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3 years ago

Which of the following are true statements?

Mathematics

2 answers:

german3 years ago

4 0

Answer:

A, D

Step-by-step explanation:

They are true statements.

puteri [66]3 years ago

3 0

Answer: The answers are (A) and (C).

Step-by-step explanation: We are given four statements related to the graphs of the functions $f(x)=\sqrt x~~\textup{and}~~f(x)=2\sqrt x$ , out of which we are to select all the correct ones.

In the attached figure, the graphs of both the functions are shown.

We can see that the domain and range of the functions are same and are equal to [0, ∞) and [0, ∞) respectively.

Also the graph of $f(x)=2\sqrt x$ looks like the graph of $f(x)=\sqrt x$ but stretched vertically by a factor of 2.

Thus, the correct statements are (A) and (C).

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Answer:

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Answer:

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Solve the given initial-value problem. (Use x as the independent variable.) 2y'y'' = 1, y(0) = 2, y'(0) = 1

elixir [45]

Answer: y(x) = (2/3)*(x + 1)^(3/2) + 1/3.

Step-by-step explanation:

We have the differential equation:

2*y'(x)*y''(x) = 1.

y(0) = 2

y'(0) = 1.

I will use the change:

u = y'

u'= y''

Then we must solve:

2*u*u' = 1.

The product does not depend on x:

u*u' = 1/2.

By looking at the problem, i know that the functions must be something like:

u = a*(x + b)^n

Where a and b are real numbers.

u' = n*a*(x + b)^(n - 1)

such that:

(x + b)^n*(x + b)^(n - 1) does not depend on x

This means that:

(x + b)^n*(x + b)^(n - 1) = (x + b)^(n + n - 1) = 0

n + n - 1 = 0

2n = 1

n = 1/2

Then:

u = a*(x + b)^(1/2)

u' = (a/2)*(x + b)^(-1/2)

The differential equation becomes:

u*u' = 1/2

a*(x + b)^(1/2)* (a/2)*(x + b)^(-1/2) = 1/2

(1/2)*a^2 = 1/2

a^2 = 1.

And by the initial conditions, we have:

y'(0) = u(0) = 1

then:

u(0) = a*(0 + b)^(1/2) = a*b^(1/2) = 1

now, if a = -1, then b^(1/2) must be negative, this can not really be then we must have:

a = 1

u(0) = 1*b^(1/2) = 1

then b = 1.

u(x) = (x + 1)^(1/2).

And remember that y'(x) = u(x).

Then we need to integrate u(x) over x.

let's use the change of variables:

w = x + 1

dw = dx

Then the integration of u(x) is:

y(w) = ∫(w)^(1/2)dw = (2/3)*w^(3/2) + c

where c is a constant of integration.

now we can go back to x:

y(x) = (2/3)*(x + 1)^(3/2) + c

And we know that:

y(0) = 1 = (2/3)*(0 + 1)^(3/2) + c

1 = (2/3)*1 + c

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Then:

y(x) = (2/3)*(x + 1)^(3/2) + 1/3.

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What is the slope of the line passing through the points (−3, 4) and (2, −1)?

kobusy [5.1K]

I think it would be D:-1

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Korolek [52]

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Given-

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