The solution to the given system of differential equations is x(t) = t + C₁ and y(t) = t²/2 + C₁t + C₂.
1. dx/dt = 2x - y
2. dy/dt = x
Substituting y = -dx/dt into the second equation,
dy/dt = x - t
-d²x/dt² = x - t
Now, assume a particular solution of the form x = At + B,
where A and B are constants.
Substituting this into the differential equation,
-A = At + B - t.
Equating the coefficients of t on both sides,
A = -1 and B = 0.
Thus, the particular solution is x = -t.
Now, integrating dx/dt = -yt,
x = -yt + C₁
Finally, substituting x into the particular solution x = -t,
-t = -yt + C₁.
Solving for y, obtain y = t²/2 + C₁t + C₂.
Therefore, the solution is x(t) = t + C₁ and y(t) = t²/2 + C₁t + C₂.
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questions attached please help me
Answer:
Step-by-step explanation:
Miko and Raj get the same salary. Every month Miko saves
9/11 of her salary while Raj saves
7/9 of his salary. Every year Miko saves $1584 more than Raj. Find the monthly salary of Miko.
Answer:
Step-by-step explanation:
The salaries are the same. Only the fraction of how much is saved is quite different.
Equation
x ( 9/11 - 7/9) = 1584
Explanation: The salary amount is x. The fractional amounts saved are also given. You have to take the difference because one of the people saves more than the other.
The amount that is more is 1584.
Solution
9/11 = 0.8182
7/9 = 0.7778
9/11 - 7/9 = 0.8182 - 0.7778 = 0.0404
Put that into the equation.
x(0.0404) = 1584 Divide by 0.0404)
x(0.0404) = 1584/0.0404
answer:x = 39204
A software designer is mapping the streets for a new racing game. all of the streets are depicted as either perpendicular or parallel lines. the equation of the lane passing through a and b is -7x 3y = -21.5. what is the equation of the central street pq? a. -3x 4y = 3 b. -1.5x − 3.5y = -31.5 c. 2x y = 20 d. -2.25x y = -9.75
The equation of the central street PQ is -1.5x - 3.5y = -31.5 option (b) is correct.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
We have a straight line:
[tex]-7x+3y=-21.5[/tex]
Convert it to the general form given below:
[tex]\rm y=mx+c[/tex]
[tex]\rm 3y=-21.5+7x\\\\ \rm y = \frac{-21.5}{3}+\frac{7}{3}x[/tex] or
[tex]\rm y = \frac{7}{3}x-\frac{21.5}{3}[/tex]
[tex]m = \frac{7}{3}[/tex] (Slope of AB line)
For the slope(m') of the PQ line:
[tex]\rm m'=-\frac{1}{m}[/tex] ( because AB and PQ are perpendicular to each other)
[tex]\rm m' = -\frac{3}{7}[/tex]
We know the:
[tex]\rm (y-y')=m'(x-x')[/tex]
Where (x', y') = (7, 6), we get:
[tex]\rm (y-6)=-\frac{3}{7} (x-7)[/tex]
[tex]\rm 7(y-6)=-3 (x-7)\\\\\rm 7y-42= -3x+21\\\\\rm 7y= -3x+21+42\\\\\rm 3x+7y=63[/tex]
[tex]\rm -1.5x-3.5y=-31.5[/tex] (multiply by -1/2 on both sides)
Thus, the equation of the central street PQ is -1.5x - 3.5y = -31.5
Learn more about the straight line.
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Each pair of shapes below are similar. Solve for each variable. Show all work necessary to justify your answer. 26 11 6 18 X = 21 a = 13 b 11 22
Answer:
x = 21
a= 22
b = 13
Step-by-step explanation:
18 / 6 = 3
3 * 7 =21
20 / 10 = 2
2 * 11 = 22
10 / 20 = 0.5
26 * 0.5 = 13
i need help with this
Answer:
Answer: (b) 5.
Step-by-step explanation:
Simple and best practice solution for (c-5)d=2 equation. ... If it's not what You are looking for type in the equation solver your own equation and let us solve it. ... 2 + 5d cd = 2 + 5d Divide each side by 'd'. c = 2d-1 + 5 Simplifying c = 2d-1 + 5 Reorder ... 11/4-t8 | | (3x^2+5x+2)+(4x^2+3x+2)= | | 4Y+7-Y=4+2Y-8 | | 10x+190=360 ...
