Derivative of log(tanhx) = 2cossec(2x)
Let us assume y = log (tan hx)
On differentiating both sides ,
[tex] \frac{dy}{dx \: } = \frac{d \: log(tanhx)}{dx} [/tex]
[tex] \frac{dy}{dx} = \frac{d log( \tan(hx) ) }{d \tan(hx).d \tan(hx) } \times dx[/tex]
[tex] \frac{dy}{dx} = \frac{1}{ \tan(hx) \times \sec( {h}^{2x} ) } [/tex]
[tex] \frac{dy}{dx} = \frac{ \cos(hx) }{ \sin(hx) } \times \frac{1 }{ \cos(h {}^{2} ) } [/tex]
[tex] \frac{dy}{dx} = \frac{2}{2 \sin(hx). \cos(hx) } [/tex]
[tex] \frac{dy}{dx} = \frac{2}{ \sin(h)(2x) } [/tex]
dy/dx = 2 cos sec (2x)
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The measure of the given angle ∠BDC or x is 55°.
What are angles?An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint.
The Latin word "angulus," which means "corner," is the source of the English term "angle."
The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation.
A geometrical shape called an angle is created by connecting two rays at their termini.
In most cases, an angle is expressed in degrees.
So, we know that:
∠ABC = 80°
∠ABD = 25°
∠BDC = x°
Calculate for ∠BDC:
∠ABC - ∠ABD = ∠BDC
80 - 25 = x
x = 55°
Therefore, the measure of the given angle ∠BDC or x is 55°.
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Tyee has 39 m of fencing to build a three-sided fence around a rectangular plot of
land that sits on a riverbank. (The fourth side of the enclosure would be the river.)
The area of the land is 169 square meters. List each set of possible dimensions (length
and width) of the field.
The dimensions of a building to be fenced off around a rectangular parcel of land are 10.5 meters and 21 meters.
How come it's called a rectangle?The Latin word rectus, which meaning "right" or "straight," is the source of the English word "rectangle." The straight sides of a rectangle are a result of its right angles. Rectitude, which refers to moral uprightness, is another term with the same root.
Explanation:
The size of a rectangle
lw = area of rectangle
where,
= length
= width
Thus, perimeter equals 2w plus l.
42 = 2w + l
l = 42 - 2w
Hence,
area = w (42- 2w)
180 = 42w - 2w²
-2w² +42w - 180 = 0
-w² + 21w - 180 = 0
The following is where to find the dimension w;
w = - b / 2a
where
a = -1
b = 21
w = - 21 / 2 × -1
W=10.5 meters.
Then,
l = 42 - 2w
l = 42 - 2(10.5) (10.5)
l=21 meters .Consequently, the measurements are 10.5 meters and 21 meters.
The dimensions of a building to be fenced off around a rectangular parcel of land are 10.5 meters and 21 meters
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What is an equation of the line that passes through the point (5, -8) and is
perpendicular to the line 5x - 4y = 16?
The equation of the line which is perpendicular to 5x - 4y = 16 is [tex]y = -\frac{4}{5}x -4[/tex].
What is Coordinate Geometry?The study of geometry using coordinate points is known as coordinate geometry (also known as analytical geometry). Finding the distance between two points, breaking lines into m:n segments, locating a line's midpoint, computing a triangle's area in the Cartesian plane, and other operations are all feasible using coordinate geometry.
Not all crossing lines are parallel ones. If the intersecting lines satisfy the following conditions, they are said to be perpendicular lines. Following are the two primary characteristics of perpendicular lines:
The intersection of perpendicular lines is always at a right angle.Two lines will always be parallel to one another if they are perpendicular to the same line.Let's say that lines AB and CD are parallel to one another. Line AB has a slope of m1, whereas line CD has a slope of m2.
If and only if the product of the slopes of the two lines equals negative of unity, two lines are perpendicular to one another.
