The general solution of the differential equation is y(x) = c1e^(-x/3) + (c2 + c3x)*e^(-2x/3), where c1, c2, and c3 are constants determined by the initial conditions.
a.) The general solution of the differential equation y'' − 2y' − 4y = 0 is y(x) = c1e^(2x) + c2e^(-2x), where c1 and c2 are constants.
To find the general solution of the differential equation, we first find the characteristic equation by assuming that the solution is of the form y(x) = e^(rx). Substituting this into the differential equation gives us r^2 - 2r - 4 = 0, which has roots r1 = 2 and r2 = -2. Therefore, the general solution of the differential equation is y(x) = c1e^(2x) + c2e^(-2x), where c1 and c2 are constants determined by the initial conditions.
b.) The general solution of the differential equation y''' + 14y'' + 49y' = 0 is y(x) = c1e^(-7x) + c2xe^(-7x) + c3x^2*e^(-7x), where c1, c2, and c3 are constants.
To find the general solution of the differential equation, we first find the characteristic equation by assuming that the solution is of the form y(x) = e^(rx). Substituting this into the differential equation gives us r^3 + 14r^2 + 49r = 0, which has a root r = -7 with multiplicity 3. Therefore, the general solution of the differential equation is y(x) = c1e^(-7x) + c2xe^(-7x) + c3x^2*e^(-7x), where c1, c2, and c3 are constants determined by the initial conditions.
c.) The general solution of the differential equation 3y''' + 16y'' + 26y' + 7y = 0 is y(x) = c1e^(-x/3) + (c2 + c3x)*e^(-2x/3), where c1, c2, and c3 are constants.
To find the general solution of the differential equation, we first find the characteristic equation by assuming that the solution is of the form y(x) = e^(rx). Substituting this into the differential equation gives us 3r^3 + 16r^2 + 26r + 7 = 0, which has roots r = -1/3 with multiplicity 1 and r = -2/3 with multiplicity 2. Therefore, the general solution of the differential equation is y(x) = c1e^(-x/3) + (c2 + c3x)*e^(-2x/3), where c1, c2, and c3 are constants determined by the initial conditions.
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PLEASE HELP!!!!!!!!!!!!!!!
Answer:
4 because 5 times 4 is 20 and 3 times 4 is 12
Answer:
c
switch them and then divide
Good luck:)
[tex]2 \sin(x) - \sqrt{3} = 0[/tex]
[tex] when\frac{\pi}{2} \leqslant x \leqslant \pi[/tex]
Given:
The equation is
[tex]2\sin x-\sqrt{3}=0[/tex]
When [tex]\dfrac{\pi}{2}\leq x\leq \pi[/tex].
To find:
The value of x.
Solution:
We have,
[tex]2\sin x-\sqrt{3}=0[/tex]
It can be written as
[tex]2\sin x=\sqrt{3}[/tex]
[tex]\sin x=\dfrac{\sqrt{3}}{2}[/tex]
It is given that [tex]\dfrac{\pi}{2}\leq x\leq \pi[/tex].
[tex]\sin x=\sin \left(\pi-\dfrac{\pi}{3}\right)[/tex]
[tex]x=\dfrac{3\pi-\pi}{3}[/tex]
[tex]x=\dfrac{2\pi}{3}[/tex]
Therefore, the value of x is [tex]\dfrac{2\pi}{3}[/tex].
What is the least common multiple of 3, 2, and 9?
Answer:
18 is the LCM
can someone help me with these three? I just need to find the unit rates for all, I’ll mark as brainliest!!
Answer:
6. 7.5/1
7. 2.4/1
8. 40/1
Step-by-step explanation:
All you have to do is divide the 2 numbers to find the unit rate.
Answer:
6: 7.5 pizzas per Classroom
7: 2.4 Liters per test
8: 40 Points per Game
"An airplane ends up 540 miles and 20 degrees north of east from its departure point. If there was a steady wind of 30 mph from the northwest during the entire flight, then find the magnitude and direction that the plane would have gone if there had been no wind".
