The value of n is 1.6 if 4.8=3n by using simplest method.
What is meant by simplest equation?A mathematical equation links the two phrases on either side of the sign. It typically simply has an equal sign and one variable. similar to 2x - 4 = 2. Simple equations are used to demonstrate the relationship between two terms when they are positioned on each side of an equal sign. Simple equations are all used to follow the four mathematical operations of addition, subtraction, multiplication, and division.
By employing the shorthand symbol for "equal to" (=), it ensures that both expressions of the equation are equal. Equations utilize arithmetic operations like addition, subtraction, division, and multiplication to balance the expressions on both sides.
4.8=3n
Dividing on both sides with 3, we get
3n/3=4.8/3
n=1.6
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it takes a boat 3 hours to travel 48 miles downstream and 4 hours to travel 40 miles upstream. What is the speed of the boat in still water?
The speed of the boat in still water is 3 miles per hour
Given that,
A boat travels 40 miles upstream in 4 hours and 48 miles downstream in 3 hours.
To find : The speed of the boat in still water
We use the distance formula. D = r * t
48/3 = 16 mph | Trip 1 |
40/4= 10mph | Trip 2 |
16-10 = 6 mph difference traveling upstream or downstream. Thus the speed of the current is 3 miles per hour.
Therefore, The speed of the boat in still water is 3 miles per hour.
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The diagram shows two different buttons and their weights.
8 grams
A
12 grams
B
The buttons are sold in bags.
Each bag contains 144 grams of buttons.
a) How many of button A are needed to fill one bag?
b) How many of button B are needed to fill one bag?
A box of buttons contains the same number of each type of button.
It contains 220g of buttons.
c)
How many of each type of button are in the box?
The number of buttons A will be equal to 11. And the number of buttons B will be equal to 11.
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.
Given that container of buttons contains a similar number of each kind of button it contains 220g of buttons.
The weight of the button is given as follows;
Button A=8 grams
Button B = 12 Grams
Consider x be the number of each button. Then the equation is;
8x + 12x = 220
20x = 220
x = 11
The number of buttons A is 11. And the number of buttons B is 11.
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The accompanying data, or the length in centimeters and girths (in centimeters) of 12 harbor seals. Find the equation of the regression line. Then construct a scatterplot of the data and draw the regression line. Then use the regression equation to predict the value of Y for each of the given X values, if meaningful, if the X value is not meaningful to predict the value of y, explain why not.
The equation of the regression line is defined as follows:
y = 0.71x + 8.27.
The estimates are given as follows:
a) x = 140 cm: 107.67 cm.
b) x = 172 cm: 130.39 cm.
c) x = 164 cm: 124.71 cm.
d) x = 158 cm: 120.45 cm.
How to obtain the linear regression equation?The linear regression equation is obtained inserting the points of the data-set into a linear regression calculator.
From the table given in this problem, the points are given as follows:
(138, 106), (168, 130), (151, 116), (144, 105), (160, 124), (159, 119), (125, 103), (137, 103), (154, 120), (147, 110), (146, 108), (147, 110).
Inserting these points into a calculator, the equation is given as follows:
y = 0.71x + 8.27.
Then the estimates are obtained replacing x into the equation and obtaining the value of y, for example, for x = 140 cm:
y = 0.71(140) + 8.27 = 107.67 cm.
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The owner of a football team claims that the average attendance for games is 67,800, he therefore justified in moving the team to a city with a larger stadium.
express the null hypothesis in symbolic form- use the correct symbol for indicated parameter
The null hypothesis is H0: μ ≤ 68,800 for the given case of The owner of a football team claiming that the average attendance for games is 67,800.
Since we know that a null hypothesis (H0) shows that no significant variation exists between variables in other words it can be said that a single variable is much not different than its mean. since from the above case we were given the information that The owner of a football team claims that the average attendance for games is 67,800. So, the null hypothesis the that the average attendance at games is less than or equal to 68,800.
H0: μ ≤ 68,800
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A projectile is fired straight up from ground level. After t seconds, its height above the ground is s feet, where s= - 161? + 112t. For what time period is the projectile at least 160 feet above the ground?
The time period the projectile at least 160 feet above the ground is 2 sec to 5sec.
What is time period?
The duration of time that a behavior lasts or a condition persists. Depending on the type of activity or situation under consideration, it may be measured in seconds or in millions of years.
