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3 years ago

Show whether or not the points with coordinates (1,3) (4,2) (-2,6) are vertices of a right triangle

Mathematics

1 answer:

katen-ka-za [31]3 years ago

8 0

Answer:

Step-by-step explanation:

See attached

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How do I differentiate this?

disa [49]

Answer:

$\frac{8}{\left(-x+2\right)^2}$ & $x = 1, x = 3$

Step-by-step explanation:

I'm sure you are familiar with the product rule,

If y = u*v => dy/dx = u * dv/dx + v * dy/dx <----- product rule

In this case:

$u=3x+2,\:v=\left(2-x\right)^{-1},\\=>\frac{d}{dx}\left(3x+2\right)\left(2-x\right)^{-1}+\frac{d}{dx}\left(\left(2-x\right)^{-1}\right)\left(3x+2\right)$

Now remember the sum rule:

$\frac{d}{dx}\left(3x+2\right) = \frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(2\right),\\\frac{d}{dx}\left(3x\right) = 3,\\\frac{d}{dx}\left(2\right) = 0\\\frac{d}{dx}\left(3x+2\right) = 3$

For this second bit we apply the chain rule:

$\frac{d}{dx}\left(\left(2-x\right)^{-1}\right) = -\frac{1}{\left(2-x\right)^2}\frac{d}{dx}\left(2-x\right),\\\frac{d}{dx}\left(2-x\right) = -1,\\\\=> -\frac{1}{\left(2-x\right)^2}\left(-1\right)\\=> \frac{1}{\left(2-x\right)^2}$

If we substitute these values back into the expression... $\frac{d}{dx}\left(3x+2\right)\left(2-x\right)^{-1}+\frac{d}{dx}\left(\left(2-x\right)^{-1}\right)\left(3x+2\right)$

...we get the following:

$3\left(2-x\right)^{-1}+\frac{1}{\left(2-x\right)^2}\left(3x+2\right)$

The rest is just pure simplification:

$3\left(2-x\right)^{-1}+\frac{1}{\left(2-x\right)^2}\left(3x+2\right)\\= \frac{3}{-x+2}+\frac{3x+2}{\left(-x+2\right)^2}\\= \frac{3\left(-x+2\right)}{\left(-x+2\right)^2}+\frac{3x+2}{\left(-x+2\right)^2}\\\\= \frac{3\left(-x+2\right)+3x+2}{\left(-x+2\right)^2}\\\\= \frac{8}{\left(-x+2\right)^2}$

Now let's equate this to equal 8 for the second bit and solve for x:

$\frac{8}{\left(-x+2\right)^2}=8,\\\frac{8}{\left(-x+2\right)^2}\left(-x+2\right)^2=8\left(-x+2\right)^2,\\8=8\left(-x+2\right)^2,\\\left(-x+2\right)^2=1,\\x = 1, x = 3$

4 0

3 years ago

The difference of a and b is?

Yakvenalex [24]

A-b
difference means subtract

8 0

4 years ago

Please help :/<br><br> 20 POINTS

Dmitry [639]

Answer:

25.1!

Step-by-step explanation:

all you have to do is C=2πr=2·π·4≈25.13274

To calculate the circumference of a circle, multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2×radius with pi (π=3.14).

Hope that helped! :)

3 0

3 years ago

Read 2 more answers

1. Which of the following is the standard form of y = (x – 3)(x – 7)?

Andrej [43]

9514 1404 393

Answer:

b. y = (x - 5)² - 4

Step-by-step explanation:

Here, we take "standard form" to mean "vertex form."

In the US, "standard form" would be ...

y = x² -10x +21

Vertex form is ...

y = (x -5)² -4 . . . . matches B

4 0

3 years ago

Solve for f.<br> 9f = 8f + 8<br> f

Svet_ta [14]

Answer:

f = 8

Step-by-step explanation:

9f = 8f + 8

9f - 8f

= f

So, f = 8

9(8) = 8(8) + 8

72 = 72

6 0

3 years ago

Read 2 more answers