Answers
The %RE value for the Improved Euler (Heun) method is zero, which means that the method is exact. The %RE value for the Explicit Euler's method is 0.14%, which means that the method is a good approximation.
How to use Explicit and Improved Euler's method?First rewrite the differential equation as follows:
[tex]\frac{dy}{dt } = (\frac{4}{t } - 6t^2)y[/tex]
Now integrate both sides of the equation:
[tex]\int\limits{\frac{dy}{dt}} \, = \int\limits\, (\frac{4}{t } - 6t^2)y dt[/tex]
This gives us:
[tex]y = 4ln(t) - 2t^3 + C[/tex]
where C = arbitrary constant.
Now, use the initial condition y(1) = 2 to find the value of C:
[tex]2 = 4ln(1) - 2(1)^3 + C[/tex]
This gives us C = 6.
Therefore, the solution of the initial-value problem is:
[tex]y = 4ln(t) - 2t^3 + 6[/tex]
Now, use the Explicit Euler's and Improved Euler (Heun) methods to compute y(1.3) numerically:
Explicit Euler's method:
First find the step size h:
h = (1.3 - 1) = 0.3
Now, use the Explicit Euler's method to compute y(1.3) as follows:
[tex]y(1.3) = y(1) + \frac{h}{2} * \frac{dy}{dt}[/tex]
[tex]y(1.3) = 2 + 0.3 * (4ln(1.3) - 2(1.3)^3 + 6)[/tex]
y(1.3) = 2.119
Improved Euler (Heun) method:
First find the step size h:
h = (1.3 - 1) = 0.3
Now, use the Improved Euler (Heun) method to compute y(1.3) as follows:
[tex]y(1.3) = y(1) + \frac{h}{2} * (\frac{dy}{dt} + \frac{dy}{dt'})[/tex]
where dy/dt' is the value of dy/dt evaluated at t = 1.3:
[tex]\frac{dy}{dt'} = 4ln(1.3) - 2(1.3)^3 + 6[/tex]
[tex]y(1.3) = 2 + \frac{0.3}{2} * (4ln(1.3) - 2(1.3)^3 + 6 + 4ln(1.3) - 2(1.3)^3 + 6)[/tex]
y(1.3) = 2.122
Now, calculate the %RE values for both methods:
Explicit Euler's method:
%RE = [tex]\frac{(y(1.3) - y_{true})}{y_{true}} * 100[/tex]
where y_true is the exact value of y(1.3) = 2.122:
%RE = (2.119 - 2.122)/2.122 × 100 = 0.14%
Improved Euler (Heun) method:
%RE = [tex]\frac{(y(1.3) - y_{true})}{y_{true}} * 100[/tex]
%RE = (2.122 - 2.122)/2.122 × 100 = 0%
The %RE value for the Improved Euler (Heun) method is zero, which means that the method is exact. The %RE value for the Explicit Euler's method is 0.14%, which means that the method is a good approximation.
Find out more on Euler (Heun) method here: https://brainly.com/question/16917818
#SPJ1
Related Questions
Review the following diagram. Calculate the area tot he nearest square foot.
Answers
The area for the figure in this problem is given as follows:
A = 1216 ft².
How to calculate the area of a circle?The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:
A = πr²
The figure in this problem is composed as follows:
Rectangle of dimensions 55.75 ft (as each ft has 12 inches, hence 9 inches = 0.75 ft) and 17.5 ft.Circle (composition of two half circles) of radius 17.5/2 = 8.75 ft.Hence the area of the figure is calculated as follows:
A = 55.75 x 17.5 + π x 8.75²
A = 1216 ft².