Given function that represents height of the projectile above the ground is s feet is s = - 16t² + 112t.
To find the time period is the projectile at least 160 feet above the ground, make an inequality:
- 16t² + 112t ≥ 160
Subtract 160 from both sides:
- 16t² + 112t - 160 ≥ 0
Divide both sides by 16:
- t² + 7t - 10 ≥ 0
- t² + 2t + 5t - 10 ≥ 0
-t(t -2) + 5(t - 2) ≥ 0
(t - 2)( -t+ 5) ≥ 0
Either, t - 2 ≥ 0 → t ≥ 2
or, -t + 5 ≥ 0 → t ≤ 5
2 ≤ t ≤ 5
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write the sum as the logarithm of a single expression. assume that variables represent positive numbers.
The sum can be written in logarithms as 6z log 6
What is logarithm ?
The word "logarithm" comes from the combination of the Greek words "logos," which means "principle or concept," and "arithmos," which means "number." A logarithm is the power that must be increased to obtain a given number. It is shown by a number's log.
Use of property
log (ab) = log a + log b
log a^b = b log a
Given that,
log 6^8 + log 6^z
=log 6^8 + log 6^z
=log (6^8*6^z)
=log (6^6z)
=6z log 6
Therefore, the sum can be written in logarithms as 6z log 6
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Given the linear equation y = -3x
Identify the:
1) Initial Value
2) Rate of Change
pls help
1) Initial value of the linear equation is 0. and 2) Rate of change is equal to -3.
What is the initial value of a linear equation?The initial value of a linear equation is the value of the y-intercept, which is the point where the equation intersects the y-axis. It is the constant term in the equation and is represented by the letter "b" in the form y=mx+b. Therefore, the initial value of a linear equation is the value of the constant "b".
The initial value of a linear equation is the y-intercept of the line.
The given linear equation is y=-3x
1) Initial value of the linear equation is the y-intercept.
the y-intercept of y=-3x is 0.
Therefore the initial value of the given equation is 0.
2) Rate of change of y=-3x is the derivative of y.
[tex]\frac{dy}{dx}=-3\frac{dx}{dx}[/tex]
⇒[tex]\frac{dy}{dx}=-3[/tex]
Therefore the rate of change is -3.
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Factor: 5x2 – 15x – 20.
Answer:
=5x2-(20-5)x-20
=5x2-20x+5x-20
=5x(x-4)+5(x-4)
=(x-4)(5x+5)
Answer:-5(2+3x)
Step-by-step explanation:
Many college graduates who are employed full-time have longer than 40-hour work weeks. Suppose that we wish to estimate the mean number of hours, H,
worked per week by college graduates employed full-time. We'll choose a random sample of college graduates employed full-time and use the mean of this
sample to estimate μ. Assuming that the standard deviation of the number of hours worked by college graduates is 6.30 hours per week, what is the minimum
sample size needed in order for us to be 90% confident that our estimate is within 1.4 hours per week of μ?
Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole
number that satisfies the requirements).
(If necessary, consult a list of formulas.)
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The minimum sample size needed in order for us to be 90% confident that our estimate is within 1.2 hours per week of is 55.
What is Statistics?Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.
Assuming that the standard deviation of the number of hours worked by college graduates is 6.30 hours per week
We need to find the minimum sample size needed in order for us to be 90% confident that our estimate is within 1.4 hours per week of.
The formula to determine sample size is n = [zs/E]²
z is standardization value indicating confidence level.
s is sample standard deviation.
E is acceptable acceptance error.
n = [invNorm(0.95)×6.3/1.4]²
n = [1.645×6.3/1.4]²
n=54.79=55
Hence, 55 is the minimum sample size needed in order for us to be 90% confident that our estimate is within 1.2 hours per week of.
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Rick is looking for an expression equal to 64 + 88. In that expression, the greatest common factor of the two numbers in the parentheses must be 1. Which expression should he choose?
The expression that Rick choose is 99 + 53.
What is parentheses?
The well-known () symbols, often known as "round brackets," are used in pairs to group things together or designate the order of operations in an equation. You will frequently need to employ brackets in math when forming or resolving equations. They support number grouping and operation definition.
Given expression is 64 + 88
The simplest form of the expression 64 + 88 is 152.
152 = 99 + 53.