As a result, the following is the formula for the perpendicular's slope:
m1.m2 = -1
The equation of the line be "y = mx + c".
Equation of the line Perpendicular to the line is 5x - 4y = 16
Therefore, 4y = 5x - 16
⇒ [tex]y = \frac{5}{4}x -4[/tex]
Slope of the line Perpendicular to the required line is [tex]\frac{5}{4}[/tex].
Slope of the required ine be m .
Therefore, m * [tex]\frac{5}{4} = -1[/tex]
⇒ [tex]m = -\frac{4}{5}[/tex].
Equation of the line is ,
[tex]y = -\frac{4}{5}x + c[/tex]
The line passes through (5,-8)
Therefore,
[tex]-8 = \frac{-4}{5}*5 + c[/tex]
⇒ c = -4
The equation of the line is [tex]y = -\frac{4}{5}x -4[/tex].
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or
Bill writes 4 pages per hour. Is the total number of pages written proportional to the number of hours spent writing?
The required proportional relationship between y = 4x, where, x it time and y is the total number of pages.
Given that,
Bill writes 4 pages per hour. The total number of pages written proportionally to the number of hours spent to be justified.
What is proportionality?Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
here,
let the number of pages written in x hours be y,
According to the question,
y = 4x
Thus, the required proportional relationship between y = 4x, where, x it time and y is the total number of pages.
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Which of the following relations between input numbers and output numbers is NOT a function?
send a picture so i know what its asking for
The diameter of a circle is 6 cm. Find its area to the nearest whole number.
Answer:
28.26
Step-by-step explanation:
A=3.14r^2
A=3.14(3)^2
A=3.14(9)
A=28.26
Answer: 28 cm
Step-by-step explanation: Area=π·r² and diameter =2r
So if we need to find what our radius is. As shown by d=2r our radius is 1/2 our diameter. If our diameter is 6cm our radius is 3cm.
Now plug 3cm into A= 2πr²⇒ A= 2(3.14)(3²) = 28.26
Now round to the nearest whole number ⇒ 28.
Charlie has twice as many brothers as Caleb.
Caleb has twice as many brothers as Angela.
Angela has 2 brothers.
How many brothers does Charlie have?
Element x decays radioactively with a half life of 8 minutes. If there are 170 grams of element x, how long, to the nearest tenth of a minute, would it take the element to decay to 5 grams?.
A time of 40.7 minutes is taken for 170 grams of element X to decay to 5 grams.
What is radioactive decay?
The release of energy in the form of ionizing radiation occurs during radioactive decay.
Ionizing radiation can harm DNA in genes and tissues because it can affect the atoms in living things.
We know that decay behaves exponentially and follows this model
[tex]m(t) = m_{0} . e^{t/T} \\[/tex]
The time constant can be described in terms of half-life (t1/2), in minutes, through the following expression
T = t1/2 /In2
If we know that t1/2 = 8 min , m₀ = 170g and m(t) = 5g then the time needed for the decay is:
τ ≈ 11.541 min
t = -τ .In m(t)/m₀
t ≈ 40.698 min
A time of 40.7 minutes is taken for 170 grams of element X to decay to 5 grams.
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Kona work at a bakery. She baked 3308 muffin. She diplayed the muffin on tray that each hold 12 muffin. How many tray did Kona ue to diplay the muffin?
Using mathematical operations, we know that Kona needs a 276 trays to display all her 3308 muffins.
What are mathematical operations?The process of calculating a value using operands and a math operator is known as a mathematical "operation."
The provided operands or integers must follow certain established rules that are associated with the math operator's symbol.
Addition, subtraction, multiplication, division, and modular forms are the five fundamental operations in mathematics.
So, a tray will be needed to display all the cakes:
The total number of muffins is 3308.
Each tray can have 12 muffins.
The total trays needed are:
3308/12
275.66
Rounding off: 276
Therefore, using mathematical operations, we know that Kona needs a 276 tray to display all her 3308 muffins.
