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ELEN [110]
3 years ago
14

The smallest integer that can be added to -2m3 − m + m2 + 1 to make it completely divisible by m + 1 is .

Mathematics
1 answer:
dangina [55]3 years ago
4 0

Recall the polynomial remainder theorem: if m-c is a factor of some polynomial p(m), then the remainder upon dividing p(m) by m-c is p(c).

Let c=-1 and p(m)=-2m^3+m^2-m+1. The remainder left from dividing p(m) by m+1 is

p(-1)=-2(-1)^3+(-1)^2-(-1)+1=5

If we subtract 5 from both sides, we'd get a "remainder" of 0, which suggests that we have to add -5 to p(m) to make m+1 a factor.

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Jasmine recorded the number of minutes she spent doing homework each day during the months of March and April.
larisa [96]

Answer:

5647

Step-by-step explanation:

You go to the store and get some chips to kill your dad

6 0
2 years ago
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
3 years ago
How do you solve 42 divided by 63
Dafna1 [17]

42  ÷ 63

  63 -> 420

63x6=378


420-378=42

       63->420


So, how many times does 63 go into 42? Well, it doesn't. So put down a zero on your paper, and then a decimal. So if we add a zero onto 42, it becomes 420. Well, 420 is divisible by 63. In fact, 63 goes into 420 6 times, making a total of 378. 420-378 = 42. Then the process begins again. So you've got a 0.6, and that six just keeps on repeating. On paper, you're gonna wanna put a dash over the six to show that it's repeating.


Anyways, the answer is .66 repeating.

6 0
3 years ago
Read 2 more answers
When 5 times a number is added to 45 the answer is the sm of 85 and 140 what is the number
zimovet [89]

Hello.

First, let the number be r.

5 times r is written like this:

\rm{5r}

Now, add 45:

\mathrm{5r+45}

Now, the sum of 5r+45 is equal to the sum of 85 and 140:

\mathrm{5r+45=85+140}

In order to solve this equation, we need to add 85 and 140:

\mathrm{5r+45=225}

Now, subtract 45 from both sides:

\mathrm{5r+45-45=225-45}

\mathrm{5r=225-45}

\mathrm{5r=180}

The last step is to divide both sides by 5:

\mathrm{r=36}

Therefore, the answer is

\rm{r=36}

I hope it helps.

Have a nice day.

\boxed{imperturbability}

8 0
2 years ago
What's the equivalent expression ​
Mkey [24]

Answer:

2^52

Step-by-step explanation:

(8^-5/2^-2)^-4 = (2^-15/2^-2)^-4= (2^-13)^-4= 2^((-13*(-4))= 2^52

3 0
3 years ago
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