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Alla [95]
3 years ago
13

I need help ASAP

Mathematics
1 answer:
Firdavs [7]3 years ago
7 0
I think it’s B I’m not sure
You might be interested in
Write one number that is a factor of 13.
maw [93]

Answer: 1 and 13

Step-by-step explanation: To find the factors of 13, begin by dividing 13 by 1 which gives us 13. This tells us that 1 and 13 are factors of 13.

13 is a prime number which means it only has two factors which are 1 and 13.

3 0
3 years ago
Read 2 more answers
Apply the method of undetermined coefficients to find a particular solution to the following system.wing system.
jarptica [38.1K]
  • y''-y'+y=\sin x

The corresponding homogeneous ODE has characteristic equation r^2-r+1=0 with roots at r=\dfrac{1\pm\sqrt3}2, thus admitting the characteristic solution

y_c=C_1e^x\cos\dfrac{\sqrt3}2x+C_2e^x\sin\dfrac{\sqrt3}2x

For the particular solution, assume one of the form

y_p=a\sin x+b\cos x

{y_p}'=a\cos x-b\sin x

{y_p}''=-a\sin x-b\cos x

Substituting into the ODE gives

(-a\sin x-b\cos x)-(a\cos x-b\sin x)+(a\sin x+b\cos x)=\sin x

-b\cos x+a\sin x=\sin x

\implies a=1,b=0

Then the general solution to this ODE is

\boxed{y(x)=C_1e^x\cos\dfrac{\sqrt3}2x+C_2e^x\sin\dfrac{\sqrt3}2x+\sin x}

  • y''-3y'+2y=e^x\sin x

\implies r^2-3r+2=(r-1)(r-2)=0\implies r=1,r=2

\implies y_c=C_1e^x+C_2e^{2x}

Assume a solution of the form

y_p=e^x(a\sin x+b\cos x)

{y_p}'=e^x((a+b)\cos x+(a-b)\sin x)

{y_p}''=2e^x(a\cos x-b\sin x)

Substituting into the ODE gives

2e^x(a\cos x-b\sin x)-3e^x((a+b)\cos x+(a-b)\sin x)+2e^x(a\sin x+b\cos x)=e^x\sin x

-e^x((a+b)\cos x+(a-b)\sin x)=e^x\sin x

\implies\begin{cases}-a-b=0\\-a+b=1\end{cases}\implies a=-\dfrac12,b=\dfrac12

so the solution is

\boxed{y(x)=C_1e^x+C_2e^{2x}-\dfrac{e^x}2(\sin x-\cos x)}

  • y''+y=x\cos(2x)

r^2+1=0\implies r=\pm i

\implies y_c=C_1\cos x+C_2\sin x

Assume a solution of the form

y_p=(ax+b)\cos(2x)+(cx+d)\sin(2x)

{y_p}''=-4(ax+b-c)\cos(2x)-4(cx+a+d)\sin(2x)

Substituting into the ODE gives

(-4(ax+b-c)\cos(2x)-4(cx+a+d)\sin(2x))+((ax+b)\cos(2x)+(cx+d)\sin(2x))=x\cos(2x)

-(3ax+3b-4c)\cos(2x)-(3cx+3d+4a)\sin(2x)=x\cos(2x)

\implies\begin{cases}-3a=1\\-3b+4c=0\\-3c=0\\-4a-3d=0\end{cases}\implies a=-\dfrac13,b=c=0,d=\dfrac49

so the solution is

\boxed{y(x)=C_1\cos x+C_2\sin x-\dfrac13x\cos(2x)+\dfrac49\sin(2x)}

7 0
3 years ago
The large bottle of nasal spray is 9.46 centimeters tall. The small bottle is 5.29 centimeters tall. How much shorter is the sma
posledela

Answer:

4.17 centimeters

Step-by-step explanation:

The large bottle of nasal spray is 9.46 centimeters tall. Assuming that the large bottle of nasal spray has the shape of cylinder, then the height of the cylinder is 9.46 centimeters.

The small bottle is 5.29 centimeters tall. Assuming that the small bottle of nasal spray has the shape of a cylinder too, then the height of the cylinder is 9.46 centimeters.

We want to know how much shorter the smaller bottle is than the big bottle. This is calculated by

Height of big bottle - height of small bottle

= 9.46 centimeters. - 5.29 centimeters

= 4.17 centimeters

5 0
3 years ago
30 points please answer honestly. Geometry help needed. <br> D is 9.32
Vadim26 [7]

Answer:

7.75 m

Step-by-step explanation:

First find the circumference. Use the formula C = 2πr

C = 2(3.14)(3)

C = 18.84

148° is a fraction of the entire circle which is 360°

Multiply

18.84/1 x 148/360

2788.32/360

7.745

4 0
2 years ago
Write a recursive rule and an explicit rule for the<br> sequence<br> 3,7,11,15
m_a_m_a [10]

Answer:

The Recursive formula for the sequence is:

aₙ = aₙ₋₁ + d

The Explicit formula for the sequence is:

a_n=4n-1

Step-by-step explanation:

Given the sequence

3,7,11,15

Here:

a₁ = 3

computing the differences of all the adjacent terms

7 - 3 = 4, 11 - 7 = 4, 15 - 11 = 4

The difference between all the adjacent terms is the same and equal to

d = 4

We know that a recursive formula basically defines each term of a sequence using the previous term(s).

The recursive formula of the Arithmetic sequence always involves the first term.

a₁ = 3

We know that, in the Arithmetic sequence, every next term can be obtained by adding the common difference and the preceding term.

so

The recursive formula of the sequence is:

aₙ = aₙ₋₁ + d

substitute n = 2 to find the 2nd term

a₂ = a₂₋₁ + d

a₂ = a₁+ d

substitute a₁ = 3 and d = 4

a₂ = 3 + 4

a₂ = 7

Thus, the recursive formula for the sequence 3,7,11,15 is:

aₙ = aₙ₋₁ + d

<u>An explicit rule for the sequence</u>

Given the sequence

3,7,11,15

We already know that

a₁ = 3

d = 4

An arithmetic sequence has a constant difference 'd' and is defined by  

a_n=a_1+\left(n-1\right)d

substituting a₁ = 3 and d = 4

a_n=4\left(n-1\right)+3

a_n=4n-4+3

a_n=4n-1

Therefore, an explicit rule for the  sequence

a_n=4n-1

6 0
2 years ago
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