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4 years ago

Fgh is a right triangle true or false

Mathematics

2 answers:

joja [24]4 years ago

7 0

We need more info like maybe a picture

Rudik [331]4 years ago

4 0

Need more info bro lol

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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

3 years ago

A college bookstore charges $60 for a yearly membership. The first book is free with membership and any book after that costs $7

brilliants [131]

Answer:

The equation representing Total money spend being as a member is $m = 60+7.6(b-1)$

Step-by-step explanation:

Given:

Memberships charges = $60

Cost of 1 book = $7.60

Let number of books be 'b'.

We need to find Total money 'm' spend yearly on buying books after becoming member.

Now we know that 1 book is free for a member.

Total money spend 'm' will be equal to Sum Memberships charges and Cost of 1 book multiplied by number of books bought yearly minus 1.

Framing in equation form we get;

$m = 60+7.6(b-1)$

Hence The equation representing Total money spend being as a member is $m = 60+7.6(b-1)$

5 0

3 years ago

Solve the quadratic function by factoring. You must fill in

Stells [14]

Answer:

5x+2=0

Step-by-step explanation:

When factoring you add or subtract your factors that are similar.

For example 9x-4x+ 5x

and this is how you get 5x+2=0

Any Questions?

4 0

3 years ago

Read 2 more answers

Plzzz help asapppppp what is the inverse of f if f(x)=^3 sqrt x-5

jasenka [17]

Hello from MrBillDoesMath!

Answer:

The first choice, y = x^3 + 5

Discussion:

Let

y = (x-5) ^ (1/3)

To find the inverse, sway x and y and then solve for y:

x = ( y - 5 )^(1/3) => cube both sides

x^3 = y - 5 => add 5 to both sides

x^3 + 5 = y

So the inverse is x^3 + 5, which is the first choice

Thank you,

MrB

4 0

3 years ago

Read 2 more answers

A stadium has 50,000 seats. Seats sell for $35 in section A, $30 in section B, and $25 in section C. The number of seats in sect

Dennis_Churaev [7]

The answer is Section A. has 25,000 seats,section B. has 12,500 seats and section C. has 12,500 seats.

How I got to the answer.
I divided 50,000÷4=12,500 then I multiplied 12,500×2=25,000.
I hope this helps.

3 0

3 years ago