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4 years ago

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. B = 46°, a = 12, b = 11

1 answer:

6 0

*Hint: The Law of Sines is Sin A/a = Sin B/b = Sin C/c

In order to solve this equation, you will have to use this equation:

A= sin^(-1)[a sinB/b]
A= sin^ (-1) [12 (sin 46°) / 11]
A = sin^ (-1) [8.632077604/11]
A = sin ^(-1) [0.7847343276]
A = 51.69611349

Therefore, Sine A would be about 52°

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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

Fiona, Dan and Stephen share £66 in a ratio 1:3:2. How much money does each person get?

Viefleur [7K]

Answer:

Fiona=11

Dan=33

Stephen=22

Step-by-step explanation:

Fiona:1/2+3+1×66

1/6×66

=11

Dan: 3/6×66=33

Stephen:2/6×66=22

8 0

3 years ago

A student took a survey of the class. There are 42 students in the class. The student surveyed favorite foods. 10 said hamburger

8_murik_8 [283]

Answer:

52.38%

Step-by-step explanation:

Given that,

Total number of students in the class is 42

Out of 42, 10 like hamburgers, 22 like pizza, 8 like french fries, and 2 like salad.

We need to find the percentage of the class chose pizza. There are 22 student who like to have pizza. Required percentage is given by :

$P=\dfrac{22}{42}\times 100\\\\P=52.38\%$

So, 52.38% of students chose pizza.

7 0

3 years ago

How do you find the area of a triangle?

scoray [572]

To find the area of a triangle, you need the formula . A= b*h divided by 2

6 0

3 years ago

Read 2 more answers

A bus travelled from location A to location B in 90 minutes. Calculate the speed of the bus in km/h

DaniilM [7]

Speed is distance over time. There’s no distance in the question and the time is 1 hr 30 mins hence 1.5 hours.

6 0

3 years ago