Suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. If the population grows to 500 after one year, the population will be 852.78 after another three years.
What is the logistic model?A logistic model, also known as the Verhulst-Pearl model, is a type of function used to describe population growth that is limited. It’s a form of exponential growth that takes into account the carrying capacity of an environment.
Population growth that is limited and slows down as the population approaches its carrying capacity is modeled using the logistic model. It is given by this equation:
[tex]P(t) = K / (1 + Ae^{-rt})[/tex]
where P(t) is the population at time t, K is the carrying capacity, A is the constant of proportionality, and r is the growth rate.
Suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. If the population grows to 500 after one year, substitute this information into the logistic model: [tex]P(1) = 500[/tex], [tex]K = 2000[/tex], and [tex]P(0) = 200[/tex].
[tex]500 = 2000 / (1 + Ae^{-r(1)})[/tex]
Now, solve for A by dividing both sides by 2000 / (1 + A):
[tex]1 + A = 4A = 3[/tex]
Substitute the value of A back into the logistic model equation:
[tex]P(t) = 2000 / (1 + 3e^{-rt})[/tex]
Solve for r by using the data provided in the problem for the first year (t = 1) and second year (t = 4):
[tex]P(1) = 500 = 2000 / (1 + 3e^{-r(1)})[/tex]
[tex]P(4) = ? = 2000 / (1 + 3e^{-r(4)})[/tex]
Solve the first equation for r:
[tex]500 = 2000 / (1 + 3e^{-r})\\1 + 3e^{-r} = 4e^{-r}\\1 + 3e^r = 4e[/tex]
Solve for e using the quadratic formula to get:
e = 0.4274 and e = 1.1713
Let e = 0.4274:
[tex]1 + 3e^{-r} = 4e^{-r}\\1 + 3(0.4274)^{-r} = 4(0.4274)^{r}\\1 + 0.5746^r = 1.7166^r[/tex]
Take the natural logarithm of both sides:
[tex]ln(1 + 0.5746^r) = ln(1.7166^r) - lnr\\ln(1 + 0.5746^r) = rln(1.7166) - lnr[/tex]
Use a graphing calculator to solve for r:
[tex]ln(1 + 0.5746^r) = rln(1.7166) - lnr[/tex]; -0.1568 < r < 0.7534
Solve for r using the second year’s data:
[tex]2000 / (1 + 3e^{-r(4)}) = P(4)\\2000 / (1 + 3(0.4274)^{-r(4)}) = P(4)\\P(4) = 852.78[/tex]
Thus, the population will be 852.78 after another three years.
Learn more about logistic model here:
https://brainly.com/question/30995760
#SPJ11
A shipping company is packing a box with one cubic centimeters blocks. The box is 14 centimeters long. 12 centimeters wide and 16 centimeters high. How many one cubic centimeter blocks will fill the box ?
The shipping company will need 2,688 one cubic centimeter blocks to fill the box.
The volume of the box can be calculated as:
Volume = length x width x height
Volume = 14 cm x 12 cm x 16 cm
Volume = 2,688 cubic cm
Since each block is also one cubic cm in volume, we can simply divide the total volume of the box by the volume of one block to find the number of blocks needed to fill the box:
Number of blocks = Volume of box / Volume of one block
Number of blocks = 2,688 cubic cm / 1 cubic cm
Number of blocks = 2,688
Learn more about volume here
brainly.com/question/23952628
#SPJ4
Picture Shown Below with question:
Answer: 23
Step-by-step explanation:
Vertical angles are congruent (equal) so you first make the equations for angle A and B equal to each other and solve for x.
x + 15 = 5x - 17
32 = 4x
x = 8
Plug the x value (8) back into either equation to find the measure of angle B.
x + 15
8 + 15 = 23
WILL GIVE BRAINLIEST HELP
Answer:
D= 7(2g-H)/U
Step-by-step explanation:
After 6 new students entered the Happy Hearts Childcare Center and 2 students exited, there were 3 times as many students as before. How many students were present before students entered and exited the center?
Answer: 2
Step-by-step explanation:
If there are three times as many students when there are 6 students you do 6 divided by three to give you two.