152 = 151 + 1
152 = 149 + 3
152 = 139 + 13
152 = 137 + 15
152 = 131 + 21
152 = 127 + 25
152 = 113 + 39
152 = 109 + 43
152 = 107 + 45
152 = 103 + 49
152 = 101 + 51
etc.
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I need help with this please help me
Answer: 45
Step-by-step explanation:
Graph triangle ABC with vertices
A( − 4, − 3), B(0, – 2),
and C(2, 2) and and its
image after a 90° clockwise
rotation about point C.
Check the picture below.
Given the functions defined by f(x)=3x2−2 and g(x)=x2−2, calculate the following: (f∘g)(−2)
Answer:
10
Step-by-step explanation:
f(x) = 3x^2 - 2
g(x) = x^2 - 2
fog(x) = 3(x^2-2)^2 - 2 = 3x^4 + 12 - 12x^2 - 2 = 3x^4 - 12x^2 + 10
fog(-2) = 3(-2)^4 -12(-2)^2 + 10
fog(-2) = 48-48+10 = 10
Burton Bush wants to retire in Arizona when he is 80 years of age. Burton, who is now 55, believes he will need $400,000 to retire comfortably. To date, he has set aside no retirement money. If he gets an interest rate of 6% compounded annually, what will he have to invest today (to the nearest dollar) to reach his goal?
Multiple Choice
$160,000
$91,243
$96,500
$93,199
Burton Bush has to invest $93,199 to get $400,000 at the end. Hence, option D is correct.
What is compound interest?Interest that is added to a loan and deposit sum is known as compound interest. In our everyday lives, it is the notion that is employed the most frequently. Compound interest is calculated as a sum using the interest and principal accrued over time. Compound interest versus simple interest differ primarily in this way.
As per the given information in the question,
Rate, r = 6%
Number of years, n = 25
Present value, PV = ?
Final value, FV = $400,000
Use the equation of compound interest:
[tex]PV = FV (1 + r)^-^n[/tex]
Put values from above in the given equation,
PV = 400,000 (1 + 0.06)⁻²⁵
PV = 400,000 × 0.23
PV = $93,199.
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Solve the equation 2y+5=y-7
Answer: -12
Step-by-step explanation:
find the value of x,y,z. show your equations and then use the variables to label the angles with their measures between a triangle and two parallel lines
The formula for the slope of parallel lines is m1 = m2, and the slopes of parallel lines are equal. The slope of parallel lines is identical because all of the parallel lines are similarly inclined with regard to the positive x-axis.
What is Equation?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including linear, quadratic, cubic, etc.
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. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.
Hence, The formula for the slope of parallel lines is m1 = m2, and the slopes of parallel lines are equal. The slope of parallel lines is identical because all of the parallel lines are similarly inclined with regard to the positive x-axis.
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The function has a maximum point at (-pi/2, 5) and a minimum point at (pi/4, -4)
The sinusoidal function is y = -4.5cos(8(x + π/2)) + 1/2
How to determine the cosine function for the functionFrom the question, we have the following parameters that can be used in our computation:
Maximum = (-π/2, 5)
Minimum = (π/4, -4)
A cosine function is represented as
y = A cos(B(x+C)) + D
Where
A = amplitude, 2π/B = Period, C = phase shift leftD = vertical shift up.The cosine function has a max and min of 1 and -1.
So, we have
Difference = |-4 - 5|
Difference = 9
This means that
Amplitude, A = 9/2
A = 4.5
Also, we have
Vertically shift = (5 - 4)/2
Vertically shift = 1/2 up
So, the function becomes
y = 4.5cos(θ) + 1/2
Next, we calculate the value of θ
The period is calculated as
Period = π/4 + π/2
Period = -π/4
This means that
2π/B = -π/4
So, we have
B = -8
This gives
y = 4.5cos(-8(x + c)) + 1/2
cos(0) = 1,
So we want -8(-π/2) - 8C = 0
Solving for c, we have
8C = 8(π/2)
Divide
C = π/2
Substitute C = π/2 in y = 4.5cos(-8(x + c)) + 1/2
y = 4.5cos(-8(x + π/2)) + 1/2
y = -4.5cos(8(x + π/2)) + 1/2
Hence, the function is y = -4.5cos(8(x + π/2)) + 1/2
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Complete question
The function has a maximum point at (-pi/2, 5) and a minimum point at (pi/4, -4)
Determine a cosine equation for this function.