More can be learned about the area of a circle at https://brainly.com/question/15673093
#SPJ1
Find the distance around each figure. Use 3.14 as an approximation for π
30. The figure is made up of a rectangle and two identical semicircles.
Answers
Answer: 1507.84ft^2
Step-by-step explanation:
Semicircle r = 16ft
Rectangle width = 22ft (because the radius of the semicircle is 16 and there are two of them, 2 x 16 = 32, 54 - 32 = 22)
Rectangle height = 32ft
Area of rectangle:
22 x 32 = 704ft^2
Area of circles:
16^2 x 3.14 = 803.84ft^2
No need to half the area for a semicircle because there are 2 of them
Therefore:
803.84 + 704 = 1507.84ft^2
URGENT
Please help
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.
P(X≥3), n=7, p=0.1
Answers
We can use the binomial probability formula to solve this problem.
P(X≥3) = 1 - P(X<3)
First, we need to find P(X<3), which means finding the probability of getting 0, 1, or 2 successes in 7 trials with a probability of success of 0.1.
P(X<3) = P(X=0) + P(X=1) + P(X=2)
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
P(X=0) = (7 choose 0) * 0.1^0 * 0.9^7 = 0.4783
P(X=1) = (7 choose 1) * 0.1^1 * 0.9^6 = 0.3830
P(X=2) = (7 choose 2) * 0.1^2 * 0.9^5 = 0.1144
P(X<3) = 0.4783 + 0.3830 + 0.1144 = 0.9757
P(X≥3) = 1 - P(X<3) = 1 - 0.9757 = 0.0243
Therefore, the probability of getting at least 3 successes in 7 trials with a probability of success of 0.1 is 0.0243.
4. What is the acceleration of the car in each section?
b
с
d
a
Answers
The acceleration for each section is shown below.
We know the formula
Acceleration = change in haste/ time taken
1. For a
= (12-0)/4
= 12/4
= 3
For b:
= (12-12)/ 5
=0
For c:
= (6-12)/ (2)
= -3
For d:
= (10-6) / 4
= 4/4
= 1
Learn more about Acceleration here:
https://brainly.com/question/2303856
#SPJ1
Find the standard form of the equation of a circle that has a center at (3, -1) and a point on the circle at (5, 2).
Answers
The standard form of the equation of a circle is,
⇒ (x - 3)² + (y + 1)² = 13
Given that;
a circle that has a center at (3, -1) and a point on the circle at (5, 2).
Hence, The value of radius is distance between (3, - 1) and (5, 2).
So, We get;
Radius = √(5 - 3)² + (2 - (- 1))²
Radius = √4 + 9
Radius = √13
So, the standard form of the equation of a circle is,
⇒ (x - 3)² + (y + 1)² = (√13 )²
⇒ (x - 3)² + (y + 1)² = 13
Learn more about the circle visit:
https://brainly.com/question/24810873
#SPJ1
Your credit card has a balance of $5400 and an annual interest rate of 12%. You decide to pay off the balance over three years. If there are no further purchases charged to the card, you must pay $179.36 each month, and you will pay a total interest of $1056.96. Assume you decide to pay off the balance over one year rather than three. How much more must you pay each month and how much less will you pay in total interest?
Answers
1006.56/2=503.28 interest total is 5,903.28
total for paid 491.94 for months
Enter the number that belongs in the green box 11 12 20 please help
Answers
The value of the missing angle obtained using the Cosine Formula is 28.2°
The Cosine FormulaThe Cosine Formula can be expressed thus ;
CosB = (a²+c²-b²) / 2ac
b = 11
a = 12
c = 20
Substituting the values into the equation
CosB = (12² + 20² - 11²) / 2(12×20)
CosB = (144-400-121)/480
CosB = 423/480
CosB = 0.88125
B =
[tex] {Cos}^{ - 1} (0.88125)[/tex]
B = 28.2°
Therefore, the value of the missing angle is 28.2°
Learn more on cosine rule;https://brainly.com/question/23720007
#SPJ1
If a horse can jump a fence that is 4 feet tall, can you jump a fence that is 7/6 of a yard (please explain algebraically how to find this) (this is from unit 8 Algebra 1 if that helps)
Answers
Answer:
3.5 feet
Step-by-step explanation:
To determine whether you can jump a fence that is 7/6 of a yard tall, we need to convert the height to feet and compare it to your own jumping ability.
