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3 years ago

Solve 4^(2x) = 7^(x−1).

1 answer:

3 0

To solve for x in the given equation, use natural logarithms. Getting the natural logarithms of both sides, will be ln 4^(2x) = ln 7^(x-1). This is also equal to 2x ln 4 = (x-1) ln 7. Rearranging the equation, 2x/(x-1) = ln 7/ln 4. The right side is equal to 1.4037. Thus, the value of x is -2.3539.

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Help pls for brainliest

KIM [24]

Answer:

8x + 2x (4)

Step-by-step explanation:

If you are trying to simplify or isolate the variables, its 4. Please tell me if this answer is wrong

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3 years ago

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What is the prime factorization of 42?

Fed [463]

Answer:

2*3*7

Step-by-step explanation:

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Graph g(x)=-5|x+2|+2

Llana [10]

This is the graph for the equation, it crosses through points (0,-8) (-2,4) (-1.6,0) and its vertex is (-2,2)

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4 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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3 years ago

What is the period of the function f(x) shown in the graph?

mixas84 [53]

Answer:

8pi

Step-by-step explanation:

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3 years ago