The largest number is 20 .
What is largest ?
There is a big number—a googolplex—that exists. It consists of 1 and 10100 zeros (googol). A googolduplex, which is an even larger number, is also present. It is 1 and over a googol zeros after that.
Let 'n' be any number, odd or even.
2n will always be even number. This is because, 2n has 2 as common factor. So, 2n is always even.
Eg: 2= 2×1, n=1 ; 4=2×2, n=2 etc
Numbers are even, consecutive.
Consecutive even numbers are 2n-2, 2n, 2n+2,
Eg : For consecutive even numbers, put n=2
2n-2=4-2=2
2n=4
2n+2 =4+2=6,
we get 2,4,6 which are consecutive even nos.
So, numbers are 2n-2, 2n and 2n+2
Their sum= 2n+2+2n+2n-2=6n
Sum=54
6n=54
n=54/6=9
So, n=9
Consecutive numbers are
2n-2= (2×9)-2=16
2n=2×9=18
2n+2=18+2=20.
So, numbers are 16, 18, 20. Their sum is 54.
The largest number is 20
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find the area of the region bounded by the given curves. y = sin2(x), y = sin3(x), 0 ≤ x ≤ π
The area of the region bounded by the given curves is 0.7123 square units
In this question we have been given two curves y = sin^2(x), y = sin^3(x), 0 ≤ x ≤ π
We need to find the area of the region bounded by the given curves.
We know that the formula for the area between two curves f and g :
A = |∫_[a to b] [f(x) - g(x)] dx|
here, a = 0, b = π, f(x) = sin^2(x) and g(x) = sin^3(x)
So, A = |∫_[0 to π] [sin^2(x) - sin^3(x)] dx|
A = |∫_[0 to π] sin^2(x) dx - ∫_[0 to π] sin^3(x) dx|
consider ∫_[0 to π] sin^2(x) dx
= ∫_[0 to π] (1 - cos(2x) / 2) dx
= π/2
Now consider ∫_[0 to π] sin^3(x) dx
= ∫_[0 to π] (1 - cos^2(x)) sin(x) dx
= 4/3
So A = |π/2 - 4/3|
= 3π - 8/2
= 0.7123
Therefore, the required area: 0.7123 square units
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In a game, the number of dominos in various rows forms an A.P. If the number of dominos
in the 3rd and 11th cell together is 68 and number of dominos in 11th cell is 24 more than of
3rd cell, then answer the following questions based on this data.
The number on the third term and the eleventh term will be 22 and 46, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
In a game, the number of dominos in different lines structures an A.P. Assuming that the quantity of dominos in the third and eleventh cell together is 68 and the quantity of dominos in the eleventh cell is 24 a bigger number than of the third cell.
Let 'x' be the third number and 'y' be the eleventh number. Then the equations are given below.
x + y = 68 ...1
y = x + 24 ...2
From equations 1 and 2, then we have
x + x + 24 = 68
2x = 44
x = 22
Then the value of the variable 'y' will be given as,
y = 22 + 24
y = 46
The number on the third term and the eleventh term will be 22 and 46, respectively.
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Establish the identity.
(csc0+ cot 0)(csc0- cot0) = 1
a. Multiply and write the left side expression as the difference of two squares: ?
b. The expression from the previous step is equivalent to 1 using what?
O A. Reciprocal Identity
O B. Quotient Identity
O C. Pythagorean Identity
O D. Cancellation Property
O E. Even-Odd Identity
pls help asap i can’t pass this class without passing this test
To answer this question, we need to first multiply the left side of the given equation and write it as the difference of two squares. This can be done by using the difference of squares formula, which states that the difference of two squares can be written as the product of the square of the sum and the square of the difference.
The left side of the given equation can be written as:
(csc0+ cot 0)(csc0- cot0)
We can then apply the difference of squares formula to this expression to get:
(csc0+ cot 0)(csc0- cot0) = (csc0+ cot 0)(csc0- cot0)
Now, we can see that this expression is equivalent to 1 using the Cancellation Property. This property states that if two numbers or expressions are equal, then their corresponding parts are also equal. In this case, since 1 = (csc0+ cot 0)(csc0- cot0), we can cancel out the corresponding parts on both sides of the equation to get 1 = 1.
Therefore, the correct answer is D. Cancellation Property.
Which of the following is an example of an arithmetic sequence?
a.1/2, 1/4, 1/6, 1/8, ...
b. 3, 5, 7, 9, 11, ...
c.2, 6, 18, 54, ...
d.64,32,16, 8, ...