1 yard = 3 feet
So, 7/6 yards = (7/6) x 3 feet = 3.5 feet
Since a horse can jump a fence that is 4 feet tall and 4 feet is greater than 3.5 feet, it is likely that the horse can jump the fence while it may be more challenging for you to do so.
Concentrated Liquid Plant Food. Bottle contains 1500ml plant food. Instructions to feed each plant - mix 15ml plant food with 1 litre of water Juba uses 15ml of plant food with 1 litre of water to feed 1 plant. She has 9 plants growing in the greenhouse that need feeding with food once a week. She has 11 plants in the vegetable plot that need feeding with food twice a week. How many bottles of plant food does Juba use in 12 weeks??
Answers
She will need to use 4 bottles of plant food in 12 weeks.
To solve this problemTo feed one plant, Juba mixes 15ml of plant food with 1 liter of water. She will therefore require the following to feed nine plants in the greenhouse once a week:
9 plants × 15 ml plant food every week = 135 ml plant food.
To feed 11 plants in the vegetable plot twice a week, she will need:
11 plants x 15 ml plant food x 2 times = 330 ml plant food per week
Juba will therefore require a total of 135 ml + 330 ml = 465 ml of plant food per week.
She will require: 465 ml x 12 weeks = 5580 ml.
Plant food comes in bottles of 1500 ml each. Juba will therefore require:5580 ml ÷ 1500 ml/bottle = 3.72
Therefore, She will need to use 4 bottles of plant food in 12 weeks.
Learn more about multiply here : brainly.com/question/28773316
#SPJ1
Annual high temperatures in a certain location have been tracked for several years. Let � represent the year and � the high temperature. Based on the data shown below, calculate the correlation coefficient (to three decimal places) between � and �. Use your calculator!
x y
1 17.17
2 22.14
3 24.61
4 24.98
5 25.95
6 32.02
7 32.69
8 36.56
9 37.33
10 40.6
11 42.67
12 45.04
13 48.01
14 51.98
�=
Answers
The correlation coefficient between the year and high temperature is approximately 0.9604,
To calculate the correlation coefficient between x (representing the year) and y (representing the high temperature), we can use the following steps:
1. Find the means of x, y, and their products.
- Mean of x, ¯ = (1+2+3+..+14)/14 = 7.5
- Mean of y, ¯ = (17.17+22.14+24.61+...+51.98)/14 ≈ 32.05
- Mean of , ¯ = [(1* 17.17)+(2* 22.14)+...+(14* 51.98)]/14 ≈ 1312.925
2. Calculate the sample standard deviations of x and y.
- Standard deviation of x, = √([∑(−¯)[tex]^2[/tex]]/(−1)) ≈ 4.3205
- Standard deviation of y, = √([∑(−¯)^2]/(−1)) ≈ 10.8629
3. Calculate the covariance of x and y.
- Covariance of x and y, cov(x,y) = [∑(−¯)(−¯)]/(−1) ≈ 51.7874
4. Calculate the correlation coefficient, r.
- Correlation coefficient, r = cov(x,y) / ( ) ≈ 0.9604
Therefore, indicating a strong positive linear relationship between x and y. The value of r being close to 1 suggests that as the year increases, so does the high temperature.
For such more questions on coefficient
https://brainly.com/question/1038771
#SPJ8
In the circle below, UV is a diameter and UX is tangent at U. Suppose m UVW=202 degrees. Find the following.
Answers
Since UX is tangent at U, we know that angle U is a right angle. Therefore, m(UX) = 90 degrees. Using the fact that the sum of angles in a triangle is 180 degrees, we can find that m(VUX) = 90 - (m(UV)/2) = 90 - (180/2) = 0 degrees.
Finally, we can use the fact that angles around a point sum to 360 degrees to find m(WUX):
m(WUX) = 360 - m(UVW) - m(VUX) = 360 - 202 - 0 = <<360-202-0=158>>158 degrees.
