Suppose f"(x) = -9 sin(3x) and f'(0) = -4, and f(0) = -2<br> Find f(pi/4)

stepan [7]

Sometimes it helps to put a number line in front of you. If one number is to the left of the other number on the number line, it's a lower number. If one number is to the right of the other number on the number line, it is greater.

-5 -4 -3 -2 -1 0 1 2 3 4 5

4 is a solution of x<-5
FALSE: 4 is not greater than -5

-3 is a solution of y>-2
FALSE: -3 is not greater than -2

y≤3 includes 3 as a possible solution
TRUE: 3 is less than OR EQUAL to 3

Hope this helps! :)

4 0

2 years ago

A line joins the point

Harrizon [31]

Intersection of the first two lines:

$\begin{cases}5x - 2y + 3 = 0\\4x - 3y + 1 = 0\end{cases}$

Multiply the first equation by 4 and the second by 5:

$\begin{cases}20x - 8y + 12 = 0\\20x - 15y + 5 = 0\end{cases}$

Subtract the two equations:

$(20x - 8y + 12)-(20x - 15y + 5)=0 \iff 7y+7=0 \iff y=-1$

Plug this value for y in one of the equation, for example the first:

$5x - 2\cdot (-1) + 3 = 0\iff 5x+5=0 \iff x=-1$

So, the first point of intersection is $(-1,-1)$

We can find the intersection of the other two lines in the same way: we start with

$\begin{cases}x=y\\x=3y+4\end{cases}$

Use the fact that x and y are the same to rewrite the second equation as

$x=3x+4 \iff 2x=-4 \iff x=-2$

And since x and y are the same, the second point is $(-2, -2)$

So, we're looking for a line passing through $(-1,-1)$ and $(-2, -2)$ . We may use the formula to find the equation of a line knowing two of its points, but in this case it is very clear that both points have the same coordinates, so the line must be $y=x$

In the attached figure, line $5x - 2y + 3 = 0$ is light green, line $4x - 3y + 1 = 0$ is dark green, and their intersection is point A.

Simiarly, line $x=y$ is red, line $x = 3y + 4$ is orange, and their intersection is B.

As you can see, the line connecting A and B is the red line itself.

5 0

2 years ago

Evaluate the following f(-2)+f(-3)=

8090 [49]

It would be =-5f
Hope this helps

7 0

2 years ago

Bryan is asked to write an inequality to represent the graph.

Fittoniya [83]

The error that Bryan has done in this inequality is that he included –14 in his solution set.

<h3>How to point out the mistake made</h3>

What Bryan has to do would be to write this inequality in such a way that the variable would appear on the left.

But the symbol that he has chosen does not move in this same direction as the graph.

The -14 should not be inclusive in the graph because it is not a part of the graph solution.

He used the wrong number in this inequality.

Suppose f"(x) = -9 sin(3x) and f'(0) = -4, and f(0) = -2 Find f(pi/4)