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Show your work, (I am stuck on this because I’m not smart lol)
Answer:
She needs to get at least 96 on the 4th test to earn an average of at least 90 in the class.
Step-by-step explanation:
(97+78+89+?) divided by 4 at\geq 90
It is divided by 4 because it is the average of 4 test scores.
To Solve: (97+78+89+?) divided by 4 at\geq 90
Multiply by 4 on both sides 97+78+89+? at\geq 360
Isolate variable: ? at\geq 96
What value of x makes the equation 1/2(5x+16)-3/2(x-8)=-4 true
Answer:
x=-24
Step-by-step explanation:
you would solve for x
1) multiply the equation out
2) put x on one side by subtracting and adding on each side (make sure to balance it out)
3) divide or multiple by the number on the number on the x
5/2x + 8 - 3/2x + 12 = -4
5/2 x - 3/2 x + 8 + 12 = -4
x + 20 = -4
x = -24
what is the probability that an electron will tunnel through a 0.50 nm air gap from a metal to a stm probe if the work function is 4.0 ev?
The probability that an electron will tunnel through a 0.50 nm air gap from a metal to a STM probe if the work function is 4.0 eV is 3.4 × 10^-5
The air gap from a metal to a STM = 0.50 nm
The work function = 4.0 eV
The probability is the ratio of the number of favorable outcomes to the total number of outcomes
The probability = Number of favorable outcomes / Total number of outcomes
The value of η = h / [tex]\sqrt{2m(U_0-E)}[/tex]
Substitute the values in the equation
= [tex]\frac{1.05(10^{-34})}{\sqrt{2(9.11(10^{-31})(4(1.6)(10^{-19})} }[/tex]
Do the arithmetic operation
= 0.0972 nm
The probability = exp (-1 / 0.972)
= 3.4 × 10^-5
Therefore, the probability is 3.4 × 10^-5
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A frog in a hemispherical pod (see fig. ) just floats without sinking into sea water with density 1. 35g / c * m ^ 3 if the pod has radius 6 cm and negligible mass, what is the mass of the frog?.
Thus, the mass of the frog is 48.6π grams when it is in a hemispherical pod which just floats without sinking into sea water.
What is meant by buoyancy?The force imposed on a body by a fluid, such as water or air, in which the body is submerged or immersed is known as buoyancy. This force is equivalent to the mass of the fluid that the body has displaced. In mathematics, buoyancy is defined as the sum of the fluid density, gravitational acceleration, and body volume. Archimedes' principle, which asserts that the buoyant force on an item is equal to the weight of the fluid it displaces, is a name for this connection. A key idea in the study of fluid mechanics, buoyancy has many uses, including the construction of boats, planes, and other floating structures.
How to solve?
V = 2/3 * π * r^3,
V = 2/3 * π * 6^3 = 2/3 * π * 216 = 36π.
F = V * d,
F = 36π * 1.35g/c * m^3 = 48.6π g.
F = m + W,
48.6π g = m + 0 g.
m = 48.6π g.
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A drawer contains one pair of brown socks and one pair of white socks. The table shows the possible outcomes, or sample space, for choosing a sock, replacing it, and then choosing another sock.
Given that the drawer includes one pair of brown socks and one pair of white socks, the likelihood of selecting one sock, replacing it, and then selecting another sock is 1/16.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Here,
n(s)=4
n(e)=1
Probability of choosing a sock, replacing it, and then choosing another sock,
=1/4*1/4
=1/16
Probability of choosing a sock, replacing it, and then choosing another sock will be 1/16 as the drawer contains one pair of brown socks and one pair of white socks.
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If 65% of a number is 208 and 15% of the same number is 48, find 80% of that number.
