If JK has endpoints (-10, 1) and K(2, -2). Point L divides JK into two parts with lengths in a ratio of 2:1 then the possible locations of L is at (-7, 0.25)
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0
L divides JK into two parts with lengths in a ratio of 2:1
so JL:LK is either 2:1 or 1:2
Let us solve the midpoint of JK
Midpoint=(-10+2/2, 1-2/2)
M=(-4,-1/2)
Midpoint of JM is (-10-4/2, 1-1/2/2)
L: (-7, 1/4)
Hence, the possible locations of L is at (-7, 0.25)
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A person invests 4000 dollars in a bank. The bank pays 5.25% interest compounded monthly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 5100 dollars?
The person must leave the money for 4 years and 8 months in the bank until it reaches 5100 dollars.
What is compound interest rate?Compound interest is computed as interest on the principle of an account plus any accrued interest.
Compound interest can be calculated using the following formula:
x = P (1+r/n[tex])^{nt}[/tex]
,where x = compound interest
P = principal (the initial deposit or loan amount)
r = annual interest rate
n = the number of compounding periods per unit of time
t = the number of time units the money is invested or borrowed for
Given:
A person invests 4000 dollars in a bank.
The bank pays 5.25% interest compounded monthly.
First, convert R as a percent to r as a decimal
r = R/100
r = 5.25/100
r = 0.0525 per year,
Then, solve the equation for t,
t = ln(A/P) / n[ln(1 + r/n)]
t = ln(5,100.00/4,000.00) / (12 × [ln(1 + 0.0525/12)])
t = ln(5,100.00/4,000.00) / (12 × [ln(1 + 0.004375)])
t = 4.638 years
t = 4 years and 8 months.
Therefore, the time is 4 years and 8 months.
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In a Biology Laboratory at the beginning of an experiment there are 100 bacteria. During the experiment it is expected that the number of bacteria will double itself every 2 hours. Under this condition how long will it take the number of bacteria to reach 3200?
The amount of time that it will take for the bacteria to reach 3,200 is given as follows:
5 hours.
How to define an exponential function?An exponential function is defined as follows:
y = ab^x.
For which the parameters are given as follows:
a is the initial value.b is the rate of change.For this problem, there are initially 100 bacteria, doubling each hour, hence the parameter values are given as follows:
a = 100, b = 2.
Hence the function is defined as follows:
y = 100(2)^x.
The amount will reach 3200 for x when y = 3200, hence:
3200 = 100(2)^x.
2^x = 3200/100
2^x = 32
2^x = 2^5
x = 5.
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______ units of measure.
Meter, kilogram and time units of measure.
What is Metric System?Everything around us has a measurement value, from the amount of sugar you put in a cake to the size of a football field. Each thing is measured differently based on its length, weight, volume, or duration. With these measurements, the idea of "Metric System" is introduced.
The Metric system has 3 main units namely, meter to measure the length, kilogram to measure the mass, and seconds to measure time.
Therefore, meter, kilogram and time units of measure.
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The population of a large city can be calculated using the function P = 227,000(.98)^t . What can you say about the rate of change from year 1 to year 2 compared to the rate of change from year 9 to year 10?
The rate of change will be greater from year 1 to year 2.
The rate of change will be the same for all years.
The rate of change will be greater from year 9 to year 10.
There is not enough information given.
Answer:
The rate of change from year 1 to year 2 is - 2%.
The rate of change from year 9 to year 10 is -0.02%
The rate of change will be the same for all years.
Step-by-step explanation:
While this seems an unlikely answer (why would the rate reamin the same every year?), it is the correct answer since we are told that one equation is valid for t years. With no other information, we must conclude the rate of change remains the same every year. The actual number by which the population shrinks is changing, but the rate remains the same.
The function P(t) = 227,000(.98)^t says that the initial population in year 0 is 227,000 [227,000(0.98)^0 = 227,000]. The factor (0.98) is the result of the expression (1-(0.02)^t). The 1 is the factor for the initial population and the -0.02 is the fraction of 1 by which the population declines each year (2%).
Initial population = 227,000 [227,000(0.98)^0 = 227,000
Year 1 population would be (227,000)*(1-0.02)^1 or (227,000)*(0.98)
Year 2 population would be (227,000)*(1-0.02)^2 or (227,000)*(0.98)^2
Year 9 population would be (227,000)*(1-0.02)^9 or (227,000)*(0.98)^9
Year 10 population would be (227,000)*(1-0.02)^10 or (227,000)*(0.98)^10
The change is the same every year (0.98).
