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3 years ago

Points X and Y are in plane Z. Any point collinear with X and Y is also in plane Z

Mathematics

2 answers:

mars1129 [50]3 years ago

8 0

Answer:

yes above statement is true

Step-by-step explanation:

mark me as brainliest ❤️

Wittaler [7]3 years ago

8 0

$\large \mathfrak{Answer : }$

Yes, it's true that Any point that is collinear to points X and Y also lies in the same Z plane among X and Y.

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What is the area of this triangle?

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Answer: 43.5

Step-by-step explanation:

$A=\frac{1}{2}(8)(12)(\sin 65^{\circ}) \approx \boxed{43.5}$

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2 years ago

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Consider the differential equation y'' − y' − 30y = 0. Verify that the functions e−5x and e6x form a fundamental set of solution

Alex Ar [27]

Answer:

Step-by-step explanation:

We have to take the derivatives for both functions and replace in the differential equation. Hence

for y=e^{-5x}:

$y(x)=e^{-5x}\\y'(x)=-5e^{-5x}\\y''(x)=25e^{-5x}\\$

for y=e^{6x}:

$y(x)=e^{6x}\\y'(x)=6e^{6x}\\y''(x)=36e^{6x}\\$

Now we replace in the differential equation y'' − y' − 30y = 0

for y=e^{-5x}:

$25e^{-5x}+5e^{-5x}-30e^{-5x}=0\\25+5-30=0$

for y=e^{6x}:

$36e^{6x}-6e^{6x}-30=0\\36-6+30=0$

Now, to know if both function are linearly independent we calculate the Wronskian

$W(f,g)=fg'-f'g$

$W(e^{-5x},e^{6x})=(e^{-5x})(6e^{6x})-(-5e^{-5x})(e^{6x})\neq 0$

I hope this is useful for you

Best regard

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3 years ago

Which equation could be used to find the length of the hypotenuse?

Allisa [31]

Answer: a^2 + b^2= c^2

Step-by-step explanation:

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2 years ago

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Just learn this throughout a quick lesson, can someone help?

suter [353]

Answer:

The Pythagorean theorem is a^2+b^2=c^2 where c is the length of the longest, diagonal side (diagonal means opposite the right angle/small square).

Step-by-step explanation:

If you're looking for a short side (i.e. next to the right angle), square the longest one and subtract the square of the other known.

If you're looking for a long side (i.e. opposite the right angle), square both you know and add them together.

In both cases, take the Square Root with your calculator, or by trial and error, find a number that squares to make your current number.

[1] A square of the number x is x times x.

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3 years ago