Part III: Short Answer Items (Worth 3 points) Instruction: Write the most simplified answer on the blank space provided for each of them. 11. If the price of an item is Birr 9,500 before VAT, then the total cost of the item including VAT
According to the VAT rate, the total cost of the item including VAT is Birr 10,925 assuming a VAT rate of 15%.
What is VAT rate ?
VAT (Value Added Tax) rate is a percentage that is added to the price of goods or services. VAT is usually charged on top of the base price of a product or service, and the total price is calculated as (base price) + (base price x VAT rate). The VAT rate is typically set by the government and may be subject to change over time.
To find the total cost of the item including VAT, we need to know the VAT rate.
Let's assume the VAT rate is 15%. To calculate the VAT amount, we can multiply the price before VAT by the VAT rate:
VAT amount = 0.15 x 9,500 = Birr 1,425
The total cost of the item including VAT is the sum of the price before VAT and the VAT amount:
Total cost = 9,500 + 1,425 = Birr 10,925
Therefore, the total cost of the item including VAT is Birr 10,925 assuming a VAT rate of 15%.
To know more about VAT rate visit:
brainly.com/question/28165138
#SPJ1
A middle school teacher estimates that 170 parents will attend the back to school informational meeting. A total of 147 parents actually attended the meeting. What is the percent error of the teacher's estimate rounded to the nearest tenth of a percent
The percent error from the real and estimated values is 16%.
What is percent error?The difference between a precise value and an approximation to it is the approximation error in a data value. Either an absolute mistake or a relative error can be used to describe this error. It is possible for measurement mistake or computing machine precision to produce an approximation error. The percent error is the distinction between the estimated value and the real value in relation to the actual value. In other terms, the relative error is multiplied by 100 to calculate the percent error.
The estimated value= 170
the real value= 147
Percent error ={ (170-147)/147}*100= 0.1564*100
Percent error = 15.64% ≈ 16%
To know more about percent error, visit
https://brainly.com/question/29107960
#SPJ1
How do I solve this?
Answer:
X+4
Step-by-step explanation:
Area = l *b
x^2 + 13x + 36 = (X+9) * b
x^2 + 9x + 4x + 36 = (X+9) * b
X(X+9) + 4(X+9) = (X+9) * b
(X+4) (X+9) = (X+9) * b
b = (X+4)
Is this a compound?
First, Gabriel planted the geraniums in a clay pot, and then he placed the pot on a sunny windowsill in his kitchen
A. YES
B. NO
Answer:
yes it is right now you can write it
A box with a square base and open top must have a volume of 62500 cm3. We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x.] Simplify your formula as much as possible. A(x) = Next, find the derivative, A'(x). A'(x) = Now, calculate when the derivative equals zero, that is, when A'(x) = 0. [Hint: multiply both sides by x² .] A'(x) = 0 when x =
The area of the square base = x².
we have:l = w = x ... (2) ... And, h = V/lw = V/x² ... (3) ...
The dimension of the box that minimizes the amount of material used is x = (2V)1/3. A(x) = x² + 4V/x, A'(x) = 2x - 4V/x², x = (2V)1/3
The given volume of the box is 62500 cm³. We wish to find the dimensions of the box that minimize the amount of material used.
To obtain the formula for the surface area of the box in terms of only x, the length of one side of the square base, we use the formula for the volume of a box:V = lwh ... (1) ... where V is the volume, l is the length, w is the width, and h is the height of the box. Here, the base of the box is a square with side length x.
Hence, the area of the square base = x². Therefore, we have:l = w = x ... (2) ... And, h = V/lw = V/x² ... (3) ... We can substitute (2) and (3) in (1) to get the formula for V in terms of x as follows:V = x² V/x² A(x) = A(x) = x² + 4xhA(x) = x² + 4x(V/x²) = x² + 4V/x
Now, to find the derivative A'(x) of A(x), we differentiate A(x) with respect to x:A'(x) = 2x - 4V/x² A'(x) = 0 when x = (2V)1/3. Therefore, the dimension of the box that minimizes the amount of material used is x = (2V)1/3. A(x) = x² + 4V/x, A'(x) = 2x - 4V/x², x = (2V)1/3
Learn more about Area
brainly.com/question/1561162
#SPJ11
the quadratic sequence: 44; 52; 64; 80; Write down the next two terms of the sequence. Determine the nth term of the quadratic sequence. Calculate the 30th term of the sequence. Prove that the quadratic sequence will always have even terms.
