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taurus [48]
3 years ago
9

In which step did Samuel make an error?

Mathematics
2 answers:
FrozenT [24]3 years ago
6 0

Answer:

In step 3

Step-by-step explanation:

Darina [25.2K]3 years ago
6 0

Answer:

step 3

Step-by-step explanation:

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Solve 5y'' + 3y' – 2y = 0, y(0) = 0, y'(0) = 2.8 y(t) = 0 Preview
mario62 [17]

Answer:  The required solution is

y(t)=-\dfrac{7}{3}e^{-t}+\dfrac{7}{3}e^{\frac{1}{5}t}.

Step-by-step explanation:   We are given to solve the following differential equation :

5y^{\prime\prime}+3y^\prime-2y=0,~~~~~~~y(0)=0,~~y^\prime(0)=2.8~~~~~~~~~~~~~~~~~~~~~~~~(i)

Let us consider that

y=e^{mt} be an auxiliary solution of equation (i).

Then, we have

y^prime=me^{mt},~~~~~y^{\prime\prime}=m^2e^{mt}.

Substituting these values in equation (i), we get

5m^2e^{mt}+3me^{mt}-2e^{mt}=0\\\\\Rightarrow (5m^2+3y-2)e^{mt}=0\\\\\Rightarrow 5m^2+3m-2=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow 5m^2+5m-2m-2=0\\\\\Rightarrow 5m(m+1)-2(m+1)=0\\\\\Rightarrow (m+1)(5m-1)=0\\\\\Rightarrow m+1=0,~~~~~5m-1=0\\\\\Rightarrow m=-1,~\dfrac{1}{5}.

So, the general solution of the given equation is

y(t)=Ae^{-t}+Be^{\frac{1}{5}t}.

Differentiating with respect to t, we get

y^\prime(t)=-Ae^{-t}+\dfrac{B}{5}e^{\frac{1}{5}t}.

According to the given conditions, we have

y(0)=0\\\\\Rightarrow A+B=0\\\\\Rightarrow B=-A~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)

and

y^\prime(0)=2.8\\\\\Rightarrow -A+\dfrac{B}{5}=2.8\\\\\Rightarrow -5A+B=14\\\\\Rightarrow -5A-A=14~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{Uisng equation (ii)}]\\\\\Rightarrow -6A=14\\\\\Rightarrow A=-\dfrac{14}{6}\\\\\Rightarrow A=-\dfrac{7}{3}.

From equation (ii), we get

B=\dfrac{7}{3}.

Thus, the required solution is

y(t)=-\dfrac{7}{3}e^{-t}+\dfrac{7}{3}e^{\frac{1}{5}t}.

7 0
2 years ago
What are the coordinates of the point (1, –6) after a counter clockwise rotation of 90° about the origin?
IgorLugansk [536]
(-6 ,-1) is the correct answer
4 0
2 years ago
Read 2 more answers
Answer choice <br> D) A worker with 15 years of service gets 5 weeks of vacation and each year.
otez555 [7]

Answer: it seems to be D, but the equation makes practically no sense!

The value of the factor changes for the different amounts of service years and vacation weeks.

Step-by-step explanation: The equation means that the employee is trying to figure out the value of the "v-factor" for how vacation time is earned.

If you substitute the number of service years into the left side of the "formula" and vacation weeks on the right side, then solve for "v", v(15)=5 you get v= 1/3 or 0.33

If you substitute other numbers, like v(2)=2, so v= 1 then v(30) = 8, v = 4/15 or 0.2667. You see the factor's value decreases. The company is much more generous to to employees with one or two years of service than with the older ones.

7 0
2 years ago
Match the correct equation for the variable n with * for number of times compound interest is figured. quarterly d.___ semi-annu
Dvinal [7]

Answer:

quarterly N = 4

semi-annually N = 2

Monthly N = 12

annually N = 1

Step-by-step explanation:

Given the following compound interest times :

N = number of times interest is compounded per period :

A period is regarded as a whole year.

Interest compounded;

QUARTERLY = Every 4 months per period = 12/3= 4

SEMI ANNUALLY = Every 6 months per period = 12/6 = 2

MONTHLY = Every month = 12 / 1 = 12

ANNUALLY = Every 12 months = 12 /12 = 1

3 0
2 years ago
Parallel lines m and n are cut by a transversal t. Which two angles are NOT corresponding angles?
Alex787 [66]
1 and 6 are not corresponding angles. They have different degrees. hope this helps :)
6 0
2 years ago
Read 2 more answers
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