Answer:
vr = [tex]540[/tex]
vp = 486.22 j + 205.9 j
Theta [tex]= 22.95[/tex]
Step-by-step explanation:
The resultant velocity vr = vp + vw
vp = vector velocity of plane and
vw = vector velocity of wind
vr = vector resultant velocity
in one hour the plane travels 540 miles and hence the speed is 540 mph
Hence vr = [tex]540[/tex]
vp = 486.22 j + 205.9 j
Theta
[tex]= tan^{-1}\frac{205.9}{486.22} \\= 22.95[/tex]
Help! What is the slope of the line represented by the equation y = 4/5 x - 3?
A) -3
B) -4/5
C) 4/5
D) 3
BRAINLIEST to wherever gets this correct
Answer:
[tex]300\pi[/tex] cubic feet
Step-by-step explanation:
Let r be the radius of cone and h be the height of cone.
Radius of cylinder=r
Height of cylinder=h
Volume of cone=[tex]100\pi ft^3[/tex]
We have to find the volume of cylinder.
We know that
Volume of cone=[tex]\frac{1}{3}\pi r^2 h[/tex]
[tex]100\pi=\frac{1}{3}\pi r^2 h[/tex]
[tex]r^2 h=300[/tex]
Volume of cylinder=[tex]\pi r^2 h[/tex]
Using the formula
Volume of cylinder=[tex]\pi (300)=300\pi ft^3[/tex]
Hence, the volume of cylinder=[tex]300\pi[/tex] cubic feet
how to find cp if loss and sp are given
Step-by-step explanation:
[tex] \tt{ \: H \: E \: Y \: \: T \: H \: E \: R\: E \: }[/tex] !
When Loss and Selling price ( SP ) are given , Cost price ( CP ) can be found out using the following formulae :
✰ [tex] \large{ \boxed{ \boxed{ \tt{CP = Loss + SP}}}}[/tex]
[tex] \text{How \: did\: we \:get \:the \: formula : \: CP \: = Loss \: + \: SP} \: [/tex] ?
We simply derived the formula from Loss = CP - SP.
First , Swap the sides of the equation :
⟶ [tex] \text{CP - SP = Loss}[/tex]
Move SP to right hand side and change it's sign :
⟶[tex] \text{CP = Loss + SP}[/tex]
This is how , CP can be obtained when we are given loss and SP.
Hope I helped ! ♡
Have a wonderful day / night ! ツ
# [tex] \underbrace{ \tt{C \: a \: r \: r \: y \: \: O \:n \: \: L \: e \: a \: r \: n \: i \: n \: g}}[/tex] !!
▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
1- The area of a parallelogram is 507 cm2. Its height is six times its base. Find the height and base.
Answer:
507=b x (3 x b)
507=b x 3b
507=3b^2
b^2=507/3
b^2=169
b=13
h=3 x b
h=3 x 13
h=39
Step-by-step explanation:
The height and base of the parallelogram is b = 13 cm and h = 78 cm
What is a Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The sum of angles of a parallelogram is 360°
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
Let the area of the parallelogram be represented as A
Now , the value of A = b x h
where the base of the parallelogram is b
The height of the parallelogram is h
So , 507 = b x h
And , height is three times its base
So , h = ( b x 3 )
On simplifying , we get
507 = b ( b x 3 )
507 = 3b²
Divide by 3 on both sides , we get
b² = 169
Taking square roots on both sides , we get
b = 13 cm
So , the height of the parallelogram is h = 78 cm
Hence , the parallelogram is solved
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(10^2 )^3
i need some help
Answer: 10^6
Step-by-step explanation:
When you take a power to a power, you can multiply the two powers:
10^6
Answer:
10^6 hope this helps you
On Monday, Florencia's hair was h centimeters long. She got a haircut on Tuesday, so her hair was only 75% percent of the length it was on Monday.
Which expressions could represent how many centimeters long Florencia's hair was after the haircut?
(The Question says to pick 2 answers out of the multiple choice options so here you go)
A. h (1-0.75)
B.(1- 75/100) h
C. 3/4 h
D. 0.75 h
E. 1/4 h
Answer:
D
Step-by-step explanation:
75/100 = .75 x the Monday length (h)
HELP QUICK whats the domain and range of g(x)=√x-3+5
Answer:
check it..
Step-by-step explanation:
domain and range...
