If DB = 18cm and AC = 24cm, Use the properties of rhombus to find the length of one side of the rhombus please helppp!!!!
Answers
Answer:
15 cm
Step-by-step explanation:
You need to remember 2 theorems about a rhombus.
1. The diagonals of a rhombus bisect each other
2. The diagonals of a rhombus are perpendicular to each other
In other words, the diagonals of a rhombus are perpendicular bisectors.
BE = 9 and AE = 12
ΔAEB is a right triangle. So, the Pythagorean theorem says
\(9^{2} + 12^{2} = AB^{2}\)
\(AB^{2}\) = 81 + 144
= 225
AB = \(\sqrt{225} = 15\) cm
Related Questions
Stephen is combining all juice shown to make fruit punch. Does the expression (64+28+76)/6 make sense’s
Answers
Yes, the expression (64+28+76)/6 makes sense as it represents the average quantity of juice per unit when combining all the shown juices.
To determine whether the expression (64+28+76)/6 makes sense, we need to evaluate the components of the expression and consider whether the mathematical operations are valid.
The expression (64+28+76)/6 represents the sum of three numbers (64, 28, and 76), divided by 6. Let's break it down step by step:
Addition: We have three numbers being added together: 64, 28, and 76. The sum of these numbers is 168 (64 + 28 + 76 = 168).
Division: The sum of the three numbers, 168, is then divided by 6. Division is a valid mathematical operation.
Now, let's analyze whether the expression makes sense in the context of Stephen combining all the juice to make fruit punch. The numbers 64, 28, and 76 may represent quantities of juice (in some units) that Stephen is combining. However, without further information or context, we cannot determine if the expression accurately represents the combination of these juices.
If the numbers 64, 28, and 76 represent quantities of juice in the same units (such as milliliters or liters), then the expression (64+28+76)/6 would represent the average quantity of juice per unit. The result, 168/6, would be 28. This would imply that each unit (e.g., glass or serving) of the fruit punch contains an average of 28 units of juice.
In summary, mathematically, the expression (64+28+76)/6 is valid. However, without additional context regarding the units or quantities being represented, it is not possible to determine whether the expression accurately describes the process of combining the juices to make fruit punch.
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Writing an equation of a parabola given the vertex and the focus
Answers
vertex (3, 1)
directrix y = 6
The equation of a parabola is
\(y=\frac{1}{4(f-k)}(x-h)^2+k\)where,
(h,k) is the vertex and (h,f) is the focus
Thus,
h = 3
k = 1
The distance from the focus to the vertex is equal to the distance from the vertex to the directrix, then f - k = k - 6
replace k=1 and solve for f,
\(\begin{gathered} f-1=1-6 \\ f=-5+1 \\ f=-4 \end{gathered}\)Thus,
h = 3
k = 1
f = -4
therefore, the equation of the parabola is,
\(\begin{gathered} y=\frac{1}{4*(-4-1)}(x-3)^2+1 \\ \\ y=-\frac{1}{20}(x-3)^{2}+1 \end{gathered}\)A 0.143-Henry Inductor is connected in series with a variable resistor to a 208-volt 400-cycle source. For what value of capacitance will the current be (a) 1.04 ampere lagging and (b) 1.04 ampere leading?
Answers
Answer:
A.)359.2, B.)2.5 uf
Step-by-step explanation:
E / I = R
208 / 1.04 = 200 ohms
2*pi*f*L = Xl
6.28*400*.143 = 359.2 ohm
1 / (2*pi*f*Xc) = c
1 /(6.28*400*159.2) = 2.5 uf
Give the domain and range of the quadratic function whose graph is described.
The vertex is (-6, -2) and the parabola opens up.
Answers
Answer:
Domain: All real #s
Range: All real numbers greater than -2
Answer:
Domain: all real numbers
Range: -2 <= y
Step-by-step explanation:
For all parabolas that open up or down, the domain is all real numbers. You could walk up and down the x-axis and always be able to find this curve forever to positive numbers and forever to the negative number side. The domain is all the x's that can be found on the curve or are allowed to be used in the equation. This is all real numbers; that's why the domain is all real numbers.
As for the range, all the y's that can be found on the graph are from the lowest point and up. So, the graph of this curve does not exist below -2. The range is -2 and up.
y >= -2 or
-2 <= y
in interval notation:
[-2, infinitysymbol)
Multiply the number by 4
Add 12 to the product
Divide the sum by 2
Subtract 6 from the quotient
Answers
By comparing the result obtained in Part B (6N) with the result obtained in Part A, we can see that the conjecture holds true. The result of the process is indeed related to the original number (N) by multiplying it by 6.