Therefore, the bold answer is: 158 degrees.
Peter has money in two savings accounts. one rate is 12% and the other 13%. if he $150 dollars more in the 13% account and the total interest is $54, how much is invested in each savings account?
Answers
Peter invested $138 in the 12% account and $288 in the 13% account.
Let x be the amount invested in the 12% account and y be the amount invested in the 13% account.
We know that the total amount invested is the sum of the two accounts, so: x + y = total amount invested
We also know that Peter has $150 more in the 13% account, so:
y = x + 150
The total interest earned is $54, which can be expressed as:
0.12x + 0.13y = 54
Substituting y with x + 150, we get:
0.12x + 0.13(x + 150) = 54
Simplifying and solving for x, we get:
0.12x + 0.13x + 19.5 = 54
0.25x = 34.5
x = 138
Therefore, Peter invested $138 in the 12% account and $288 in the 13% account.
To learn more about interests click here:
brainly.com/question/25857212
#SPJ1
100 Points! Algebra question. Graph the function. Describe the key characteristics. Only looking for an answer to A. Photo attached. Thank you!
Answers
The graph of function is shown in image.
We have to given that;
The Function is,
f (x) = ∛ (x + 1)
Now, We can find the domain and range as;
Since, We know that the set of all inputs of the function is called Domain of set.
Hence, Domain of function is,
D = (- ∞,∞)
And, Range is,
R = (- ∞,∞)
Here, In the function there is no inflection point in present.
And The end behavior of the function y =∛ (x + 1) is as x approaches negative infinity, y approaches negative infinity, and as x approaches positive infinity, y approaches positive infinity.
Thus, The graph of function is shown in image.
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ1
the area of the base of a rectangular prism is 15m2 and the height measures 5m. what is the volume of the pyramid with the same dimensions as the rectangular prism?
Answers
Answer:
V = 25 cm³
Step-by-step explanation:
the volume (V) of a rectangular prism is calculated as
V = Ah ( A is the area of the base and h the height )
V = 15 × 5 = 75 cm³
the volume of the pyramid is one third the volume of the prism , then
V = 75 × [tex]\frac{1}{3}[/tex] = 25 cm³
For the second week of November, Donald Miller worked 52 hours. Donald earns $13 an hour. His employer pays overtime for all hours worked in excess of 40 hours per week and pays 1.5 times the hourly rate for overtime hours.
Calculate the following for the second week of November (round your responses to the nearest cent if necessary):
Answers
For the second week of November, Donald Miller earned $754.
Let's calculate Donald Miller's earnings for the second week of November using the given information:
1. Determine the number of regular and overtime hours:
Donald worked 52 hours in total, with overtime paid for hours above 40. So he worked 40 regular hours and 12 overtime hours (52 - 40 = 12).
2. Calculate regular pay:
Donald earns $13 per hour for the regular hours. To find his regular pay, multiply the hourly rate by the number of regular hours worked: 40 hours * $13/hour = $520.
3. Calculate overtime pay:
The overtime rate is 1.5 times the hourly rate, so the overtime pay is $13 * 1.5 = $19.5 per hour. To find the total overtime pay, multiply the overtime rate by the number of overtime hours worked: 12 hours * $19.5/hour = $234.
4. Calculate the total pay for the second week of November:
Add the regular pay and overtime pay together: $520 (regular pay) + $234 (overtime pay) = $754.
So, for the second week of November, Donald Miller earned $754 (rounded to the nearest cent if necessary).
For more questions on earning
https://brainly.com/question/30910943
#SPJ11
Find an equation for the perpendicular bisector of the line segment whose endpoints are (7,−1) and (−9,3)
Answers
Answer:
y = 4x + 5--------------------
Find the slope of the line passing through the given points:
m = (3 - (-1)) / (-9 - 7)m = 4/ (-16)m = - 1/4Perpendicular lines have negative- reciprocal slopes, so the perpendicular bisector has a slope of m = 4.
