Answer:
Step-by-step explanation:
[tex]t^2 \dfrac{dy}{dt}+ y^2 = ty \\ \\ t^2 \dfrac{dy}{dt}-ty = -y^2[/tex]
[tex]\text{by dividing both sides by }{y^2},\text{ we have:}[/tex]
[tex]\dfrac{t^2}{y^2}\dfrac{dy}{dt}- \dfrac{ty}{y^2}= -1[/tex]
[tex]\dfrac{t^2}{y^2}\dfrac{dy}{dt}- t\dfrac{1}{y}= -1[/tex]
[tex]\text{by dividing both sides by }t^2; \text{we have;}[/tex]
[tex]\dfrac{1}{y^2}\dfrac{dy}{dt}- \dfrac{1}{t}\dfrac{1}{y}= -\dfrac{1}{t^2}--- (i)[/tex]
[tex]Let \ v = \dfrac{1}{y}[/tex]
[tex]\dfrac{dv}{dt}= -\dfrac{1}{y^2}\dfrac{dy}{dt}[/tex]
[tex]-\dfrac{dv}{dt}= \dfrac{1}{y^2}\dfrac{dy}{dt}[/tex]
[tex]\text{replace in equation (1); we have}[/tex]
[tex]- \dfrac{dv}{dt}-\dfrac{1}{t}v = -\dfrac{1}{t^2}[/tex]
[tex]- \Big ( \dfrac{dv}{dt}+ \dfrac{1}{t}v \Big) = -\dfrac{1}{t^2}[/tex]
[tex]\dfrac{dv}{dt}+\dfrac{1}{t}v = \dfrac{1}{t^2}[/tex]
[tex]\text{relating above with} \dfrac{dv}{dt}+ P(t) v = Q(t) \text{, we have:}[/tex]
[tex]P(t) = \dfrac{1}{t} \ \ \ , \ \ \ \ Q(t) = \dfrac{1}{t^2}[/tex]
[tex]\mu (t) = e^{\int P(t) \ dt }= e ^{\int \dfrac{1}{t} \ dt}= e^{In|t|}= t[/tex]
[tex]v\mu(t) = \int \mu(t) Q(t) dt + C[/tex]
[tex]vt = \int (t) (\dfrac{1}{t^2})dt + C[/tex]
[tex]vt = \int \dfrac{1}{t}dt + C[/tex]
[tex]vt = Int+C[/tex]
[tex]v = \dfrac{In \ t + C}{t}[/tex]
[tex]\text{substitute } v = \dfrac{1}{y}}, we \ get}[/tex]
[tex]\dfrac{1}{y}=\dfrac{In \ t +C}{t}[/tex]
[tex]\mathbf{y = \dfrac{t}{In \ t + C}}[/tex]
Which of the following circles have their centers on the x-axis?
Check all that apply.
A. (x-4)2 + (y-0)² = 22
B. (x-0)2 + (v-0)² = 25
C. (x + 1)² + (y-7)² = 16
D. (x-0)2 + (v-5)2 = 49
The equations of the circles that have centers on the x-axis are;
A. (x - 2)² + (y - 0)² = 22
B. (x - 0)² + (y - 0)² = 25
What is the general form of the equation of a circle?The equation of a circle is; (x - h)² + (y - k)² = r², where;
(h, k) = The coordinates of the center of the circle
r = The radial length of the circle
The center of the circle is on the x-axis when the y-coordinate of the center of the circle is; k = 0, therefore, the circle that have their centers on the x-axis are the circles with the term (y - 0)²
The option of the circle that has the term (y - 0)² are the first and second option, where the v is actually a y; option A and .
The correct option is therefore;
A. (x - 4)² + (y - 0)² = 22
B. (x - 0)² + (y - 0)² = 25
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STRUCTURE Gustavo sets up tables for a caterer on weekends. Each round table can seat 8 people. Each rectangular table can seat 10 people. One weekend, his boss asked him to set up tables for 124 people. He uses 2 more round tables than rectangular tables. Write a system of equations to find the number of round tables and rectangular tables Gustavo used. Then graph the system on a separate sheet of paper to solve the system. Let x = the number of round tables and let y = the number of rectangular tables. y = x+ x+ y= WHAT DO I PUT IN THE BOXES
The system of equation of the tables used is 8x + 10y = 124 and x = y + 2
He used 8 round tables and 6 rectangular tables
How to determine the system of equation of the tables usedFrom the question, we have the following parameters that can be used in our computation:
Each round table = 8 peopleEach rectangular table = 10 peopleTotal number of table = 124Using the above as a guide, we have the following:
8x + 10y = 124
Where
x = round tables
y = rectangular tables
We understand that
He uses 2 more round tables than rectangular tables
This means that
x = y + 2
So, the system of equations is 8x + 10y = 124 and x = y + 2
The graph of the system is attached, where we have x = 8 and y = 6
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imagine that a friend asks you for investment advice. he bas $10,000 to invest and he has about 35 years before he will be ready for his financial goal of early retirement. what types of investments would you recommend to your friend? why? what other investing advice would you give him to help him achieve his financial goals?
