The sum of even numbers between 105 and 351 is 28,044 .
What is arithmetic progression ?An additive or arithmetic sequence is a sequence of numbers such that the difference between consecutive terms is constant. For example, the sequence 5, 7, 9, 11, 13, 15 ... is an exponent plus the common difference of 2.
Calculationeven numbers between 105 and 351
the series will start like
106 , 108 , 110 , .................................. , 346 , 348 , 350
this is a arithmetic progression
a = 106 d = 2 l = 350
we need to find n
350 = 106 + ( n - 1 ) 2
350 - 106 = (n -1 ) 2
244/2 = n -1
n = 123
now sum = 123/2 ( 106 + 350)
= 28,044
so the sum of even numbers between 105 and 351 is 28,044 .
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write equations for each line given the following points. Remember you must first find the slope and then determine the Y intercept, then write out the equation in slope intercept form. Remember if the Y intercept b is zero, then, there is no need to put it there, and if the slope is one, then you only need to write x, not 1 X
(-3,2) and (5,7)
The slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is: [tex]y = \frac{5}{8} x + \frac{1}{8}[/tex]
What is the slope-intercept form?One of the most popular ways to represent a line's equation is in the slope-intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope-intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfills. There are several ways to solve the straight line equation given as,Slope-intercept formPoint slope formTwo-point formIntercept formCalculation
from ( - 3, 2) and (5, 7)
slope(m) = [tex]\frac{y_{2}- y_{1} }{x_{2}- x_{1} }[/tex]
[tex]=\frac{7 - 2}{5 - (-3)}[/tex]
[tex]= \frac{5}{8}[/tex]
from slope-intercept equation
⇒y = mx+ c
⇒( - 3, 2) , [tex]2 = \frac{5}{8} * (-3) + b[/tex]
⇒[tex]2 = \frac{15}{8} + b[/tex]
⇒[tex]2 - \frac{15}{8} = b[/tex]
⇒[tex]\frac{16+15}{8} = b[/tex]
⇒[tex]\frac{31}{8} = b[/tex]
Therefore, the slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is :
⇒[tex]y = \frac{5}{8} x +\frac{31}{8}[/tex]
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The slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is:
What is the slope-intercept form?One of the most popular ways to represent a line's equation is in the slope-intercept form of a straight line.
When the slope of the straight line and the y-intercept are known, the slope-intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis).
The equation of a line is the equation that each point on the line fulfills. There are several ways to solve the straight line equation given as,
Slope-intercept form
Point slope form
Two-point form
Intercept form
from ( - 3, 2) and (5, 7)
slope(m) = y²-[tex]y^{1}[/tex]/x²-[tex]x^{1}[/tex]
=7-(-2)/5-(-3)
=5/8
from slope-intercept equation
⇒y = mx+ c
⇒( - 3, 2) , 2=5/8*(-3)+b
⇒2=15/8+b
⇒2-15/8=b
⇒16+15/8
31/8=b
Therefore, the slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is :
⇒y=5/8x +31/8
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An animal shelter has 2 cats for every 3 dogs. If there are 45 animals in the shelter, how many dogs are there?
Answer: 27 dogs
Step-by-step explanation: 2 cats + 3 dogs= 5 in total for animals. 2/5x45=18 cats
3/5x45= 27 dogs
27+18=45 animals
There is 27 dogs in the shelter
A small publishing company is releasing a new book. The production costs will include a one-time fixed cost for editing an additional cost for each book printed. The total production cost C (in dollars) is given by the function C=650+17.95N, where N is the number of books.
The total revenue earned (in dollars) from selling the books is given by the function R=31.90N.
Let P be the profit made (in dollars). Write an equation relating P to N. Simplify your answer as much as possible.
P = ?
Homework help lolol
Answer: 67
Step-by-step explanation:
do the math
This shows a figure.
What is the value of x?
57
63
86
95
Answer:
57
Step-by-step explanation:
Straight line is 180 degrees
x+2x+9=180
3x=171
x=171/3
x=57
pls mark as brainliest
Please help me (see attachment)
A graph of the given equation (x - y = 6) is shown in the image attached below.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.