Find the first three terms of the sequence below. T n = n 2 − 2 n − 4
The first three terms of the sequence is -5,-4,-1.
What is sequence of the number?
The fundamental concepts in mathematics are series and sequence. A series is the total of all elements, but a sequence is an ordered group of elements in which repetitions of any kind are permitted. One of the typical examples of a series or a sequence is a mathematical progression.
Here the given sequence nth term formula is,
=> [tex]T_n=n^2-2n-4[/tex]
Now put n=1 into given formula then
=>[tex]T_1=1^2-2*1-4=1-2-4 =-5[/tex]
Now put n=2 into given formula then
=> [tex]T_2=2^2-2*2-4=4-4-4=-4[/tex]
Now put n=3 into given formula then
=> [tex]T_3=3^2-2*3-4=9-6-4=-1[/tex]
Hence the first three term of the sequence i -5,-4,-1.
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Sydney invests $100 every month into an account that pays 0.8% annual interest, compounded monthly. Benny invests $80 every month into an account that pays 2.2%
annual interest rate, compounded monthly.
a. Determine the amount in Sydney's account after 10 years.
b. Determine the amount in Benny's account after 10 years.
c. Who had more money in the account after 10 years? Sydney
d. Determine the amount in Sydney's account after 30 years. $40,672.12
e. Determine the amount in Benny's account after 30 years.
f. Who had more money in the account after 30 years? Benny
Answer:
a. $20,442.09
b. $47,981.82
c. Benny
d. $211,063.58
e. $9,583,450.63
f. Benny
In a triangle, the measure of the first angle is six times a number. The measure of the second angle is nine less than the first angle. The measure of the third angle is three times the number more than the measure of the first angle. Which equation best represents this description of the triangle
The equation 10x + 9 = 180 can be used to represent the description of the triangle, and solving for x gives x = 17.1.
x + 6x + 3x + 9 = 180
10x + 9 = 180
10x = 171
x = 17.1
The measure of the first angle is represented by x, and the measure of the second angle is represented by 6x - 9. The measure of the third angle is represented by 3x + 9. We can add these three equations together to get the equation 10x + 9 = 180. We can then solve for x by subtracting 9 from both sides of the equation to get 10x = 171. Finally, we can divide both sides of the equation by 10 to get x = 17.1.
The equation 10x + 9 = 180 can be used to represent the description of the triangle, and solving for x gives x = 17.1.
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The volume of a cylinder is 90 cm3. If the radius is 3 cm, what is the height of the cylinder?
(A) 15 cm
(B) 5cm
(C) 30 cm
(D) 10 cm
Answer:
10 cm
Step-by-step explanation:
Data :
Volume = V = 90π cm³
Radius = r = 3cm
Area = A = π(3)²
Formula for volume is
V = πr² h
Solve for height h
h = V/(πr²)
h = 90π / π3² = 90π /9π
h = 10 cmData :
Volume = V = 90π cm³
Radius = r = 3cm
Area = A = π(3)²
Formula for volume is
V = πr² h
Solve for height h
h = V/(πr²)
h = 90π / π3² = 90π /9π
h = 10 cmData :
Volume = V = 90π cm³
Radius = r = 3cm
Area = A = π(3)²
Formula for volume is
V = πr² h
Solve for height h
h = V/(πr²)
h = 90π / π3² = 90π /9π
h = 10 cmv
evaluate the double integral. 7xy2 da, d is enclosed by x = 0 and x = 4 − y2 d
The value of the double integral of the expression is 2/15.
The term integral in math is defined as a method of adding or summing up the parts to find the whole and it is basically used to find the volume, area and the central values of many things.