The number is 320 and 80 % of the number is 256
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the equation A is
65% of a number is 208 and 15% of the same number is 48
So , 65% of n = 208 be equation (1)
15% of n = 48 be equation (2)
Now , on simplifying the equations , we get
( 15 / 100 ) x n = 48
15n/100 = 48
Multiply both sides by 100 . we get
15n = 4800
Divide by 15 on both sides of the equation , we get
n = 320
The number n can also be determined by
( 65% - 15% ) of n = 208 - 58
50 % of n = 160
So , 100 % on n = 160 x 2
n = 320
Therefore , the number n is 320
Now , the 80 % of the number n is A = 80/100 x 320
A = 320 x 0.8
A = 256
Therefore , the value of A is 256
Hence , The number is 320 and 80 % of the number is 256
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O
Nolan is going to a carnival that has games and rides. Each game costs $2.50 and
each ride costs $3.50. Nolan spent $52.50 altogether on 17 games and rides. Write a
system of equations that could be used to determine the number of games Nolan
played and the number of rides Nolan went on. Define the variables that you use to
write the system.
Answer: g + r = 17
2.5g + 3.5r = 52.5
Step-by-step explanation: Let g be the number of games Nolan played and r be the number of rides Nolan went on. We can write the following system of equations to represent the problem:
g + r = 17
2.5g + 3.5r = 52.5
We can solve this system of equations using elimination, substitution, or graphing.
The production rate per hour of a purse factory that can manufacture 200 purses in 8 hours.
Answer:
>:)
Step-by-step explanation:
200 purses, 8 hours
200/8 = 25
25 purses per hour!
Pls mark me as brainliest and give me 20 points I need it :) Hope this answer helped!!
Answer: The Factory manufactures 25 purses per hour
Step-by-step explanation:
200 purses / 8 hours
25 purses per hour
One of the roots of the equation 10x^2-33x=c=0 is 5.3. Find the other root and the coefficient c.
Answer:
another root=-2,c=-106
Step-by-step explanation:
let q and r be two roots of eqn 10x²-33x-c=0,--(1)
then,q=5.3
comparing eqn--(1) with ax²+bx+c=0,we get
a=10,b=-33,C=-c
we know,
q+r=-b/c
or,5.3+r=33/10
or,53+10r=33
or,10r=-20
or,r=-2
hence, another root=-2
again,we know
q×r=-C/a
or,5.3×-2=c/10
or,-106=c
hence,c=-106.
(a) Find the three consecutive natural numbers whose sum is 66.
(b) Find the three consecutive odd natural numbers whose sum is 39.
Answer:
(a) 21, 22, 23
(b) 11, 13, 15
Step-by-step explanation:
Natural numbers are the set of numbers 1, 2, 3... Not numbers that we think of as fractions or decimals or negative numbers.
Let x = the first number
Let x+ 1 = the second number
Let x+ 2 = the third number
x + x+ 1 + x + 2 = 66 Combine like terms
3x + 3 = 66 Subtract 3 from both sides
3x = 63 Divide both sides by 3
x = 21
Check:
21 + 22 + 23 = 66
Let x + the first number
Let x + 2 = the second number
Let x + 4 = the thirds number
x + x + 2 + x + 4 = 39 Combine like terms
3x + 6 = 39 Subtract 6 from both sides
3x = 33 Divide both sides by 3
x = 11
Check: 11 =+ 13 + 15 = 39
Andrew invests $2834 in a savings account with a fixed annual rate of 2.5% compounded daily. What will the account balance be after 28 years?
The account balance(i.e. compound amount) will be $5706.84 after 28 years.
What is daily compounded interest?
Daily compounded interest is defined as an interest that is accrued daily and is computed by charging interest on principal plus interest earned daily. Due to the frequent compounding, daily compounded interest is higher than interest compounded on a monthly or quarterly basis.
Given, Principal = $2834
the annual rate = 2.5% = 0.025
time = 28 years
For compounded daily, n = 365
Now, the compound amount is calculated by
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
or, A = [tex]2834(1 + \frac{0.025}{365} )^{365*28}[/tex]
A = $5706.84
Hence, the account balance will be $5706.84 after 28 years.