Next, we would rewrite the given equation in standard form as follows:
x - y = 6
Adding y to both sides of the equation, we have the following:
x - y + y = 6 + y
x = 6 + y
Rearranging the equation, we have the following:
y = x - 6
By critically observing the graph (see attachment), the y-intercept is equal to -6 and the x-intercept is equal to 6.
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Write 0.0000509 in standard form.
Answer:
5.090 x 10^-5
Step-by-step explanation:
Please show all work
The volume of the composite solid is 340.4 cubic inches
How to calculate the volume of the composite solidThe composite solid is made up of two parts one has
uniform height varying heightThe volume for the uniform height
= base area * height
base area = 0.5 base * height = 0.5 * 8 * 6.9 = 27.6
= 27.6 * 10
= 276 cubic inches
The volume for the varying height
= 1/3 base area * height
base area = 27.6 (both share same base)
= 1/3 * 27.6 * 7
= 64.4 cubic inches
The total volume
= 276 + 64.4
= 340.4 cubic inches
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are these expressions equivalent
4(2a+7) and 8a +7
7y + 2y+y and 10y
8m-4m+4m and 8m
9e+2(e+5 and 11 +5
The equivalent expressions are 7y + 2y+y and 10y & 8m-4m+4m and 8m.
Other expressions are not equivalent
How to determine the equivalent expressions?Expressions 1
The expressions are given as
4(2a+7) and 8a +7
Open the brackets
8a+28 and 8a +7
The above expressions are not equal
Expressions 2
Here, we have
7y + 2y+y and 10y
Evaluate the like terms
10y and 10y
The above expressions are equal
Expressions 3
Here, we have
8m-4m+4m and 8m
Evaluate the like terms
8m and 8m
The above expressions are equal
Expressions 4
Here, we have
9e+2(e+5) and 11 +5
Open the brackets
9e+2e+10 and 11 +5
Evaluate the like terms
11e + 10 and 11 + 5
The above expressions are not equal
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Trevor is a high school quarterback. On
average, out of each 16 attempts, he
completes 5 out of 8 passes and throws 1
pass that is intercepted. If Trevor passes
40 times, how many completions would
he be expected to make? (setting up proportions )
The total number of completions Trevor be expected to make is 25.
Define the term proportions?Proportion is mostly discussed using ratios and fractions. A fraction is written as a/b, while a ratio is represented as a:b, and a proportion implies that two ratios remain equal. In this case, a and b can be any two integers. According to the notion of proportion, two ratios are in proportion when they are equivalent. It is a formula or statement that shows that two ratios and fractions are equivalent.For the given question.
Let the number of completion by Trevor be 'x'.
Trevor completes 5 out of 8 passes.
Total passes are 40
Then, proportions set up is-
5/8 = x/40
x = 25
Thus, the total number of completions Trevor be expected to make is 25.
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Please help me
Slope=
Y- intercept=
Equation=
Slope:
The slope is found with m = (y2 - y1) / (x2 - x1).
You can use any two points, so I'd pick ones with positive x and y values.
Using (1,5) and (3,3):
m = (3 - 5) / (3 - 1) = (-2)/(2) = -1
The slope is -1.
To find the y-intercept, we can go to the point (-1,7) and use the slope of -1. A slope of -1 means that if x goes up by 1, then then y goes down by 1. So if we go from x=-1 to x=0, then the y-value of 7 will go down by 1.
y-intercept (0,6)
The equation in slope-intercept form is y = -x + 6, since we already found the slope and y-intercept.
you are taking out candies one by one from a jar that has 10 red candies, 20 blue candies, and 30 green candies in it. what is the probability that there are at least 1 blue candy and 1 green candy left in the jar when you have taken out all the red candies?
The required probability that there are at least 1 blue candy and 1 green candy left in the jar when you have taken out all the red candies is 7/12 .
Probability is defined as the ratio of total numbers of outcomes of an event to the favouable outcomes of an event.
