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Ganezh [65]
2 years ago
12

Use one of the triangles to approximate PQ in the triangle below.

Mathematics
1 answer:
s2008m [1.1K]2 years ago
4 0

Answer:

The answer is B 5.4 units

Step-by-step explanation:

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Find the general solution of the differential equation and check the result by differentiation. (Use C for the constant of integ
atroni [7]

Answer: y=Ce^(^3^t^{^9}^)

Step-by-step explanation:

Beginning with the first differential equation:

\frac{dy}{dt} =27t^8y

This differential equation is denoted as a separable differential equation due to us having the ability to separate the variables. Divide both sides by 'y' to get:

\frac{1}{y} \frac{dy}{dt} =27t^8

Multiply both sides by 'dt' to get:

\frac{1}{y}dy =27t^8dt

Integrate both sides. Both sides will produce an integration constant, but I will merge them together into a single integration constant on the right side:

\int\limits {\frac{1}{y} } \, dy=\int\limits {27t^8} \, dt

ln(y)=27(\frac{1}{9} t^9)+C

ln(y)=3t^9+C

We want to cancel the natural log in order to isolate our function 'y'. We can do this by using 'e' since it is the inverse of the natural log:

e^l^n^(^y^)=e^(^3^t^{^9} ^+^C^)

y=e^(^3^t^{^9} ^+^C^)

We can take out the 'C' of the exponential using a rule of exponents. Addition in an exponent can be broken up into a product of their bases:

y=e^(^3^t^{^9}^)e^C

The term e^C is just another constant, so with impunity, I can absorb everything into a single constant:

y=Ce^(^3^t^{^9}^)

To check the answer by differentiation, you require the chain rule. Differentiating an exponential gives back the exponential, but you must multiply by the derivative of the inside. We get:

\frac{d}{dx} (y)=\frac{d}{dx}(Ce^(^3^t^{^9}^))

\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*\frac{d}{dx}(3t^9)

\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*27t^8

Now check if the derivative equals the right side of the original differential equation:

(Ce^(^3^t^{^9}^))*27t^8=27t^8*y(t)

Ce^(^3^t^{^9}^)*27t^8=27t^8*Ce^(^3^t^{^9}^)

QED

I unfortunately do not have enough room for your second question. It is the exact same type of differential equation as the one solved above. The only difference is the fractional exponent, which would make the problem slightly more involved. If you ask your second question again on a different problem, I'd be glad to help you solve it.

7 0
2 years ago
A manufacturer compares its income f(x) to its expenses g(x) for x number of units sold. What does the solution to f(x) = g(x) r
Aliun [14]

Answer: The number of units sold when the manufactures home income equals the manufactures expenses

Step-by-step explanation:

3 0
2 years ago
Write the equation of a line in - form that contains the point (- 1, - 2) and is perpendicular to the line y = 5x - 10 degrees
galina1969 [7]

Answer:

y+2= -1/5(x+1)

Step-by-step explanation:

if lines are perpendicular their slopes are negative reciprocal

y=mx+b where m is the slope

y=5x-10 has the slope 5 so a perpendicular line will have slope -1/5

equation point slope form

(y-y1) = m(x-x1) where m is slope, and (x1,y1) any point that belongs to the line

y+2= -1/5(x+1)

3 0
2 years ago
State the vertex and axis of symmetry of the graph of y=ax2+c.
Neporo4naja [7]

State the vertex and axis of symmetry of the graph of y=ax^2+c

General form of quadratic equation is y=ax^2 + bx +c

There is no bx in our given equation, so we put 0x

Given equation can be written as y=ax^2 + 0x +c

a=a , b=0

Now we use formula to find vertex

x=\frac{-b}{2a}

x=\frac{-0}{2a}=0

Now we plug in 0 for 'a' and find out y

y=a(0)^2 + 0x +c= c

So our vertex is (0,c)

The axis of symmetry at x coordinate of vertex

So x=0 is our axis of symmetry


3 0
2 years ago
Read 2 more answers
Solve:<br> y" + 14y' + 49y = 8xe^-7x
erma4kov [3.2K]
The answer is 7x^2e-/8

8 0
2 years ago
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