Parallel lines s and t are cut by a transversal, r, as shown. Parallel lines s and t are cut by transversal r. Clockwise from top left, the angles formed with r and s are blank, blank, 1, (5 x minus 4) degrees; the angles formed with r and t are blank, blank, 94 degrees, blank. What is the value of x to the nearest whole number? 18 20 86 94
Answer:
18
Step-by-step explanation:
From the above question,
We have the Algebraic expression
(5x - 4)° + 94° = 180°
5x - 4° + 94° = 180°
5x + 90° = 180°
5x = 180° - 90°
5x = 90°
x = 90°/5
x = 18
Answer:
18
Step-by-step explanation:
Help?
1. List the terms in the expression using a comma to separate each term.
This question will be graded by your teacher. *
10x + 5 + 3x + 1
Vhur answer
2. list the coefficients in the expression,
Answer:
10x, 5, 3x, 1 There are four terms
2) The coefficients are 10 and 3
A 12-inch diameter pizza has 22 calories per square inch.
About how many calories are in the entire pizza?
Use 3.14 for pi.
Select from the drop-down menu to correctly complete the statement.
There are about
Choose...
calories in the pizza. optains : 264, 414, 2487, 9948
Answer:
the answer is 2487
Step-by-step explanation: i took the test
PLEASE HELP I WILL MARK BRAINLIEST
name 2 rights of someone accused of a crime that you observe in the pic above.
A. right to a trial and lawyer
B. right to a lawyer and providing evidence
C. Trial with a judge and witness
D. Right to take notes and provide evidence for defence
Answer:
it is b the right to evidence lawyer.
Answer:
B. right to lawyer and providing evidence
Step-by-step explanation:
Which rational expression is equal to a positive whole number when evaluated?
8 1/3
15 1/5
212
12 1/4
Can someone please help me with this question.Select all the expressions equivalent to:
20a + 10b
a:5(4a + 2b)
b:10(2a + b)
C:2(10a + 5)
D:2(10a + 5b)
E:5(4a - 2b)
Answer:
a
b
d
i did this for notes really helps
will give brainliest please help
Answer:
16g + 24 - (13g- 15)
length - width
perimeter = 2(length) - 2(width)
2(16g+ 24) + 2(13g-15)
32g + 48 + 26g - 30
58g + 18
An observer (O) spots a plane flying at a 42° angle to his horizontal line of sight. If the plane is flying at an altitude of 15,000 feet, what is the distance (x) from the plane (P) to the observer (O)?
A right triangle is shown with angle O marked 42 degrees, hypotenuse marked x, and height marked 15,000 feet.
10,035 feet
16,648 feet
20,188 feet
22,417 feet
Answer:
22,417
Step-by-step explanation:
Just took the test.
Pythagoras theorem states that for a right angle triangle the square of the hypotenuse is equal to the sum of the other two sides of the plane. The distance (x) from the plane (P) to the observer (O) is 22417.75 feet.
Given information-The observer angle to the plane is 42 degrees.
The height of the plane is 15000 feet.
As angle O is 42 degree and the height is 15000. Let suppose the base is y feet long. Thus angle O can be given as,
[tex]\begin{aligned} \tan42^o&=\dfrac{15000}{y} \\ y&=\dfrac{15000}{\tan42^o} \\ y&=16660\\ \end[/tex]
Thus the base of the right triangle is 16660 feet.
Pythagoras theoremPythagoras theorem states that for a right angle triangle the square of the hypotenuse is equal to the sum of the other two sides of the plane.
For the given problem the the hypotenuse side is x feet.
[tex]\begin{aligned}\\ x^2&=15000^2+16660^2\\ x&=22417.75\\ \end[/tex]
Thus the distance (x) from the plane (P) to the observer (O) is 22417.75 feet.
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Which equation represents a line which is parallel to the line y=2x-5
1. 2x+y=8
2.x+2y=-4
3.y-2x=-8
4.x-2y=6
Answer:
3
Step-by-step explanation:
when two lines are parallel, they have the same slope
you can find slop by changing the equation to slope intercept form (y=mx+b), m being the slope
slopes:
1. -2
2. -1/2
3. 2
4. 1/2
Answer:
3. y-2x=-8
Step-by-step explanation:
jane takes 4 hours to do a job that Alice can do in 3 hours. if jane works 1/2 hour before Alice joins her, how long will it take the two of them to finish the job
Answer:
2.4 hours
Step-by-step explanation:
Please answer this immediately pleasee
Please i need it now
f (x) = 3x+2 / x-1 untuk x ≠ 1, maka invers fungsi f (x) adalah
Answer:
Step-by-step explanation:
hello : F (x) = 3x+2 / x-1
let : F (x) = y.....x ?