We have , Red candies in the jar = 10
green canides in the jar = 30
blue candies in the jar = 20
total number of candies in jar = 60 i.e total number of outcomes = 60
The Probability that the last of sixty candies drawn is one of thirty green candies = 30/60 = 1/2
Ignoring green canides, probability that the last of the thirty other candies drawn is one of twenty blue = 20/30 = 2/3
The Probability that the last of sixty candies drawn is one of twenty blue candies = 20/60 = 1/3
The Probability that the last of sixty candies drawn is not one of twenty blue candies = 1 - 1/3
= 2/3
Probability that last draw would be blue and the last not blue would be green = 20/60 × 30/40
= 1/4 ----(1)
Probability that last draw would be green and the last not green would be blue = 30/60× 20/30
= 1/3 ------(2)
Now , Required probability that last draw would be either blue or green canidy = sum of above probabilty from equation (1)and (2)
= 1/4 + 1/3 = 7/12
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Determine the equation of the line.
(Write the answer in slope-intercept form.)
Answer:
y = 1x + -2
Step-by-step explanation:
Step 1: Calculating Slope (m).
m = y2 - y1 / x2 - x1
m = -4 - 0 / -2 - 2
m = -4 / -4
m = 1
Now put value of m in equation...
y = 1x + b
Step 2: Calculating Y-intercept (b).
Lets choose the first point, ( 2, 0) for calculating y-intercept:
y = m ( x ) + b
0 = 1 ( 2 ) + b
0 = 2 + b
-2 = b
b = -2
Now put value of b in equation for your final answer...
y = 1x + -2
Hope this helps!
30°
(5y-8)°
(6x-2)°
(11x-9)
72⁰
Answer:
x = 7°y = 18°Step-by-step explanation:
Find x:-
[tex]\sf 11x-9+72+6x-2=180[/tex]
[tex]\sf 17x+61=180[/tex]
[tex]\sf 17x=119[/tex]
[tex]\sf x=7[/tex]
Find y:-
[tex]\sf 30+11(7)-9+5y-8=180[/tex]
[tex]\sf 5y+90=180[/tex]
[tex]\sf 5y=90[/tex]
[tex]\sf y=18[/tex]
So, therefore, x = 7° & y = 18°!!
____________________
Hope this helps!
Have a great day! :)
5 oranges and 14 bananas cost me $1.30 and 8 oranges and 9 bananas
cost me $1.41.
a) Represent this information as a matrix equation.
b) Find the cost of a banana and an orange.
A) The matrix equation that represents the given information is;
[tex]\left[\begin{array}{ccc}5&14\\8&9\\\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right] = \left[\begin{array}{ccc}1.30&\\1.41\\\end{array}\right][/tex]
B) The cost of a banana is; $0.05
The cost of an orange is; $0.12
How to create and solve a matrix equation?A matrix equation is defined as an equation where a variable stands for a matrix .
Let x represent cost of oranges
Let y represent cost of bananas
5 oranges and 14 bananas cost me $1.30 and 8 oranges and 9 bananas
cost me $1.41. Thus, the equations are;
5x + 14y = 1.30 ----(1)
8x + 9y = 1.41 -----(2)
A) Now, the matrix form of the simultaneous equation above will be;
[tex]\left[\begin{array}{ccc}5&14\\8&9\\\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right] = \left[\begin{array}{ccc}1.30&\\1.41\\\end{array}\right][/tex]
B) Multiply the first equation by 8 and the second one by 5 to get;
40x + 112y = 10.4
40x + 45y = 7.05 Subtract to get;
67y = 3.35
Divide both sides by 67 to get;
y = $0.05 per banana
Plug in 0.05 for y into eq 1 to get;
5x + 14(0.05) = 1.30
5x + 0.7 = 1.3
5x = 1.3 - 0.7
5x = 0.6
x = 0.6/5
x = $0.12
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Write a polynomial function with rational coefficients so that P(x) has given roots: -4 and 2i.
P(x) is a polynomial function having rational coefficients that has given roots is: P(x) = x³ + 2x² + 4x + 8.
Define the term roots of polynomial?The values of a variables for which the provided polynomial equals zero are referred to as the roots of a polynomial. If an is the polynomial p(x) root, then p(a) = 0.P(x) has given roots: -4 and 2i.
A radical is always preceded by a pair of plus & minus signs.
As a result, there would be another root -2i.
All of the roots are -4, -2i, + 2i.
As, the number of roots given are 3, thus the polynomial formed ill be cubic.