Find the midpoint of the segment with the endpoints (7, - 1) and (- 9,3).
x = (7 - 9)/2 = -2/2 = - 1y = (-1 + 3)/2 = 2/2 = 1Now, we need to find the line with a slope of 4 and passing through the point (- 1, 1). Use point-slope form and find the equation:
y - 1 = 4(x - (-1))y - 1 = 4x + 4y = 4x + 5Solve for n. n/n_1 +2/n+1 =2
Answers
Answer:
Step-by-step explanation:
[tex]\frac{n}{n-1}+\frac{2}{n+1} = 2\\\frac{n^2+n + 2n-2}{n^2-1} = 2\\ n^2+3n-2 = 2n^2-2\\n^2=3n\\n^2-3n= 0\\n(n-3) = 0\\n = 0 \\or\\ n = 3[/tex]
R
S
57°
15
T
find sidelength of RS and RT
Answers
The side lengths of RS and RT are 4 and 5 units
Finding the side lengths of RS and RTFrom the question, we have the following parameters that can be used in our computation:
The right triangles (See attachment)
The side lengths of RS and RT are calculated using
RT = KS = 4
Then we apply the pythagoras theorem for RS as follows
RS² = RK² + KS²
substitute the known values in the above equation, so, we have the following representation
RS² = 3² + 4²
So, we have
RS = 5
Hence, the side lengths of RS and RT are 4 and 5 units
Read more about right triangles at
https://brainly.com/question/2437195
#SPJ1
root((sqrt(7 ^ 4)) ^ 6, 3) * sqrt((root(7 ^ 8, 6)) ^ 3)
Answers
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
Jada and Mackenzie are hosting events that are catered by the same company. Jada plans to have 78 adults and 78 children attend, so the total projected cost of her meals is $3,354. Mackenzie has 58 adults and 76 children on her guest list, so she will pay the caterer $2,800. How much does the caterer charge for each meal?
Every adult's meal costs $____, and every child's meal costs $____.
Answers
Every adult's meal costs $26, and every child's meal costs $17.
How to write system of equation?Let
cost of adults = x
Cost of child = y
78x + 78y = $3,354
58x + 76y = $2,800
From (1)
Divide through by 78
x + y = 43
x = 43 - y
Substitute into (2)
58x + 76y = $2,800
58(43 - y) + 76y = 2800
2494 - 58y + 76y = 2800
- 58y + 76y = 2800 - 2494
18y = 306
y = 306/18
y = 17
Substitute the value of y into
x = 43 - y
x = 43 - 17
x = 26
Therefore, the cost of adults meal is $26 and child's meal is $17
Read more on system of equation:
https://brainly.com/question/13729904
#SPJ1
What is the previous term for: -6, 1, 8, 15...
Answers
Answer:
- 13---------------------
Given sequence:
-6, 1, 8, 15...This is a AP since the difference is common:
1 - (-6) = 7,8 - 1 = 7,15 - 8 = 7.The previous term is going to be 7 less than the subsequent term:
- 6 - 7 = - 13For the right triangles below, find the values of the side lengths h and a.
Round your answers to the nearest tenth.
60°
(a) h=
h
(b) a=
a= 0
30°
5
X
45°
a
7
45%
Answers
(a) The value of h in the right triangle is 5.8.
(b) The value of a in the right triangle is 9.9.
What is a right triangle?Right triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle), i.e, in which two sides are perpendicular.
(a) To find the value of h in the right triangle, we use the formula below
Formula:
h = A/sin∅.................. Equation 1Where:
A = 5∅ = 60°Susbtituet these values into equation 1
h = 5/sin60°h = 5/0.8660h = 5.8(b) Also, to calculate the value of a in the right triangle, we us the formula below
a = B/sinθ................................. Equation 2Where:
B = 7θ = 45°Substitute these values into equation 2
a = 7/sin45°a = 7/0.7071a = 9.9Learn more about right triangle here: https://brainly.com/question/31203729
#SPJ1
A rectangular field is 125 meters long and 85 meters wide.
