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3 years ago

What is the center and radius of the circle? * (x - 2)² + (y – 9)^2= 4

Mathematics

1 answer:

Rudiy273 years ago

5 0

the center is (2,9)

and the radius is 2

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Find the greatest common factor of 24, 36, and 48. help

Dimas [21]

Answer:

24, 36, and 48

Step-by-step explanation:

those numbers are the most high common factor of 24, 36, and 48.

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3 years ago

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Which shape has parallel lines and at least one acute angle

galina1969 [7]

Answer:

Step-by-step explanation:

c is the only shape on here with acute angles, the top and bottom bases are parallel w/ each other

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2 years ago

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Find T, N, and kappa for the plane curve Bold r left parenthesis t right parenthesis equalsleft parenthesis 7 Bold cos t plus

pickupchik [31]

Answer:

Step-by-step explanation:

r(t) = (7 cost + 7t sin t)i + (7 sin t - 7t cos t)j

$\frac{d \bar r t}{dt} =(7\frac{d}{dt}\cos t + 7\frac{d}{dt} (t \sin t)i+(7\frac{d}{dt} \sin t-7\frac{d}{dt} t \cos t)j$

$=(7(-\sin t)+7(1* \sin t+t \cos t))i+(7 \cost -7(1*\cos t - t \sin t))j\\\\=7((-\sin t+\sin t+t \cos t)i+(\cos t-\cos t+t \sin t)j)\\\\=7((t\cos t)i+(t\sin t)j)$

$\bar r'(t)=\frac{d \bar r t}{dt} =(7t\cos t)i+(7t\sin t)j---(1)\\\\11\bar r(t)=\sqrt{(7t\cos t)^2+(7t\sin t)^2}\\\\=\sqrt{49t^2(\cos^2t+\sin^2 t)} \\\\=7t$

$\bar T (t)=\frac{\bar r'(t)}{11\bar r(t)11} =\frac{(7t\cos t)i+(7t\sin t)j}{7t} \\\\\barT(t)=(\cos t)i+(\sin t)j$

$\bar T'(t)=\frac{d}{dt} (\cos t)i+\frac{d}{dt} (\sin t) j\\\\\bar T'(t)=(-\sin t)i+(\cos t)j---(2)\\\\11\bar T'(t)=\sqrt{(-\sin t)^2+(\cos t)^2} \\\\=\sqrt{\sin^2t+\cos^2t} \\\\=1$

$\bar N(t)=\bar T'(t)=\frac{(-\sin t)i+(\cos t)j}{(1)} \\\\ \large \boxed {\bar N(t)=(-\sin t)i+(\cos t)j}$

$K(t)=\frac{|\b\r T'(t)|}{\bar r (t)|} \\\\=\frac{|-\sin t i+\cos t j|}{|7t\cos t +7t \sin t j|}$

Using eq (1) and (2)

$K(t)=\frac{\sqrt{(-\sin t)^2+(\cos t)^2} }{\sqrt{(7t\cos t)^2+(7t\sin t)^2} }\\\\=\frac{\sqrt{\sin^2 t+\cos^2t} }{\sqrt{49t^2(\cos^2 t+\sin^2t)} }\\\\=\frac{\sqrt{1} }{\sqrt{49t^2\times 1} } \\\\ \large \boxed {K(t)=\frac{1}{7t} }$

7 0

3 years ago

F(x) = -2|x-2|+4 vertical stretch by a factor of 2

stepladder [879]

A vertical stretch by a factor of 2 of F(x) = -2|x-2|+4 would result in the revised function G(x) = -4|x-2|+4. The vertex would stay in the same place (2,4).

5 0

3 years ago

Find AD. Show how you got your answer.

stealth61 [152]

Notice the picture below
the AD line is a bisector, cutting the 36 degrees A in half,
18 and 18 degrees each half

notice the tickmarks, the triangle is an isosceles,
if those two sides are equal, so are the angles they make
down below with the base

now, the base is 8, AD is bisecting that too, to 4 and 4

now, using the Law of Sines

$\bf \textit{Law of sines}
\\ \quad \\
\cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c}\\\\
----------------------------\\\\
\cfrac{sin(18^o)}{4}=\cfrac{sin(72^o)}{\overline{AD}}\implies \overline{AD}=\cfrac{4\cdot sin(72^o)}{sin(18^o)}$

keep in mind, the angles are in degrees, so, when taking the sines, make sure your calculator is in Degree mode

4 0

3 years ago