The roots in terms of the polynomial can be written as-
P(x) = (x - (-2))(x - 2i)(x + 2i)
P(x) = (x + 2)(x - 2i)(x + 2i)
Simplifying,
P(x) = x³ + 2x² + 4x + 8
Thus, P(x) is a polynomial function having rational coefficients that has given roots is P(x) = x³ + 2x² + 4x + 8.
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2. Maria earns a $50,000 salary plus a 10% commission on any sales over $20,000. Last year
Maria made $40,000 in sales. How much did Maria earn in salary plus commission?
Last year, Maria earned $54,000
In this question, we have been given Maria earns a $50,000 salary plus a 10% commission on any sales over $20,000.
Last year Maria made $40,000 in sales.
This means, she got 10% commission
We find the 10 percent of 40000.
40000 * (10/100) = 4000
Her total earning would be,
$50,000 + $4000(commission) = $54,000
Therefore, Maria earned $54,000
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Solve for n.
5(n+4)
3
O-24
24
22
O-22
=n-8
The value of n is -22.
What is a variable?
Any traits, figures, or amounts that may be gauged or counted are considered variables.
Given:
5(n+4)/3=n-8
Move 3 to the right
5(n+4)=3(n-8)
5n+20=3n-24
5n-3n= -24-20
2n=-44
n=- 44/2=-22
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at a certain university, the average attendance at basketball games in the previous year was 3000 spectators per game. the athletic director claims that the attendance this season is up from last year. for the first 14 games of the current year, there has been an average of 3200 spectators per game with a standard deviation of 450. using a significance level of .05, does this sample data provide evidence to support the athletic director's claim?
The p-value is higher than 0.05, so we are unable to rule out the null hypothesis. There is little proof to back up the director's claim.
Hypothesis:
H₀ : μ = 3000
H₁ : μ > 3000
The t-test should be employed when the population mean and standard deviation are unknown. Since the sample size is high, we can infer that the sample mean's sampling distribution is normal.
The following information is provided:
s = 450
x = 3200
n = 14
Therefore, test statistics will be:
t = (x - μ) / (s / √n) = (3200 - 3000) / (250 / √14) = 1.66
The test in this instance is right-tailed, and its degree of freedom is df=n-1=14-1=13.
0.0601 is the p-value.
We are unable to reject the null hypothesis since the p-value is higher than 0.05. The director's allegation is not supported by a lot of evidence.
Since p =.0601, the director's assertion cannot be supported by the available data.
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Which answer is correct?
(A) y = 3x − 2
y = 2x + 5
(B) y = −3x + 2
y = 2x − 5
(C) y = −3x − 2
y = −2x − 5
(D)y = 3x + 2
y = −2x + 5
Step-by-step explanation:
the slow of a line is the factor of x in a "y = ..." firm of equation.
the line going through (1, 5) has a slope of 3 (when x increases by +1, then y increases by +3, so the slope y/x = 3).
(B) and (C) are out, because there is no line with slope 3 (only -3).
the line going through (-2, 9) has a slope of -2 (when x increases by 1, y decreases by 2, so the slope y/x = -2/1 = -2).
(A) is out, as there is no line with the slope -2 (only +2).
so, (D) is the correct answer.
I need help with this question ASAP
Answer:
X = 14
Hope this helps!
Step-by-step explanation:
The small red square means the angle is 90°.