An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a fixed number, called the common difference, to the previous term. For example, the sequence 1, 2, 3, 4, … is an arithmetic sequence because each term is obtained by adding 1 to the previous term, which is the common difference.
Out of the four given options, only the sequence 1/2, 1/4, 1/6, 1/8, … is an arithmetic sequence. The common difference of this sequence is 1/4-1/2 = -1/4, so each term is obtained by subtracting 1/4 from the previous term. The other three sequences, 3, 5, 7, 9, 11, …, 2, 6, 18, 54, …, and 64, 32, 16, 8, … are not arithmetic sequences because the difference between each consecutive pair of terms is not constant. Therefore, the correct answer is a.
delivered.
a. What is the constant rate of change? What does it represent?
b. What is the initial value? What might that represent?
The constant rate of change and initial value for the given graph are 40 and 20 respectively. the initial value might represent the fixed cost of the soil.
What is the slope of straight line?The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference. The negative slope indicates the rate of decrease while the positive shows the rate of increase.
The given problem can be solved as follows,
(a) The graph given is a straight line that passes through (0, 40) and (10, 240).
The constant rate of change is equivalent to the the slope of the line given as,
⇒ (240 - 40)/(10 - 0) = 20
(b) The initial value of the graph is given as the y-intercept of the line.
Which is given as 40.
It might represent the fixed cost.
Hence, the constant rate of change is given as 40 and the initial value is 20 which might represent the fixed cost.
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The missing graph is attached here.
question 4 while verifying cleaned data, a data analyst encounters a misspelled name. which function can they use to determine if the error is repeated throughout the dataset? 1 point case counta check count
To determine if a misspelled name is repeated throughout a dataset, a data analyst can use the COUNT function. This function counts the number of occurrences of a value in a range of cells.
Alternatively, the data analyst could use the COUNTA function, which counts the number of cells in a range that contain data (including text and numbers, but not empty or blank cells). The COUNTA function would also count the number of occurrences of the misspelled name in the dataset.
What is a dataset, using an example?
A collection of numbers or values pertaining to one subject constitutes a data set. An example of a data set might be each student's test scores for a certain class. The amount of fish that each dolphin eats in an aquarium is a data set.
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two arithmetic sequences $a$ and $b$ both begin with $30$ and have common differences of absolute value $10$, with sequence $a$ increasing and sequence $b$ decreasing. what is the absolute value of the difference between the $51$st term of sequence $a$ and the $51$st term of sequence $b$?
The difference between 51th term of a and 51th term of b is 1000.
nth term of an arithmetic series is given by [tex]a_n = a_0 +( n-1)* d[/tex]
where [tex]a_0[/tex] is first term of arithmetic series , [tex]a_n[/tex] is nth term of the series and d is the common difference
given [tex]a_0 = b_0 = 30[/tex]
and given that both series have common difference have absolute value of 10.
common difference of series a is 10 as this series is increasing
similary common difference of series b is -10 as it is decreasing
putting the values in the above equation we get:
[tex]a_5_1[/tex] = [tex]a_0[/tex] +(n-1)*d
=> 30 + (51-1)*10
=> 30 + 500
so [tex]a_5_1[/tex] = 530
[tex]b_5_1[/tex] = [tex]b_0[/tex] +(n-1)*d
=> 30 + (51-1)*-10
=> 30 -500
so [tex]b_5_1[/tex] = -470
so we have to find value of [tex]a_5_1 - b_5_1[/tex] which is 530 - (-470) =530 +470 =1000
so the differnce of 51th term of a and b is 1000
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question and ente your response in the box provided. Use the
Factor the following expression: x² + x - 6
Answer:
-3
Step-by-step explanation:
x² + x = 3
3 - 6 = -3
a
b
c
whuch is the answer look at the picture
d
Answer:
Step-by-step explanation:
[very easy] [100 pt and brainliest]
The table shows the weights of apples at a grocery store. There is a proportional relationship between the number of apples and their weight. What is the weight of TWO apples?
TYPE ONLY THE NUMBER
Answer:
2 apples = 0.24 kg
12 apples = 1.44 kg
Step-by-step explanation:
Find the weight of one apple.
If 5 apples weigh 0.60 kg, then 1 apple weighs:
[tex]\implies \sf 1\;apple=\dfrac{0.60}{5}=0.12\; kg[/tex]
Therefore:
2 applies = 2 × 0.12 - 0.24 kg12 apples = 12 × 0.12 = 1.44 kgA bakery old 26 vanilla cupcake in a day which wa 13 percent of the total number of cupcake old that day. How many total cupcake did the bakery ell that day
The bakery sold total 200 cupcake in that day.
