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3 years ago

Is the orthocenter of a triangle on the inside ?

Mathematics

2 answers:

Olegator [25]3 years ago

8 0

It isn’t always in the triangle

likoan [24]3 years ago

7 0

Answer:

It turns out that all three altitudes always intersect at the same point - the so-called orthocenter of the triangle. The orthocenter is not always inside the triangle. If the triangle is obtuse, it will be outside. To make this happen the altitude lines have to be extended so they cross.

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The interest rate r required to increase your investment p to the amount a in t years is found by . Find the interest rate r for

Dahasolnce [82]

Answer:

The interest rate was of 0.1173 = 11.73%.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

$E = P*I*t$

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

$A = E + P$

In this problem, we have that:

$A = 10000, P = 8100, t = 2$

$A = E + P$

$10000 = E + 8100$

$E = 1900$

$1900 = 8100*I*2$

$I = \frac{1900}{8100*2}$

$I = 0.1173$

The interest rate was of 0.1173 = 11.73%.

7 0

3 years ago

What’s X and how did you find it?

Gre4nikov [31]

Answer:

X=12

Step-by-step explanation:

2/3x-5=1/2x-3

2/3x=1/2x+2

2/3x-1/2x=2

(6)1/6x=2(6)

X=12

I am not sure

8 0

4 years ago

Sin(x+2y)=cos(2x -y)

patriot [66]

$~~~~~~~\sin (x+2y) = \cos (2x-y)\\\\\\\implies \dfrac{d}{dx} \sin(x+2y) = \dfrac{d}{dx} \cos (2x-y)\\\\\\\implies \cos(x+2y)\dfrac{d}{dx}(x+2y) = -\sin(2x-y) \dfrac{d}{dx}(2x-y)~~~~~~~~~~~;[\text{Chain rule}]\\\\\\\implies \cos(x+2y) \left(1+2 \dfrac{dy}{dx}\right) = -\sin(2x-y)\left(2-\dfrac{dy}{dx} \right)\\\\\\\implies \cos(x+2y) + 2\cos(x+2y)\dfrac{dy}{dx} = -2\sin(2x-y)+\sin(2x-y) \dfrac{dy}{dx}\\ \\\\$

$\implies \sin(2x-y) \dfrac{dy}{dx} - 2\cos(x+2y) \dfrac{dy}{dx} = \cos(x+2y) + 2\sin (2x-y)\\\\\\\implies \left[\sin(2x-y) -2\cos(x+2y) \right] \dfrac{dy}{dx} = \cos(x+2y) + 2\sin (2x-y)\\\\\\\implies \dfrac{dy}{dx} = \dfrac{\cos(x+2y) + 2\sin (2x-y)}{\sin(2x-y) -2\cos(x+2y) }$