I bet the ODE is supposed to read
[tex]x^2y''-14xy'+56y=0[/tex]
Then if [tex]y=x^r[/tex], we have [tex]y'=rx^{r-1}[/tex] and [tex]y''=r(r-1)x^{r-2}[/tex], and substituting these into the ODE gives
[tex]r(r-1)x^r-14rx^r+56x^r=0\implies r(r-1)-14r+56=r^2-15r+56=0[/tex]
Solving for r, we find
[tex]r^2-15r+56=(r-8)(r-7)=0\implies \boxed{r=8\text{ or }r=7}[/tex]
so that [tex]y_1=x^8[/tex] and [tex]y_2=x^7[/tex] are two fundamental solutions to the ODE. Thus the general solution is
[tex]\boxed{y(x)=C_1x^8+C_2x^7}[/tex]
Given that [tex]y(1)=4[/tex] and [tex]y'(1)=3[/tex], we get
[tex]\begin{cases}4=C_1+C_2\\3=8C_1+7C_2\end{cases}\implies C_1=-25\text{ and }C_2=29[/tex]
So the particular solution is
[tex]\boxed{y(x)=29x^7-25x^8}[/tex]
3x(x + 2) ......................
Answer:
3x^2+6x
Step-by-step explanation:
3x(x+2)
First distribute the 3x
You end up with
(3x^2+6x)
and that is the answer.
Using calculus, it can be shown that if a ball is thrown upward with an initial velocity of 16 ft/s from the top of a building 704 ft high, then its height h above the ground t seconds later will be h = 704 + 16t − 16t2. During what time interval (in seconds) will the ball be at least 32 ft above the ground? (Enter your answer using interval notation.)
Answer:
[0, 7]
Step-by-step explanation:
We want the height to be greater than or equal to 32 ft, so ...
704 +16t -16t^2 ≥ 32
t^2 -t -42 ≤ 0 . . . . . . . . . . . subtract 32, divide by -16
(t -7)(t +6) ≤ 0
This inequality will be true for values of t between -6 and +7. Since we're only concerned with times t ≥ 0, the appropriate solution interval is ...
0 ≤ t ≤ 7 . . . . [0, 7] in interval notation
How many hours are there in 360 mins
Answer: 6 hours
Step-by-step explanation:
You have to divide 360 by 60 minutes.
Answer:
There are 360 minutes in 6 hours.
Hope this helps :)
Find the 10th term of the geometric sequence a9=-5 r=-1/2
Answer:
2.5
Step-by-step explanation:
multiply -5 by -1/2
find simple interest on #1200 for 3 years at 4.25% per anum
Answer:
$153.00
Step-by-step explanation:
A = $1,353.00
(I = A - P = $153.00)
Equation:
A = P(1 + rt)
Calculation:
First, converting R percent to r a decimal
r = R/100 = 4.25%/100 = 0.0425 per year.
Solving our equation:
A = 1200(1 + (0.0425 × 3)) = 1353
A = $1,353.00
The total amount accrued, principal plus interest, from simple interest on a principal of $1,200.00 at a rate of 4.25% per year for 3 years is $1,353.00.
Answer:
$153
Step-by-step explanation:
Simple Intrest = P ( money invested ) * R ( percentage ) * T ( year )
I = P * R * T / 100
I = 1200 * 4.25 * 3 = 15300 / 100 = $153
This is the easiest method for me and I hope it helps :)
range of 2.45 3.50 2.89 2.99
Answer:
[tex]\huge\boxed{\mathrm{Range = 1.05}}[/tex]
Step-by-step explanation:
Given Data:
2.45 , 3.50 , 2.89 , 2.99
Arrange it in ascending order.
2.45 , 2.89 , 2.99 , 3.50
Range = Highest No - Lowest No.
Range = 3.50 - 2.45
Range = 1.05
Answer:
Range=largest value-smallest value
Range=2.99-2.45
Range=0.54
Step-by-step explanation:
hope it is helpful for you
if it is please follow
Solve for y: 3x - 4y = 12
Answer:
y = 3/4x -3
Step-by-step explanation:
[tex]3x-4y=12\\[/tex]
Move 3x to the right and change its sign
[tex]-4y = -3x+12[/tex]
Divide both sides of the equation by -4
[tex]\frac{-4y}{-4} =\frac{-3x}{-4} + \frac{12}{-4} \\\\y = \frac{3}{4} x -3[/tex]
-5/10 + 7/10 . what is the answer
Answer:
2/10
Step-by-step explanation:
-5+7=2, since the denominator stays the same.