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)
an= 1-(0.6)^n lim n tends to infinite an=n^3/7n^3+1lim n tends to infinite an=an= 7+2n^2/n+7n^2 lim n tends to infinite an=n^3/5n+8 lim n tends to infinite an= an=e^6/n lim n tends to infinite an= Square root n+5/25n+5 lim n tends to infinite an=n^2 /square root n^3+9n lim n tends to infinite an=
The given series diverges.
Given:
aₙ = n²/√n³+7n
using series divergence test
If limₙ→∞ aₙ ≠0, then ∑ aₙ diverges .
limₙ→∞ (n²/√n³+7n) = limₙ→∞ (n²/√n³(1+7/n²)
= limₙ→∞ (n²/n³/²√1+7/n²)
= limₙ→∞ (√n/√1+7/n²)
= (∞/√1+0)
= ∞
Therefore the series diverges.
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when graphing x is greater than or equal to 1, where does the shading occur
Find the total income produced by a continuous income stream in the first 15 years if the rate of flow is given by the following function, where t is time in years.
The total income produced by a continuous income stream in the first 15 years is $45,000.
What is continuous income stream?
We can see the money flowing into the account continuously rather than in a lot of discrete payments if the deposits are made often enough and the intervals between deposits are short compared to the account's overall lifespan. This scenario will be referred to as a constant revenue stream.
Given function is
f(t) = 3000
Now integrate both side of the function and the lower limit is t = 0 and upper limit is t = 15.
[tex]= \int^{15}_{0}3000 dt[/tex]
[tex]=3000[t]_0^{15}[/tex]
= 3000 [ 15 - 0]
=45000
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PLEASE HELP I WILL DO ANYTHING
Find the constant of proportionality for the proportional relationship shown on the graph.
graph of a line going through 0 comma 0 and one half comma 8
p = 0.5
p = 0.625
p = 16
p = 8
The proportionality constant of the given graph is k = 16.
How to find the proportionality constant of a graph?The proportionality constant of a graph is the ratio of the y-coordinates to the x-coordinates.
Thus, it is written as k = y1/x1 = x2/y2 = ... = yn/xn
Calculation:The given graph has the coordinates as
x = 0; y = 0 i.e., (0, 0)
x = 0.5; y = 8 i.e., (0.5, 8)
x = 1; y = 16 i.e., (1, 16)
x = 1.5; y = 24 i.e., (1.5, 24)
and so on.
Then, the ratio of y - coordinate to the x - coordinate is
k = 8/0.5 = 16
or
k = 16/1 = 16
or
k = 24/1.5 = 16
and so on.
So, the proportionality constant for the given graph is k = 16.
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Find the exact value of sec 30^0 - sin 45^0 + sin 90^0
The exact value of sec 30°- sin 45° + sin 90° is 1.45.
What is the trigonometric ratio?
The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
Here, we have
sec 30°- sin 45° + sin 90°
we have to find the exact value of the given expression,
sec 30° = 2/√3
sin 45° = 1/√2
sin 90° = 1
Put all values in the given expression, and we get
sec 30°- sin 45° + sin 90° = 2/√3 - 1/√2 + 1
sec 30°- sin 45° + sin 90° = 1.15 - 0.70 + 1
sec 30°- sin 45° + sin 90° = 1.45
Hence, the exact value of sec 30°- sin 45° + sin 90° is 1.45.
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Vinnie's Mini-Golf hosts children's birthday parties. Parents can reserve the party room for kids to eat pizza and cake after playing golf. The total price for a party with c children is 8.5c + 35 dollars. Mrs. Kim scheduled her son's party for 8 children.
What price will Mrs. Kim pay for her son's party?
Mrs Kim will pay 103 dollars for her son's party.
What is a substitution method?
The algebraic approach to solving simultaneous linear equations is known as the substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.
Given, the total price for the party with c children = 8.5c + 35 dollars
For 8 children, c = 8 then,
Total price = 8.5*8 + 35 = 103 dollars
Hence, Mrs Kim will pay 103 dollars for her son's party.
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On the first day of vacation, you read one-quarter of a novel. On the second day, you read half of the remaining pages. On the third day, you read the last 126 pages of the novel.
