Applying Euler's method:
Let f(x, y) = 2x - 3y + 1, and consider the following recurrence relations:
[tex]\begin{cases}x_0=1\\x_n=x_{n-1}+h&\text{for }n\ge1\end{cases}[/tex]
[tex]\begin{cases}y_0=5\\y_n=y_{n-1}+f(x_n,y_n)h&\text{for }n\ge1\end{cases}[/tex]
For step size h = 0.1, we can approximate y (1.2) with just 2 steps:
[tex]\begin{cases}x_0=1\\y_0=5\end{cases}\implies y_1=5+f(1,5)\times0.1=3.8[/tex]
[tex]\begin{cases}x_1=1+0.1=1.1\\y_1=3.8\end{cases}\implies y_2=3.8+f(1.1,3.8)\times0.1=\boxed{2.98}[/tex]
For step size h = 0.05, we need 4 steps:
[tex]\begin{cases}x_0=1\\y_0=5\end{cases}\implies y_1=5+f(1,5)\times0.05=4.4[/tex]
[tex]\begin{cases}x_1=1+0.05=1.05\\y_1=4.4\end{cases}\implies y_2=4.4+f(1.05,4.4)\times0.05=3.895[/tex]
[tex]\begin{cases}x_2=1.05+0.05=1.1\\y_2=3.895\end{cases}\implies y_3=3.895+f(1.1,3.895)\times0.05=3.47075[/tex]
[tex]\begin{cases}x_3=1.1+0.05=1.15\\y_3=3.47075\end{cases}\implies y_4=3.47075+f(1.15,3.47075)\times0.05\approx\boxed{3.1151375}[/tex]
(Compare these to the value of y (1.2) found using the exact solution to the differential equation, about 3.22832.)
3. If a week is 7 days, what fraction of a week is 2 days?
In a room at a museum, we want to tile the floor. If the floor measures 15 feet by 55 feet, what is the largest-size square tile that we can use to tile the floor without having to cut tiles?
A) 11 ft by 11 ft
B) 5 ft by 11 ft
C) 5 ft by 3 ft
D) 3 ft by 3 ft
E) 11 ft by 3 ft
F) 5 ft by 5 ft
Answer:
B. 5 foot by 11 foot
the numbers have to be divisible in both directions.
11x11 doesn't work, because at 15 feet wide one tile isn't wide enough, and 2 is too wide.
5x11 works- 3x5= 15 and 11x5=55. you'd use 15 tiles.
the rest are all smaller.
Genesis has an action figure collection. She keeps some in a display case and the rest on the wall. 253 of her action figures are on the wall, and 45% of her action figures are in the display case. What is the total number of action figures in Genesis's collection?
Answer:460
Step-by-step explanation:on delta math
The total number of action figures in Genesis's collection will be 460.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that, Genesis offers a variety of action figures. She hangs the remainder and keeps some in a display cabinet. 253 of her action figures are hung on the wall, and the display case holds 45% of her collection.
The obtained expression for the given condition,
=253 / (1-0.45)
=253/0.55
=25300/55
=460
Thus, the total number of action figures in Genesis's collection will be 460.
Learn more about the arithmetic operation here:
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Fine the slope of the line through (20, -8), (9, -8)
Answer: The slope is 0
Find the vertex of the function. ill mark brainlist
Answer:
(2,-9)
Step-by-step explanation:
PLEASE HELP DUE TODAYYYY ..100 PTS!
Answer:
i got 65.8/9. i hope this is correct , if not, i wish you the besy<3
Answer:
62.7
Step-by-step explanation:
Sarah makes $3000 contributions at the end of each half-year to a retirement account for 8 years. For the next 20 years, she makes no additional contributions and no withdrawals. If the account earns 7.5%, compounded semi-annually, find the value of the account after the 28 years.
(b) If the above account is used to set up an annuity that pays her an amount at the beginning of each 6-month period for the next 20 years, how much will each payment be?
Answer:
I think its aa.... I think its aa.... Carrot
Step-by-step explanation:
100 POINTS!!!!!
Two cylinders are similar with diameters 6 in and 9 in.
a. Find the ratio of the circumference of their bases
b. Find the ratio of the surface areas.
c. Find the ratio of the volumes.