2/10, simplified is 1/5
Answer:
2/10 or 1/5
Step-by-step explanation:
Because -5/10 and 7/10 both have 10 as the denominator we don't have to do anything about that, so you just add and simplify.
If you need me to go through it in depth let me know, but I hope that helps!
Have a great day!
Please help!
Add [-6-2 2] + [-3 2 1].
Answer:
Step-by-step explanation:
[-6 + -3 -2 + 2 2 + 1} = [-9 0 3}
Write 20% as a decimal.
Answer ?
Answer:
0.2
Step-by-step explanation:
Step 1:
20 divided by 100 = 0.2
Answer:
0.2
If you want to get a decimal from a percent you need to divide the percent by 100.
Hope This Helps :)
Remember all decimal are basicaly,
x% = (x)/(100)
so
20%=(20)/(100)=0.20
Death Valley is the location of the lowest land elevation in the USA which is 282 feet below sea level.The location with the highest level is 20,320 feet above sea level.What is the difference in the elevations of these two locations
Answer:
20,038
Step-by-step explanation:
20,320 - 282
Given f(x) = 52x, evaluate f-1), f(o), and K2).
01/25, 1, 625
Answer:
[tex]f(-1) = \frac{5}{2}[/tex]
[tex]f(0) = 5[/tex]
[tex]f(2) = 20[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 5(2^x)[/tex]
Required
Determine f(-1); f(0) and f(2)
Solving f(-1)
In this case, we simply take x as;
[tex]x = -1[/tex]
Substitute -1 for x in [tex]f(x) = 5(2^x)[/tex]
[tex]f(-1) = 5(2^{-1})[/tex]
Apply law of indices
[tex]f(-1) = 5 * \frac{1}{2}[/tex]
[tex]f(-1) = \frac{5}{2}[/tex]
Solving f(0)
In this case, we simply take x as;
[tex]x = 0[/tex]
Substitute 0 for x in [tex]f(x) = 5(2^x)[/tex]
[tex]f(0) = 5(2^0)[/tex]
[tex]f(0) = 5(1)[/tex]
[tex]f(0) = 5[/tex]
Solving f(2)
In this case, we simply take x as;
[tex]x = 2[/tex]
Substitute 2 for x in [tex]f(x) = 5(2^x)[/tex]
[tex]f(2) = 5(2^2)[/tex]
[tex]f(2) = 5(4)[/tex]
[tex]f(2) = 20[/tex]
A cylindrical can has a volume of 16 cm 3. What dimensions yield the minimum surface area? 1. The radius of the can with the minimum surface area is ______ cm. (Simplify your answer.) 2. The height of the can with the minimum surface area is ______ cm. (Simplify your answer.)
Answer:
radius = 1.37 cm
height = 2.71 cm
Step-by-step explanation:
We are given volume = 16 m³.
Formula for volume of a cylinder is;
V = πr²h
Thus,
πr²h = 16
h = 16/πr²
Now formula for the surface area is;
S = 2πr² + 2πrh
Putting 16/πr² for h gives;
S = 2πr² + 2πr(16/πr²)
S = 2πr² + 2π(16/πr)
S = 2π(r² + 16/πr)
To minimize, we will find the derivative of S and equate to zero
S' = 2π(2r - 16/πr²) = 0
4πr - 32/r² = 0
4πr = 32/r²
r³ = 32/4π
r = ∛(32/4π)
r = 1.37 cm
From h = 16/πr²;
h = 16/(π × 1.37²)
h = 2.71 cm
morgan bought a pair of shoes at a sale of 25% . if the amount she paid was $1000 , find the market price ?
Answer:
$4,000
Step-by-step explanation:
to find the market price you:
1000x100=100000
100000/25=4000
Answer:
4,000
Step-by-step explanation:
Which of the following is the solution of the equation 3x + 4=19 use substitution to identify the correct answer
Answer:
5
Step-by-step explanation:
Step 1:
3x + 4 = 19
Step 2:
3x = 19 - 4
Step 3:
3x = 15
Answer:
x = 5
Hope This Helps :)
Find the domain and range. {(-2,0), (1,-2), (3,4)}
Answer:
[tex] \boxed{ \bold{ \boxed{ \sf{domain = { (- 2 \: , \: 1 \: , \: 3)}}}}}[/tex]
[tex] \boxed{ \bold{ \boxed{ \sf{range = ( \: - 2 \: , \: 0 \: , \: 4)}}}}[/tex]
Step-by-step explanation:
Domain is the set of all x values.
