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3 years ago

What is the exponential function (0,25) (1,50) (2,100) (3,200) (4,400)

Mathematics

1 answer:

Rina8888 [55]3 years ago

4 0

Answer:

Step-by-step explanation:

If it is exponential dividing any term by the preceding term will be a constant, the common ratio or rate. 50/25=100/50...=2 The initial value, a, (at x=0) is 25 so the general form is

y=ar^x we have a=25 and r=2 so

y=25(2^x)

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Find the particular solution to y'=2sin(x) given the general solution is y=C-2cos(x) and the initial condition y(pi/3)=1

mezya [45]

ANSWER

The particular solution is:

$y=2-2 \cos(x)$

EXPLANATION

The given Ordinary Differential Equation is

$y'=2 \sin(x)$

The general solution to this Differential equation is:

$y=C-2 \cos(x)$

To find the particular solution, we need to apply the initial conditions (ICs)

$y( \frac{\pi}{3} ) = 1$

This implies that;

$C-2 \cos( \frac{\pi}{3} ) = 1$

$C-2( \frac{1}{2} )= 1$

$C-1= 1$

$C= 1 + 1 = 2$

Hence the particular solution is

$y=2-2 \cos(x)$

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