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jolli1 [7]
3 years ago
10

Can someone plss help me

Mathematics
1 answer:
puteri [66]3 years ago
7 0
0/3 is the same thing as 0, so write those nxt to each other. Then 1/3, 2/3. Lastly 3/3 is the same as 1, so write those nxt to each other.
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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
Joe would like to paint a rectangular shaped wall. The measures of dimensions of the wall are 8 inches by 4 inches. Every 1 inch
Sergio [31]

Answer:

$90

Step-by-step explanation:

8 + 4 = 12

12 x 3 (3 feet for each inch) = 36

36 x 2.50 (cost per square foot) = $90

3 0
3 years ago
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Find the missing measure for a right circular cone given the following information. Find L.A. if r = 6 and h = 8
Masja [62]
\bf \textit{lateral area of a cone}\\\\
LA=\pi r\sqrt{r^2+h^2}\quad 
\begin{cases}
r=radius\\
h=height\\
-----\\
r=6\\
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6 0
3 years ago
Please see questions below.
Norma-Jean [14]
The answer is C sin50...
6 0
3 years ago
100 points gor correct answer Identify the base of a triangle in which h=(3x+15) ft and A=(15x+75) ft^2.
ivolga24 [154]

Answer:

b = 10

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = \frac{1}{2} bh ( b is the base and h the height )

Here h = 3x + 15 and A = 15x + 75, thus

\frac{1}{2} × b × (3x + 15) = 15x + 75

Multiply both sides by 2 to clear the fraction

b(3x + 15) = 30x + 150

Divide both sides by (3x + 15)

b = \frac{30x+150}{3x+15} ← factor numerator and denominator

  = \frac{30(x + 5)}{3(x+5)} ← cancel the factor (x + 5) on numerator/denominator

  = \frac{30}{3}

  = 10

7 0
3 years ago
Read 2 more answers
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