Answer:
a. Ratio of their circumference = 2:3
b. The ratio of their surface areas = 2:3
c. The ratio of their volume = 4:9
Step-by-step explanation:
Let the cylinders be labelled as A and B respectively.
Diameter of cylinder A = 6 in,
its radius = [tex]\frac{diameter}{2}[/tex]
= [tex]\frac{6}{2}[/tex] = 3 in
Diameter of cylinder B = 9 in,
its radius = [tex]\frac{diameter}{2}[/tex]
= [tex]\frac{9}{2}[/tex] = 4.5 in
Thus,
a. circumference of a circle = 2[tex]\pi[/tex]r
Circumference of cylinder A = 2[tex]\pi[/tex]r
= 2 x [tex]\pi[/tex] x 3
= 6[tex]\pi[/tex] in
Circumference of cylinder B = 2[tex]\pi[/tex]r
= 2 x [tex]\pi[/tex] x 4.5
= 9[tex]\pi[/tex]
Ratio of their circumference = [tex]\frac{circumference of cylinder A}{circumference of cylinder B}[/tex]
= [tex]\frac{6\pi }{9\pi }[/tex]
= 2:3
b. The surface area of a cylinder = 2[tex]\pi[/tex]rh
the surface area of cylinder A = 2[tex]\pi[/tex]rh
= 6[tex]\pi[/tex]h
the surface area of cylinder B = 2[tex]\pi[/tex]rh
= 9[tex]\pi[/tex]h
The ratio of their surface areas = [tex]\frac{surface area of cylinder A}{surface area of cylinder B}[/tex]
= [tex]\frac{6\pi h}{9\pi h}[/tex]
= 2:3
c. Volume of a cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h
volume of cylinder A = [tex]\pi[/tex][tex]r^{2}[/tex]h
= [tex]\pi[/tex] x [tex]3^{2}[/tex] x h
= 9[tex]\pi[/tex]h
volume of cylinder b = [tex]\pi[/tex][tex]r^{2}[/tex]h
= [tex]\pi[/tex] x [tex]4.5^{2}[/tex] x h
= 20.25[tex]\pi[/tex]h
The ratio of their volume = [tex]\frac{volume of cylinder A}{volume of cylinder B}[/tex]
= [tex]\frac{9\pi h}{20.25\pi h}[/tex]
= 4:9
d=6in,9in
r=3in,4.5in
circumference:-
[tex]\\ \sf\longmapsto \dfrac{2\pi r_1}{2\pi r_2}[/tex]
[tex]\\ \sf\longmapsto \dfrac{6\pi}{9\pi}[/tex]
[tex]\\ \sf\longmapsto \dfrac{2}{3}[/tex]
[tex]\\ \sf\longmapsto 2:3[/tex]
LSA:-
[tex]\\ \sf\longmapsto \dfrac{2\pi r_1h}{2\pi r_2h}[/tex]
[tex]\\ \sf\longmapsto \dfrac{6}{9}[/tex]
[tex]\\ \sf\longmapsto \dfrac{2}{3}[/tex]
[tex]\\ \sf\longmapsto 2:3[/tex]
TSA
[tex]\\ \sf\longmapsto \dfrac{2\pi r_1(h+r_1)}{2\pi r_2(h+r_2)}[/tex]
[tex]\\ \sf\longmapsto \dfrac{6(h+6)}{9(h+9)}[/tex]
[tex]\\ \sf\longmapsto \dfrac{6h+36}{9h+81}[/tex]
[tex]\\ \sf\longmapsto \dfrac{h(6+36)}{h(9+81)}[/tex]
[tex]\\ \sf\longmapsto \dfrac{42}{90}[/tex]
[tex]\\ \sf\longmapsto \dfrac{7}{15}[/tex]
[tex]\\ \sf\longmapsto 7:15[/tex]
Volume:-
[tex]\\ \sf\longmapsto \dfrac{\pi r_1^2h}{\pi r_2^2h}[/tex]
[tex]\\ \sf\longmapsto \dfrac{3^2}{4.5^2}[/tex]
[tex]\\ \sf\longmapsto \dfrac{9}{20.25}[/tex]
[tex]\\ \sf\longmapsto 4:9[/tex]
Which three lengths can NOT be the lengths of the sides of a triangle?