Range is the set of all y - values.
{ ( - 2 , 0 ) , ( 1 , -2 ) , ( 3 , 4 )}
Domain = { -2 , 1 , 3 }
{ ( -2 , 0 ) , ( 1 , -2 ) , ( 3 , 4 )}
Range = { - 2 , 0 , 4 }
Hope I helped!
Best regards! :D
What can you conclude about the slope of the values in
the table? Check all that apply.
lope
The slope is 0.
The slope is undefined.
The graph will be a horizontal line.
The graph will be a vertical line.
The graph will have a line with a positive slope.
Answer:
The slope is undefined.
The graph will be a vertical line.
Step-by-step explanation:
just did it
The graph will be a vertical line. Option C is correct.
Given that,
The slope of the line is zero we have to determine what are the conditions.
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
What is simplification?
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The slope of the line is zero,
m = 0
tanФ = 0
y / x = 0
for the above condition, Δy must be zero or Δx must be infinite and the line will be a verticle.
Thus, the graph will be a vertical line. Option C is correct.
Learn more about slopes here:
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A car can travel 38 miles on each gallon of gasoline. At that rate, how many gallons of gasoline will it take to travel
190 miles?
2
5
20
50
Answer:
5 gallons of gasoline
Step-by-step explanation:
since we have the number of miles the car drives per gallon (38) we can set up an equation
the equation would be the number of miles per gallon (38) times the number of gallons it would take to drive 190 miles (x) equals 190 miles
38x = 190
you then divide 190 by 38
x = 5 gallons
Five gallons of gasoline must be taken to travel 190 miles.
What is the unitary method?The unitary method is a problem-solving methodology that involves first finding the value of a single unit and then finding the necessary value by multiplying the single unit value.
How many gallons of gasoline will it take to travel 190 miles?On one-gallon gasoline, the car can travel 38 miles.
Let x gallons of gasoline be taken to travel 190 miles.
So, 38x=190
⇒x=190/38=5
Hence, 5 gallons of gasoline is taken to travel 190 miles.
Learn more about the unitary method from- https://brainly.com/question/22056199?referrer=searchResults
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The expression 3A + 2.5S gives the cost in dollars of A adult tickets and S student tickets. What is the cost of 2 adult tickets and 4 student
Answer:
16
Step-by-step explanation:
A = 2; S = 4
3A + 2.5S =
= 3(2) + 2.5(4)
= 6 + 10
= 16
Solve the following proportion for
5/11=y/6
Round your answer to the nearest tenth
Answer:
Step-by-step explanation:
5 y
_ = _
11 6
Cross multiply to get:
11y = 30
y = 2.7272
y = 2.7
Factor this trinomial 4x^2-6x-10 If you can please try to show me how to do it.
Answer:
[tex]=2(2x-5)(x+1)[/tex]
Step-by-step explanation:
So we have the trinomial:
[tex]4x^2-6x-10[/tex]
First, factor out a 2:
[tex]=2(2x^2-3x-5)[/tex]
Now, factor within the parentheses.
To do so, we want to find two numbers. When multiplied, these two numbers must equal (a)(c) and when added, they must equal b
(a)(c) is 2(-5) or -10 and b is -3. So, we want two numbers that when multiplied together gives -10 and when added gives -3.
-5 and 2 works. Therefore:
[tex]=2(2x^2-3x-5)[/tex]
Replace -3x with 2x and -5x:
[tex]=2(2x^2+2x-5x-5)[/tex]
Factor out a 2x for the first two terms. And factor out a negative 5 for the remaining two:
[tex]=2(2x(x+1)-5(x+1))[/tex]
Grouping:
[tex]=2(2x-5)(x+1)[/tex]
And we're done!
You bought a magazine for $2 and three candy bars. You spent a total of $11. How much did each candy bar cost?
Answer:
$3 each
Step-by-step explanation:
Minus the $2 from $11 gives you $9. So $9÷3=$3 per candy bar.