For example, let's say with have the equation x+5 ... If we evaluate the same expression when x=10, we get 3(10)+7=30+7=37. Here's a variable expression with two variables: 3x−2y ... How do you express the phrase "a number z divided by 19" as an algebraic expression? ... How do you simplify 11c+5d−9c−9d?Let the number of cows be x and their legs be 4x. ... or, x = 7 [dividing by 2 on both sides]. ... The roots of the equation ax2 + bx + c = 0 will be reciprocal if: ... A circle of radius 10 inches has its center at the vertex C of an equilateral triangle ABC ... (a) 15, (b) 30, (c) 60, (d) 90, (e) 120. Circle Problem Answers. Answer: (b) 5.
Please help me this is due in 20 mins
Answer:
35cm
120cm^2
Step-by-step explanation:
Answer:
1. The perimeter of figure a is 36 cm.
2. The area of figure a is 60 cm².
3. The perimeter of figure b is 14.25 in.
4. The area of figure b is 7.031 in².
If it's wrong tell me
Use the graph that shows the solution to f(x)=g(x).
f(x)=−(x+2)(x−2)
g(x)=2|x+2|
What is the solution to f(x)=g(x)?
Select each correct answer.
−2
0
2
4
Answer: -2, 0
Step-by-step explanation:
The graph this represents this system is the second graph since the vertex of the absolute value function is at x=-2.
So, to find the solutions, we can find the intersection points. These are at x=-2 and x=0.
A rectangle is inscribed in a circle of radius r. What is the maximum area of the rectangle
Use the right triangular prism to find the total surface area of the prism. Leave label off answer.
Step-by-step explanation:
the total surface area is the sum of the 5 individual areas in the surface :
2 triangle sides (left and right).
1 back rectangle side
1 rectangle floor
1 inclined rectangle front side
to get the length of the baseline (Hypotenuse) of the right-angled triangles on the side. we use Pythagoras
c² = a² + b²
where c is the Hypotenuse (the side opposite of the 90° angle).
c² = 3² + 4² = 9 + 16 = 25
c = 5
so, now, we have everything we need.
the area of a triangle side (since it is right-angled) :
4×3/2 = 6
2 sides, that makes 12
the area of the back side
6×3 = 18
the area of the floor
6×4 = 24
the area of the inclined front side
6×5 = 30
so, the total surface area is
12+18+24+30 = 84
Y is the midpoint of XZ and W is the midpoint of VX.
If VZ=s+52 and WY=7s, what is the value of s?
Answer:
4
Step-by-step explanation:
By the triangle midsegment theorem, 2(WY)=VZ.
So, 2(7s)=s+52, meaning s=4.
Which statement about a rotation is true? A. Rotating a right trapezoid around its vertical axis will form a cone. B. Rotating a square around its vertical axis will form a sphere. C. Rotating a right triangle around its vertical axis will form a cone. D. Rotating a rectangle around its vertical axis will form a sphere.
Rotating a shape involves moving it in a circular way around its axis
The true statement about the rotation is (c) Rotating a right triangle around its vertical axis will form a cone.
How to determine the rotation?When a two-dimensional shape such as triangles, trapezoid, square, rectangles, etc are rotated about their axes, the new shape formed is a three-dimensional shape
As a general rule, the rotation of a right triangle around its axis would form a cone.
Hence, the true statement about the rotation is (c)
Read more about rotation at:
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Answer: C. Rotating a right triangle around its vertical axis will form a cone.
Step-by-step explanation: CORRECT on Plato/Edmentum.
Type SSS, SAS, ASA, AAS, or HL to
justify why the TWO LARGER triangles are congruent.
m
BE = BC
Answer: AAS
Step-by-step explanation:
3/4 plus 4/5 subtract 7/10
Hey There! Happy to Help! Your answer is below.