What is percent value?The word percent means per hundred and percent value of a quantity refers to the hundred parts of that quantity. Percent value is expressed by sign %.
How to calculate percentage value?In order to determine a percent value of a quantity, we divide the quantity by the total quantity and finally the resultant value is multiplied by 100.
In the other hand, when we need to calculate total quantity from a percentage value, we multiply the specific quantity by 100 and finally the resultant is divided by the percentage value.
Given, Number of cupcakes sold at a specific time =26 which was 13 percent of total number of cupcakes sold in that day.
Therefore, number of total cupcakes sold in that day = 26× 100/13 =200
the total number is 200
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If the exponent of the leading term of the numerator is higher than the exponent of the leading term of the denominator, what can we conclude?.
If the degree on x in the denominator is larger than the degree on x a bigger leading exponent than the polynomial in the numerator.
After then the graph to the value found by dividing the leading coefficients of the two polynomials.
To find horizontal asymptotes:
1. If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0).
2. If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote.
3. Rational functions (a polynomial divided by a polynomial) and exponential functions have horizontal asymptotes.
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x + 2y = 5; P = (2,-5)
Answer:
....................
Find the value of the variable
A. 180 degree
B. 25 degree
C. 55 degree
D. 125 degree
Help!!!!!
Answer:
120°
Step-by-step explanation:
125° + ( y + 5 )° + y = 360°
or, 125° + y + 5° + y = 360°
or, 2y + 130° = 360°
or, 2y = 360° - 130°
or, 2y = 230
or, y = 230/ 2
. y = 115°
. .
. ( y + 5 )°
. . ( 115 + 5 )°
.
. . 120°
Option are wrong.
what is the power of the lens that has a focal length of 40 cm and a diameter of 5.0 cm?
The power of the lens is 2.5D
The focal length of 40 cm and a diameter of 5.0 cm.
Optical power (also referred to as dioptric power, refractive power, focusing power, or convergence power) is the degree to which a lens, mirror, or other optical system converges or diverges light. It is equal to the reciprocal of the focal length of the device: P = 1/f.
Power of lens = 1 / focal length (in meters)
For a thin lens in air, the focal length is the distance from the center of the lens to the principal foci (or focal points) of the lens. For a converging lens (for example a convex lens), the focal length is positive and is the distance at which a beam of collimated light will be focused to a single spot.
we have focal length 40cm (.4 m)
so
Converging lenses have positive optical power, while diverging lenses have negative power.
Power of lens = 1/0.4 m
=2.5 D [The unit of Power of lens is Dioptre]
Therefore, the power of the lens that has a focal length and a diameter of 5.0 cm is 2.5D
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9x+7y=256 and 3x+5y=125
Answer:
y= 14.875
x= 16.875
Step-by-step explanation:
simultaneous equation
substitution method
20. Keith is offered an interest rate of 8.27% for a
loan with continuous compounding. Calculate
his equivalent rate with simple compounding.
[A] 0.0795 or 7.95%
[B] 0.0998 or 9.98%
[C] 0.0106 or 1.06%
[D] 0.0863 or 8.63%
[E] 0.1108 or 11.08%
To calculate Keith's equivalent rate with simple compounding, we need to use the following formula:
r = (e^(i/n) - 1) * n
where r is the equivalent rate with simple compounding, i is the interest rate with continuous compounding, and n is the number of compounding periods per year.
In this case, we are given that i = 8.27% and we can assume that the number of compounding periods per year is 12, since many loans are compounded monthly. Plugging these values into the formula, we get:
r = (e^(0.0827/12) - 1) * 12
= (1.0082 - 1) * 12
= 0.0082 * 12
= 0.0984 or 9.84%
Therefore, Keith's equivalent rate with simple compounding is [B] 0.0998 or 9.98%.
If angle D is 22 degrees, what is the measure of angle B?
Answer:
22 degrees
Step-by-step explanation:
D=B and C=A
molly is playing a game that requires her to roll a fair die repeatedly until she first rolls a 1, at which point she must stop rolling the die. what is the probability that molly will roll the die less than four times before stopping?
The probability that molly will roll the die less than four times before stopping is 91/216
Probability is the calculation of an outcome or the chance of an event ever happening.
Probability determines the likelihood of an event occurring: P(A) = f / N.
