Principal + Interest = $2500 + $68.75 = $2568.75
Therefore, the maturity value of the loan is $2568.75.
Finding the area and perimeter
Answer:
Lion area: 60
Lion Perimeter: 34
Tiger Area: 60
Tiger perimeter: 64
Step-by-step explanation:
Please help i’ll give brainlist!!
Solve each proportion.
Answer: 12, 32/11
Step-by-step explanation:
3 12
4 32/11
How do l do this help
Answer:
130
Step-by-step explanation:
Answer: y=130 x=130
Step-by-step explanation:
The diameter of the base of a cone is shown on the grid. Each square unit on the grid has a side length of 1 foot. The volume of the cone is approximately 200.96 cubic feet. Determine the height of the cone, and construct it vertically on the grid with respect to the center of the cone's base.
Use 3.14 for .
Answer:
First, we need to find the radius of the base of the cone. We can see from the grid that the diameter is 8 units, so the radius is 4 units (or 4 feet).
Next, we can use the formula for the volume of a cone to find the height:
V = (1/3)πr^2h
Substituting the given volume and radius, and using 3.14 for π, we get:
200.96 = (1/3) x 3.14 x 4^2 x h
Simplifying and solving for h, we get:
h = 200.96 / (1/3 x 3.14 x 4^2)
h = 200.96 / 53.02
h ≈ 3.79 feet (rounded to two decimal places)
To construct the cone vertically on the grid with respect to the center of the base, we can draw a circle with radius 4 units (or 4 feet) centered at the point (4,4) on the grid. Then, we can draw a line from the center of the circle (point (4,4)) up to a point above the circle that is 3.79 units (or 3.79 feet) away from the center. This line represents the height of the cone. Finally, we can connect the endpoint of the line to the points where the circle intersects the grid to complete the cone.
Perry's patio is 6 meters long and 53 meters wide. What is the area of his patio?
Help please I got 5.76 I don’t know if that’s right
Answer:
trust yourself cuh
Step-by-step explanation:
please help with these 2 questions in math
The correct answer is E (-1,-3). Reflection across the x-axis is a transformation that flips the object across an imaginary line that runs through the center of the x-axis.
What is transformation?Transformation in mathematics is the process of changing an object or figure in some way. This includes changing the size, position, rotation or reflection of an object. Transformations can also be used to move a figure from one coordinate system to another. Common transformations include translation, rotation, reflection and scaling.
In this case, the x-axis is the line y = 0. The figure ABCD is reflected across this line, resulting in point A being reflected to E.
When a figure is reflected, the x-coordinates remain the same, while the y-coordinates change sign. This means that the x-coordinate of point A (-1) remains the same, but the y-coordinate (3) changes to its opposite (-3). Therefore, the resulting coordinates of point A are (-1,-3).
Reflection across the x-axis is an example of a transformation. Transformations involve changing the position, size or orientation of a figure, but not its shape. This means that the figure ABCD is still the same shape after being reflected, but its position has changed. After being reflected, the figure is now located on the opposite side of the x-axis.
For more questions related to reflection
https://brainly.com/question/26494295
#SPJ1
Find the probability of rolling an even number on a single die
The probability of rolling an even number on a single die is 1/2, or 50%. This can be calculated by considering the possible outcomes of rolling the die.
There are six possible outcomes, and three of these are even numbers (2, 4, and 6). Therefore, there is a 3/6, or 1/2, chance of rolling an even number. In terms of probability, this can be expressed as a fraction, percentage, or decimal. As a fraction, the probability of rolling an even number on a single die is 3/6, or 1/2. As a percentage, the probability of rolling an even number on a single die is 50%. As a decimal, the probability of rolling an even number on a single die is 0.5. No matter how it is expressed, the probability of rolling an even number on a single die is 1/2, or 50%. This can be easily remembered by considering that there are six possible outcomes, and three of them are even numbers.