(a) How many pages does the novel have?
(b) How many pages did you ready by the end of the second day?
Answer:
A. 336
B. 210
Step-by-step explanation:
To solve, we need to first multiply 126 by 2, which gives us 252. This is how many pages we had left after the first day. Then, since we read one-quarter on the first day, 252 is three-quarters, or 75% of the book. To find what number 252 is 75% of, we multiply both sides by 100 and divide by 75. This gives us 336, and the total amount. Next, we need to find how many pages we read on the first day. To do this, we find 25% of 336, which is 84. Then add 84 (how much we read on the first day) to 126 (how much we read on the second day), which gives us 210.
Answer:
(a) 336 pages
(b) 210 pages
=======================================================
Work Shown:
Part (a)
x = number of pages
x/4 = amount read on day 1
3x/4 = amount left to read after day 1 is over
(1/2)*(3x/4) = 3x/8 = amount read on day 2
(x/4) + (3x/8) = (2x/8)+(3x/8) = 5x/8 = amount read on days 1 and 2
x - (5x/8) = 8x/8 - (5x/8) = 3x/8 = amount left after day 2 is over
3x/8 = 126
3x = 8*126
3x = 1008
x = 1008/3
x = 336
There are 336 pages total
-------------------
Check:
336 pages total.
You read one-quarter of that on day one, so you read 336/4 = 84 pages on the first day.
There are 336-84 = 252 pages left (note that 3/4 * 336 = 252)
Then on day two, you read half of what's left, so you read 252/2 = 126 pages. The other half (126) is the last 126 pages mentioned for day 3, so the answer to part (a) is confirmed.
-------------------
There are at least three ways we can solve part (b)
Add up the number of pages read on days 1 and 2 to get 84+126 = 210 (refer to the "check" section above).In the first section we found that 5x/8 represents how many pages have been read by the end of day 2. Plug in x = 336 to find that 5*336/8 = 210Since we know there are 336 pages total, and 126 is what needs to be read on the third day to finish up the book, this must mean 336-126 = 210 pages have been read so far for days 1 and 2 combined.Either way, 210 pages have been read by the end of the 2nd day.
when you graduated from high school you had a choice between coming to jmu and working at walmart where you would earn $37,870 per year. suppose tuition at jmu is $20,000 per year, textbook expenses are $2,699 per year, and room and board expenses are $15,000 per year. assume that when you graduate you will get a job that pays you $75,000 per year.
Therefore , the best choice is you to join jmu and after that you will able to earn the same amount you spend on the graduation in 2 year.
What is equation ?Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.
Here,
Given:
You would earn $37,870 per year at walmart
Tuition at jmu is $20,000 per year, textbook expenses are $2,699 per year, and room and board expenses are $15,000 per year.
and you will get a $75,000 per year after graduation.
So the total expense is = 20,000 + 15000 + 2699 =37,699
Therefore , the total expense at jmu = $37,699
and total 4 year graduation course fees = 37,699 * 4=1,50,796
Thus, total fees you have to pay = $1,50,796
and after this you will get a job of $75,000 per year.
you will able to earn the same amount you spend on the graduation in 2 year.
Therefore , the best choice is you to join jmu and after that you will able to earn the same amount you spend on the graduation in 2 year.
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let g be a group and h be a subgroup such that the index is finite. aha-1 prove that is a finite set
The assertion that there exists a normal subgroup N of G such that N is of finite index in G and [N ⊂ H] is true and can be proved if "G" is a group and "H" is a subgroup of finite index.
Given,
The statement, "G" is a group and "H" is a subgroup of finite index.
We have to prove that there exists a normal subgroup N of G such that N is of finite index in G and [N ⊂ H].
Group: A group is a finite or infinite collection of elements and a binary operation (referred to as the group operation) in discrete mathematics that together meet the four essential qualities of closure, associativity, identity, and inverse.
Subgroup: If a subgroup "H" also satisfies the four essential criteria of closure, associativity, identity element, and inverse, it is a subset of a group, let's say "G" [denoted by (H ≤ G)].
Here,
By left multiplication, the group G affects the collection of left co-sets (G/H).
Hence it induces the permutation representation [ρ:G→Sₙ], where
[n = |G : H|].
(A permutation representation is a group homomorphism, it should be noted.)
Now, let (N = kerρ) be the kernel of the homomorphism (ρ). Then [N◃G].