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The general form of an parabola is 4y2 + 40y + 3x + 103 = 0
What is the standard form of the parabola?
The standard form of the parabola is x = -4/3y² -40/3y -103/3
What is parabola?
A parabola is an approximately U-shaped, mirror-symmetrical planar curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. One way to describe a parabola is with a point and a line.
x = -4/3(y +5)² -1
Solve for x.
x = (4y² +40y +103)/(-3)
x = -4/3y² -40/3y -103/3 . . . . 'standard form' in the US
__
Taking our clues from the graph*, we can write the vertex form equation as ...
x = -4/3(y +5)² -1 . . . . . . 'standard form' in other places
____
* The vertex is (-1, -5), so for some leading coefficient, the equation will be ...
x = a(y -(-5))² +(-1) = a(y +5)² -1
The value of 'a' is the scale factor. Here, that is the difference between the parabola value (x = -2 1/3) and the vertex value (x = -1) one unit away from the vertex.
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Question 2
The average distance from Jupiter to the Sun is about 5 x 10^8 miles. The average
distance from Venus to the Sun is about 7 x 10^7 miles.
The average distance from Jupiter to the Sun is about how many times as great as
the average distance from Venus to the Sun?
1. 1.4 times
2.7.1 times
3. 10 times
4. 430,000,000 times
When the average distance from Jupiter to the Sun is about 5 x 10^8 miles and the average distance from Venus to the Sun is about 7 x 10^7 miles. The average distance from Jupiter to the Sun is about 7.1 as great as the average distance from Venus to the Sun.
How to compare the distancesThe distances is compare using the mathematical operation called division,
the procedure is done as follows
= (The average distance from Jupiter to the Sun) / (The average
distance from Venus to the Sun)
= 5 x 10^8 miles / 7 x 10^7 miles.
= 7.14285
= 7.1
the comparison showed that the distance from Jupiter to Sun is 7.1 times greater than the distance form Venus to Sun
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Janet made 7 1/3 pounds of trail mix. If she puts 1 5/6 pounds into each bag, how many
bags can Janet fill?
geomtrynnnnnnnnnnnnnnnnnn
Answer:
D
Step-by-step explanation:
[tex]10x+6y=0\\\-7x+2y=31[/tex]solve the system by using substitution or elimination
The value of x= 93/11 and y=-155/11 when the system of equation are 10x+ 6y=0 and 7x+ 2y=31.
Given that,
The system of equation are 10x+ 6y=0 and 7x+ 2y=31.
We must resolve the equation system.
We know that,
Take the system of equations.
10x+ 6y=0 ------>equation(1)
7x+ 2y=31 ------->equation(2)
Multiply 3 to the equation(2) and subtract with equation(1)
3×(7x+ 2y=31)
21x+ 6y=93
10x+ 6y=0
----------------- (subtract)
11x+0=93
11x=93 (divide)
x=93/11
Substitute x=93/11 in equation(1)
10(93/11)+6y=0
930/11+6y=0
6y=-930/11
y=-155/11
Therefore, The value of x= 93/11 and y=-155/11 when the system of equation are 10x+ 6y=0 and 7x+ 2y=31.
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0.27 times 35 = 9.45 because i just said so bye
Answer:
Yes, you're right.
Step-by-step explanation:
Just by doing the math, 0.27 times 35 is 9.45.
Plugging it in a calculator also says it's 9.45.
A food truck did a daily survey of customers to find their food preferences. The data is partially entered in the frequency table. Complete the table to analyze the data and answer the questions:
Likes hamburgers Does not like hamburgers Total
Likes burritos 39 77
Does not like burritos 95 33
Total 134 205
Part A: What percentage of the survey respondents liked hamburgers but do not like burritos? Show all work. (3 points)
Part B: What is the marginal relative frequency of all customers who like hamburgers? Show all work. (3 points)
Part C: Which category has the lowest joint relative frequency? Show all work. (4 points)
A: The percentage of respondents who like hamburgers but dislikes burritos is 46.34%
B: Marginal relative frequency of all who like hamburgers is 0.65.
