Find the mean for this of data: 18, 26, 16, 14, 26

Find the area of the following figure below

icang [17]

140
explanation: ......

6 0

2 years ago

Question 5: prove that it’s =0

mamaluj [8]

Answer:

Proof in explanation.

Step-by-step explanation:

I'm going to attempt this by squeeze theorem.

We know that $\cos(\frac{2}{x})$ is a variable number between -1 and 1 (inclusive).

This means that $-1 \le \cos(\frac{2}{x}) \le 1$ .

$x^4 \ge 0$ for all value $x$ . So if we multiply all sides of our inequality by this, it will not effect the direction of the inequalities.

$-x^4 \le x^4 \cos(\frac{2}{x}) \le x^4$

By squeeze theorem, if $-x^4 \le x^4 \cos(\frac{2}{x}) \le x^4$

and $\lim_{x \rightarrow 0}-x^4=\lim_{x \rightarrow 0}x^4=L$ , then we can also conclude that $\im_{x \rightarrow} x^4\cos(\frac{2}{x})=L$ .

So we can actually evaluate the "if" limits pretty easily since both are continuous and exist at $x=0$ .

$\lim_{x \rightarrow 0}x^4=0^4=0$

$\lim_{x \rightarrow 0}-x^4=-0^4=-0=0$ .

We can finally conclude that $\lim_{\rightarrow 0}x^4\cos(\frac{2}{x})=0$ by squeeze theorem.

Some people call this sandwich theorem.

6 0

2 years ago

A local hamburger shop sold a combined total of hamburgers and cheeseburgers on Thursday. There were fewer cheeseburgers sold th

myrzilka [38]

Answer:

the number of hamburgers sold on Thursday were 325.

Step-by-step explanation:

The total number of hamburger and cheese burger is missing

i will replace it with any figure, you can replace it wit your given data and you will get the solution.

A local hamburger shop sold a combined total of 593 hamburgers and cheeseburgers on Thursday

There were 57 fewer cheeseburgers sold than hamburgers

How many hamburgers were sold on thursday

Let h be the number of hamburgers and c be the number of cheeseburgers.

Using this information we can set up two equation as:

$h+c=593\\c=h-57$

Now we need to solve these two equations to get the value of number of hamburgers. For that we use substitution method as shown below:

$h+h-57=593\\2h-57=593\\2h=650\\h=325$

Therefore, the number of hamburgers sold on Thursday were 325.

6 0

2 years ago

2. Graph the following equation: y = - 1/2 x + 4

Murljashka [212]

Answer:

Step-by-step explanation:

y = (-1/2)x + 4 is the equation of a straight line with y-intercept (0, 4) and slope -1/2.

To graph this, first plot the y-intercept (0, 4).

Recall that slope m = rise / run, and notice that the slope in this particular case is -1/2 = rise / run, or rise = -1 and run = 2.

Starting with your pencil point on (0, 4), move the point 2 units to the right (run = 2), arriving at (2, 4). Next, move your pencil point 1 unit down, to (2, 3).

Draw a straight line through (0, 4) and (2, 3).

8 0

2 years ago

Which of the following is a solution to the differential equation xy′−3y=6 ?

ololo11 [35]

Answer:

$y = 5 {x}^{3} - 2$

Step-by-step explanation:

The given differential equation is :

xy′−3y=6

We want to determine which of the following options is a solution to the differential equations.

The function that satisfies the differential equation is a solution.

We can verify that

$y = 5 {x}^{3} - 2$

satisfy this differential equation.

We differentiate to get:

$y' = 15 {x}^{2}$

We substitute the function and its derivative into the differential equation to get:

$x(15 {x}^{2}) - 3(5 {x}^{3} - 2) = 6$

We expand and simplify on the left:

$15 {x}^{3}- 15 {x}^{3} + 6= 6$

This simplifies to:

$6 = 6$

Verified.

We can show that all the other functions do not satisfy this differential equation

4 0

3 years ago