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yulyashka [42]
3 years ago
9

Help I will be marking brainliest!!!

Mathematics
1 answer:
baherus [9]3 years ago
3 0

Answer:

Angle k is 34.5 degrees

Step-by-step explanation:

a circle makes 360 degrees total.  okay so u have to consider the angles given. m arc go= 127

m<0 = 54.5

54.5 times 2 = 109

109 is arc gk

109 + 127+ 55= 291

360-291=69= arc OU

69 divided by 2 is 34.5

Angle k is 34.5 degrees

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Find the length of the following curve. If you have a​ grapher, you may want to graph the curve to see what it looks like.
stepladder [879]

The length of the curve y = \frac{1}{27}(9x^2 + 6)^\frac 32 from x = 3 to x = 6 is 192 units

<h3>How to determine the length of the curve?</h3>

The curve is given as:

y = \frac{1}{27}(9x^2 + 6)^\frac 32 from x = 3 to x = 6

Start by differentiating the curve function

y' = \frac 32 * \frac{1}{27}(9x^2 + 6)^\frac 12 * 18x

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The length of the curve is calculated using:

L =\int\limits^a_b {\sqrt{1 + y'^2}} \, dx

This gives

L =\int\limits^6_3 {\sqrt{1 + [x(9x^2 + 6)^\frac 12]^2}\ dx

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L =\int\limits^6_3 {\sqrt{1 + x^2(9x^2 + 6)}\ dx

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L =\int\limits^6_3 {\sqrt{9x^4 + 6x^2 + 1}\ dx

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brainly.com/question/14015568

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Step-by-step explanation:

A parabola is written in the form

f(x)=a((x-h)^2+k) (1)

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ak is the y-coordinate of the vertex of the parabola

a is a scale factor

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Substituting (2) and (3) into (1) we get the new expression:

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f(x)=\frac{1}{2}((x^2-8x+16)-6)=\frac{1}{2}(x^2-8x+10)=\frac{1}{2}x^2-4x+5

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