C:Lowest joint frequency is of the respondents who like both.
What are relative frequencies?The word "relative" is used to describe how something is being viewed in connection to or in comparison to another event. How frequently an event occurs can be determined by looking at its frequency. On the other hand, relative frequency is a means to compare the frequency of a specific event to all other occurrences.
The ratio of the total number of events occurring in a scenario to the number of times an event occurs is known as relative frequency.
Two facts must be known in order to determine the relative frequency:
>>Number of total events/trials
>>Frequency count for a category/subgroup
Calculation:
Like Ham↓ Does Not Like Ham Total↓
Likes burritos → 39 38 77
Does not like burritos → 95 33 128
Total → 134 71 205
So, according to the above table, a total of 77 customers like burritos, out of which 38 do not like hamburgers, hence, the remaining 39 like Hamburgers.
A total of 128 customers do not like burritos, out of which 95 do like hamburgers, hence, the remaining 33 do not like Hamburgers.
A total of 134 customers like hamburgers, but 71 do not like it, hence, the total respondents are 205.
A:
Total people who liked hamburgers are 134 and those who doesnot like burritos and liked hamburgers are 95 and the total people participated in the survey are 205.
So the percentage of people is [tex]\frac{95}{205}*100[/tex] = 46.34%
B:
The marginal relative frequency is nothing but total people who like hamburgers out of the total respondents.. which is
[tex]\frac{134}{205}[/tex] = 0.65
C:
The category that has lowest joint relative frequency is
Case 1:
Likes both burritos and hamburgers:
[tex]\frac{39}{134}=0.29[/tex]
Likes burritos and dislikes hamburgers:
[tex]\frac{38}{71} = 0.53[/tex]
Likes hamburgers and dislikes burritos:
[tex]\frac{95}{134} = 0.71[/tex]
Who dislike both are:
[tex]\frac{33}{71}=0.47[/tex]
So the category which lowest joint frequency is Likes both burritos and Hamburgers.
A: The percentage of respondents who like hamburgers but dislikes burritos is 46.34%
B: Marginal relative frequency of all who like hamburgers is 0.65.
C:Lowest joint frequency is of the respondents who like both.
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Answer:
look at the link so you can get the straight up answers
Step-by-step explanation:
I did the same test got it all right
PLS give BRAINLIST mean the world
X is a normally distributed random variable with mean 26 and standard deviation 1.
What is the probability that X is between 24 and 28?
Use the 0.68-0.95-0.997 rule and write your answer as a decimal. Round to the nearest
thousandth if necessary.
Answer: give me brainliset
(
X
>
42
)
=
P
(
Z
>
−
1.1429
)
=
1
−
P
(
Z
<
1.1429
)
=
1
−
Φ
(
1.1429
)
=
1
−
0.8729
(from tables)
=
0.1271
Step-by-step explanation:
Order these numbers from least to greatest.
1.4 comma space 1.04 comma space 16 over 10 comma space 1 1 half
Answer:
1.04, 1.4, 1.5 (one and a half), 10, 16
Answer:
1.04, 1.4, 1.5, 1.6
Step-by-step explanation:
1 1 half = 1.5
16 over 10 = 1.6
hope this helps!
A recipe requires 1 1 cup of sugar for every 6 6 cups of flour. How many cups of sugar will be required for 18 18 cups of flour? enter the answer in the box.
Both 3 and 6 cups of sugar are used.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Tw dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.
According to our question-
2 cups of flour and 1 cup of sugar
Add the sugar and flour together for three cakes.
2 cups of wheat and 1 cup of sugar equals 3.
6 cups of flour and 3 cups of sugar
Hence, Both 3 and 6 cups of sugar are used.
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