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3 years ago

Mrs.Kunkleman asks her students to write the Pythagorean theorem in their own words

Mathematics

1 answer:

masha68 [24]3 years ago

5 0

Step-by-step explanation:

The Pythagorean theorem can be understood as a mathematical relationship between the sides of a right triangle that helps to understand geometric problems in real situations, such as finding measurements, calculating areas, etc.

The theorem says that the square of the hypotenuse is equal to the sum of the squares on the other sides.

In a right triangle the hypotenuse is the longest side of the triangle, on the side opposite to its longest angle, and the other two sides will be the sides. So the Pythagorean theorem formula is:

a² = b² + c²

where a represents the hypotenuse and b and c the other sides.

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For what positive values of k does the function y=sin(kt) satisfy the differential equation y''+144y=0 ?

lina2011 [118]

Answer:

The positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12

Step-by-step explanation:

To determine the positive values of k that the function y = sin(kt) satisfy the differential equation y''+144y=0.

First, we will determine y''.

From y = sin(kt)

y' = $\frac{d}{dt}(y)$

y' = $\frac{d}{dt}(sin(kt))\\$

y' = kcos(kt)

Now for y''

y'' = $\frac{d}{dt}(y')$

y'' = $\frac{d}{dt}(kcos(kt))$

y'' = $-k^{2}sin(kt)$

Hence, the equation y'' + 144y = becomes

$-k^{2}sin(kt)$ + $144(sin(kt))$ $= 0$

$(144 - k^{2})(sin(kt)) = 0$

$(144 - k^{2})= 0$

∴ $k^{2} = 144\\$

$k =$ ± $\sqrt{144}\\$

$k =$ ± $12$

∴ $k = +12$ or $-12$

Hence, the positive value of k that the function y = sin(kt) satisfies the differential equation y'' + 144y = 0 is +12

7 0

4 years ago

59, 61, 61, 69, 72, 74, 80 What is the median of the data?

Thepotemich [5.8K]

Answer:

Step-by-step explanation:

It's 69 because 69 is in the middle of all of this data when it is put in order from least to greatest.

5 0

3 years ago

what is the slope of a line that is perpendicular to the line that contains points (5,4) and (-7,9). explain please

Luba_88 [7]

Answer:

$\frac{12}{5}$

Step-by-step explanation:

First find the slope of the line containing points (5,4) and (-7,9). To find the slope use the formula $\frac{y_{2} -y_{1}}{x_{2}-x_{1}}$ . Putting those values in, you have

$\frac{9-4}{-7-5}$

Simplify

$\frac{5}{-12}$

$-\frac{5}{12}$

Then, to find the slope of the line perpendicular to that, find the negative reciprocal.

$\frac{12}{5}$

3 0

3 years ago

A.)ii. and iii. B.)ii. C.)i. D.)i. and iv.

Vlad [161]

The answer is B) ii

The notation "p --> q" means "if p, then q". For example

p = it rains
q = the grass gets wet

So instead of writing out "if it rains, then the grass gets wet" we can write "p --> q" or "if p, then q". The former notation is preferred in a math class like this.

So when is the overall statement p --> q false? Well only if p is true leads to q being false. Why is that? It's because p must lead to q being true. The statement strongly implies this. If it rained and the grass didn't get wet, then the original "if...then" statement would be a lie, which is how I think of a logical false statement.

If it didn't rain (p = false), then the original "if...then" statement is irrelevant. It only applies if p were true. If p is false, then the conditional statement is known to be vacuously true. So this why cases iii and iv are true.

4 0

3 years ago

Scale 1 in=8 feet So 1.24 in =

zepelin [54]

Answer:

9.92 feet or 9 feet 11 1/16 inches

Step-by-step explanation:

1.24X8 feet=9.92 feet or 9 feet 11 1/16 inches

4 0

2 years ago