Give the length and width of another rectangular field that has the same perimeter but a larger area.
Answers
Answer: Length 105 Width 105
There are other possible answers
Step-by-step explanation:
Perimeter of the field is = (2)*(125) + (2)*(85) = 420
Area of the field is = (85)*(125) = 10,625
You need to find two other numbers that when doubled add up to 420, and when multiplied together are greater than 10,625. Guess and check can work, however making a square will yield the highest results, you can find the dimensions of said square by dividing 420 by 4 to get 105.
(2)*(105) + (2)*(105) = 420
(105)(105) = 11,025
420 = 420
11,025 > 10,625
6. Tell whether the sequence is arithmetic. If it is, what is the common difference?
-19, -11, -3, 5,...
Oyes; 5
Oyes; 6
Oyes; 8
O no
Answers
The sequence -19, -11, -3, 5,... is arithmetic with a common difference of 8.
An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a constant value, called the common difference (d), to the preceding term. To determine if the given sequence is arithmetic, we can find the differences between consecutive terms.
The difference between the second and first terms is 11 - (-19) = 30, and the difference between the third and second terms is -3 - (-11) = 8. The difference between the fourth and third terms is 5 - (-3) = 8. Since the differences between consecutive terms are the same, the sequence is arithmetic.
The common difference can be found by subtracting any term from the term that follows it. For example, the common difference can be obtained by subtracting the second term (-11) from the third term (-3), or by subtracting the third term (-3) from the fourth term (5).
In both cases, we get a common difference of 8. Therefore, the common difference of the given sequence is 8.
For more information regarding arithmetic sequence, click below:
https://brainly.com/question/28583639#
19. A bag contains 5 red marbles, 8 white marbles, and
7 green marbles. What is the probability of randomly selecting
a white marble, replacing it, then randomly selecting another
white marble?
30 Ton
re numbered from 1 to 10 and placed in a box.
Answers
The required probability of randomly selecting a white marble, replacing it, then randomly selecting another white marble is 4/25.
The probability of randomly selecting a white marble from the bag is 8/20, or 2/5, since there are 8 white marbles out of a total of 20 marbles (5 red, 8 white, and 7 green).
After replacing the first marble, there are still 8 white marbles and a total of 20 marbles in the bag. Therefore, the probability of randomly selecting another white marble is also 2/5.
To find the probability of both events happening (selecting a white marble, replacing it, and then selecting another white marble), we multiply the probabilities of the two events:
The probability of selecting a white marble and replacing it, then selecting another white marble = (2/5) x (2/5) = 4/25
Therefore, the probability of randomly selecting a white marble, replacing it, then randomly selecting another white marble is 4/25.
Learn more about probability here:
https://brainly.com/question/32004014
#SPJ1
Figure A is a scale image of figure A. Enter the scale factor applied to figure A to produce figure B
Answers
The scale factor here is 2.1.
To calculate the scale factor, you need two corresponding measurements from two similar objects or figures. The scale factor is the ratio of the corresponding lengths or dimensions between the two objects.
Now, the scale factor is
= 12.5 / 5
= 125/50
= 21/10
= 2.1 : 1
Thus, the scale factor here is 2.1.
Learn more about Scale Factor here:
https://brainly.com/question/30215044
#SPJ1
Urgent!!!!!
Help please I have to answer these questions using the graph.
Answers
a.) The concentration of the drug after 8 hours in the blood would be = 24 mg/L.
b.) The concentration increases over the interval of 0-2 hours.
c.) The maximum concentration of the drug is at 2 hours after intake which is 64 mg/L.
d.) After the drug reaches its maximum concentration, it will take 8 hours to decrease to 16mg/L.
e.) The concentration of the drug in the blood after one week will be zero.
f.) In summary, the concentration of the drug in the blood stream after the first 20 hours will be done below.