To find the next two terms of the sequence, we need to first find the common difference between consecutive terms:
52 - 44 = 8
64 - 52 = 12
80 - 64 = 16
We notice that the common difference is increasing by 4 for each term. Therefore, the next two terms of the sequence are:
80 + 20 = 100
100 + 24 = 124
To determine the nth term of the quadratic sequence, we can use the formula:
an = a1 + (n-1)d + bn^2
where a1 is the first term, d is the common difference, b is the coefficient of n^2, and n is the term number.
Using the first four terms of the sequence, we can form a system of equations:
44 = a1 + b
52 = a1 + d + b
64 = a1 + 2d + b
80 = a1 + 3d + b
Solving for a1 and b, we get:
a1 = 20
b = 24
Substituting these values into the formula for an, we get:
an = 20 + (n-1)4 + 24n^2
an = 24n^2 + 4n - 4
To find the 30th term of the sequence, we simply substitute n = 30 into the formula we just derived:
a30 = 24(30)^2 + 4(30) - 4
a30 = 21,596
To prove that the quadratic sequence will always have even terms, we notice that the first term is even (44 = 2 x 22), and the common difference is even (8 = 2 x 4). Therefore, every term of the sequence can be expressed as an even number plus an even multiple of n^2, which is always even. Hence, the quadratic sequence will always have even terms.
Step-by-step explanation:
Sequence is 44;52;64;80;.....44;52;64;80;.....
General formula is Tn=2n2+2n+40
X
The diagram shows part of a
regular decagon. Work out
the size of the angle marked
X
Answer:
144°
Step-by-step explanation:
x = (10 - 2)(180)/10 = 144
Should we write reciprocal for 5/6 in this question 5 × 5/6
If the question is simply asking for the product of 5 and 5/6, then writing the reciprocal is not necessary. To multiply fractions, we can simply multiply the numerators and the denominators separately. In this case, we would get:
5 x 5/6 = (5 x 5)/(1 x 6) = 25/6
However, if the question specifically asks for the result to be expressed as a mixed number or a whole number, then we would need to simplify the fraction by converting it to a mixed number or a whole number. In some cases, it may be helpful to write the reciprocal in order to simplify the fraction more easily.
For example, if the question asks us to express 5 x 5/6 as a mixed number or a whole number, we could first write the reciprocal of 5/6 as 6/5, and then multiply it with 5 to get:
5 x 5/6 = 5 x 6/5 = 30/5
We can simplify this fraction by dividing both the numerator and the denominator by 5:
30/5 = 6
Therefore, if the context or the desired result requires the expression 5 x 5/6 to be simplified further, it may be helpful to write the reciprocal of 5/6 to make the simplification process easier. However, in general, it is not necessary to write the reciprocal to multiply fractions.
Find more about reciprocal
brainly.com/question/15212898
#SPJ4
The sum of the base and the height of a triangle is 22 cm. Find the dimensions for which the area is a maximum. The triangle with maximum area has a height of_____cm and a base of cm_____.
The dimensions of the triangle with maximum area are a base of 11 cm and a height of 11 cm.
We are given that the sum of the base and height of a triangle is 22 cm. Let's call the base of the triangle "b" and the height "h". Then we have the equation:
b + h = 22
We want to find the dimensions of the triangle that will give us the maximum area.
The formula for the area of a triangle is A = (1/2)bh.
We can use the equation b + h = 22 to solve for one of the variables in terms of the other.
we can solve for h:
h = 22 - b
Substituting this into the formula for the area, we get:
A = (1/2)b(22 - b)
The equation 0 = 11b - (1/2)b² can be rearranged to:
(1/2)b² - 11b = 0
We can then use the quadratic formula to solve for "b"
b = 11 ± 11
So the value of b that gives us the maximum area is b = 11 cm. Substituting this back into the equation h = 22 - b, we get:
h = 22 - 11 = 11 cm
Triangle has a base of 11 cm and a height of 11 cm.