( 2x + 22 ) + ( 3x - 2 ) = 90°
2x + 22 + 3x - 2 = 90
( 2x + 3x ) + ( 22 - 2 ) = 90
5x + 20 = 90
5x + 20 - 20 = 90 - 20
5x = 70
x = 14
Answer: x = 14
Step-by-step explanation:
When you have a right angle, they add up to 90 degrees
So you add up the two angles that you have that equal a total of 90 degrees
2x+22 + 3x-2 = 90
5x+20 = 90
5x = 70
x = 14
I hope this helps :D
i need help please!!! i dont know
The locations of the destinations given by the angles formed between parallel lines and their common transversal in the question are;
1) US Capitol
2) CIA Building
3) US Capitol
4) US Treasury
5) Walmart
What are the relationships between the angles formed by parallel lines that have a common transversal?The relationship between the angles formed are;
Corresponding angles are congruentSame side interior angles are supplementaryAlternate interior angles are congruentAlternate exterior angles are congruentVertical angles are congruent1) The location that is at a corresponding angle to the White House is the Supreme Court
The location at the vertical angle to the Supreme Court is the Smithsonian Institute
The location that is at the angle right adjacent to the Smithsonian Institute is the US Capitol
The destination location is the US Capitol2) The location that is vertical angles to the FBI Building is the National Zoo
The same side interior angle to the National Zoo is the National Coffee shop
The location at the alternate interior angle to the National Coffee Shop is the CIA Building
The location is the CIA Building3) The location at the alternate exterior angles to Lincoln Memorial is Walmart
The adjacent location that is a right angle to Walmart is the White House Gardens
The location that is at the corresponding angle to the White House Gardens is the US Capitol
The location is the US Capitol4) The location that is at the corresponding angle location to the Smithsonian Institute is the National Zoo Gift Shop
The location that is at the same side interior angle to the national gift shop is the US Capitol
The location that is at the vertical angle location to the US Capitol is the US Treasury
The current location is the US Treasury5) The location that is at alternate interior angle location to the Ford's theater is the US Capitol.
The location that is supplementary with the Vietnam War Memorial and the National Zoo is the National Coffee Shop
The location at the angle that is vertical from the National Coffee Shop is the Lincoln Memorial
The location that is at alternate exterior angle with the Lincoln Memorial is Walmart
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Amir want to proportionally increae the ize of a photo to create a poter for hi room. The ize of the original photo i hown. Complete the tatement and then anwer the quetion to repreent way that Amir can increae the ize of hi photo
The height of the poster is 20 inches.
The original width of the poster was 6 inches. The original height of the poster was 4 inches. The size of the poster is scaled up. This is a transformation of the size of the poster. The width of the scaled-up poster is 30 inches. We need to find out the height of the scaled-up poster.
The scaling transformation preserves the shape of the object. This means the sides must still be in the same proportion. Let the constant of proportionality be represented by the variable "k".
30 = k*6
k = 30/6
k = 5
Hence, the poster is scaled up by a factor of five.
H = k*4
H = 5*4
H = 20
Hence, the height of the scaled-up poster is 20 inches.
The complete question is given below.
Amir wants to scale up a photo to create a poster for his room. The original picture is 6 inches in width and 4 inches in height. What will be the height of the poster if its width is 30 inches?
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g with normalcdf if 15% of adults in a certain country work from home, what is the probability that fewer than 60 out of a random sample of 500 adults will work from home?
The probability that fewer than 60 out of a random sample of 500 adults will work from home is 0.03
In the given probability case we have;
What is the likelihood that, out of a random sample of 500 persons, fewer than 60 will work from home if 15% of adults in a particular country do so?
Let,
P = 15% = 0.15
n = 500
By considering the binomial distribution case the formula is given by
P( X = x ) = ⁿCₓ * Pˣ * (1 - P)ⁿ⁻ˣ
P( X ≤ 60 ) = ⁿCₓ * Pˣ * (1 - P)ⁿ⁻ˣ
= ⁶⁰∑ₓ=₀ (⁵⁰⁰Cₓ) (0.15)ˣ (1 - 0.15)⁵⁰⁰⁻ˣ
= 0.031
≅ 0.03
Hence, the probability that fewer than 60 out of a random sample of 500 adults will work from home is 0.03
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18) 7-(-1)²-(-9)
Whoever explains the best I will give Brainlyist or whatever it’s called
ANSWER: 137
Step-by-step explanation:
This can be rewritten as:
18 × 7 - (-1)² -(-9)
Using BODMAS
firstly open the brackets using the negative sign, we have;
18 × 7 +1² + 9
Now you can apply your BODMAS.
126 + 1 + 9
ANS = 137
a person can play 1/6 of a song in 1/3 of a minute.
how many minutes does it take the person to play the whole song at once at this rate?
Answer:
2 minutes for a whole song.
Step-by-step explanation:
Given that,
→ (1/6) song = (1/3) minutes
Parts of whole song is,
→ (1/6) × 6 = 1
Then the required minutes taken to play whole song will be,
→ x/6 = 1/3
→ x = (1/3) × 6
→ x = 6/3
→ [ x = 2 min ]
Hence, 2 minutes for a whole song.