When it comes to long-term investment goals like early retirement, it is generally recommended to focus on investments that offer potential growth over an extended period of time. Here are some investment options and advice that could be beneficial for your friend:
Stock market investments: Investing in a diversified portfolio of stocks can provide the potential for long-term growth. Your friend can consider investing in individual stocks or exchange-traded funds (ETFs) that represent a basket of stocks.
Mutual funds: Mutual funds offer diversification by pooling money from multiple investors to invest in a variety of assets. They are managed by professionals who make investment decisions on behalf of the investors.
Index funds: Index funds are a type of mutual fund that aims to replicate the performance of a specific market index, such as the S&P 500. They offer broad market exposure and generally have lower expense ratios compared to actively managed funds.
Retirement accounts: Encourage your friend to take advantage of tax-advantaged retirement accounts like a 401(k) or an individual retirement account (IRA). These accounts provide tax benefits and can help grow savings faster.
Dollar-cost averaging: Advising your friend to invest regularly, regardless of market conditions, through a strategy called dollar-cost averaging can help mitigate the impact of market volatility. By investing a fixed amount at regular intervals, your friend will buy more shares when prices are low and fewer shares when prices are high.
Rebalancing: As time goes on, it's important to periodically review and rebalance the investment portfolio. This involves adjusting the asset allocation to maintain the desired level of risk and return. Regularly rebalancing ensures that the investments stay aligned with the financial goals and risk tolerance.
Emergency fund: Remind your friend about the importance of building an emergency fund with three to six months' worth of living expenses. This will provide a safety net and help prevent the need to tap into long-term investments during unforeseen circumstances.
Seek professional advice: Depending on your friend's knowledge and comfort level with investing, it may be helpful to recommend consulting with a financial advisor who can provide personalized advice based on their specific financial situation and goals.
Remember, investing involves risks, and it's crucial for your friend to carefully evaluate investment options, consider their risk tolerance, and have a long-term perspective. Regularly monitoring and adjusting the investment strategy over time will help ensure progress towards achieving their financial goals.
Find the solution set for the equation. |9x-5|+3=8
Answer: 10/9, 0
Step-by-step explanation:
Sofia and ella are both writing expressions to calculate the surface area of a rectangular prism however they wrote different expressions.
a. examine the expressions below, and determine if they represent the same value. explain why or why not.
sofia's expression
(3 cm x 4 cm ) + (3 cm x 5 cm) + (4 cm x 5 cm) + (4 cm x 5 cm)
ella's expression:
2(3 cm x 4 cm) + 2(3 cm x 5 cm) + 2(4 cm x 5 cm)
b. what fact about the surface area of a rectangular prism does ella's expression show more clearly than sofia's?
a ) The given expression from Sofia and Ella represents two different values.
b.) The fact about the surface area of prism that Ella's expression shows that is not in Sofia's expression is that the expression is according to the formula.
How to determine the surface area of a rectangular prism?To determine the surface area of a rectangle prism, the formula that should be used would be given below:
That is;
Surface area of rectangular prism;
= 2(wl+hl+hw)
when the formula is multiplied out the following is gotten;
= 2wl + 2hl + 2hw
From Ella's expression,
2(3 cm x 4 cm) + 2(3 cm x 5 cm) + 2(4 cm x 5 cm). This follows the order of the formula. And it's final answer = 94cm²
From Sofia's expression,
(3 cm x 4 cm ) + (3 cm x 5 cm) + (4 cm x 5 cm) + (4 cm x 5 cm). This doesn't follow the order of the formula and therefore is not correct and not the same final value with Ella's expression.
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1. Identify the variable that is contained in the expression.
7y+2y² +3
7
x
y
3
The variable that is contained in the given expression is y. Therefore, option C is the correct answer.
