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Marat540 [252]
3 years ago
9

Suppose two adjacent endpoint of a rotated square are located at (-4, -6) and (5, -1) on the coordinates axes. What is the lengt

h of the side of the square?

Mathematics
1 answer:
Rufina [12.5K]3 years ago
8 0
To find the length of the side of the square, we just need to find the distance between the two endpoints. This problem can quickly be solved by using the distance formula, but for those who are not familiar with it, we can simply solve it by analyzing a triangle.

Take a look at the diagram below. We are interested in x. To find this we have created a right triangle. The horizontal component is just the distance between the x coordinates of the two points while the vertical component is the distance between the y coordinates.

The horizontal component is 9 and the vertical component is 5. We can now get x by using the pythagorean theorem:

x^{2}= 9^{2} + 5^{2} =81+25=106
x= \sqrt{106} which is approximately equal to 10.30 units.

ANSWER: 
The length of the side of the square measures 10.30 units.

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The point-slope form: y-y_0=m(x-x_0)

m = -1; (2; 4) \to x_0=2;\ y_0=4

subtitute

y - 2 = -1(x - 4)
6 0
3 years ago
Find the length of the curve y = integral from 1 to x of sqrt(t^3-1)
Arlecino [84]
y=\displaystyle\int_1^x\sqrt{t^3-1}\,\mathrm dt

By the fundamental theorem of calculus,

\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm d}{\mathrm dx}\displaystyle\int_1^x\sqrt{t^3-1}\,\mathrm dt=\sqrt{x^3-1}

Now the arc length over an arbitrary interval (a,b) is

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\displaystyle\int_a^bx^{3/2}\,\mathrm dx=\frac25x^{5/2}\bigg|_{x=a}^{x=b}=\frac25\left(b^{5/2}-a^{5/2}\right)
6 0
3 years ago
An angle measuring 3.5 radians is equal to which of the angle measures given below? Round your answer to 2 decimal places after
Vaselesa [24]
2 x pi radians = 360 degrees, [remember this formula]
2 x 3.14 = 6.28 radians = 360 degrees
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closest answer would be b ) 200.54 degrees 
 

3 0
3 years ago
Read 2 more answers
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katen-ka-za [31]

Answer:

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Step-by-step explanation:

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Vertices of K ≡ (-8 , -1) which shows K is in third quadrant. When K is reflected across the line y = -1, the point K remains where it is (in the third quadrant) as it is on the line y = -1 only.

Vertices of L ≡ (5 , 1) which shows L is in first quadrant. When L is reflected across the line y = -1, the point L moves to fourth quadrant as L' with coordinates (5 , -3).

Thus each of the first, fourth and third quadrant contains a vertex except the second quadrant.

4 0
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Lilit [14]

Answer:

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Step-by-step explanation:

5 0
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