Here we have given the expression that can be written as
=> [tex]\int_{1}^{-1}\int_{0}^{\sqrt{1-y^{2}}}xy^2dxdy[/tex]
When we integrate the equation, then we get the simplified form as follows:
=>[tex]\int_{1}^{-1}\mathrm{[\frac{x^2y^2}{2}]}_{0}^{\sqrt{1-y^2}}[/tex]
Here we have to apply the values on the expression then we get the resulting expression as,
=>[tex]\frac{1}{2}\int_{1}^{-1}(y^2-y^4)dy[/tex]
Now, we have to Integrate with respect to y, then we get the expression as follows:
=>[tex]\frac{1}{2}\mathrm{[\frac{y^3}{2} - \frac{y^5}{5}]}_{-1}^{1}[/tex]
Then the resulting value of double integral is written as,
=> 2/15
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we roll a fair 6-sided die 5 times. what is the probability that exactly 3 of the 5 rolls are either a 1 or a 2?
Therefore , the solution of the given problem of probability comes out to be the result of adding these five times is: 5 x (1/32) = 5/32.
What does probability mean as a process?Probability theory is a branch of mathematics that deals with estimating the likelihood of an event occurring or of a claim being true. A probability is just a value between 0 and 1 and 1, with 0 approximately denoting the possibility of an event occurring and 1 denoting certainty. The likelihood or chance that an event will occur is expression numerically as a probability.
Here,
There are five options since you need one additional set and four even numbers:
5 C 4 ==5
OEEEE, EOEEE, EOEOE, EEEOE, and EEEEO
Three-sixths of the time, you'll obtain an odd number.
Three-sixths of the time, you'll obtain an even number.
As a result, the likelihood of OEEEE is (3/6)5=1/32.
This also represents the likelihood of each additional possibility.
The result of adding these five times is: 5 x (1/32) = 5/32.
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the rate of interest for 5 years is 2.5 and the interest is 2400. what is the total amount deposited?
The total amount deposited is $300.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that rate of interest for 5 years is 2.5 and the interest is 2400
We have to find the total amount deposited.
Simple interest=PNR/100
Principal P=2400Rs
Rate =2.5 per annum
N=time in year=5
Now plu in the value in the formula.
simple Interest=2400×2.5×5/100
=300
Hence, 300 is the amount which is deposited.
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The system of equations below has no solution.
StartLayout enlarged left-brace 1st row two-thirds x + five-halves y = 15 2nd row 4 x + 15 y = 12
An equation that could represent a linear combination of the given system of equations is: B. 0 = -78.
What is no solution?In Mathematics, no solution is also referred to as zero solution, and an equation is said to have no solution when the left hand side and right hand side of the equation are not the same or equal.
Generally speaking, a linear combination of any system of equations can be obtained by either adding or subtracting a multiple of the equations of the system.
2x/3 + 5y/2 = 15 ......equation 1.
4x + 15y = 12 ......equation 2.
By multiplying equation 1 with 6 and equation with 1, we have the following system of equations:
4x + 15y = 90 ......equation 3.
4x + 15y = 12 ......equation 4.
By subtracting equation 3 from equation 4, we have the following:
0 = -78
In this context, we can reasonably infer and logically conclude that 0 = -78 is an equation that would most likely represent a linear combination of the given system of equations.
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Complete Question:
The system of equations below has no solution.
2x/3 + 5y/2 = 15
4x + 15y = 12
Which equation could represent a linear combination of the system?
A) 4/3x=42
B) 0= -78
C)15/2y=33
D)0=0
The population of a city increases by 1.6% per year. If this year's population is 237,000, what will next year's population be, to the nearest individual?
The population next year is 240792
How to determine the population next yearFrom the question, we have the following parameters that can be used in our computation:
Initial population = 237,000
Rate = 1.6% per year
The population next year can be calculated as
Population = Initial * (1 + Rate)
Substitute the known values in the above equation, so, we have the following representation
Population = 237000 * (1 + 1.6%)
Evaluate
Population = 240792
Hence, the new population is 240792
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13. The cost of 7 shirts and 3 pairs of trousers is shs. 2950 while that of 5 pairs of trousers and 3 shirts is less by 200. How much will Dan pay for 2 shirts and 2 pairs of trousers? 14 A father is twice as old as his
Dan paid for 2 shirts and 2 pairs of trousers will be shs 1300.
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.
The cost of 7 shirts and 3 pairs of trousers is 2950 while that of 5 pairs of trousers and 3 shirts is less by 200.