A.23 m, 17 m, 14 m
B. 5m, 7m, 8m
C. 21m, 6m, 10m
D.11 m, 11 m, 12 m
Answer:
C. 21m, 6cm, 10m
Step-by-step explanation:
Help please !! due in 1 hour
3^2x+1 +9 = 3^x+3 +3^3
Answer:
-4
Step-by-step explanation:
Since they all have the same base;
2x+1+9=x+3+32x-x=3+3-1-9x=6-1-9x=6-10x=-4John wants to earn $30. He already has $12. What percent is he at his goal?
Answer:
40%
Step-by-step explanation:
40%
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hope it helps
I don't really know how to explain sorry
please help me i really need help please
Answer:
d
Step-by-step explanation:
helpp me plzzzzzz plzz
Answer:
I would help but I don’t know what all of those symbols are.
What is the Median of this data set: 6, 10, 12, 5, 16, 11.
Answer: 10.5
Step-by-step explanation:
The median is the middle number in a data set, so in this set 5,6,10,11,12,16
the mean of 10 and 11 would be the median.
Helen makes 6 friendship bracelets . She gave 1/3 of the bracelets to sami which expression can i use
Answer:
6 x 1/3 = 2
Step-by-step explanation:
What is the area of the triangle?
what's the answer! Consider having a personal loan that spans 5 years. The loan was only taken out for $6000, but the interest rate was a higher fixed percentage of 5.99%. How much interest will you have paid after it is paid off?
Answer: $179.70
Step-by-step explanation:
The simple interest will be:
= (Principal × Rate × Time) / 100
= ($6000 × 5.99% × 5) / 10
= ($6000 × 0.0599 × 5) / 10
= $1797 / 10
= $179.70
Therefore, the total interest on the loan is $179.70
What is the answer and the work i have to do to get to it
Answer:
B
Step-by-step explanation:
someone help meee nowww pleasee
Answer:
149.28 m²
Step-by-step explanation:
Bottom and two sides of the rectangle: 3x4x6=72
Two square ends of the rectangle: 2x4x4=32
Two triangular sides of the prism: 2x1/2x2x6=12
Back of prism: 2x4=8
Top of prism: 4x6.32=25.28
72+32+12+8+25.28=149.28
Find the length of the side and area of the square who perimeter is given below
(a) 44 cm
Answer:
Side length:11
Area: 121
Step-by-step explanation:
if its a square all sides should be equal so you can divide 44 by 4 which gives you 11 and then to find area you just multiply the two sides together which would be 11x11 and that equals 121
I'm pretty sure this is what it would be but it also seems over simplified and i might be missing something?
Every Month the average number of books borrowed by a class of 24 from a library is 4.What is the total number of books borowed by the class for the month
Answer:
96
Step-by-step explanation:
24*4=96
The following tables represent a function and its inverse.
Compare the functions.
h(x)
Which statements describe the functions? Check all
that apply.
х
-4
-2
0
N
4
y
-6
1
6
11
16
The domain of h-1(x) is the range of h(x).
The range of h-l(x) is the range of h(x).
The x-intercept of h-1(x) is the x-intercept of h(x).
The x-coordinate of the x-intercept of h-1(x) is the y-
coordinate of the y-intercept of h(x).
The maximum of h(x) is the largest x-value of
h-4(x).
х
1
6.
11
16
y
-4
-2
0
2
4.
Intro
Answer:
These are all that apply
- The domain of h-1(x) is the rand of h(x)
- The x-coordinate of the x-intercept of h-1(x) is the y- coordinate of the y-intercept of h(x).
- The maximum of h(x) is the largest x-value of h-4(x).
Step-by-step explanation:
The correct statements describing the given functions are -
The domain of h⁻¹(x) is the range of h(x).The x-coordinate of the x-intercept of h⁻¹(x) is the y- coordinate of the y-intercept of h(x).The maximum of h(x) is the largest x-value of h⁻¹(x).What is function?A function is a relation between a dependent and independent variable. We can write the examples of functions as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
Given are the functions. It is asked to identify the statements that describe these functions.