Learn more about probability here:
https://brainly.com/question/15124899
#SPJ1
Select the correct answer. The product of two numbers is 21. If the first number is -3, which equation represents this situation and what is the second number? A. The equation that represents this situation is x − 3 = 21. The second number is 24. B. The equation that represents this situation is 3x = 21. The second number is 7. C. The equation that represents this situation is -3x = 21. The second number is -7. D. The equation that represents this situation is -3 + x = 21. The second number is 18.
Answer:
The product of two numbers is 21.
Step-by-step explanation:
If the first number is -3, which equation represents this situation and what is the second number? A. The equation that represents this situation is x − 3 = 21.
Ann thought of a number, n . She multiplied it by 5 and then added 7. Then she told Jim the result, r
Start with the formula you wrote in part (b). Use it to write another formula that could help Jim find Ann’s number, n as soon as he is given the result, r
The formula that could help Jim find Ann’s number, n as soon as he is given the result, r is n = (r - 7) / 5.
How to write formula?Formula 1;
Let the unknown number Ann thought of = n
(n × 5) + 7 = r
5n + 7 = r
If Jim is given Ann's number n if given the results, r
This means Jim will make Ann's number n the subject of the formula;
5n + 7 = r
Subtract 7 from both sides
5n = r - 7
divide both sides by 5
n = (r - 7) / 5
Therefore, the formula written in terms of n is n = (r - 7) / 5
Read more on formula:
https://brainly.com/question/19041791
#SPJ1
Martha made 2 2/3 pounds of pasta. she divided the pasta into fourths. how much pasta is in each portion?
Step-by-step explanation:
2 2/3 = 8/3
8/3 * 1/4 = 8/12 = 2/3 pound in each portion
Can someone help me, please?
how do i solve this problem?
Option A correctly describes the area of the graph of the function.
How is an area of the graph calculated?
The area of a graph is the area under the function curve enclosed within the X-axis of the graph. Thus, it is the area of the figure formed by enclosing the function graph with the X-axis.
It is the integration of the function polynomial of the possible values of x that the function curve lies in.
Here the function equation is : [tex]f(x) = ( 25 - x^{2} )[/tex]
From the figure, we can see that the value of x varies from -5 to 5.
Initial x-value of integration = minimum value of x
= -5
Final x-value of integration = maximum value of x
= 5
Thus, the area of the graph can be correctly calculated as. :
[tex]Area = \int\limits^{maxX}_ {minX} \, f(x)dx[/tex]
[tex]Area = \int\limits^5_ {-5} \, (25-x^{2} )dx[/tex]
Hence, Option A correctly calculates the area of the graph given.
To learn more about Graphs, visit
https://brainly.com/question/29548482
#SPJ1
BEAINEST IF CORRECT
if x= 60 would they be similar or not? explain ur answer.
Answer: no they wouldn't be similar
Step-by-step explanation: if x=60 if triangle 1 then the third angle would be (180-(58+60)) =180-118=62
if we decide to calculate the third angle in triangle 2 we will have 180-(50+58) = 180-108=72
therefore not all angles in 1 are similar to angles in 2 so the triangles aren't similar
14 yd
21 yd find the area of the triangle
Answer:
147
Step-by-step explanation:
A= h^b b=21*14= 147
which is more 7,000 millimeters or 7 liters?
Increase the number 15/16 by 3/5 of it of it. Then increase the resulting number by 3/5 of it
The resulting number is 12/5
What are arithmetical operations?Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.
Given that we need to, increase the number 15/16 by 3/5 of it, then increase the resulting number by 3/5 of it
So, performing the operations,
15/16+15/16×3/5
= 15/16(1+3/5)
= 15/16(8/5)
= 120/80
= 3/2
Now,
3/2+3/2×3/5
= 3/2(1+3/5)
= 3/2(8/5)
= 24/10
= 12/5
Hence, the resulting number is 12/5
Learn more about arithmetical operations, click;
https://brainly.com/question/30553381
#SPJ2