Let 'x' and 'y' be the cost of a shirt and trousers, respectively. Then the equations are given as,
7x + 3y = 2950 ....1
5y + 3x = 2950 - 200
3x + 5y = 2750 ....2
Multiply equation 1 by 5 and equation 2 by 3, then we have
35x + 15y = 14750 ...3
9x + 15y = 8250 ...4
Subtract equation 4 from equation 3, then we have
35x - 9x = 14750 - 8250
26x = 6500
x = 250
Then the value of 'y' is given as,
3(250) + 5y = 2750
750 + 5y = 2750
5y = 2000
y = 400
Then Dan pay for 2 shirts and 2 pairs of trousers will be given as,
⇒ 2 x 250 + 2 x 400
⇒ 500 + 800
⇒ 1300
Dan paid for 2 shirts and 2 pairs of trousers will be shs 1300.
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When solving a system of linear equations, try to algebraically form one equation that has only one variable. T/F
False. Solving a system of linear equations requires solving for multiple variables.
To solve for a single variable, you would only need to solve one equation.
To solve a system of linear equations, you need to use methods such as elimination, substitution, or graphing. For example, consider the system of equations:
3x + y = 7
2x - y = 4
To solve this system, you could use elimination by adding the equations together. This would give you the equation 5x = 11. To solve for x, you would then divide both sides by 5, giving you x = 11/5.
Once you have solved for x, you can substitute this value into either of the original equations to solve for y. In this example, substituting 11/5 for x into the first equation would give you 3(11/5) + y = 7. Simplifying this equation gives you y = -2/5.
Therefore, the solution to this system of linear equations is x = 11/5 and y = -2/5.
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a pharmaceutical company wants to conduct a survey of individuals who have high cholesterol. the company has obtained a list from primary care physicians throughout the country of individuals who are known to have high cholesterol. design a sampling method to obtain the individuals in the sample. be sure to support the choice.
A good sampling method for this scenario would be a probability-based method called Simple Random Sampling.
In Simple Random Sampling, each individual from the population of individuals who have high cholesterol has an equal chance of being selected for the sample. This ensures that the sample is representative of the population and that each individual in the population has a known non-zero probability of being selected.
This method can be supported by the fact that it is easy to implement, and it does not require any prior knowledge of the population characteristics. It also ensures that the sample is unbiased and has a good chance of being representative of the population.
Additionally, Simple Random Sampling is also a cost-effective sampling method as it is less expensive and time-consuming than other sampling methods such as stratified random sampling or cluster sampling.
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Indicate if each equation in the table has no solutions, one solution, or
infinitely many solutions.
- 2(x - 2) = 4 - 2x
A
B
C
A. No Solution
B. One Solution
C.
Infinitely many
solutions
The linear equation -2(x - 2) = 4 - 2x has infinitely many solutions
What is a Linear EquationA linear equation is a mathematical statement that describes a relationship between two or more variables and is written in the form of ax + by = c, where a, b and c are constants and x and y are variables. The equation is called "linear" because it is a first degree equation and it describes a straight line when graphed on a coordinate plane.
In this problem, we have to solve for the value of x
-2(x - 2) = 4 - 2x
Open the bracket
-2x + 4 = 4 - 2x
collect like terms
-2x + 2x = 4 - 4
0 = 0
This has an infinitely many solution
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pls help due tomorrow!!!!
Answer:
Any real value.
Step-by-step explanation:
Ok, so I am just gonna simplify the question a little bit.
[tex]\frac{x-8+3}{5}[/tex] = (x - 5)/5 or x/5 - 1..
Wait a minute, the question doesn't make sense.
The question is true for any value of x as | x | > 0 and - | x | will be < 0 no matter what.
ap stats let the random variable b represent the number in the sample who have a bachelor's degree. what is the probability that b will equal 40
The probability that B will equal 40, where random variable B represent the number in the sample who have a bachelor’s degree is 1.1340323e-12, that is 1.1340323 × 10⁻¹².
The question is asking for the probability that B, the number of residents in the sample of 50 who have a bachelor's degree, will equal 40. To calculate this probability, we need to use the binomial probability formula, which is:
P(B = x) = (n choose x) × pˣ × (1-p)⁽ⁿ⁻ˣ⁾
where:
n = sample size (50)
p = probability of success (31%)
x = number of successes (40)
So, the probability that B will equal 40 is:
P(B = 40) = (50 choose 40) × (0.31)⁴⁰ × (0.69)⁽⁵⁰ ⁻ ⁴⁰⁾
P(B = 40) = 1.1340323e-12
This is a very small probability, which means that it is very unlikely that exactly 40 of the 50 residents in the sample will have a bachelor's degree.