What is the drug blood concentration?Drug blood concentration is defined as the amount of drug that is absorbed into the blood stream that contains a particular quantity per liter of blood.
The graph above represents the relationship between the concentration of a drug in the blood and the time it was taken.
For a ) The concentration of the drug after 8 hours in the blood would be = 24 mg/L.
For b.) The concentration increases over the interval of 0-2 hours.
For c.) The maximum concentration of the drug is at 2 hours after intake which is 64 mg/L.
For d.) After the drug reaches its maximum concentration, it will take 8 hours to decrease to 16mg/L.
For e.) The concentration of the drug in the blood after one week will be zero.
For f.) In summary, the concentration of the drug in the blood stream after the first 20 hours is not the same as observed in the graph above. There is a spike increase after the first two hours of intake after which a decrease in concentration was observed through our the remaining hours.
Learn more about graph here:
https://brainly.com/question/25799000
#SPJ1
4x3 = -5x - 21 solve for x
Answers
To solve for x in the equation 4x3 = -5x - 21, we can follow these steps:
1. Move all the terms containing x to one side of the equation, and move the constant term to the other side. We can do this by adding 5x to both sides and then adding 21 to both sides:
4x3 + 5x = -21
2. Factor out x from the left-hand side of the equation:
x(4x2 + 5) = -21
3. Divide both sides by (4x2 + 5):
x = -21 / (4x2 + 5)
So the solution for x is x = -21 / (4x2 + 5). Note that this is a rational function, which means that the value of x depends on the value of the variable x. This equation has no real solutions because the denominator is always positive, and the numerator is negative.
5
Functional Volume Questions ACCESS MATHS
1) James has a swimming pool in the shape of a prism.
Diagram NOT
18m
Accurately drawn
3m
6m
1m
топол хочите
9m
The swimming pool is empty.
It is filled with water at a constant rate.
It takes 4 hours for the water to be 2 meters deep from the deepest
point.
a) How long will it take to completely fill the pool?
Give your answer in hours.
(1m³ = 1000litres)
You must show all your working.
Answers
The amount of time it will take to completely fill the pool would be = 18 hours.
How to calculate the amount of time taken to fill the pool?To determine the amount of time it will take to fill the pool, the volume of the pool is first calculated by dividing the figure to obtain two regular shapes of a trapezoidal prism and a square prism.
The volume of a trapezoidal prism = 1/2(a+b)×h×l
where;
a = 3m
b = 1m
h = 18-6 = 12m
l = 9m
Volume of the trapezoidal prism = 1/2(3+1)×12×9
= 4×12×9 = 432m³
Volume of square prism = length×width×height
where;
length = 6m
width = 9m
height = 1 m
Volume = 6×9×1 = 54m³
Therefore the volume of the pool = 432+54 = 486m³
If 4 hours = 2 m up from the deepest part
The volume filled for 4 hours = 1/2×2×12×9 = 108m³
If 4 hours = 108
X hours = 486
make X the subject of formula;
X = 4×486/108
= 1944/108
= 18 hours.
Learn more about volume here:
https://brainly.com/question/27710307
#SPJ1
Natalie borrowed money from her parents to pay for a trip.
Natalie will pay her parents in equal amounts every week until she pays back the entire amount she borrowed.
The table below shows the amount of money Natalie still owes her parents at the end of every two weeks for the first eight weeks.
Answers
Natalie owes $18 at the end of every two weeks.
To find the weekly payment amount, we can use the given data to write a system of equations. Let's assume that Natalie borrowed x amount from her parents.
From the given table, we can write the following equations:
At the end of 2 weeks, Natalie still owes:
x - 2d = 180 ...(1)
At the end of 4 weeks, Natalie still owes:
x - 4d = 144 ...(2)
Solving equations (1) and (2), we get:
2d = 36
d = 18
Therefore, Natalie owes $18 at the end of every two weeks.
Learn more about equation here:
https://brainly.com/question/29657983
#SPJ1