Probability(Event) = Favorable Outcomes/Total Outcomes
She can do this in 1 roll, 2 rolls, or 3 rolls.
Probability of getting 1 in the first roll: 1/6
Probability of getting 1 on the second roll: 5/6∗1/6=5/36
Probability of 1 on the third roll: 5/6∗5/6∗1/6=25/216
As it can happen in 1, 2, or 3 rolls we add the probabilities: 1/6+5/36+2/52
⇒26/216+30/216+25/216
⇒91/216
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What is 5 times 10000
Answer:
50000
Step-by-step explanation:
find an equation of the tangent line to the given curve at the specified point. y = e^x / x , (1, e)
y = e is the equation of the tangent line to the given curve at the specified point , y = [tex]e^{x}[/tex] / x , (1, e)
Through the coordinate geometry formal of point-slope form, the equation of tangent and normal can be calculated.
The tangent has the equation (y - y1) = m(x - x1), and a normal travelling through this point and perpendicular to the tangent has the equation (y - y1) = -1/m (x - x1).
thus , y' = [tex]\frac{e^{x}-xe^{x} }{x^{2} }[/tex]
y'(1) = 0 = m
Our slope is indicated by the horizontal line.
y−[tex]y_{1}[/tex]=m(x−[tex]x_{1}[/tex])
Our line will simply be our y-coordinate because our slope(m) is 0:
e
Therefore:
The tangent line's equation is y=e.
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What is the circumference of the following circle?
Use 3.14 for \piπpi and enter your answer as a decimal.
Answer:
9.42cm
Step-by-step explanation:
according to fig :
diameter (d) =3cm so ,
radius (r) = d/2 =3/2 = 1.5cm
solution:
as we know that ,
circumference of a circle = 2πr
=2×3.14×1.5
=9.42 cm
Answer:
21.98 cm
Step-by-step explanation:
The circumference formula is [tex]2\pi r[/tex] which can be expressed as [tex]\pi d[/tex], where r is radius and d is the diameter length.
Since we know the diameter is 3 cm, that means we can plug in that value for d and get [tex]7 \pi[/tex] as the circumference
However, the question tells us to use 3.14 for [tex]\pi[/tex], so we must find the value of [tex]7 * 3.14[/tex]. By doing mental math or by using a calculator we can find this value to be 21.98.
Thus, the circumference of the circle is 21.98 cm
The printer at Seneca office can print out one A1 page every 5 seconds. In 4.3 hours time, how many pages can be printed out? Add any workings here
Answer: There are 4.3 hours * 60 minutes per hour = 4.360=258minutes in 4.3 hours.
There are 258 minutes * 60 seconds per minute = 25860=15480 seconds in 258 minutes.
Therefore, the printer at Seneca office can print out 15,480 pages / 5 seconds per page =15480/5=3096 pages in 4.3 hours. Answer: 3096
Step-by-step explanation:
Annual salary at r rupees per month along with a Christmas bonus of Rs2000. Find the total annual salary with a festive bonus.
The total annual salary with a festive bonus is Rs (12r+2000)
What is multiplication?In maths, multiply means the repeated addition of groups of equal sizes.
Given that, there is an annual salary at r rupees per month along with a Christmas bonus of, Rs 2000.
Here, a person is getting monthly salary = Rs r
Therefore, his annual salary = Rs r × 12
= Rs 12r
He is also getting a bonus for Christmas = Rs 2000
So, in total, he will get = Rs (12r+2000)
Hence, The total annual salary with a festive bonus is Rs (12r+2000)
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PLEASE HELP QUICK I WILL GIVE BRAINLIEST
Answer:
z > 1 1/3
Step-by-step explanation:
See picture
The sum of two numbers is 62, and their difference is
12. What are the numbers?
Answer:
25 and 37
Step-by-step explanation:
x+y=62
y-x=12
+x. +x
y=12+x
x+(12+x)=62
2x+12=62
-12. -12
2x=50
/2. /2
x=25
25 is one of the numbers
y-25=12
+25 +25
y=37
hopes this helps
find the value of x in the figure?