--The question is incomplete, answering to the question below--
"According to a recent survey, 31 percent of the residents of a certain state who are age 25 years or older have a bachelor’s degree. A random sample of 50 residents of the state, age 25 years or older, will be selected. Let the random variable B represent the number in the sample who have a bachelor’s degree. What is the probability that B will equal 40 ?"
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The area of a rectangle is 2 square feet: The perimeter of the rectangle is 9 ft. Find the length, /, and width, W, of the rectangle. What is /2 + w2 ?
The length and breadth of a rectangle with an area of 2 square feet and a perimeter of 9 feet are 4 feet and 0.5 feet, respectively.
What is area?The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. Draw a square on a sheet of paper using a pencil. It is a two-dimensional figure. The area of the form on the paper is referred to as its Area. Consider your square to be made up of smaller unit squares.
Here,
area=2
perimeter=9
lw=2
w=2/l
2l+2w=9
2l+2*(2/l)=9
2l+4/l=9
2l²+4=9l
2l²-9l+4=0
2l²-8l-1l+4=0
2l(l-4)-1(l-4)=0
(2l-1)(l-4)=0
l=1/2, 4
l=4 feet
w=2/l
w=2/4
w=0.5 feet
l²+w²=4²+(0.5)²
=16.25
The length and width of rectangle whose area is 2 square feet and perimeter as 9 feet is 4 feet and 0.5 feet.
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a probabilistic skip list is generated using a fixed probability of 1/2. if nis the number of items in the skip list, what is the average number of layers in the skip list?
If a probabilistic skip list is generated by a fixed probability of 1/2 and n is number of items in skip list then average number of layers in skip list is [tex]log2(n)[/tex] .
let the size of the list be = n ;
So , the first iteration the length of list is = n ;
the list reduces to 1/2 , because the list is using fixed probability of 1/2 ;
So , the second iteration : the length of list is = n/2 ;
similarly , the length of list is = [tex]\frac{n}{2^{2} }[/tex] ;
following the pattern ,
we can say that after "k" iteration , the size of the list is 1 .
where "k" represents number of layers ;
So , [tex]\frac{n}{2^{k} } =1[/tex] ;
simplifying further ,
we get ;
⇒ [tex]N = 2^{k}[/tex] ;
⇒ [tex]k=log2(n)[/tex] .
Therefore , The average number of layers in skip list is [tex]log2(n)[/tex] .
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Factorise 6-y^2
Please help
Answer:
6-y^2 can be factored by using the difference of squares formula which states that:
a^2 - b^2 = (a+b)(a-b)
We can factorize 6-y^2 by using the following:
6 - y^2 = (sqrt(6) + sqrt(-y^2))(sqrt(6) - sqrt(-y^2))
= (sqrt(6) + yi)(sqrt(6) - yi)
where i is the imaginary unit.
So, 6-y^2 = (sqrt(6) + yi)(sqrt(6) - yi) is the factored form of 6-y^2
Please note that the factorization is only true for real values of y, when y is not real the expression can't be factorized.
At a community barbecue, Mrs. Vance and Mr. Coleman are buying dinner for their families. Mrs. Vance purchases 1 hot dog meal and 3 hamburger meals, paying a total of $36. Mr. Coleman buys 2 hot dog meals and 2 hamburger meals, spending $32 in all. How much do the meals cost?
The cost of one hamburger meal is $10 and the cost of one hot dog meal is $6.
What is the cost of one meal?The first step is to form a system of equations using the information in the question:
a + 3b = 36 equation 1
2a + 2b = 32 equation 2
Where:
a = cost of one hot dog meal
b = cost of one hamburger meal
The elimination method would be used to determine the cost of each meal
Multiply equation1 by 2
2a + 6b = 72 equation 3
Subtract equation 2 from equation 3
4b = 40
Divide both sides of the equation by 4
b = 40 / 4
b = 10
Substitute for b in equation 1:
a + 3(10) = 36
a + 30 = 36
a = 36 - 30
a = 6
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5.jill is 9 kilometers away from joe. both begin to walk toward each other at the
same time. jill walks at 1.5 kilometers per hour. they meet in 2 hours. how fast is
joe walking?
Joe moves along at a speed of 2.5 km/h.