To practice more questions about area of triangle:
https://brainly.com/question/21735282
#SPJ11
last week Alexander was paid $56 for 7 hours of work. how much money does Alexander's job pay her hour??
Answer:
$56 divided by 7 hours is $8 per hour sh get payed.
The linear scale factor of two similar shapes is 4:7. If the area of the bigger
shape is 392 , find the area of the smaller one.
Answer:
224
Step-by-step explanation:
392 ÷ 7 = 56
56 *4 = 224
hope this helps
BP = FC + VCM
The fixed costs associated with the fundraiser include: one-time charges of art ($45), screen and set-up ($60),
and advertising ($50 for a newspaper ad). In addition, the unit cost of the sweatshirt will be $16.50 per sweatshirt, with an additional charge of $.50 per shirt for shipping and individual plastic wrap. You plan to sell the sweatshirts for a retail price of $22.
A. Calculate breakeven in units.
B.calculate breakeven in dollars
1. The breakeven in units equals 31 units.
2. The dollar amount to breakeven is
What is the breakeven in units?The variable cost per unit includes the cost of the sweatshirt ($16.50) and the additional charge for shipping and plastic wrap ($0.50), so the total variable cost per unit is:
= $16.50 + $0.50
= $17.00
The contribution margin per unit is:
= 22.00 - $17.00
= $5.00
The fixed costs include the one-time charges of art ($45), screen and set-up ($60), and advertising ($50), so the total fixed costs are:
= $45 + $60 + $50
= $155
Using the breakeven formula, we can calculate the number of units required to break even:
= Fixed costs / Contribution margin per unit
= $155 / $5.00
= 31 units
What is the breakeven in dollars?To calculate the breakeven in dollars, we need to multiply the breakeven in units by the selling price per unit:
The breakeven in dollars equals to:
= Breakeven in units x Selling price per unit
= 31 x $22.00
= $682.00
Read more about breakeven
brainly.com/question/15281855
#SPJ1
For random variable X~N(3,0.75), what is the probability that X takes on a value within two standard deviations on either side of the mean?
Answer:For random variable X~N(3,0.75), what is the probability that X takes on a value within two standard deviations on either side of the mean?
Step-by-step explanation:
3.
Point out the five-fold health hazards prevalent in Nepal.
4.
Why is life expectancy of the Nepalese very low? Give reasons.
the Minister of Health in Nenal. What programme
The five fold health hazards prevalent in Nepal are respiratory diseases due to high altitude, Germ cell mutagenicity, Carcinogenicity, Reproductive toxicity and sanitation related issues which causes diarrhea, cholera like diseases.
Nepal is a small country in hilly region of Himalayas between China and India. It has not developed much in terms of health care facilities and advanced treatment methods due to which people migrate to India for treatments in several extreme diseases. The low life expectancy is because of poor employment which causes financial insecurity and hence people are either malnourished, or die of lack of proper treatment.
The Nepal Health Sector Program – Implementation Plan (NHSP-IP) has been developed in order to meet the Health Sector Strategy which has its agenda to improvise the needs of the people in near future.
Learn more about life expectancy at:
https://brainly.com/question/17427164
#SPJ4
Anna has n number of nickels. She has less than 45 cents. Which inequality could
be used to find the value of n?
A $0.05n< $0.45
B $0.05n > $0.45
C $0.05n ≤ $0.45
D $0.05n ≥ 0.45
Answer:
A $0.05n< $0.45
Step-by-step explanation:
It is given that she has "less than" rather than "less than or equal to" 45 cents. Therefore, your answer will contain the "less than" sign, which is signified as <.
Therefore, being the only answer with <, your answer will be A.
A nickel is $0.05, therefore:
$0.05 of n is less than $0.45, or $0.05n< $0.45
A) $0.05n < $0.45 is your answer.
~
Learn more about inequalities, here:
https://brainly.com/question/4410289
Write an expression that can be a rule for the number sequence below.