The given expression is 7y+2y² +3.
In the given expression there are 3 terms, so it is called trinomial.
In the term 7y, y is the coefficient of 7.
In the term 2y², y² is the coefficient of 2.
3 is the constant term.
Therefore, option C is the correct answer.
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A recipe uses 5 cups of flour to 1-1/10 cups of milk. If you have two cups of flour, how much milk should you use.
The quantity of milk that should be used for the given amount of flour would be = 11/25
How to calculate the amount of milk to use for the recipe?The following steps are being taken to calculate the amount of milk that would be needed for the recipe.
The number of cups of flour for 1⅒ of milk = 5
The quantity of milk needed for 2cups of flour= X
That is;
1⅒milk = 5 flour
X milk = 2 flour
cross multiply;
X milk = 2×1⅒/5
= 11/25
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A TV station is going to air a movie marathon with 11 movies. It will consist of 6 science fiction movies and 5 horror movies. The horror movies will be aired later in the evening. So, all of the horror movies will be aired last (after all of the science fiction movies). In how many ways can the station air the movie marathon?
The solution is: In 86400 ways can the station air the movie marathon.
Given:
Number of total movies = 11
Number of science fiction movie = 6
Number of horror movie = 5
Computation:
Number of science fiction movies way air = 6!
so, we get,
Number of science fiction movies way air = 720
Number of horror movies way air = 5!
so, we have,
Number of horror movies way air = 120
The number of ways the station air the movie marathon is:
720 * 120
=86400
so, we get,
Final answer is 86400 ways.
Hence, The solution is: In 86400 ways can the station air the movie marathon.
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What is the total cost of 20 books at R25 each?
Answer:
R500
Step-by-step explanation:
20 books x R25 each = R500.
I NEED HELP WITH STATISCTICS
Answer:
20cm
Step-by-step explanation:
The scatterplot above displays the relationship between the amount of food hippopotamuses eat per day and their age. Describe and explain any associations and data features on the scatterplot. Then, use the variables on the graph to interpret the relationship that is shown.
The scatter plot shows a [positive linear] association.
How to determine the association of the scatterplotFrom the question, we have the following parameters that can be used in our computation:
The image of the scatter plot
On the scatter plot, we can see that
The points appear to be on a straight line
Also, we can see that
As the x values increases the y values increases
This represents a positive linear association.
Hence, the association is a positive linear association.
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I need help finding the Component form and Magnitude of the vector V.
To find the magnitude of the vector, we can use the Pythagorean theorem: ||V|| = sqrt((5 * √2 / 2)^2 + (5 * √2 / 2)^2) = 5.
To find the component form of a vector, you need to break it down into its x and y components. Let's say our vector V has a magnitude of 5 and is pointing in the direction of 45 degrees (measured from the positive x-axis).
To find its x component, we can use cosine: Vx = V cos(45) = 5 * √2 / 2. To find its y component, we can use sine: Vy = V sin(45) = 5 * √2 / 2. So the component form of vector V is (5 * √2 / 2, 5 * √2 / 2).
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Can someone help me? The velocity of a sound in air is given by the equation v=20 radical273+t where v is the velocity in meters per second and t is the temperature in degrees Celsius find the temperature when the velocity is 348 meters per second round the answer to the nearest degree
when the velocity is 348 meters per second, the approximate temperature is 18 degrees Celsius.
How to find the temperature when the velocity is 348 meters per secondTo find the temperature when the velocity is 348 meters per second, we can substitute the given velocity into the equation v = 20√273 + t and solve for t.
Given: v = 348 meters per second
Substituting this value into the equation:
348 = 20√273 + t
Now, let's solve for t. We can start by isolating the term with t:
t = 348 - 20√273
Calculating the value:
t ≈ 348 - 20 * 16.523
t ≈ 348 - 330.46
t ≈ 17.54
Rounding the answer to the nearest degree, we have:
t ≈ 18 degrees Celsius
Therefore, when the velocity is 348 meters per second, the approximate temperature is 18 degrees Celsius.
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14. The graph below represents the number of books checked out at a library. What
is the constant of proportionality (unit rate per hour)?
The required constant of proportionality is 5.
A graph is shown, we have to find out the constant of proportionality.
In the given case, the constant of proportionality is given by the slope of the curve.
So, the slope is given as,
m = rise/run
From the graph put the value for any point, we choose (2, 10)
So,
m = 10/2
m = 5
Thus, the required constant of proportionality is 5.
