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Y_Kistochka [10]
2 years ago
14

The product of 5 and a number, decreased by 9, is 306. What is the number?

Mathematics
2 answers:
densk [106]2 years ago
7 0

Answer:

The number is 63

Step-by-step explanation:

Product means multiply

5n

Decreased by 9

5n-9

Is means equals

5n-9 = 306

Solve

5n-9 = 306

Add 9 to each side

5n-9+9 = 3-6+9

5n = 315

Divide by 5

5n/5 = 315/5

n = 63

steposvetlana [31]2 years ago
5 0

Step-by-step explanation:

bsbdjdkksnsbsvsvns NC Ricans Roxane Isiah

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Find the Center and the radius of the circle<br> x2 + y2 - 6x + 8y- 7 = 0.
777dan777 [17]

Answer:

C(3,-4), r=4*sqrt(2)

Step-by-step explanation:

C(p, q)

x^2+y^2+dx+ey+f=0

p=-d/2, q=-e/2, r^2=p^2+q^2-f

x^2+y^2 - 6x+8y-7=0

p=-(-6)/2=6/2=3

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r^2=9+16+7

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r=sqrt(32)

r=sqrt(16*2)

r=4*sqrt(2)

8 0
3 years ago
Solve y'' + 10y' + 25y = 0, y(0) = -2, y'(0) = 11 y(t) = Preview
svetlana [45]

Answer:  The required solution is

y=(-2+t)e^{-5t}.

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

y^{\prime\prime}+10y^\prime+25y=0,~~~~~~~y(0)=-2,~~y^\prime(0)=11~~~~~~~~~~~~~~~~~~~~~~~~(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

m^2e^{mt}+10me^{mt}+25e^{mt}=0\\\\\Rightarrow (m^2+10y+25)e^{mt}=0\\\\\Rightarrow m^2+10m+25=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow m^2+2\times m\times5+5^2=0\\\\\Rightarrow (m+5)^2=0\\\\\Rightarrow m=-5,-5.

So, the general solution of the given equation is

y(t)=(A+Bt)e^{-5t}.

Differentiating with respect to t, we get

y^\prime(t)=-5e^{-5t}(A+Bt)+Be^{-5t}.

According to the given conditions, we have

y(0)=-2\\\\\Rightarrow A=-2

and

y^\prime(0)=11\\\\\Rightarrow -5(A+B\times0)+B=11\\\\\Rightarrow -5A+B=11\\\\\Rightarrow (-5)\times(-2)+B=11\\\\\Rightarrow 10+B=11\\\\\Rightarrow B=11-10\\\\\Rightarrow B=1.

Thus, the required solution is

y(t)=(-2+1\times t)e^{-5t}\\\\\Rightarrow y(t)=(-2+t)e^{-5t}.

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