W/4+12.5-7z
What which term has a coefficient?
Answer:
The coefficient is 7 and the term that has it.
3x - 7 = 11 what does x equal
Answer:
6
Step-by-step explanation:
3x-7=11
3x-7=113x=11+7
3x-7=113x=11+73x=18
3x-7=113x=11+73x=183x/3=18/3
3x-7=113x=11+73x=183x/3=18/3 X=6
Factor the expression
27 + 33 how do work it out
The factor of the expression 27 + 33 is 3.
What is meaning of factor?
A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.
Factors can be found using either division or multiplication. Rules of divisibility can also be applied.
What meaning of expression?
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.
Given expression is 27 + 33
The factors of 27 are 1, 3, 9, 27.
The factors of 33 are 1, 3, 11, 33.
The common factor of 27 and 33 is 3.
Taking common 3 from the given expression:
27 + 33 = 3 (9 + 11)
The factor of the given expression is 3.
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Halp for a cookie :) ♥ ♥❣ ❣
*Piece-Wise Defined Functions*
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The function shown in the graph above is a discontinuous function, at x = -2
For values of x less than -2, the left side of the graph is applicable. whose equation is :
[tex]\qquad \sf \dashrightarrow \: y - 0 = \cfrac{1 - 0}{ - 3 - ( - 2)} (x - ( - 2))[/tex]
[tex]\qquad \sf \dashrightarrow \: y = \cfrac{1}{ - 3 + 2} (x + 2)[/tex]
[tex]\qquad \sf \dashrightarrow \: y = - 1(x + 2)[/tex]
[tex]\qquad \sf \dashrightarrow \: y = - x - 2 \:\: ; \:\:x<-2[/tex]
For values of x greater than -2, the right side of the graph is applicable. whose equation is :
[tex]\qquad \sf \dashrightarrow \: y - 4= \cfrac{4 - 2 }{0 - (-2)} (x -0)[/tex]
[tex]\qquad \sf \dashrightarrow \: y - 4 = \cfrac{2}{2} (x)[/tex]
[tex]\qquad \sf \dashrightarrow \: y - 4 = x[/tex]
[tex]\qquad \sf \dashrightarrow \: y = x + 4 \: \: ;\: \: x > - 2[/tex]
So, the correct choice will be Option " A "
Answer:
[tex]\textsf{A.} \quad \begin{cases}-x -2 \quad \text{if}\;x < -2\\x + 4 \quad \;\;\;\text{if}\;x \geq -2\end{cases}[/tex]
Step-by-step explanation:
When graphing piece-wise functions:
An open circle indicates the value is not included in the interval.A closed circle indicates the value is included in the interval.An arrow show that the function continues indefinitely in that direction.From inspection of the given graph:
The equation for the line on the left side of the function has a negative slope and an x-intercept at x = -2.There is an open circle at x = -2 and the line continues to the left.Therefore, the definition of the function is:
[tex]\begin{cases}-x + a \quad \text{if}\;x < -2\\x + 4 \quad \;\;\;\text{if}\;x \geq -2\end{cases}[/tex]
where a is some constant.
The only answer option that matches the given parameters is option A.
a square tile is expanding as it is heated. right now, the 29 cm tile is growing by 1.625 cm per hour. at what rate is the area of the tile changing?
Using the concept of application of derivative it is concluded that the rate of change in the area of square tile is 94.25 cm²/hour.
What is the area of a square?The area of the square is defined as the square of its sides.
Let the side of the square is a then its area will be a².
Area of square figure = Side².
Let the side of the square is x= 29cm.
It is given that the side 29 cm tile is growing by 1.625 cm per hour on heating.
And the rate of change in side of square dx/dt = 1.625 cm/hour
We have to calculate the rate of change in an area of the square (A).
hen, area A = x²
On differentiating A with respect to time(t) we get a rate of change in area
dA/dt = d(x²)/dt
= 2x dx/dt
= 2×29×1.625
= 94.25 cm²/hour
Hence, the rate of change in the area of the square tile is 94.25 cm²/hour.
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