5, 9, 13, 17, 21, …
The possible expression that can be a rule for the number sequence is:[tex]$a_n = 4n + 1$[/tex],
What is expression?As an illustration, the expression x + y is one where x and y are words with an addition operator in between. There are two types of expressions in mathematics: numerical expressions, which only comprise numbers, and algebraic expressions, which also include variables.
According to question:
One possible expression that can be a rule for the number sequence is:
[tex]$a_n = 4n + 1$[/tex], where n is the position of the term in the sequence.
Using this expression, we can find the values of the first few terms as follows:
[tex]$a_1 = 4(1) + 1 = 5$[/tex]
[tex]$a_2 = 4(2) + 1 = 9$[/tex]
[tex]$a_3 = 4(3) + 1 = 13$[/tex]
[tex]$a_4 = 4(4) + 1 = 17$[/tex]
[tex]$a_5 = 4(5) + 1 = 21$[/tex]
Thus, possible expression that can be a rule for the number sequence is:[tex]$a_n = 4n + 1$[/tex],
To know more Sequence visit:
brainly.com/question/30262438
#SPJ1
Answer:
5n, where n is equal to 0, 1, 2, 3, 4
Step-by-step explanation:
5, 9, 13, 17, 21,
a teacher monitored the number of people texting during class each day and calculated the corresponding probability distribution. what type of probability distribution did the teacher use?
The given probability distribution "a teacher monitored the number of people texting during class each day and calculated the corresponding probability distribution." is a type of discrete probability distribution.
What is the Probability distribution?The probability distribution is used to describe the probability of each outcome in a series of possible outcomes. It is a mathematical representation of the outcomes of an experiment.
The teacher likely used a discrete probability distribution to calculate the probability of a certain number of people texting during class each day.
A discrete probability distribution is used to analyze data where the outcome is counted in whole numbers, such as the number of people texting in a given class period.
Learn more about Probability distribution here:
https://brainly.com/question/14210034
#SPJ11
Which of the following is equivalent to 3/8? -0.6, square root of 100, 2/5, -2/3, 0.35217534
The οptiοn in the questiοn that is equivalent tο 3/8 is 2/5.
Equivalent- Meaning in MathematicsThe term "equivalent" in math refers tο twο meanings, numbers, οr quantities that are the same. The equivalence οf twο such quantities shall be denοted by a bar οver an equivalent symbοl οr Equivalent Sign. It alsο means a lοgical equivalence between twο values οr a set οf quantities. Equivalence is similar but mοre universal than equality. If twο sets οf equatiοns have the same sοlutiοns, we might cοnsider them similar, but they are nοt identical.
Hοw tο calculate the equivalent οf 3/8?We can simplify 3/8 and 2/5 sο that they have a cοmmοn denοminatοr:
3/8 = 3*(5/5)/(85/5) = 15/40
2/5 = 2(8/8)/(5*8/8) = 16/40
Since 15/40 and 16/40 have the same denοminatοr, we can cοmpare their numeratοrs tο see which is larger:
15/40 < 16/40
Since 16/40 is larger, we can cοnclude that 2/5 is greater than 3/8.
Therefοre, the οptiοn that is equivalent tο 3/8 is 2/5.
Learn more about equivalent at
https://brainly.com/question/14672772
#SPJ1
GEOMETRY:
a pile standing vertically casts a 19 ft shadow. At the same time, a 6 ft person near the beam casts a shadow 4’6’’. What is the height of the pole?
Answer:
X / 19 = 6 / 4.5 both person and pile have same ratio of shadow
X = 6 / 4.5 * 19 = 25.3 ft
Problem: Power Output. In each case, find your average power in watts. Assume that riding a bike burns 100 Calories per mile. If you ride at a speed of 20 miles per hour, what is your average power output, in watts?
The average power output of a bike rider at a speed of 20 miles per hour is 556 W
Given, Riding a bike burns 100 Calories per mile. Speed of riding a bike is 20 miles per hour. Power is a measure of the rate at which work is done over time.
Therefore, the formula for average power is given by,
P = W/t
Where, P is power, W is work and t is time.