The quotient group G/N is isomorphic to a subgroup of Sn according to the first isomorphism theorem.
In particular, G/N is a finite group, hence the index [G:N] is finite.
Finally, we show that [N ⊂ H].
For any (x ∈ N) = [ker (ρ)], we have [x(gH) = gH] for any [g ∈ G].
In particular we have (xH = H),
Hence (x ∈ H).
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A credit card account had a balance of $939 on May 5. A purchase of $216 was made on May 17, and a payment of $100 was made on May 20. The interest on the average daily balance is 1.4%
per month.
Find the average daily balance on the June 5 bill.
The average daily balance on the June 5 bill is $1,037.32, including the finance charge.
What is the average daily balance?The average daily balance is the total balance divided by the number of days in the billing cycle.
May has a 31-day billing cycle.
The average daily balance determines the finance charge, which is a product of the monthly interest rate (MPR) and the ending average daily balance.
Daily Balance
May 5 Credit card balance $939 $11,260 ($939 x 12)
May 17 Purchase 216 $4,620 ($1,155 x 4)
May 20 Payment -100 $15,825 ($1,055 x 15)
Total daily balances $31,705
Average daily balance $1,023 ($31,705 ÷ 31)
Interest rate per month = 1.4%
Finance charge for the month = $14.32 ($1,023 x 1.4%)
June 5 balance = $1,037.32 ($1,023 + $14.32)
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Which functions are increasing?; How to know if a function is increasing or decreasing?; Which section of the function is increasing?; Which type of increasing function eventually exceeds all other increasing functions?
Linear, polynomial, and quadratic functions can be both increasing or decreasing functions. Exponential function is monotonically increasing function. The derivative of a function may be used to determine whether the function is increasing or decreasing. Exponential functions eventually exceed all other increasing functions.
Function, in mathematics, refers to an expression or rule that describes a relationship between two or more variables. A function is said to be an increasing function when the y-value increases as the x-value increases and vice versa. In order to determine whether the function is increasing or decreasing, the derivative of a function may be used on any intervals in its domain. If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I. From the given function options, Exponential functions eventually exceed all other increasing functions as the one of variable is in the exponential leading an exponential increase and not a constant increase.
Note: The question is incomplete. The complete question probably is: From the following, Which functions are increasing? How to know if a function is increasing or decreasing?; Which section of the function is increasing?; Which type of increasing function eventually exceeds all other increasing functions? A) linear B) exponential C) polynomial D) quadratic.
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a rectangle has its base on x-axis and its upper two vertices on the parabola y= 12 - x2. What is the largest area of rectangle?
A rectangle's greatest area is 32 square units.
Given:
A parabola's equation is y = 12 - x2, which is an even function
As a result, its rectangular shape is also even at the origin.
We are aware that the area of a rectangle is equal to its length times its width.
Here,
width = y, length = 2x
A = 2x, where (12 - [tex]x^{2}[/tex])
⇒ A = 24x - 2[tex]x^{3}[/tex]
Consider the A derivative with regard to x.
⇒ A' = 24 - 6 [tex]x^{2}[/tex]
When A' = 0, the area is the largest.
⇒ 24 - 6x2 = 0
⇒ [tex]x^{2}[/tex] = 4
⇒ x = 2
Replace x with its value in y = 12 - [tex]x^{2}[/tex].
⇒ y = 12 - 4
⇒ y = 8
Area = 2(2)(8) = 32
Hence, a rectangle's greatest area is 32 square units.
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Samuel is buying a pair of boots with an original price of $80 ...
Based on the information , the store that gives the best deal is Store A .
Inn the question ,
it is given that ,
the original price for the shoes that Samuel is buying is = $80 .
the discount offered by Store A is = 25% ,
So , the effective price is = 80 - 0.25 of original price
Substituting the values ,
we get ,
= 80 - 20
= $60
the discount offered by Store B is = $10
So , the effective price is = 80 - 10 = $70 .
So , the price of shoe is less in store A in comparison to store B .
Therefore , the best deal is given by Store A .
The given question is incomplete , the complete question is
Samuel is buying a pair of boots with an original price of $80. Store A is offering a 25% discount off the original price of all boots. Store B is offering a $10 discount off the original price of all boots .
Based on this information, which store gave the best deal ?
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