y= 3x+2 / x-1
y(x-1) =3x+2
yx-y= 3x+2
yx-3x = y+2
x(y-3) = y+2
for y ≠ 3
x= (y+2)/(y-3)
invers fungsi f (x) : g(x) = (x+2)/(x-3) ..... x ≠ 3
You need to cross a canal and want to determine the distance across the opposite side. Since you're able to take measurements on your side of the canal, you come up with 40 ft. and 16 ft. Find the distance x across the canal . Show all work
Answer:
36.7 ft
Step-by-step explanation:
Measurements for the sides of the canal is given as: 40 ft. and 16 ft.
You solve the above question using Pythagoras Theorem
The distance across the canal is calculated as:
√(40² - 16²)
= √(1344)
= 36.66060556 ft
Approximately = 36.7 ft
Therefore, the distance x across the canal = 36.7 ft
Jean and Sarah are buying tubs of ice cream. 2 scoops of ice cream are twice the price of 1 scoop of ice cream. Jean buys 4 tubs with 2 scoops in them and 2 tubs with 1 scoop each. Sarah buys 2 tubs of 2 scoops and 4 tubs of 1 scoop. Sarah spends 2.50 € less than Jean.
Answer:
The answer is below
Step-by-step explanation:
Let x represent the cost of 1 scoop of ice cream. Since the cost of 2 scoops of ice cream are twice the price of 1 scoop of ice cream, therefore the cost of 2 scoops of ice cream = 2x
Jean buys 4 tubs with 2 scoops in them and 2 tubs with 1 scoop each. Therefore the money spent by Jean is:
Money spent by Jean = 4(2x) + 2(x) = 8x + 2x = 10x
Sarah buys 2 tubs of 2 scoops and 4 tubs of 1 scoop. The money spent by Sarah is:
Money spent by Sarah = 2(2x) + 4(x) = 4x + 4x = 8x
Sarah spends 2.50 € less than Jean. Therefore:
Money spent by Sarah = Money spent by Jean - 2.5
8x = 10x - 2.5
2x = 2.5
x = €1.25
Therefore the cost of 1 scoop of ice cream is €1.25, the cost of 2 scoops of ice cream is €2.50.
Money spent by Jean = 10x = 10(1.25) = €12.5
Money spent by Sarah = 8x = 8(1.25) = €10
A cheesecake recipe says:
Mix 12 ounces of cream cheese with 15 ounces of sugar.
1. What is the unit rate of cream cheese for sugar?
2. what is the unit rate of sugar for cream cheese?
(CORRECT ANSWER GETS A GOOD 5 STARS AND BRAINLESST)
Answer:
the unit rate of cream cheese for sugar is .8
the unit rate of sugar for cream cheese is 1.25
Step-by-step explanation:
I hope this is correct / helps! :)
compllete the values for x + 2y = 7
what is2/3b - 1/4b? Please help- also has to be simplified
Answer:5/12b
Step-by-step explanation:
Answer:
5/12b
Step-by-step explanation:
2/3= 8/12
1/4= 3/12
8/12-3/12= 5/12 then put the b at the end,
5/12b
5/12 is already in simplest form
After dinner 1-3 of the corn bread is left suppose 2 friends want to share it equally what fraction names how much of the whole pan of corn bread each f riend will get
Answer:
Each friend will get [tex]\frac{1}{18}[/tex] of whole pan of corn bread
Step-by-step explanation:
As given,
Corn bread left = [tex]\frac{1}{3}[/tex]
Total number of friends = 2
So the left bread will divide into 2 parts
So, each person will get = [tex]\frac{1}{2}[/tex] ( [tex]\frac{1}{3}[/tex] ) = [tex]\frac{1}{6}[/tex] of the left bread
Now,
Left bread = [tex]\frac{1}{3}[/tex] of whole bread
And
Each person get = [tex]\frac{1}{6}[/tex] of the left bread
= [tex]\frac{1}{6}[/tex] ×[tex]\frac{1}{3}[/tex] of whole bread
= [tex]\frac{1}{18}[/tex]of whole bread
∴ we get
Each friend will get [tex]\frac{1}{18}[/tex] of whole pan of corn bread