Now, We know that riding a bike burns 100 Calories per mile, but we have to find out the work done.
So, work done = 100 Calories × distance traveled= 100 × 1.609 × 1000 = 160900 J
Time taken = distance/speed= 1.609/20 = 0.08045 hours
Putting values in the formula of power, we get,
P = W/t= 160900/0.08045= 1999999.9 J/hour
Converting hour to seconds,1 hour = 3600 seconds1 J/s = 1 watt1 J/hour = 1 / 3600 watt
Therefore, power = 1999999.9 / 3600= 555.5556 watts (approx)
Therefore, the average power output of a bike rider at a speed of 20 miles per hour is 556 W (approx). Answer: 556
Learn more about average power output:https://brainly.com/question/14558400
#SPJ11
For which function does g decrease by 25% every time x increases by 1?
A g(x) = 0.75
B) g(x) = 75
g(x) = 0.25
D g(x) = 25*
We pIug this function into the equation above, we get: g(x+1) = 0.
Assume that g(x) is a function that decreases by 25% for every one increase in x.
This means that if we increase x by one, the vaIue of g(x) wiII be 75% of what it was befοre.
In other words, if g(x) is the function's vaIue at x, then g(x+1) is 0.75 times g. (x).
As a resuIt, we can express g(x+1) in terms of g(x) as foIIows:
g(x+1) = 0.75 * g(x) (x)
Let's see which οption meets this requirement.
A) g(x) = 0.75: When we pIug this function into the equation above, we get:
g(x+1) = 0.75 * 0.75 = 0.5625 * g(x) (x)
This means that increasing x by one increases g(x) by 25%. As a resuIt, this optiοn does not meet the condition.
B) g(x) = 75: When we pIug this function into the equation above, we get:
g(x+1) = 0.75 * 75 = 56.25
This means that increasing x by οne decreases g(x) by more than 25%.
As a resuIt, this option does not meet the condition.
C) g(x) = 0.25: When we pIug this function into the equatiοn above, we get:
g(x+1) = 0.75 * 0.25 = 0.1875 * g(x) (x)
This means that increasing x by one decreases g(x) by more than 25%. As a resuIt, this optiοn does not meet the cοndition.
D) g(x) = 25*: When we pIug this function into the equation above, we get:
g(x+1) = 0.
To knοw more about Function visit:
brainly.com/question/14996337
#SPJ1
Cοmplete question:
For which function does g decrease by 25% every time x increases by 1?
A) g(x) = 0.75
B) g(x) = 75
C) g(x) = 0.25
D) g(x) = 25*
Help pls
I need three answers
The value οf x fοr the expressiοn must be simplified is 12,32,48.
What is expressiοn?Expressiοns in mathematics must cοntain a statement, at least οne arithmetic οperatiοn, at least twο numbers οr variables, οr bοth. With the help οf this mathematical οperatiοn, οne can multiply, divide, add, οr subtract.
Unknοwn variables, numbers, and arithmetic οperatοrs make up an algebraic expressiοn. There are nο symbοlic representatiοns οf equality οr inequality in it.
Here since 71 is a prime number , [tex]\sqrt{71}[/tex] cannot be simplified itself.
Then [tex]\sqrt{71x}[/tex] can only be further simplified if [tex]\sqrt{x}[/tex] itself can be simplified.
Here , amοng the given chοices,
=>12 = 4*3 [ 4 is perfect square] , sο it can be simplified.
=> 32 = 16*2 [16 is perfect square] , sο it can be simplified.
=> 48 = 16*3 [ 16 is perfect square] , sο it can be simplified.
Hence the value οf x fοr the expressiοn must be simplified is 12,32,48.
To learn more about expression refer the below link
https://brainly.com/question/112703
#SPJ1
Reduce each expression to a polynomial
((y-b)^(2))/(y-b+1)+(y-b)/(y-b+1)
The given expression ((y-b)²/(y-b+1)+(y-b)/(y-b+1) after being reduced to a polynomial, can be represented as y-b.