10 times as many as 5 tens is 5thousand
Answer:
This question does not make sense for very specific reasons
Step-by-step explanation:
1. 5,000 does not look like 5thousand
2. 10 times as many as 5 tens is not really a question at all
3. the question itself already contains the answer 5,000
The double box plot shows the test scores for Miss Robinson's second and fourth period
classes. Based on the double box plot, which sentence is true?
Answer: The second period class has the greater first quartile.
The second-period class has the greater first quartile. Then the correct option is A.
What is a double box?Like the other twin graph styles discussed in earlier sections, double package plots provide for a fast detailed evaluation of two sets of data.
The double box plot shows the test scores for Miss Robinson's second and fourth-period classes.
Based on the double box plot. Then the true sentence will be
The second-period class has the greater first quartile. Test Scores
Then the correct option is A.
More about the double box link is given below.
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If you borrow $450.00 at a 5% interest, how much will you pay in one month?
Answer: Between about 31 and 33 dollars per month
Step-by-step explanation:
If a =5, 0, −1,find a vector b such that compab = 2.b = _______.
Answer:
[tex]b = (q,r , 5q-2\sqrt{26} )[/tex]
Step-by-step explanation:
From the question we are told that
The vector given is
[tex]a = (5,0,-1)[/tex]
Also [tex]comp_a b = 2[/tex]
Generally
[tex]comp_a b = \frac{a \cdot b}{|a|}[/tex]
Here [tex]|a|[/tex] is the magnitude of a which is mathematically represented as
[tex]|a| = \sqrt{5^2 + 0^2 +(-1)^2 }[/tex]
=> [tex]|a| = \sqrt{26}[/tex]
b is vector which we will assume to have the following parameters
[tex]b = (q , r , x)[/tex]
So
[tex]comp_a b = \frac{(5,0,-1) \cdot (q,r,x)}{\sqrt{26} } = 2[/tex]
=> [tex]\frac{5q + 0 -x}{\sqrt{26} } = 2[/tex]
=> [tex]x = 5q-2\sqrt{26}[/tex]
Hence the vector be can be mathematically represented as
[tex]b = (q,r , 5q-2\sqrt{26} )[/tex]
This means that the vector b is more than one value since it is made up of variable
This means that if
[tex]q = 1\\r=1\\x =1[/tex]
Then
[tex]b = (1,1,5-2\sqrt{26} )[/tex]
A quantity has magnitude but not position, that's why in this the vector [tex]b =(0,0, -2\sqrt{26}).[/tex]
Vector:If[tex]a =(5,0,-1)[/tex] Our goal is to determine a vector b that will allow comp to work properly [tex]_{a}b = 2.[/tex]
Allow the vector to flow naturally [tex]b =(x, y,z)[/tex]
Recalling
comp[tex]_{a}b =\frac{a.b}{|a|}[/tex]
Therefore,
comp [tex]_{a}b= 2 \\\\[/tex]
[tex]\to \frac{a.b}{|a|}= 2\\\\[/tex]
[tex]\to \frac{(5,0,-1)\cdot (x,y,z)}{ |(5,0,-1)|} =2\\\\\to \frac{5x+0-z}{5^2+0+(-1)^2}=2\\\\ \to \frac{5x-z}{\sqrt{26}}= 2 \\\\\to 5x-z = 2\sqrt{26}\\\\ \to z=5x-2\sqrt{26}\\\\[/tex]
As a result, the vector b can be expressed as,
[tex]\to b =(x,y,z) =(x, y, 5x-2\sqrt{26}) \\\\[/tex]
As a result, this aforementioned form can be found in an endless number of vectors.
One of them is [tex]b =(0,0, -2\sqrt{26}).[/tex]
Find out more about the vector here:
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Write 0.0000002711 in scientific notation. (Use 2 numbers after the decimal point.)
