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satela [25.4K]
3 years ago
13

Determine the equation of the tangent line to the given path at the specified value of t. (sin(7t), cos(7t), 2t9/2); t=1

Mathematics
1 answer:
Reptile [31]3 years ago
4 0

Answer:

P(t) = {sin7, cos7, 2} + (7cos7, -7sin7, 9)(t-1)

Step-by-step explanation:

The equation of the tangent line to the given path at the specified value of t is expressed as;

P(t) = f(t0) + f'(t0)(t - t0)

f(t0) = (sin(7t), cos(7t), 2t^9/2)

at t0 = 1;

f(t0) = {sin7(1), cos7(1), 2(1)^9/2}

f(t0) = {sin7, cos7, 2}

f'(t0) = (7cos7t, -7sin7t, 9/2{2t^9/2-1}

f'(t0) = (7cos7t, -7sin7t, 9t^7/2}

If t0 = 1

f'(1) = (7cos7(1), -7sin7(1), 9(1)^7/2)

f'(1) =(7cos7, -7sin7, 9)

Substituting the given function into the tangent equation will give:

P(t) = f(t0) + f'(t0)(t - t0)

P(t)= {sin7, cos7, 2} + (7cos7, -7sin7, 9)(t-1)

The final expression gives the equation of the tangent line to the path.

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What is the vertex of y<∣x−3∣+5​
Tcecarenko [31]

Answer:

(3, 5)

Step-by-step explanation:

The graph is is the standard y=|x| except the values tells you that x shifts 3 (within the absolute value or parentheses x does the opposite) to the right and the y value shifts 5 up (numbers outside parentheses affects y and does what it says). You can try using a table of values then graphing to check your answer.

3 0
2 years ago
A tennis ball has a radius of about 1.4 inches What is the volume of the tennis ball to the nearest half inch.? Use 3.14 as an a
Ilya [14]

Answer:

Volume of tennis ball = 11.49 inch³

Step-by-step explanation:

Given:

Radius of tennis ball = 1.4 inches

Value of π = 3.14

Find:

Volume of tennis ball

Computation:

Volume of sphere = [4/3][π][r]³

Volume of tennis ball = [4/3][π][Radius of tennis ball]³

Volume of tennis ball = [4/3][3.14][1.4]³

Volume of tennis ball = [1.333][3.14][1.4]³

Volume of tennis ball = [1.333][3.14][2.744]

Volume of tennis ball = [4.1856][2.744]

Volume of tennis ball = 11.4852

Volume of tennis ball = 11.49 inch³

6 0
3 years ago
Whats 14.635 rounded to the nearest cent?
Nutka1998 [239]
The cents are .635 and the greatest cent is 6. So, when it is rounded to the greatest value like estimating it will be 14.600 or 14.6. As easy as that. :)
7 0
2 years ago
Cmon y'all i only have 3 more questions
Afina-wow [57]

1.25

the exponent is to the 6th because there are six zeros

4 0
3 years ago
Read 2 more answers
What is the domain of the function y=-720t + 3600 ?
Colt1911 [192]

Answer:

We conclude that:

\mathrm{Domain\:of\:}\:-720t+3600\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:

Please also check the attached graph.

Step-by-step explanation:

Given

Given the function

y=-720t\:+\:3600

To determine

What is the domain of the function y=-720t + 3600

We know that the domain of the function is the set of input argument values for which the function is real and defined.

Given the function

y=-720t\:+\:3600

From the given function, it is clear that the function has no undefined points nor domain constraints.

Therefore, the domain of the function is

-\infty \:

Thus, we conclude that:

\mathrm{Domain\:of\:}\:-720t+3600\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:

Please also check the attached graph.

3 0
2 years ago
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