Answer:
17/20 = 0.85000
Step 1:
Simplify 7/10⇒ (3/4 + 4/5) - 7/10
Step 2:
Simplify 4/5⇒ (3/4 + 4/5) - 7/10
Step 3:
Simplify 3/4⇒(3/4 + 4/5) - 7/10
Step 4:
Calculating the Least Common Multiple⇒ Find the Least Common Multiple
The left denominator is : 4 The right denominator is : 5Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 2 0 2
5 0 1 1
Product of all
Prime Factors 4 5 20
Least Common Multiple:
20
Calculating Multipliers⇒ Calculate multipliers for the two fractions
⇒ Denote the Least Common Multiple by L.C.M
⇒ Denote the Left Multiplier by Left_M
⇒ Denote the Right Multiplier by Right_M
⇒ Denote the Left Deniminator by L_Deno
⇒ Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 5 Right_M = L.C.M / R_Deno = 4Making Equivalent Fractions⇒ Rewrite the two fractions into equivalent fractions
⇒ Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. 3 • 5
----------------------------- = ------------
L.C.M 20
R. Mult. • R. Num. 4 • 4
----------------------------- = -------
L.C.M 20
Adding fractions that have a common denominatorAdding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
3 • 5 + 4 • 4 31
------------------ = ---
20 20
Equation at the end of step 4:
31 7
---- - ----
20 10
Step 5:
Calculating the Least Common Multiple :Find the Least Common Multiple
The left denominator is : 20
The right denominator is : 10
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 2 1 2
5 1 1 1
Product of all
Prime Factors 20 10 20
Least Common Multiple:
20
Calculating Multipliers :
Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 1
Right_M = L.C.M / R_Deno = 2
Making Equivalent Fractions :
Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 31
------------------------- = ----
L.C.M 20
R. Mult. • R. Num. 7 • 2
---------------------------- = -----
L.C.M 20
Adding fractions that have a common denominator :
Adding up the two equivalent fractions
31 - (7 • 2) 17'
-------------- = ---
20 20
17
—— = 0.85000
20
The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. which of the following equations can be used to model the height as a function of time, t, in hours? assume that the time at t = 0 is 12:00 a.m. h = 0.5 cosine (startfraction pi over 12 endfraction t) 9.5 h = 0.5 cosine (startfraction pi over 6 endfraction t) 9.5 h = cosine (startfraction pi over 12 endfraction t) 9 h = cosine (startfraction pi over 6 endfraction t) 9
The equation can be used to model the height as a function is[tex]\rm h = 0.5\ cos(\frac{\pi}{6} t)+9.5[/tex] where t is time, the second option is correct.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We know the general equation for the cosine function:
[tex]\rm y = A\ cos(bx-c)+d[/tex]
Where A is the amplitude
We have a wall clock that varies from 9 feet to 10 feet.
The value of 'A' is given by:
[tex]\rm A = \frac{10-9}{2} \Rightarrow 0.5[/tex]
b is the cycle speed, we know:
[tex]\rm T = \frac{2\pi}{b}[/tex] (T is period)
[tex]\rm12 = \frac{2\pi}{b}[/tex]
[tex]\rm b=\frac{\pi}{6}[/tex]
The value of d is given by:
[tex]\rm d = \frac{10+9}{2}[/tex]
d = 9.5
The equation can be modeled:
[tex]\rm h = 0.5\ cos(\frac{\pi}{6} t)+9.5[/tex] (c =0 and y =h)
Thus, the equation is [tex]\rm h = 0.5\ cos(\frac{\pi}{6} t)+9.5[/tex]
Know more about trigonometry here:
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Answer: B, h = 0.5 cosine (StartFraction pi Over 6 EndFraction t) + 9.5
Step-by-step explanation: edge :)
When you use a (______________), you pay for your purchases later.
A credit card
B checking account
C deposit
D credit score
Answer:
A. credit card
Step-by-step explanation:
When using a credit card, the bank is paying for you. Overtime through bills you will pay that amount back usually with interest.
What is m _BEC
OB) 70°
OA) 65°
OD) 120°
OC) 50°
Answer:
C) 50°
Step-by-step explanation:
[tex]m\angle BEC= 180\degree-(65\degree+65\degree)[/tex]
[tex]\implies m\angle BEC= 180\degree-130\degree[/tex]
[tex]\implies m\angle BEC= 50\degree[/tex]
Can pls someone help me? and show how it did it?
Answer:
You have no image so how could i solve?
Step-by-step explanation:
Can somebody please help me? :(
Answer:
143 square meters
Step-by-step explanation:
The surface has a width of 11 meters and a length of 13 meters.
13 x 11 = 143.
Is this correct?
Tanner made his father a quilt. The width is 6 5 /7 meters by 7 3/ 5 meters what is the area of the quilt?
Answer:
51.0285714…
Step-by-step explanation:
you just multiply them together.
Answer:
Step-by-step explanation:
→ Multiply the 2 lengths together
[tex]6\frac{5}{7} *7\frac{3}{5}[/tex]
→ Convert both to improper
[tex]\frac{47}{7} *\frac{38}{5}[/tex]
→ Multiply
[tex]\frac{1786}{35}[/tex]
→ Convert to mixed fraction
[tex]51\frac{1}{35}[/tex]
Please help fast! (I'm not trying to rush ya)
Answer:
"LOCATION: Most temperate, deciduous (leaf-shedding) forests are located in the eastern United States, Canada, Europe, China, Japan, and parts of Russia. Deciduous forests are broken up into five zones."
Step-by-step explanation:
✖ Brazil
✓ China
✓ United States
✓ Russia
✖ Chile
Hopefully this helps you!
-Keira
A rectangular bathroom mirror is 4 feet wide and 2 feet tall. What is its perimeter?
Answer:
The perimeter is 24 feet :]
hope this helps! <33
Answer:
12 feet
Step-by-step explanation:
The perimeter of a rectangle is just the sum of all the sides. There are four sides, two that represent the width, and two that are the length. Basically, the easiest way for us to find the perimeter of this shape is to add together the length and the width 2 times.