Part A:
Based on the given process, the conjecture that relates the result of the process to the original number (represented as N) is as follows:
Start with the original number N.
Multiply N by 4.
Add 12 to the product.
Divide the sum by 2.
Subtract 6 from the quotient.
The result of this process is the final number obtained.
Part B:
To prove the conjecture using deductive reasoning, we will follow the steps given in Part A:
Start with the original number N.
Multiply N by 12.
Add 4 to the product.
Divide the sum by 2.
Subtract 2 from the quotient.
We will simplify the steps using algebraic notation:
Step 1: N
Step 2: 12N
Step 3: 12N + 4
Step 4: (12N + 4) / 2
Step 5: [(12N + 4) / 2] - 2
Now, let's simplify Step 5:
Step 5: (12N + 4) / 2 - 2
= (12N + 4 - 2*2) / 2
= (12N + 4 - 4) / 2
= 12N / 2
= 6N
Therefore, the result of this process is 6N.
We may verify that the supposition is correct by comparing the result from Part B (6N) with the result from Part A. By multiplying the outcome by 6, the process does in fact relate to the original number (N).
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The complete question is:
Multiply the number by 4. Add 12 to the product. Divide this sum by 2. Subtract 6 from the quotient. 1st number is 3 and the results 2nd number is 6 and the results 3rd number is 8 and the results 4th number is 12 and the results part A. Write a conjecture that relates the result of the process to the original number selected. Represent the original number as N. What is the result part b Represent the original number as N, use deductive reasoning to prove the conjecture in part (a) multiply the number by 12 and the results add 4 to the product and the results divide the sum by 2 subtract 2 from the quotient
Amanda tiene 4 bolitas más que Rodrigo, y Patricio tiene una bolita más que el doble de Amanda y Rodrigo juntos. Si en total tienen 103 bolitas, cuantas bolitas tiene Amanda
Answers
Las cantidades de bolitas para cada una de las tres personas son las siguientes:
Amanda: 19 bolitas
Rodrigo: 15 bolitas
Patricio: 69 bolitas
¿Cuántas bolas tienen Amanda, Rodrigo y Patricio?En este problema tenemos a tres personas (Amanda, Rodrigo y Patricio) que se reparten 103 bolitas, en términos algebraicos, cada persona es representada por las siguientes ecuaciones:
Amanda
x = y + 4
Rodrigo
y
Patricio
z = 2 · (x + y) + 1
Total
x + y + z = 103
A continuación, determinamos la cantidad de bolitas asociada con Rodrigo:
x + y + 2 · (x + y) + 1 = 103
3 · x + 3 · y = 102
x + y = 34
y + 4 + y = 34
2 · y = 30
y = 15
Luego, determinamos las cantidades de bolitas de Amanda y Patricio:
x = 15 + 4
x = 19
z = 2 · (19 + 15) + 1
z = 2 · 34 + 1
z = 68 + 1
z = 69
ObservaciónEl enunciado se encuentra escrito en español y el lenguaje de la respuesta es el mismo del enunciado.
The statement is written in Spanish and the language used in the answer is the same of the statement.
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which of the four triangles efG
Answers
The failure of a circuit board interrupts work that utilizes a computing system, until a new board is delivered. The delivery time, Y, is uniformly distributed on the interval two to six days. The cost of a board failure and interruption includes the fixed cost c0 of a new board and a cost that increases proportionally to Y2. If C is the cost incurred, C = c0 + c1Y2.
A) Find the probability that the delivery time exceeds two days.
B) In terms of c0 and c1, find the expected cost associated with a single failed circuit board.
Answers
Answer:
a) 1 ( 100% )
b) Co + 46/3 C1
Step-by-step explanation:
Delivery time = Y
Interval = 2 to 6 days
cost incurred ( C ) = Co + C1 Y^2
a) determine the probability that the delivery time exceeds two days
since the delivery time is uniformly distributed on the interval 2 to 6 days the probability of having a delivery time > 2 days will be = 1
b) Determine the expected cost associated with a single failed circuit board
E ( Y^2 ) = 46/3
hence the cost associated with a single failed circuit board =
E ( C ) = Co + 46/3 C1
attached below is a detailed solution
The company also has plans to open a third obstacle course, The Gridiron, where the first three checkpoints will have coordinates A′′(0,−5), B′′(9,−5), and C′′(4,−5). What relationship could this location have to the previous locations? Select all answers that apply.
Answers
Answer: It is a reflection of Reflections of You (second location) in the x-axis.
Step-by-step explanation: Based on the given information, the relationship between the new location (The Gridiron) and the previous locations can be determined.
The correct answer is:
It is a reflection of Reflections of You (second location) in the x-axis.
The coordinates of the first three checkpoints of The Gridiron (A''(0,−5), B''(9,−5), and C''(4,−5)) indicate that they have the same y-coordinate (-5) as the corresponding checkpoints in the second location, Reflections of You. However, there is no indication of a reflection in the y-axis or any transformation related to the first location, Transformation Fitness Studios. Therefore, the correct answer is that The Gridiron is a reflection of Reflections of You in the x-axis.
Write an expression that would have a value less than 3/4
Answers
Answer: 1/2
Step-by-step explanation:
1/2 is 2/4 which is smaller than 3/4
Find all the values of x where the tangent line is horizontal.
f(x) = 2x^3 + 42x^2 + 270x + 11
Answers
Answer:
If I calculated correctly, the tangent line is horizontal where x ≈ -5.3 + 9.3i, and -5.3 - 9.3i
I'm somewhat concerned at having gotten complex numbers, and strongly recommend going through the steps to see if I missed anything. I checked it myself and don't see any errors.
Step-by-step explanation:
You can do this by taking the derivative of the function and solving for zero:
f(x) = 2x³ + 32x² + 220x + 11
f'(x) = 6x² + 64x + 220
f'(x) = 2(3x² + 32x + 110)
We can't factor that further, so let's do it the long way, starting by letting f'(x) equal zero:
0 = 2(3x² + 32x + 110)
0 = 3x² + 32x + 110
0 = 9x² + 96x + 990
0 = 9x² + 96x + 256 + 734
0 = (3x + 16)² + 734
(3x + 16)² = -734
3x + 16 = ± i√734
3x = -16 ± i√734
x = (-16 ± i√734) / 3
x ≈ (-16 + 27.9i) / 3, and (16 - 27.9i) / 3
x ≈ -5.3 + 9.3i, and -5.3 - 9.3i
I'm always wary when I end up with complex numbers. I'd suggest double checking everything here, but I'm fairly certain I did everything correctly.
A rectangular prism has a width of x2 inches and a length of xy2 inches and a height of xy inches.
Which expression represents the volume of the rectangular prism in cubic inches?
2x^2y^2
2xy^3 + 2x^2y
2x^4y^3
x^3y^2
Answers
In this case, the width is x^2 inches, the length is xy^2 inches, and the height is xy inches.
Substituting these values into the formula, we get:
V = (xy^2)(x^2)(xy)
Simplifying, we get:
V = x^4y^3
Therefore, the expression that represents the volume of the rectangular prism in cubic inches is x^4y^3.
an airplane takes 3 hours to travel a distance of 1440 miles with the wind. The return trip takes 4 hours against the wind. Find the speed of the plane in the still air and the speed of the wind.
Answers
Answer:
The speed of the plane in the still air is 420 miles/hour
The speed of the wind 60 miles/hour
Step-by-step explanation:
Let the speed of the plane with the wind be v
Let the speed of the plane against the wind be u
Now, speed = distance/time
With the wind,
v = (1440 miles)/(3 hours) = 480 miles/hour
v = 480 miles/hour
Against the wind,
u = (1440 miles)/(4 hours) = 360 miles/hour
u = 360 miles/hour
Now, let the speed of plane be p, and speed of wind be w,
Now, with the wind, the speed is 480 mph,
so,
speed of plane + speed of wind = 480 mph
p + w = 480 (i)
and against the wind, the speed is 360 mph,
so,
speed of plane - speed of wind = 360mph
p-w = 360 (ii)
adding equations (i) and (ii), we get,
p+w + p-w = 480 + 360
2p = 840
p = 840/2
p = 420 miles/hour
Then, the speed of the wind will be,
p + w = 480,
420 + w = 480
w = 480 - 420
w = 60 miles/hour
The speed of the plane in still air is calculated to be 420 mph, and the speed of the wind is calculated to be 60 mph by solving the two simultaneous equations obtained from the time, rate, and distance relationship.
Explanation:This problem is about the rate, time, and distance relationships. The rate at which the airplane travels in still air is r (unaffected by wind), and the speed of the wind is w. When the plane flies with the wind, it is 'assisted' and therefore travels faster - at a speed of (r + w); against the wind, it travels slower - at a speed of (r - w).
From the problem, we know that:
The trip with the wind covers 1440 miles in 3 hours, so (r + w) * 3 = 1440The return trip against the wind covers the same 1440 miles in 4 hours, so (r - w) * 4 = 1440By solving these two equations, we get the following:
r + w = 480r - w = 360Adding these two gives 2r = 840 => r = 420 mph (the speed of the plane in still air), and subtracting gives 2w = 120 => w = 60 mph (the speed of the wind).
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Question 4 A study has been conducted to compare male and female test performance on a standardised science exam. In this hypothetical study, the researchers reported with a sample size of n = 50, the 95% confidence interval was found to be between 0.15 and 0.55.
What would happen to the 95% confidence interval if the sample size was increased?
The 95% confidence interval would remain the same Cannot be determined from the information provided The 95% confidence interval would decrease The 95% confidence interval would increase
Answers
If the sample size was increased, the 95% confidence interval would decrease. A larger sample size would provide more precise and accurate data, resulting in a narrower confidence interval.
A confidence interval is a range of values within which a population parameter is estimated to lie with a certain level of confidence. It is commonly used in statistical inference to estimate the true value of a population parameter based on a sample from that population.
If the sample size was increased, the 95% confidence interval would likely decrease. This is because a larger sample size typically leads to more precise estimates and less variability in the data, resulting in a narrower confidence interval. However, the exact size of the decrease would depend on various factors such as the amount of variability in the data and the level of statistical significance chosen for the study.
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Find the area of the regular pentagon with apothem 3.5 and side. Not drawn to scale.
100 POINTS
SHOW WORK PLEASE
Answers
Answer:
52.5 inch square
Step-by-step explanation:
Area of pentagon: A = 1/2 × p × a;
where 'p' is the perimeter of the pentagon and 'a' is the apothem of the pentagon.
A = 1/2 x (6 x 5) x 3.5 = 1/2 x 30 x 3.5 = 15 x 3.5 = 52.5
The area of the regular pentagon with apothem 3.5 and side 6 is 52.5
What is the area of the regular pentagon?In Mathematics, a pentagon is a polygon with 5 sides. A pentagon can be classified as a regular pentagon and irregular pentagon. When all the sides and the angles of a pentagon are of equal measure, then it is called a regular pentagon.
How to find the area of the regular pentagonGiven the question, we need to find the area of the regular pentagon with apothem 3.5 and side 6.
In order to find the area, the formula to calculate the area of the regular pentagon is given by:
\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)
Where “s” is the side length. And “a” is the apothem length.Now,
\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)
\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times 6 \times 3.5\)
\(\text{Area of pentagon} =52.5\)
Therefore, the area of the regular pentagon with apothem 3.5 and side 6 is 52.5
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\(16-2t=5t+9\)
Answers
You divide each side by factors
Find the present value of an annuity which pays ` 200 at the end of each 3 months for 10 years assuming
money to be worth 5% converted quarterly?
(a) ` 3473.86
(b) ` 3108.60
(c) ` 6265.38
(d) None of thes
Answers
The present value of the annuity is approximately `7032.08. The correct answer is option (d) None of these.
To find the present value of an annuity, we can use the formula:
PV = PMT * (1 - (1 + r)^(-n)) / r
Where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.
In this case, the periodic payment is `200, the interest rate is 5% (or 0.05) converted quarterly, and the number of periods is 10 years, which equals 40 quarters.
Plugging in these values into the formula, we get:
PV = 200 * (1 - (1 + 0.05)^(-40)) / 0.05
Simplifying the equation, we find:
PV ≈ 200 * (1 - 0.12198) / 0.05
PV ≈ 200 * 0.87802 / 0.05
PV ≈ 35160.4 / 0.05
PV ≈ 7032.08
Therefore, the present value of the annuity is approximately `7032.08.
None of the provided answer options (a), (b), or (c) match this result. The correct answer is (d) None of these.
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Cars and trucks are the most popular vehicles. Last year, the number of cars sold was 39,000 more than three times the number of trucks sold. There were 216,000 cars sold last year. Write an equation that can be used to find the number of trucks, t, sold last year.
Answers
Answer:
(39,000 + 3t = 216000.) t = 59000
Step-by-step explanation:
(How to find t) First, subtract 39000 from 216000. Divide that by 3. Your answer is 59000.
A data set contains an independent and a dependent variable. Which must be true of the data set if a linear function can
be used to represent the data?
O The set must have a constant additive rate of change.
The set must have a constant multiplicative rate of change.
O The values in the set must be positive.
O The values in the set must be increasing.
Mark this and return
Save and Exit
Next
Submit
Answers
The answer choice which must be true regarding the linear function is; The set must have a constant additive rate of change.
Which is true about a linear function?Since a linear function typically takes the slope-intercept form; f(x) = mx +c.
It therefore follows that the equation must have a constant slope m, which is the described additive constant rate of change.
It therefore follows that, the answer choice which is true regarding the linear function is therefore; The set must have a constant additive rate of change.
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5. Joel sells cotton candy at the Magic games
for $4 per bag. He also sells peanuts at the
games for $2.50 per bag. One day he sold
160 bags and collected $460. How many of
each item did he sell?
Answers
The number of peanuts sold is 140 and the number o cotton candies sold is 40.
Two equations that can be used to solve the equation
$4c + $2.5p = $460 equation 1
c + p = 160 equation 2
Where:
c = cotton candy
p = peanuts
How many peanuts did he sell?
Multiply equation 2 by 4
4c + 4p = 640 equation 3
Subtract equation 1 from equation 3
$1.50p = 180
p = 120
How many cotton candies did he sell?120 + c = 160
c = 160 - 120
c= 40
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. Why is the following arrangment of squares not an array?
Answers
When it comes to arrays in mathematics, it usually involves objects or numbers that are arranged in rows and columns.In order for a set of squares to be considered an array, it must meet certain requirements. These requirements are:All rows must have the same number of squares. All columns must have the same number of squares. Squares must be organized in an orderly manner. A set of squares that does not meet these requirements is not an array.
An array is a set of objects or values that are organized in a specific order. It is used in programming, mathematics, and other fields to make data manipulation and analysis easier.
When it comes to arrays in mathematics, it usually involves objects or numbers that are arranged in rows and columns.In order for a set of squares to be considered an array, it must meet certain requirements. These requirements are:All rows must have the same number of squares. All columns must have the same number of squares. Squares must be organized in an orderly manner. A set of squares that does not meet these requirements is not an array.
For example, if a set of squares is arranged in a random or disorganized manner, it cannot be considered an array because it does not meet the orderly requirement. Additionally, if the number of squares in each row or column is different, it cannot be considered an array because it does not meet the uniformity requirement.
Overall, it is important to remember that an array is a specific type of organization and cannot be applied to any random set of objects or values.
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In the diagram a person who is ft tall is standing on the ground ft away from point . A line segment drawn from the top corner of the building to point creates two similar triangles.
Answers
The height of the building, using similar triangles, is given by:
36 feet.
What are similar triangles?Similar triangles are two triangles that share these two features, which are listed as follows:
Same angle measures.Proportional side lengths.The second bullet point, regarding proportional side lengths, is especially relevant in the context of this problem, as a proportional relationship is built to find the height h of the building.
From the similar triangles, the equivalent side lengths are presented as follows:
3 ft and 18 ft.6 ft and h ft.Hence the proportional relationship that models this situation is presented as follows:
3/18 = 6/h.
Applying cross multiplication, the height of the building is obtained as follows:
3h = 18 x 6
h = 6 x 6 (simplifying by 3)
h = 36 feet.
Missing InformationThe diagram is given by the image shown at the end of the answer.
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Which of the following statements is true regarding that equation |x+3|-2=k?
Answers
The true statement is if k = - 1 there are solutions, but if k = - 3 there are no solutions
How to determine which statement is true regarding the equation |x+3|-2=k?
Given: |x+3|-2=k
Below are rules for solving absolute value equations:
1. If p is positive and |y| = p, then
x = p OR y = -p
(two equations are set up)
2. If p is negative and |y| = p, then
No solution
3. If p is zero and |y| = p, then
One solution
Using the rules:
|x+3|-2=k
when k = -1
|x+3|-2= -1
|x+3| = 1
Rule 1 is applicable here. Thus, there are solutions
when k = -3
|x+3|-2 = -3
|x+3| = -1
Rule 3 is applicable here. Thus, no solution
Therefore, if k = - 1 there are solutions, but if k = - 3 there are no solutions. The 2nd option is the true statement
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Find the derivative of:f(x)=ln (x^2sin(x)/arctan(x))
Answers
Solution
Write the function
\(f(x)\text{ = }\ln\left(\frac{x^2\sin\left(x\right)}{\arctan\left(x\right)}\right)\)Next
Apply the chain rule
\(\begin{gathered} Let\text{ u =}\left(\frac{x^2\sin\left(x\right)}{\arctan\left(x\right)}\right) \\ \mathrm{Apply\:the\:Quotient\:Rule}:\quad \left(\frac{f}{g}\right)^'=\frac{f\:'\cdot g-g'\cdot f}{g^2} \\ =\frac{\frac{d}{dx}\left(x^2\sin \left(x\right)\right)\arctan \left(x\right)-\frac{d}{dx}\left(\arctan \left(x\right)\right)x^2\sin \left(x\right)}{\left(\arctan \left(x\right)\right)^2} \\ \frac{d}{dx}\left(x^2\sin\left(x\right)\right)=\frac{d}{dx}\left(x^2\sin\left(x\right)\right) \\ \\ \frac{d}{dx}\left(\arctan\left(x\right)\right)\text{ = }\frac{1}{x^2+1} \\ \\ =\frac{\left(2x\sin \left(x\right)+\cos \left(x\right)x^2\right)\arctan \left(x\right)-\frac{1}{x^2+1}x^2\sin \left(x\right)}{\left(\arctan \left(x\right)\right)^2} \\ \\ Simplify \\ \\ \frac{du}{df}=\frac{\arctan\left(x\right)\left(2x\sin\left(x\right)+x^2\cos\left(x\right)\right)\left(x^2+1\right)-x^2\sin\left(x\right)}{\arctan^2\left(x\right)\left(x^2+1\right)} \end{gathered}\)Next
\(\begin{gathered} f(x)\text{ = In\lparen u\rparen} \\ \frac{df}{du}\text{ = }\frac{1}{u} \\ \\ From\text{ chain rule} \\ \\ f^{\prime}(x)=\text{ }\frac{du}{dx}\text{ }\times\text{ }\frac{df}{du} \\ \\ =\frac{1}{\frac{x^2\sin\left(x\right)}{\arctan\left(x\right)}}\frac{d}{dx}\left(\frac{x^2\sin\left(x\right)}{\arctan\left(x\right)}\right) \\ \\ =\frac{1}{\frac{x^2\sin \left(x\right)}{\arctan \left(x\right)}}\cdot \frac{\arctan \left(x\right)\left(2x\sin \left(x\right)+x^2\cos \left(x\right)\right)\left(x^2+1\right)-x^2\sin \left(x\right)}{\arctan ^2\left(x\right)\left(x^2+1\right)} \\ \\ =\frac{\arctan \left(x\right)\left(x^2\cos \left(x\right)+2x\sin \left(x\right)\right)\left(x^2+1\right)-x^2\sin \left(x\right)}{x^2\sin \left(x\right)\arctan \left(x\right)\left(x^2+1\right)} \\ \\ \end{gathered}\)Final answer
The derivative of the function is given below:
\(f^{\prime}(x)\text{ }=\frac{\arctan\left(x\right)\left(x^2\cos\left(x\right)+2x\sin\left(x\right)\right)\left(x^2+1\right)-x^2\sin\left(x\right)}{x^2\sin\left(x\right)\arctan\left(x\right)\left(x^2+1\right)}\)A fancy restaurant put dishes of butter at each table. They divided 4/5 of a kilogram of butter evenly to put 1/5 of a kilogram in each dish. How many butter dishes did they fill?
Answers
Answer: 4
This problem requires basic division. If the restaurant divided 4/5 kg of butter with 1/5 kg on each dish, you would need to compute 4/5 divided by 1/5.
4/5 ÷ 1/5
Using the "KFC" method, or Keep, Change, Flip, you would keep the first number (in this case, 4/5), change the division sign, and flip the fraction to 5/1, or 5. We now have this:
4/5 x 5
To compute this equation, you must multiply the numerators of both of the numbers together. In this case, you would compute (4x5)/5, resulting with 20/5, or 4.
