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3 years ago

NEED ASAP

Mathematics

1 answer:

Lera25 [3.4K]3 years ago

5 0

Answer:

Step-by-step explanation:

Rational numbers come in 3 different forms; integers, fractions and terminating or recurring decimals such as

Irrational numbers are quite 'messy'. They can't be written as fractions, they are never-ending, non-repeating decimals. An example of this is the value of

A whole number can be called an integer and is either a positive or negative number, or zero. An example of this is

and

−

365

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Find the point on the hyperbola xy= 8 that is closet to the point (3,0)

son4ous [18]

The distance $l$ between $(x, y)$ and $(3, 0)$ is:
$l=\sqrt{(0-y)^{2}+(3-x)^{2}}=\sqrt{y^{2}+(3-x)^{2}}$

Since the equation of the hyperbola is $xy=8$ , we can get $y$ by itself and end up with
$y=\frac{8}{x}$

which we can plug into our distance formula:
$l=\sqrt{(\frac{8}{x})^{2}+(3-x)^{2}}$

To make calculation easier, we'll square both sides:
$l^{2}=(\frac{8}{x})^2+(3-x)^{2}$
and create a new variable $m=l^{2}$ :
$m=(\frac{8}{x})^2+(3-x)^{2}$
$\rightarrow m=\frac{64}{x^{2}}+9-6x+x^{2}$

Differentiate both sides:
$\frac{dm}{dx}=-\frac{128}{x^{3}}-6+2x$
Minimum distance is achieved when $\frac{dm}{dx}=0$ :
$-\frac{128}{x^{3}}-6+2x=0$
$\rightarrow -128-6x^{3}+2x^{4}=0$
$\rightarrow 2(x^{4}-3x^{3}-64)=0$
$\rightarrow x^{4}-3x^{3}-64=0$

To find a value of $x$ , you can use methods like synthetic division and get the answer $x=4$

Plug into $xy=8$ :
$4y=8$
$\rightarrow y=2$

So the closest point on the hyperbola to $(3, 0)$ is $(4, 2)$

7 0

3 years ago

What percent of the boxes have x's in them

Sveta_85 [38]

It is a 4 by 8 grid. So there are 32 squares total.
Now, count how many x's are on the boxes.
I counted 14 x'ed boxes.
Divide 14 by 32
14/32=0.4375
Now convert to a percent. Move the decimal two places to the left.
You get 43.75% as the answer.

6 0

4 years ago

Read 2 more answers

PLEASE HELP FOR BRAINLIEST

Ratling [72]

Answer:

232

Step-by-step explanation:

The formula for a triangle is base x height x 1/2

The triangles on the top and bottom have a base and height of 6 and 12 so: 6x12x1/2= 36 There are 2 of them so: 36 + 36 = 72

The triangles on the sides have a base and height of 8 and 14 so: 8x14x1/2=56 There are also 2 of them so: 56 + 56 = 112

The formula for the area of a rectangle is length x width