Answer:
x = 11
Step-by-step explanation:
the sum of the 3 angles in the triangle = 180°
sum the 3 angles and equate to 180
80 + 60 + 3x + 7 = 180
147 + 3x = 180 ( subtract 147 from both sides )
3x = 33 ( divide both sides by 3 )
x = 11
Answer:
x = 11
Step-by-step explanation:
The sum of the angles of a triangle is 180 degrees
60 + 80 + 3x+7 = 180
Combine like terms
3x+147=180
Subtract 147 from each side
3x+147-147=180-147
3x = 33
Divide each side by 3
3x/3 = 33/3
x = 11
5x2 to the power of 5
find the exact length of the curve. x = et − t, y = 4et/2, 0 ≤ t ≤ 4
The exact length of the curve is [tex]& \mathbf{L}=\mathbf{e}^5+\mathbf{4}[/tex].
Let the given equation is [tex]x=e^t-t, y=4 e^{\frac{t}{2}}, 0 \leq t \leq 5[/tex].
Length of Parametric Curve: A parametric curve is a function expressed in components form, such that x=f(t),y=g(t). The length of a parametric curve on the interval a ≤ t ≤ b is given by the definite integral [tex]$L=\int_a^b \sqrt{\left(\frac{d x}{d t}\right)^2+\left(\frac{d y}{d t}\right)^2} d t$[/tex]
Let’s begin by getting the first derivative of the components of the function with respect to the variable t.
[tex]$$\begin{aligned}x & =e^t-t, y=4 e^{\frac{t}{2}} \\\frac{d x}{d t} & =\frac{d}{d t}\left(e^t-t\right)=\frac{d}{d t}\left(e^t\right)-\frac{d}{d t}(t)=e^t-1 \\\frac{d y}{d t} & =\frac{d}{d t}\left(4 e^{\frac{t}{2}}\right)=\left(4 e^{\frac{t}{2}}\right) \frac{d}{d t}\left(\frac{t}{2}\right)=\left(4 e^{\frac{t}{2}}\right)\left(\frac{1}{2}\right)=2 e^{\frac{t}{2}}\end{aligned}$$[/tex]
Substitute the derivatives into the following definite integral which computes the length of the parametric curve on the interval [a,b]=[0,5].
[tex]$$\begin{aligned}L & =\int_a^b \sqrt{\left(\frac{d x}{d t}\right)^2+\left(\frac{d y}{d t}\right)^2} d t \\& =\int_0^5 \sqrt{\left(e^t-1\right)^2+\left(2 e^{\frac{t}{2}}\right)^2} d t \\& =\int_0^5 \sqrt{\left(e^{2 t}-2 e^t+1\right)+\left(4 e^t\right)} d t \\& =\int_0^5 \sqrt{\left(e^{2 t}+2 e^t+1\right)} d t \\& =\int_0^5 \sqrt{\left(e^t+1\right)^2} d t \\& =\int_0^5\left(e^t+1\right) d t\end{aligned}$$[/tex]
We need to find the value of the definite integral to get the exact length of the curve.
Take out the limits of integration and evaluate the resulting indefinite integral to solve.
[tex]$$\begin{aligned}L & =\left.\left[\int\left(e^t+1\right) d t\right]\right|_0 ^5 \\& =\left.\left[\int e^t d t+\int 1 d t\right]\right|_0 ^5 \\& =\left.\left[e^t+t\right]\right|_0 ^5\end{aligned}$$[/tex]
Evaluate the solution at the limits of integration to get the length.
[tex]$$\begin{aligned}& L=\left[e^{(5)}+(5)\right]-\left[e^{(0)}+(0)\right] \\& L=\left(e^5+5\right)-\left(e^0+0\right) \\& L=e^5+5-(1+0) \\& L=e^5+5-1 \\& \mathbf{L}=\mathbf{e}^5+\mathbf{4}\end{aligned}$$[/tex]
Therefore, the exact length of the curve is [tex]& \mathbf{L}=\mathbf{e}^5+\mathbf{4}[/tex].
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Mai is putting money into a checking account. Let y represent the total amount of money in the account (in dollars). Let x represent the number of weeks Mai has been adding money. Suppose that x and y are related by the equation y= 550 + 40x.
Answer the questions below.
Note that a change can be an increase or a decrease.
For an increase, use a positive number. For a decrease, use a negative number.
What is the change per week in the amount of money in the account?
What was the starting amount of money in the account?
The change per week in the amount of money in the account is 40
The starting amount of money in the account is 550.
How to illustrate the equation?The statement that exemplifies the provided variables is called an equation. In this instance, the scenario is described by taking into account two or more factors. The definition of an equation as a mathematical statement that consists of two expressions joined by an equal sign must be understood.
In this instance, x and y are connected by the formula y=550 + 40x. In light of this, the weekly change in the account's balance is 40 dollars, while the initial balance was 550.
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