4 + 2 + 4 + 2 = 12
So, the perimeter of the mirror is 12 feet! I hope this helps! Have a lovely day!! :)
Write down one prime number that lies between each of the following pairs of numbers: a) 45 and 55 b) 62 and 72
==============================================
Remember, prime numbers have only 2 factors: 1 & themselves.
For example, 5 is a prime number because it's only divisible by 1 and 5 (itself)
Now, write down some primes.
1) between 45 and 55
- 47
- it's only divisible by 1 and itself, so it IS prime
2) 62 and 72
67, because it is divisible by 1 and itself only.
====================================================
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)
i need help this is due in 10 mins
Answer:
180 degree rotation
Step-by-step explanation:
Answer:
Reflect across the y-axis
Translate horizontally 7 units right
Step-by-step explanation:
Alright I'll try to quickly answer this for you.
Firstly you could try reflecting figure P across the y axis. That would mean multiplying the whole function times -1.
So a point like (-2,3) would be come (-2,-3), and then visualize moving that point to where it would be on figure Q. It looks like it would be on (5,-3) on figure Q. So to take (-2,-3) to (5,-3) you translate it horizontally 7 units right.
45/100•72=45/72•100
True or false
Answer:
False
Step-by-step explanation:
45/100 × 72 = 32.4
45/72 × 100 = 62.5
62.5 ≠ 32.4
Answer:
false
Step-by-step explanation:
45/100x72=32.4%
45/72X100=62.5%
Please help me with this math problem!! Will give brainliest!! NO links please!! Thanks! :) (Please draw a picture)
Answer:
0.64
Step-by-step explanation:
Given the sides of a triangle, we can solve for any angle using the Law of Cosines: [tex]a^2=b^2+c^2-2bc(cosA)[/tex]
Our variables:
a = 27
b = 36
c = 45
B = 90°
[tex]a^2=b^2+c^2-2bc(cosA)[/tex]
[tex](27)^2=(36)^2+(45)^2-2(36)(45)(cosA)[/tex]
[tex]720=1296+2025-3240(cosA)[/tex]
[tex]720-3321=-3240(cosA)[/tex]
[tex]-2601=-3240(cosA)[/tex]
[tex]\frac{2601}{3240} =cosA[/tex] ≈ [tex]0.80278[/tex]
[tex]cos^-(A)=cos^-(\frac{2601}{3240})[/tex]
[tex]< A = 0.63885708[/tex]
This might be wrong, but you get the method. I would repost for a better answer from someone else because I'm practically half asleep. Very sorry but I hope you get some help soon! Best of luck
Need it ASAP PLEASE HELP!!!!
Answer:
25π + 30m which is approx. 108.54m
Step-by-step explanation:
First, we can work out the angle of the middle of the playground. 360 - 60 = 300°
Next, we can find out the arc length of the playground using the formula:
θ/360 × πd → 300/360 × 30π = 25π
Finally, we need to add on the two radii to find the perimeter of the playground: 25π + 15 + 15 = 25π + 30m which is approx. 108.54m
Hope this helps!
Thomas lives more than 0. 55 km and less than 0. 75 km from his school.
Thomas lives from his school?
A. 0. 06 km
B 0. 50 km
c. 0. 60 km
D. 1. 30 km
Which choice could be the distance Thomas lives from school?
Answer:
D. answer po
Step-by-step explanation:
Tama yan na D
IMAGE BELOW I WILL GIVE BRAINLIEST
Answer:
A' (- 4, 6 )
Step-by-step explanation:
Since the dilatation is centred at the origin then multiply each coordinate by the scale factor , that is
A (- 6, 9 ) → A' ([tex]\frac{2}{3}[/tex] (- 6), [tex]\frac{2}{3}[/tex] (9) ) → A' (- 4, 6 )
find the HCF of 50and70 by using euclids algorithm
Answer:
10
Step-by-step explanation:
To find,
HCF of 50 & 70 using Euclid's Division Algorithm.
Solution,
HCF(50 & 70) -- 70 = 50 × 1 + 20.
50 = 20 × 2 + 10
20 = 10 × 2 + 0.
Therefore their HCF is 10.
Answer:
10
Step-by-step explanation:
According to Euclid's Algorithm, c = dq + r , 0 ≤ r < d (where r is the remainder)
As 70 > 50, c = 70 and d = 50
Substituting values of c and d:
70 = (50 x 1) + 20
⇒ 50 = (20 x 2) + 10
⇒ 20 = (10 x 2) + 0
Therefore, the HCF is 10
Please help me with my home work
2.334567890 x 3.04576879 =