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A shirt company has 3 designs each of which can be made with short or long sleeves. There are 6 color patterns available. How many different shirts are available from this company?
Answer:
36 different shirts-----------------
Given that there are 3 designs, 2 sleeve lengths, and 6 color patterns, we can multiply these values together:
3 designs × 2 sleeve lengths × 6 color patterns = 36So, there are 36 different shirts available from this company.
There are 36 different types of shirt available for this company.
Given that;
Number of design Company has = 3
Number of color pattern available = 6
Types of shirt (short or long sleeves) = 2
Now, We need to find the number of different types of shirts are available from this company.
Since, the number of different types of shirts can be calculated by multiplying Number of design Company has with Number of color pattern available also multiplying with Types of shirt (short or long sleeves).
Hence, By framing in equation form we get;
the number of different types of shirts is,
⇒ 3 × 6 × 2
⇒ 36
Therefore, We get;
There are 36 different types of shirt available for this company.
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Harper recorded the heights of plants, in inches, as shown in the table.
nd the mean of the data.
11 12 13 14 15 16 17 18 19 20 21
Heights of Plants (in.)
The mean height of the plants whose heights are shown by the data set is 16 in.
Calculation of meanTo find the mean:
Sum of the values = 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 = 176
Total number of values = 11 (since there are 11 values in the data set)
Mean = Sum of the values / Total number of values
= 176 / 11
= 16
In other words, the mean of the given data set is 16 in and thus, the mean height of the plant is 16 in.
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Help me with this problem please.
The product of matrices A and B are:
[tex]AB = \left[\begin{array}{ccc}-50&7\\44& -10\\\end{array}\right][/tex]
[tex]BA = \left[\begin{array}{ccc}-12&-30\\-16& -48\\\end{array}\right][/tex]
How to find the product of two matrices?A matrix (plural matrices) is a set of numbers arranged in rows and columns so as to form a rectangular array.
The number of rows of a matrix can be determined by counting from top to bottom and the number of columns can be determined by counting from left to right.
The product of matrices A and B are:
AB = A * B
[tex]AB = \left[\begin{array}{ccc}-3&-8\\2& 8\\\end{array}\right] * \left[\begin{array}{ccc}6&3\\4& -2\\\end{array}\right][/tex]
To get the product, multiply each row by the column. That is:
(-3 * 6) + (-8 * 4) = -50
(-3 * 3) + (-8 * (-2)) = 7
(2 * 6) + (8 * 4) = 44
(2 * 3) + (8 * (-2)) = -10
[tex]AB = \left[\begin{array}{ccc}-50&7\\44& -10\\\end{array}\right][/tex]
BA = B * A
[tex]BA = \left[\begin{array}{ccc}6&3\\4& -2\\\end{array}\right] * \left[\begin{array}{ccc}-3&-8\\2& 8\\\end{array}\right][/tex]
To get the product, multiply each row by the column. That is:
(6 * (-3)) + (3 * 2) = -12
(6 * (-8)) + (3 * 8) = -30
(4 * (-3)) + ((-2) * 2) = -16
(4 * (-8)) + ((-2) * 8) = -48
[tex]BA = \left[\begin{array}{ccc}-12&-30\\-16& -48\\\end{array}\right][/tex]
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100 Points! Algebra question. Photo attached. Find the exact value of the expression. Please show as much work as possible. Thank you!
The exact value of the expression tan 15⁰ is determined as 2 - √3.
What is the exact value of the expression?The exact value of the expression is calculated by applying trigonometry identity as shown below;
The trig ratio is simplified as;
SOH CAH TOA;
SOH ----> sin θ = opposite side / hypothenuse side
CAH -----> cos θ = adjacent side / hypothenuse side
TOA ------> tan θ = opposite side / adjacent side
The given trigonometry expression;
tan 15⁰
The expanded trigonometry expression;
tan 15⁰ = tan (60 - 45)
Apply tan addition formula;
tan(A - B) = (tan A - tan B) / (1 + tan A×tan B).
Simplify as follows;
tan (60 - 45) = (tan 60 - tan 45) / ( 1 + tan60 x tan45)
tan 60 = √3
tan 45 = 1
Substitute this value back into the tan formula;
tan (60 - 45) = (√3 - 1 ) / ( 1 + √3)
Rationalize the surd expression as follows;
(√3 - 1 ) / (√3 + 1) x (√3 - 1 ) / (√3 - 1 )
= ( 4 - 2√3) / 2
= 2 - √3
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HELP PLS DUE IN 5 MINUTES!!!!!!!!!!
Answer:
Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.
Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.
Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.
Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.
Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.
Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.
Step-by-step explanation:
The sum of Jerry's and Carrie's ages is 52. Jerry is 4 years older than Carrie. What is Jerry's age?
Answer:
28
Step-by-step explanation:
let's assumed that
x = Jerry's age
y = Carrie's age
if Jerry 4 years older that Carrie
x = y + 4
x + y = 52
(y + 4) + y = 52
2y + 4 = 52
2y = 48
y = 24
x = y + 4
x = 24 + 4
x = 28
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�
<
0
x<0x, is less than, 0.
The graph of the inequality is x < 0 and is plotted
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
A = x is less than 0
So , on simplifying , we get
x < 0
Hence , the inequality of x is all numbers less than 0 without including 0
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Can someone help find the surface area, then round the answer to the nearest whole number please?
The Surface Area of cylinders are: 100 yd² , 264 m², 226 mm²
The Surface Area of Can is 219 cm².
We know the formula for Surface Area of Cylinder
= 2πrh
1. Radius = 2 yd
Height = 8 yd
So, Surface Area of Cylinder
= 2πrh
= 2 x 3.14 x 2 x 8
= 100 yd²
2. Radius = 7 m
Height = 6 m
So, Surface Area of Cylinder
= 2πrh
= 2 x 3.14 x 6 x 7
= 264 m²
3. Radius = 3 mm
Height = 12 mm
So, Surface Area of Cylinder
= 2πrh
= 2 x 3.14 x 3 x 12
= 226 mm²
4. Radius = 3.5 cm
Height = 10 cm
So, Surface Area of Can
= 2πrh
= 2 x 3.14 x 3.5 x 10
= 219 cm²
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p, q and r are prime numbers such that pqr3=270.
Work out the values of p, q and r.
b. Work out the highest common factor of 270 and 105.
The highest common factor of 270 and 105 is 15.
How to find the highest common factorfinding the prime factorization of 270.
The prime factorization of 270 can be written as:
270 = 2 * 3^3 * 5
From the equation pqr^3 = 270, we can see that p, q, and r are prime numbers. Therefore, p must be 2, q must be 3, and r must be 5.
So the values of p, q, and r are:
p = 2
q = 3
r = 5
Moving on to part B, let's work out the highest common factor (HCF) of 270 and 105.
The prime factorization of 270 is:
270 = 2 * 3^3 * 5
The prime factorization of 105 is:
105 = 3 * 5 * 7
To find the HCF, we need to find the common factors and choose the highest one.
The common factors of 270 and 105 are 3 and 5.
The highest common factor of 270 and 105 is 3 * 5 = 15.
Therefore, the highest common factor of 270 and 105 is 15.
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Please help me out on this question
The relative frequency distribution is:
Income ($) | Frequency Relative | Frequency200-300 | 51 | 18.82%301-400 | 58 | 21.40%401-500 | 74 | 27.30%501-600 | 69 | 25.46%More than 600 | 19 | 7.01%The correct option is A.
What is a relative frequency?A relative frequency is the proportion of the total number of outcomes to the number of times a certain value of the data happens in the set of all outcomes.
Relative frequency = frequency of given data/total frequency * 100%The relative frequency distribution of the given data is constructed below:
Total number of students = 51 + 58 + 74 + 69 + 19
Total number of students = 271
The relative frequency of each class interval will be:
200-300; 51/271 * 100% = 18.82%
301-400; 58/271 * 100% = 21.40%
401-500; 74/271 * 100% = 27.30%
501-600; 69/271 * 100% = 25.46%
More than 600; 19/271 * 100% = 7.02%
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You deposit $5000 in an account earning 6% interest compounded monthly. How much will you have in the
account in 15 years?
Answer:
$12270.46----------------------
Use the compound interest formula:
[tex]A = P(1 + r/n)^{nt}[/tex]Where:
A = final amount;P = initial deposit = $5000;r = annual interest rate = 6%;n = number of times the interest is compounded per year = 12;t = time period in years = 15.Plugging in the values, we get:
A = 5000(1 + 0.06/12)¹²*¹⁵ A = 12270.46f(x) = x²/x² 2x+3 find Vertical asymptote find horizontal asymptote
The vertical asymptote of the equation does not exist, the horizontal asymptote of the equation is 1.
To calculate vertical asymptote,
Putting the denominator equal to zero,
x²+2x+3 = 0
Using Quadratic formulae,
b² - 4ac
where,
b = 2
a = 1
c = 3
putting value,
4-12 = -8<0
therefore, the solution is negative
Hence, no vertical asymptote of the given equation exists,
To calculate the horizontal asymptote,
the degrees of the numerator and denominator are the same. we can compare the coefficients of the highest power terms.
The coefficient of x² in the numerator is 1
Hence, the horizontal asymptote is y = 1.
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PLEASE HELP ON VOLUME! ASAP❗️ I BEG❗️❗️❗️
The volume of the cylinder A = 1006.76 m³
The volume of the cylinder B = 2893.82 ft³
The volume of the cylinder C = 2712.96 in³
The volume of the cylinder D = 111.78 in³
The Volume of the cylinder = πr²h
Where r = radius , h = height
A) r = 15/2 = 7.5
h = 5.7
Volume = 3.14 × (7.5)² × 5.7
Volume = 1006.76
B) r = 8
height = 14.4
Volume = 3.14 × (8)² × 14.4
Volume = 2893.82
C) r = 6
h = 24
Volume = 3.14 × (6)² × 24
Volume = 2712.96
D) r = 2
h = 8.9
Volume = 3.14 × (2)² × 8.9
Volume = 111.78
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First to find correct answer will get brainly
The surface area of the dilated solid is 2,880 square units
What is the surface area of the dilated solid?Multiply each side of the shape by 4
Surface area of a rectangular prism = 2(LH + LW + WH)
Where,
Length, L = 8 × 4 = 32 units
Width, W = 6 × 4 = 24 units
Height, H = 3 × 4 = 12 units
Surface area of a rectangular prism = 2(LH + LW + WH)
= 2(32×12 + 32×24 + 24×12)
= 2(384 + 768 + 288)
= 2(1,440)
= 2,880 square units
Therefore, 2,880 square units is the surface area of the solid.
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four students are trying to find the rule that translates point N(-2,-4) to N'(2,4)
The student that gets the rule of the transformation correctly is Raheem
How to determine the student that gets the rule correctlyFrom the question, we have the following parameters that can be used in our computation:
Point N = (-2, -4)
Image of the point N = (2, 4)
This means that
N = (-2, -4)
N' = (2, 4)
From the above, we can see that
N' = -1 * N
This means that
N' = (-2, -4) * -1
So, we have
N' = (-2* -1 , -4 * -1)
So, the rule is (x * -1, y * 1)
Hence, the student that gets the rule correctly is Raheem
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Question
Four students are trying to find the rule that translates point N(-2,-4) to N'(2,4). Each student’s reasoning is shown below.
Raheem: The rule is (x * -1, y * -1)
Casey: The rule is (x + 2, y + 4)
Andrew: The rule is (x + 4, y + 0)
Lo: The rule is (x + 4, y + 8)
Which student is correct?
Raheem
Casey
Andrew
Please help. Any unnecessary answers will be reported.
You are in a competition that involves building card towers. The quickest person to reach 100 stories wins the competition. After reaching 5 stories of cards as shown in the picture below, you needed to use 40 cards.
How many cards will be necessary to build , in a similar way, a tower with 100 stories. Make sure you include work.
Answer:
To determine the number of cards necessary to build a tower with 100 stories, let's analyze the pattern observed in the given information.
From the information provided, we know that building 5 stories of cards required 40 cards. Now, let's examine the relationship between the number of stories and the number of cards used:
Number of stories: 5
Number of cards used: 40
To find the number of cards needed for 100 stories, we can calculate the ratio of the number of stories to the number of cards used for the 5-story tower and then apply that ratio to the target number of stories (100).
Ratio = Number of stories / Number of cards used
Ratio = 5 / 40
Now, we can use this ratio to calculate the number of cards needed for 100 stories:
Number of cards for 100 stories = Ratio * Number of stories
Number of cards for 100 stories = (5 / 40) * 100
Calculating the result:
Number of cards for 100 stories = (0.125) * 100
Number of cards for 100 stories = 12.5
Since it is not possible to use a fraction of a card, we need to round up to the nearest whole number. Therefore, we would need a minimum of 13 cards to build a tower with 100 stories using a similar pattern.
Please note that the actual number of cards required may vary depending on the specific construction technique and stability of the tower.