The given functions are h(x) and its inverse h⁻¹(x). For the given functions, as we can see in the table, the following statements are true -
The domain of h⁻¹(x) is the range of h(x).The x-coordinate of the x-intercept of h⁻¹(x) is the y- coordinate of the y-intercept of h(x).The maximum of h(x) is the largest x-value of h⁻¹(x).Therefore, the correct statements describing the given functions are -
The domain of h⁻¹(x) is the range of h(x).The x-coordinate of the x-intercept of h⁻¹(x) is the y- coordinate of the y-intercept of h(x).The maximum of h(x) is the largest x-value of h⁻¹(x).To solve more questions on functions, visit the link below-
https://brainly.com/question/30194223
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The straight-line distance between the points is ___ units, rounded to the nearest tenth.
Answer:
The straight-line distance between the points is approximately 8.6.
Step-by-step explanation:
The straight-line distance ([tex]d[/tex]) between the points is determined by the following Pythagorean identity:
[tex]d = \sqrt{x^{2}+y^{2}}[/tex] (1)
Where:
[tex]x[/tex] - Horizontal distance between the points.
[tex]y[/tex] - Vertical distance between the points.
Let consider that each square has a distance of 1 unit. If we know that [tex]x = 5[/tex] and [tex]y = -7[/tex], then the straight-line distance is:
[tex]d = \sqrt{5^{2}+(-7)^{2}}[/tex]
[tex]d \approx 8.6[/tex]
The straight-line distance between the points is approximately 8.6.
Which expression below is equivalent to -2(5x-8)?
-10x+16
-10x-8
3x-10
3x-8
-2(5x-8)
-10x+16
So A.
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hope it helps
Darren had 20 minutes to do a three-problem quiz. He spent 11
7
10
minutes on question A and 4
2
5
minutes on question B. How much time did he have left for question C?
Answer:
He had 5 minutes left for question C.
Step-by-step explanation:
20 minutes to do the quiz.
He spent:
11 minutes on question A
4 minutes of question B.
So, for the first 2 questions, he used 15 minutes.
How much time did he have left for question C?
Total of 20 minutes, in the first two questions he used 15. So
20 - 15 = 5
He had 5 minutes left for question C.
Activity
Part A
Match the factors affecting cost to their definitions. Write the name of the factor next to its definition
Answer:
cost of materials - the value of all things needed to create the good or service
opportunity cost - the value of a product given up to produce or obtain another product
fixed cost - costs that are not affected by the level of production
sunk cost - past costs that cannot be recovered
marginal cost - change in total cost that arises when the quantity produced changes by one unit
Step-by-step explanation:
Answer:
cost of materials: the value of all things needed to create the good or service
opportunity cost: the value of a product given up to produce or obtain another product
fixed cost: costs that are not affected by the level of production
sunk cost: past costs that cannot be recovered
marginal cost: change in total cost that arises when the quantity produced changes by one unit
giving brainliest *easy*
Step-by-step explanation:
The formula is given by :
[tex]s=\dfrac{m}{360}\times 2\pi r[/tex]
We have,
m = 19° and d = 9 cm
So,
[tex]s=\dfrac{19}{360}\times 2\pi \times \dfrac{9}{2}\\\\s=1.49[/tex]
Hence, this is the required soltion.
(2,2) and (2,-2) slope?
Answer:
Undefined.
Step-by-step explanation:
Slope is equal to the change in y over the change is x, or rise over run.
[tex]m=\frac{change in y }{ change in x}[/tex]
The change in x is equal to the difference in x-coordinates, and the chnage in y is equal to the difference in y-coordinates.
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Substitute in the values of x and y into the equation to find the slope.
[tex]m= \frac{-2-(2)}{2-(2)}[/tex]
Simplify it. since -2-(2) and 2-(2) = nothing, the Slope is Undefined.
Hence, the slope is Undefined.
Answer:
Undefined
Step-by-step explanation:
Hope this helps
Dr. Toliver has 6 fossils.
Dr. Cook has 5 times as many fossils as Dr. Maranan.
They have 90 fossils altogether. How many fossils does Dr. Maranan have?
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(hp
Answer:
dude 30 fossils are left
Step-by-step explanation: