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SIZIF [17.4K]
3 years ago
13

5 times the sum of the digits of a two digit number is 9 less than the number formed by reversing its digits. If 4 times the val

ue of the digit at ones place is equal to the half of the place value of the digit at tens place, find out the number. ​
Mathematics
1 answer:
Ganezh [65]3 years ago
4 0

Answer:

5 times the sum of the digits of the number is 9 less than the number formed by reversing digits. → x = (5y - 9)/4 -- equation (1). Case - 2 : And, 4 times the value of the digits at ones place is equal to half the place value of digit at tens place (10x/2).

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A) Find a particular solution to y" + 2y = e^3 + x^3. b) Find the general solution.
Reptile [31]

Answer:

a.P.I=\frac{e^{3x}}{11}+\frac{1}{2}(x^3-3x)

b.G.S=C_1Cos \sqrt2 x+C_2 Sin\sqrt2 x+\frac{1}{11}e^{3x}+\frac{1}{2}(x^3-3x}

Step-by-step explanation:

We are given that a linear differential equation

y''+2y=e^{3x}+x^3

We have to find the particular solution

P.I=\frac{e^{3x}}{D^2+2}+\frac{x^3}{D^2+2}

P.I=\frac{e^{3x}}{3^2+2}+\frac{1}{2} x^3(1+\frac{D^2}{2})^{-2}

P.I=\frac{e^{3x}}{11}+\frac{1-2\frac{D^2}{4}+3\frac{D^4}{16}+...}{2}x^3

P.I=\frac{e^{3x}}{11}+\frac{x^3-2\frac{\cdot3\cdot 2x}{4}}{2}+0} (higher order terms can be neglected

P.I=\frac{e^{3x}}{11}+\frac{1}{2}(x^3-3x)

b.Characteristics equation

D^2+2=0

D=\pm\sqrt2 i

C.F=C_1cos \sqrt2x+C_2 sin\sqrt2 x

G.S=C.F+P.I

G.S=C_1Cos \sqrt2 x+C_2 Sin\sqrt2 x+\frac{1}{11}e^{3x}+\frac{1}{2}(x^3-3x)

3 0
3 years ago
Class of 50 students dressed up 38% have white shirts. How many are wearing white shirts?
shutvik [7]

Step-by-step explanation:

☥ \underline{ \underline{ \text{Given} }}:

  • Total number of students = 50
  • Percentage of students who are wearing white shirts = 38 %

☥ \underline{ \underline {\sf{To \: find} }}:

  • Total number of students who are wearing white shirts

☥ \underline{ \underline{ \sf{Solution} }} :

⟹ \sf{38\% \: of \: 50} =  \frac{38}{100}  \times 50 =  \boxed{ \sf{19}}

\red{ \boxed{ \boxed{ \tt{⟿ \: Our \: final \: answer : 19}}}}

Hope I helped ! ♡

Have a wonderful day / night ツ

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3 0
3 years ago
What is number pattern
anyanavicka [17]
A number patter is a list of numbers that follow a certain pattern like 2,4,6,8,10 is a pattern of 2's 
7 0
3 years ago
Bob is a realtor who specializes in high-end properties. In an advertising campaign, he wants to point out that his properties a
madreJ [45]

Answer:

D.

Bob should use the mean to make his selling price look like it's the greatest.

8 0
2 years ago
Is 3x+12-2x equivalent to x +12? Use two properties of operations to justify your answer.
aev [14]

Answer:

Yes, x + 12

Step-by-step explanation:

Simplify the following:

3 x - 2 x + 12

Grouping like terms, 3 x - 2 x + 12 = (3 x - 2 x) + 12:

(3 x - 2 x) + 12

3 x - 2 x = x:

Answer: x + 12

8 0
3 years ago
Read 2 more answers
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