Answer:
[tex]Number = 2.71 * 10^{-7}[/tex]
Step-by-step explanation:
Given
[tex]Number = 0.0000002711[/tex]
Required
Write, using scientific notation
The scientific notation is written in the form:
[tex]Form = a * 10^n[/tex] Where n is an integer and [tex]1 \leq a \leq 10[/tex]
To start with; Represent the given number as fraction
[tex]Number = \frac{2711}{10000000000}[/tex]
Represent the denominator as an exponent
[tex]Number = \frac{2711}{10^{10}}[/tex]
This can be rewritten in form of:
[tex]Number = 2711 * 10^{-10}[/tex]
Remember that: [tex]Form = a * 10^n[/tex] Where n is an integer and [tex]1 \leq a \leq 10[/tex]
This implies that; we need to adjust 2711 to a number between 1 and 10;
This gives:
[tex]Number = 2.711 * 1000 * 10^{-10}[/tex]
Write 1000 as an exponent
[tex]Number = 2.711 * 10^3 * 10^{-10}[/tex]
Apply law of indices
[tex]Number = 2.711 * 10^{3-10}[/tex]
[tex]Number = 2.711 * 10^{-7}[/tex]
The question requires 2 numbers after the decimal point;
So, 2.711 will be approximated to 2.71
[tex]Number = 2.71 * 10^{-7}[/tex]
Hence;
[tex]0.0000002711[/tex] is equivalent to [tex]2.71 * 10^{-7}[/tex]
Bepotastine besilate (BEPREVE) ophthalmic solution contains 1.5% w/v of the therapeutic agent. Express this concentration in mg/mL.
Answer:
15mg/ml
Step-by-step explanation:
Percent mass per volume ( % m/v) is unit expression that tells us how many grams of a solute that we can find 100 ml of a particular solution.
In the above question, we are asked to express 1.5%w/v Bepotastine besilate (BEPREVE) ophthalmic solution as mg/mL
Step 1
1.5% w/v = 1.5 g of Bepotastine besilate (BEPREVE) in 100ml ophthalmic solution
Hence, if
100ml = 1.5g
1 ml = y g
We Cross Multiply
100ml × yg = 1 ml × 1.5g
yg = 1 ml × 1.5g/100ml
= 0.015g
Therefore, in 1 ml we have 0.15 g.
Step 2
Since we are asked to express as mg/ml
We convert 0.015g to mg
1 gram = 1000 milligrams
0.015 grams =
Cross Multiply
0.015grams × 1000 milligrams/ 1 gram
= 15 mg
Therefore, the concentration in mg/ml of 15% m/v of Bepotastine besilate (BEPREVE) ophthalmic solution is 15mg/ml
Find the slope of the line containing the pair of points. (5,-7) and (-4,-4)
Answer:
1/-3
Step-by-step explanation:
Find the slope of the curve below at the given points. Sketch the curve along with its tangents at these points. R = sin 2 theta: theta = plusminus pi/4, plusminus 3 pi/4 The slope of the curve at theta = pi/4 is:__________
Answer:
-1
Step-by-step explanation:
Given that:
r = sin 2θ , θ = ± π/4 , ± 3π/4
Recall that:
x = r cosθ
y = r sinθ
The differential of y with respect to x
[tex]\dfrac{dy}{dx} = \dfrac{\dfrac{dy}{d \theta}}{\dfrac{dx}{d \theta}}[/tex]
[tex]\dfrac{dy}{dx} =\dfrac{\dfrac{dy}{d \theta}}{\dfrac{dx}{d \theta}} = \dfrac{ r cos \theta + sin \theta* \dfrac{dr}{d \theta} } {\dfrac{dr}{d \theta} *cos \theta- sin \theta \ r}[/tex]
at θ = π/4 , r = sin π/2
r = 1
[tex]\dfrac{dy}{dx} = \dfrac{ r cos \theta + 2 cos (2 \theta)*sin \ \theta } {2 \ cos (2 \theta) *cos \theta- sin 2 \theta * sin \theta}[/tex]
where;
θ = π/4
[tex]\dfrac{dy}{dx} = \dfrac{ 1 \times cos (\dfrac{\pi}{4}) + 2 cos (\dfrac{\pi}{2})*sin (\dfrac{\pi}{4}) } {2 \ cos (\dfrac{\pi}{2})*cos (\dfrac{\pi}{4})- sin (\dfrac{\pi}{2}) * sin (\dfrac{\pi}{4})}[/tex]
[tex]\dfrac{dy}{dx} = \dfrac{\dfrac{1}{\sqrt{2}}+0 }{0-1 * \dfrac{1}{\sqrt{2}}}[/tex]
[tex]\dfrac{dy}{dx} = \dfrac{\dfrac{1}{\sqrt{2}} }{- \dfrac{1}{\sqrt{2}}}[/tex]
[tex]\mathbf{\dfrac{dy}{dx} =-1}[/tex]
slope of the curve (dy/dx) at theta(θ) = pi/4 is -1