Please answer i added extra points

10 fish are in a tank, 3 fish drown, how many fish are left?

taurus [48]

10. Fish don't drown (; nice try tho

6 0

2 years ago

Read 2 more answers

Show that every triangle formed by the coordinate axes and a tangent line to y = 1/x ( for x > 0)

vfiekz [6]

Answer:

Step-by-step explanation:

given a point $(x_0,y_0)$ the equation of a line with slope m that passes through the given point is

$y-y_0 = m(x-x_0)$ or equivalently

$y = mx+(y_0-mx_0)$ .

Recall that a line of the form $y=mx+b$ , the y intercept is b and the x intercept is $\frac{-b}{m}$ .

So, in our case, the y intercept is $(y_0-mx_0)$ and the x intercept is $\frac{mx_0-y_0}{m}$ .

In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph $(x_0,\frac{1}{x_0})$ . Which means that $y_0=\frac{1}{x_0}$

The slope of the tangent line is given by the derivative of the function evaluated at $x_0$ . Using the properties of derivatives, we get

$y' = \frac{-1}{x^2}$ . So evaluated at $x_0$ we get $m = \frac{-1}{x_0^2}$

Replacing the values in our previous findings we get that the y intercept is

$(y_0-mx_0) = (\frac{1}{x_0}-(\frac{-1}{x_0^2}x_0)) = \frac{2}{x_0}$

The x intercept is

$\frac{mx_0-y_0}{m} = \frac{\frac{-1}{x_0^2}x_0-\frac{1}{x_0}}{\frac{-1}{x_0^2}} = 2x_0$

The triangle in consideration has height $\frac{2}{x_0}$ and base $2x_0$ . So the area is

$\frac{1}{2}\frac{2}{x_0}\cdot 2x_0=2$

So regardless of the point we take on the graph, the area of the triangle is always 2.

6 0

2 years ago

Find the area of a regular pentagon with the apothem of 24.3 cm and a side length of 35.3

steposvetlana [31]

Answer: $A=2144\ cm^2$

Step-by-step explanation:

For this exercise you need to use the following formula for calculate the area of regular polygon:

$A=\frac{s^2n}{4tan(\frac{180}{n})}$

Where is "s" the length of any side, "n" is the number of sides.

Int this case you know that it is regular pentagon, which means that it has five sides. Then you can identify that the values of "n" and "s":

$s=35.3cm\\n=5$

Therefore, substituitng values into the formula, you get that the area f the pentagon is:

$A=\frac{(35.3cm)^2(5)}{4tan(\frac{180}{5})}\\\\A=2144\ cm^2$

8 0

2 years ago

How do I solve The sum of a number and 3 is subtracted from 10 the result is 5

meriva

State the given in the question

Given that the sum of a number and 3 is subtracted from, the result is 5

State what is to be found in the question

We are to find the number. In other to achieve this, we would follow the steps below:

Step 1: Represent the number with an unknown

Let x represent the number

Step 2: Interpret the given statement mathematically

If x is the number, then the sum of the number and 3 would be

$x+3$

Then the sum of a number and 3 subtracted from 10 would be

$10-(x+3)$

Finally, when the sum of a number and 3 subtracted from 10, the result is 5, would be

$10-(x+3)=5$

Step 3: Solve for x in the mathematical interpretation of the given statement

The value of x is as calculated as shown below:

$\begin{gathered} 10-(x+3)=5 \\ \text{Open the bracket or the parenthesis} \\ 10-x-3=5 \\ \text{collect like terms} \\ 10-3-5=x \\ 7-5=x \\ 2=x \\ \text{Therefore:} \\ x=2 \end{gathered}$

Hence, the number is 5

4 0

8 months ago

Grace is at a bookstore with $75 to spend. She has plans to buy a reference book that cost $18 and some novels that cost $12 how

elixir [45]

Answer:

Step-by-step explanation:

12x+18=75

-18=-18

12x= 57

Divide by 12.

57/12=4.75

Grace can buy 5 books including the reference book

7 0

2 years ago