You can check this answer by re-multiplying the numbers together. 1/5 kg of butter per dish, multiplied by the total amount of dishes, 4, you would result in the original 4/5 kg of butter.
Hope this helps!
Carol and Peter walk to school. Carol walks 3/5 of a mile to walk to school,
Peter walks 0.65. Which student has a father walk?
Answers
For Carols situation, I divided one mile into 5 parts. 1 mile divided by 5 equals .2 miles. Since she walked 3/5 of a mile, I multiplied .2 with 3 which equals 0.6. Carol walked 0.6 Miles.
Peter walked 0.65 mile, so he walked .05 miles farther then Carol
Peter had a farther walk
Let sets A and B be defined as follows.
A is the set of integers greater than -14 and less than -5.
B={h,i,s,x,z}
a) find the cardinalities of A and B
n(A)=
n(B)=
b) select true or false
-12 ∈ A
-21 ∈ A
s ∈ B
m ∉ B
Answers
A is the set of integers greater than -14 and less than -5. B={h, i, s, x, z}. The cardinalities of A and B are, n(A) = 8 and n(B) = 5.
-12 ∈ A, s ∈ B, and m ∉ B are True statements. Since, -21 does not belong to A, 21 ∈ A is a False statement.
Cardinalities of A and B
It is given that,
A = {n : -14 < n < -5, n ∈ Z} ............ (1)
B = {h, i, s, x, z} ......... (2)
Thus, from (1),
A = {-13, -12, -11, -10, -9, -8, -7, -6} ........... (3)
Cardinalities of A and B are the number of members in the set A and B, respectively. Therefore,
n(A) = 8
n(B) =5
Reason Behind True or False
As seen from (3), set A contains the element -12. Thus, -12 ∈ A is True.Again from (3), we can see that -12 does not belong to the set A. Thus, -21 ∈ A is FalseFrom (2), s is present in set B. Hence, s ∈ B is TrueSimilarly, m is not present in set B. Therefore, m ∉ B is TrueLearn more about cardinalities here:
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Y=2x^2 - 8x+3 graph the equation
Answers
Answer:
Graph is below.
Step-by-step explanation:
The solutions of the equations are : x = [8 ± √ 40] / 4
Given,
Y=2x² - 8x+3
Now,
To get the solution of equation equate it to 0 .
2x² - 8x+3 = 0
By quadratic formula,
x = -b ± √ b² - 4ac/2a
Substitute the values in the formula,
x = [8 ± √ 64 - 4(2)(3)] / 2* 2
x = [8 ± √ 40] / 4
Now plot the points in the graph. The graph is attached below.
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Metalfab Pump and Filter expects the cost of steel bodies for 6-inch valves to increase by $1.5 every 3 months. If the cost for the first quarter is expected to be $80, what is the present worth of the costs for a 3-year time period at an MARR of 7% per year compounded quarterly?
Answers
Answer:
120
Step-by-step explanation:
n= 5*4= 20
Final cost= 80*(2*20)= 120
Now, we can calculate the present value:
PV= FV/(1+i)^n
PV= 120/ (1.011^20)= $96.42
5/11 divided 4/11 =
29 divided by 6/7=
5/9 divided by 1 2/3=
5 3/5 divided by 3 1/2=
please help me!
Answers
Using division and multiplication, the values of the operation are 5/4, 203/6, 1/3 and 32/21 respectively
What are Division of NumbersDivision of numbers is the process of breaking down a number into definite proportions of value. In dividing a number, we are reducing it's size by a specific factor. The number to be divided is the dividend. The number by which we divide is the divisor.
In the question given, we have several division operations to carry out.
A) 5/11 ÷ 4/11
Since this are fractions, when we take the inverse of one of the values, we change the sign to multiplication.
5/11 * 11 / 4
This becomes 5/4
B) 29 ÷ 6 / 7
We can also do the same thing we did above by simply taking the inverse of the divisor and then change the sign to multiplication.
29 × 7 / 6 = 203/6
C) 5/9 ÷ 1 2/3
We have to first convert the mixed fraction into an improper fraction and the take the inverse of it and multiply.
5/9 ÷ 5/3
5/9 × 3/5 = 3/ 9 = 1/3
D) 5 3/5 ÷ 3 1/2
We also change the mixed fraction into improper fraction and then take inverse before multiplying.
16/3 ÷ 7/2
16/3 × 2/ 7 = 32/21
Learn more on division here;
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