What is speed?Speed is what it means. the speed at which an object's location changes in any direction.
The distance traveled in relation to the time it took to travel that distance is how speed is defined.
Since speed simply has a direction and no magnitude, it is a scalar quantity.
So, calculate walking speed of Joe as follows:
Jill covers 9 kilometers in 3 hours while moving at a 3-kilometer-per-hour pace.
Joe covers 7.5 kilometers in 3 hours while walking at a speed of x miles per hour.
Applying the formula, D = R * T.
We can determine Joe's rate by replacing D, which is 7.5 kilometers, and T, which is 3 hours:
7.5 = R * 3
Both sides by 3: Divide
R = 2.5
Therefore, Joe moves along at a speed of 2.5 km/h.
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Correct question:
Jill is 16.5 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill is 16.5 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill is walking 3 kilometers per hour. They meet in 3 hours. How fast is Joe walking?
A realtor wishes to enclose 600 of land in a rectangular plot and then divide it into two plots with a fence parallel to one of the sides. What are the dimensions of the rectangular plot that require the least amount of fencing
The dimensions of the rectangular plot that require the least amount of fencing is :
A(17.32, 17.32) = 600
P(17.32, 17.32) = 121.24
Now, According to the question:
Optimization using Derivatives:
Suppose the function F(x) has continuous first- and second-order derivatives, F′(x) and F″(x).
At a point x=c in the domain of F(x), the function:
has a relative minimum if F′(c)=0 (critical point) and F″(c)>0 (concave up); and,has a relative maximum if F′(c)=0 (critical point) and F″(c)<0 (concave down).600 [tex]u^2[/tex] of land to be enclosed by fence
Area inside plot should be maximized, amount of fence should be minimized
If we draw a quick sketch, we get something like this:
_____ _____
| | |
| | |
| | |
| | |
The two rectangles could be different sizes but if one rectangle size maximizes area then it would make sense to use that some rectangle for both sides.
Let's put some variables into our picture so we can define our constraints.
y y
| | |
x | x | x |
| | |
| | |
Now we just need an equation to connect our unknowns (how much fence to use) to our constraint (it has to have an exact area of 600 u^2.
A = x × 2y = area = 600
P = 3x + 4y = perimeter = a minimum
First we solve the area equation for y:
y = [tex]\frac{600}{2x}[/tex] = [tex]\frac{300}{x}[/tex]
and then we substitute that result into our perimeter equation:
P = 3x + 4 (300/x)
P = 3x + 1200/x
Our perimeter equation is: P(x) = 3x + 1200/x OR P(x) = 3x +1200[tex]x^-^1[/tex]
We can find what value of x makes our perimeter as small as possible (a minimum) by graphing or by using Calculus.
In Calculus we know that maximums and minimums always occur when the derivative is zero. This is because the slope (rate of change) at these points in a graph are always flat or zero. Our derivative is
P'(x) = 3 - 1200[tex]x^-^2[/tex]
When set equal to zero, we can solve for x:
3 - 1200[tex]x^-^2[/tex]= 0
1 - 400[tex]x^-^2[/tex] = 0
1 = 400/[tex]x^{2}[/tex]
[tex]x^{2}[/tex] = 400
x = ± 20
Our fence length can't be a negative number so our answer must be 20u.
If our x length is 20, then our y length must be 300/x to ensure our area is 600 u^2.
The y length is 300/(20) = 15
Let's put all of our numbers into our picture to see if it make sense.
15 15
| | |
20 | 20 | 20 |
| | |
| | |
15 15
Sure enough our area is 600.
Here's what we have right now:
A(20, 15) = 600
P(20, 15) = 120
How about we try something a little bigger like 20.5 for x and 14.63 for y?
A(20.5, 14.63) = 600
P(20.5, 14.63) = 120.02
How about we try something a little smaller like 19.5 for x and 15.38 for y?
A(19.5, 15.38) = 600
P(19.5, 15.38) = 120.02
It looks like if we try to change x, even a little, to make it bigger or smaller the perimeter only gets bigger.
You might have guessed at the beginning that a square is the best shape to use to maximize area, so let's try that as well.