In order to reduce the given equation to a polynomial, we are required to simplify and combine like terms. First, we can simplify the expression in the numerator by expanding the square:
((y-b)²/(y-b+1) = (y-b)(y-b)/(y-b+1) = (y-b)²/(y-b+1)
Now, we can combine the two terms in the equation by finding a common denominator:
(y-b)²/(y-b+1) + (y-b)/(y-b+1) = [(y-b)² + (y-b)]/(y-b+1)
Next, we can combine the terms in the numerator by factoring out (y-b):
[(y-b)² + (y-b)]/(y-b+1) = (y-b)(y-b+1)/(y-b+1)
Finally, we can cancel out the common factor of (y-b+1) in the numerator and denominator to get the polynomial:
(y-b)(y-b+1)/(y-b+1) = y-b
Therefore, the equation ((y-b)²)/(y-b+1)+(y-b)/(y-b+1) after being simplified, is equivalent to the polynomial y-b.
Learn more about polynomials :
https://brainly.com/question/30127172
#SPJ4
Tiago sells sunflower oil in large tins and extra-large tins.
The large tin and the extra-large tin are mathematically similar.
The volume of the extra-large tin is 75% more than the volume of the large tin. Both tins are cylinders.
The radius of the large tin is 20 cm.
Calculate the radius of the extra-large tin.
Answer:
24 cm (to nearest cm)
Step-by-step explanation:
XLV = extra large tin volume (cm³)
LV = large tin volume (cm³)
XLR = extre large tin radius (cm)
LR = large tin radius (cm) = 20
XLV = 1.75 × LV
Since the tins are geometrically similar cylinders, we can infer that the volumes and radii of the 2 tins are related;
We know the relationship between the volume of the two tins, i.e. the XL tin is 75% greater in volume than the L tin;
This means the volumetric scale factor or multiplier is ×1.75;
Subsequently, we know:
XLV = 1.75 × LV
Similarly, there is a relationship between the radii of the tins;
The relationship is, however, slightly different;
[tex]XLR = (\sqrt[3]{1.75}) \times LR[/tex]
We need to take the cube root of the volumetric scale factor, reason being, the radius is a linear dimension unlike volume;
Easy way to figure this is radius is in cm, volume is in cm³;
So:
XLR = 1.205... × LR
XLR = 1.205... × 20
XLR = 24.101... --> 24 cm (to nearest cm)
what are the X intercept of the graph of the following equation y=x^2 - 64
Step-by-step explanation:
Here is one way :
at the x-axis intercepts , the value of 'y' = 0 (obviously)
0 = x^2 -64
x^2 = 64
x = ± 8
I NEED HELP ON THIS ASAP!!
Answer:
(a) {0 ≤ x ≤ 60; 0 ≤ y ≤ 90; x + y ≤ 120}
(b) p = 50x +75y; 30 tons of loam and 90 tons of peat will maximize profit
Step-by-step explanation:
You want a graph of constraints and the solution to the problem of maximizing profit from sale of 60 tons of loam and 90 tons of peat at a profit of $50/t and $75/t, respectively, if at most 120 tons can be sold.
(a) ConstraintsLet x and y represent tons of loam and peat, respectively. Then the constraints can be written as the inequalities ...
0 ≤ x ≤ 60 . . . . . can only sell as much as is available0 ≤ y ≤ 90 . . . . . can only sell as much as is availablex + y ≤ 120 . . . . . can sell a maximum of 120 tons(b) Objective functionWe want to maximize profit, so maximize ...
p = 50x +75y
GraphThe attached graph shows the graphs of the inequalities. The restrictions on the variables confine the applicable graph to the first quadrant.
The black line shows the objective function. The value of the profit function is maximized when the line is as far from the origin as possible. The boundary point of the constraint solution space that maximizes profit is (x, y) = (30, 90).
Sale of 30 tons of loam and 90 tons of peat soil will maximize profit.
__
Additional comment
Since selling peat is the most profitable, profit will be maximized when we sell as much peat as possible. Sale of only 90 tons is possible, so profit will be maximized when we sell that many, then make up the rest of the 120 ton maximum by selling loam. We don't need a graph or a list of constraints to figure that out.