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2 years ago

Find the slope of the line containing the points (-2,-2) and (-4,-2).

Mathematics

1 answer:

Galina-37 [17]2 years ago

7 0

Answer:

Step-by-step explanation:

Use the formula ( $\frac{y_1-y_2}{x_1-x_2}$ )

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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

2 years ago

If F(x) = 4%-3, which of the following is the inverse of F(x)?

Brums [2.3K]

I assume you meant to type x for %.

If not, basically back-substitute at the end of the solution.

F(x) = 4x - 3

Let y = F(x)

y = 4x - 3

x = 4y - 3

x - 3 = 4y

(x - 3)/4 = y

Let y = F^(-1)x

F^(-1)x = (x - 3)/4

If you want % in your answer, just replace x for % in your answer.

8 0

2 years ago

A differential equation that is a function of y only

Pachacha [2.7K]

ANSWER
<span>will produce a slope field with rows of parallel tangents
</span>
EXPLANATION
A differential equation that is a function of y only does not depend on x, i.e. of the form dy/dx = f(y), where f is a function.

Therefore, the slope field will be independent of the horizontal position. This means that there will be rows where the slopes will be of the same rise/run ratio. When two slopes are the same, they are said to be parallel.

7 1

2 years ago

X is an integer.

vivado [14]

Answer:

*44+44468

Step-by-step explanation:

54+85588255)(5(5))55)5)

6 0

2 years ago

There is a total of 100 calories in 15 of Mei's favorite crackers. What is

borishaifa [10]

Answer:

2,100

Step-by-step explanation:

first you want divide 140 by 20 to find the the amount of calories per cracker so 140 divided by 20 is 7 then all you need to do is multiply 7 time the 300 crackers to get you total of 2,100.

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Hope it helps! 0.0

6 0

2 years ago

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