Each rectangle is 300[tex]u^2[/tex]. We want a square so each side would be √(300) = 17.32
17.32 17.32
| | |
17.32 | 17.32 | 17.32 |
| | |
17.32 17.32
A(17.32, 17.32) = 600
P(17.32, 17.32) = 121.24
Hence, The dimensions of the rectangular plot that require the least amount of fencing is :
A(17.32, 17.32) = 600
P(17.32, 17.32) = 121.24
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a standard interior staircase has steps each with a rise (height) of 22 cm and a run (horizontal depth) of 23 cm. research suggests that the stairs would be safer for descent if the run were, instead, 28 cm. for a particular staircase of total height 4.57 m, how much farther into the room would the staircase extend if this change in run were made?
The staircase would extend 104.3cm farther into the room if the run were made 28cm instead of 23cm.
To find out how much farther into the room the staircase would extend if the run were 28 cm instead of 23 cm, we need to calculate the difference in the run and then multiply it by the number of steps.
The difference in the run is 28cm - 23cm = 5cm
To find the number of steps, we need to divide the total height of the staircase by the height of each step:
4.57m / 0.22m = 20.86 steps.
So the difference in the run multiplied by the number of steps is:
5cm * 20.86 steps = 104.3cm.
Therefore, the staircase would extend 104.3cm farther into the room if the run were made 28cm instead of 23cm.
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What is the equation of a circle with a center (8, 4) and radius of 7?
The equation of a circle with a center (8, 4) and radius of 7
(x - 8)² + (y - 4)² = 49How to determine the equation the circleInformation given in the question
the equation of a circle with a center (8, 4) and radius of 7
Equation of a circle is given as
(x - h)² + (y - k)² = r²
The equation of the circle is written by substituting for h and k and r where
h = 8
k = 4
r = 7
substituting the values of h k and r into the equation results to
(x - 8)² + (y - 4)² = 7²
(x - 8)² + (y - 4)² = 49
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The formula for the lateral area of a right cone is LA = rs, where r is the radius of the base and s is the slant height of the cone. Which are equivalent equations?
The formula of lateral area of a cone can be equivalent to the formulas:
LA = r√(r^2 + h^2) and
LA = πrl
The formula for the lateral area of a right cone is LA = rs, where r is the radius of the base and s is the slant height of the cone.
The slant height (s) of a cone is the distance from the apex of the cone to the center of the base along a line that is perpendicular to the base and passes through the apex. The slant height of a cone can be found using the Pythagorean theorem using the radius (r) and the height (h) of the cone:
s = √(r^2 + h^2)
So, the formula for lateral area of a cone can be equivalent to the formula:
LA = r√(r^2 + h^2)
Another equation that is equivalent to the lateral area formula is
LA = (1/2)(2πr)(l)
LA = πrl
where l is the slant height of the cone.
This is because the lateral area of a cone is equal to (1/2) of the circumference of the base multiplied by the slant height, and we know that the circumference of a circle is equal to 2πr.
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Which of the following is NOT a solution to the system of inequalities?
(1,2)
(0,4)
(2,1)
(1,5)
Answer:
(2, 1 ) is not a solution to the system
Step-by-step explanation:
the solution lies in the shaded region between the 2 lines.
(1, 2 ) lies within this region and is a solution
(0, 4 ) lies within this region and is a solution
(2, 1 ) does not lie inside the region and is therefore not a solution
(1, 5 ) lies within this region and is a solution
Thus
(2, 1 ) is the only point that is not a solution to the system
Jamie's brother Nick is 10 years older than jaime is. Two years ago, Nick was three times older than Jaime was. In how many years will Nick be twice Jaimes age?
The number of years Nick will be twice as Jaime's age is 3 years time.
How to find the number of years Nick will be twice the age of Jamie?Jamie's brother Nick is 10 years older than Jaime is. Two years ago, Nick was three times older than Jaime was.
The number of years Nick will be twice as Jamie's age can be calculated as follows:
let
Jamie age = x
Nick age = x + 10
Two years ago:
3(x - 2) = x + 10 - 2
3(x - 2) = x + 8
3x - 6 = x + 8
3x - x = 8 + 6
2x = 14
x = 14 / 2
x = 7
Nick age = 7 + 10 = 17
Let's find the number of years Nick years will be twice as Jamie's age.
Let
y = number of years
2(7 + y) = 17 + y
14 + 2y = 17 + y
2y - y = 17 - 14
y = 3
y = 3
Hence, in 3 years time Nick age will be twice of Jaime's age.
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