Find the domain of the vector function. (Enter your answer in interval notation.) r(t) = t − 2 t + 2 i + sin(t)j + ln(36 − t2)k

Answers

Answer 1

Answer:

The domain of the vector function is :  ( -6, -2) ∪ ( -2, 6)

Step-by-step explanation:

The given vector function  can be correctly expressed as:

[tex]r(t) = \dfrac{t-2}{t+2}i + sin \ tj + In(36-t^2) k[/tex]

The domain of the given function can be determined by finding the domain of each respective component.

To start with [tex]\dfrac{t-2}{t+2}[/tex]

Not defined, t = -2

Thus, the domain of the first component of the vector = [tex]( - \infty , -2) \cup ( 2, \infty )[/tex]

The 2nd component = sin t

No restriction on t

The 3rd component of the function is ㏑(36 - t²)

Let recall that natural is defined for +ve numbers,

i.e.

36 - t² > 0

(6 + t) (6 - t) > 0

Thus, it satisfies the inequality  -6 < t < 6

The third domain = (-6,6)

Overall;

The domain of the vector function is :  ( -6, -2) ∪ ( -2, 6)

Answer 2

Domain of a function is the set all possible inputs for that function.The domain of the given vector function is,

[tex](-6, -2) \cap (-2,6)[/tex]

What is domain?

Domain of a function is the set all possible inputs for that function.

Given information-

The vector function given in the problem is,

[tex]r(t)=\dfrac{t-1}{t+2} \hat i++sin(t)\hat j+ln(49-t^2)\hat k[/tex]

To find the domain of the above vector function, we need to find the domain of each function of vector quantity.

Lets find the domain of [tex]\hat i[/tex] first which is given by,

[tex]\dfrac{t-2}{t+2}[/tex]

This function is defined at all values except, t equals to -2 as the function is not defined at,

[tex]t=-2[/tex]

Hence the domain of component [tex]\hat i[/tex] is,

[tex](-\infty, -2) \cap (\infty,2)\\[/tex]

Lets find the domain of [tex]\hat j[/tex] first which is given by,

[tex]\sin(t)[/tex]

Two trigonometry function sine and cosine defined for all real number.

This function is defined at all real numbers. Hence the domain of component [tex]\hat j[/tex] is

Lets find the domain of [tex]\hat k[/tex] first which is given by,

[tex]\ln(36-t^2)[/tex]

Set the above argument greater than zero to find where the expression is defined.Thus,

[tex](36-t^2)>0\\(6+t)(6-t)>0[/tex]

Therefore,

The domain of it should be [tex](-6,6)[/tex]

Hence the domain of the given vector function is,

[tex](-6, -2) \cap (-2,6)[/tex]

Learn more about the domain here;

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Step-by-step explanation:

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Answer:

[tex] \huge \boxed{ \boxed{ - \frac{6}{7} }} \\ [/tex]

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

[tex]m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\[/tex]

From the question we have

[tex]m = \frac{ - 3 - - 9}{ - 5 - 2} = \frac{ - 3 + 9}{ - 5 - 2} = - \frac{6}{7} \\ [/tex]

We have the final answer as

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Hope this helps you

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Answer:

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first put the points, then just draw the line that goes throw that row of dots.

Step-by-step explanation:

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Answers

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Step-by-step explanation:

1. -1.66666666667

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X
-2
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0
1
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у
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Answer:

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कम्प्युटरको गति मापन गर्ने एकाइहरूलाई वर्णन गर्नुहोस् ।​

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Answer:

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Answer:

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Step-by-step explanation:

95342 * 8% = 7627.36

Answer:

Marcus earns 15% commission on his total sales at work.

Suppose Marcus's sales totaled $725 last week. How much did he earn in commission?

A.

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Step-by-step explanation:

If a is half b , and b is twice c , then a:c=​

Answers

Answer: a/c = 1

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b/c = 2 => c = 1/2 .b

=> a/c = (1/2.b)/(1/2.b) = 1

Step-by-step explanation:

If a is half b, and b is twice c, then the fraction a:c will be 1.

What is a fraction?

In such a fraction, the value that appears above the horizontal line is referred to as the numerator.

In another word, if we divide two numbers by each other then the upper word is called the numerator, and the lower word is called the denominator.

As per the given,

a is half b ⇒ a = b/2

b is twice c ⇒ b = 2c

By substitution,

a = (2c)/2

a = c

a:c = 1:1 = 1

Hence "If a is half b, and b is twice c, then the fraction a:c will be 1".

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Step-by-step explanation:

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I'm confused too I'm sorry

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Answers

Answer:

A car takes 4 hours to reach a destination travelling at the speed of 63 km/h.

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The time varies inversely with the speed. The more the speed, the lesser the time and the lesser the speed, the more the time.

Let speed = s and let time = t

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

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17550 solutions

Step-by-step explanation:

Given that:

y1 +y2+y3+y4=27

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(yi  ≥ 0 and yi [tex]\epsilon[/tex] [tex]{\displaystyle \mathbb {Z} }[/tex]  )

The no. of a nonnegative integer determines the number of ways to choose 27 objects from (4) distinct objects with repetition regardless of the order.

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Step-by-step explanation:

Kensington was selling Girl Scout cookies and a customer offered her a deal. The customer would place three $1 bills, one $5 bill and one $10 bill in a bag. Kensington would reach into the bag and take one bill from the bag and get paid that instead of the $5 it would cost for one box of Girl Scout cookies. Should she take the deal? Or should she insist on getting the regular cost of $5?

Answers

Answer:

no she should take the deal

Step-by-step explanation:

there are 5 bills in that bag and only 1 of them has a chance of being over the regular price where as 3 have a chance of being under the regurla price the odds a not in the girl scouts favor as she has a 60%chance of not getting a $1 and only a 20% chance of getting the $10.

three times the difference of two times m and five is equal to eight times m to the second power increased by four

Answers

Answer: 3*(2m-5)=8m^2+4

Step-by-step explanation:

The mathematical expression of the given statement is 3(2m-5) = 8m²+4.

What is an mathematical expression?

Expression in mathematics is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Here, the given mathematical statement is given as :

three times the difference of two times m and five is equal to eight times m to the second power increased by four , which can be written as :

3(2m-5) = 8m²+4

Therefore, the mathematical expression of the given statement is 3(2m-5) = 8m²+4.

Read more about  mathematical expression at:

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Consider u = ⟨5, –2⟩ and v = ⟨10, –4⟩. What is the relationship between u and v?

The vectors point in the same direction.
The vectors form an acute angle.
The vectors form an obtuse angle.
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Answers

Answer: A. The vectors point in the same direction

Step-by-step explanation:

edge2020

Answer:

A) The vectors point in the same direction.

Step-by-step explanation:

got it right on edge :)

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Answers

[tex]\textsf{Hey there!}[/tex]

[tex]\mathsf{81^2=81\times81\rightarrow\bf{6,561}}[/tex]

[tex]\mathsf{(6,561)^{\dfrac{1}{8}}= \bf{3}}[/tex]

[tex]\boxed{\boxed{\mathsf{Therefore, your\ answer\ is: \boxed{\huge\textsf{\bf{C. 3}}}}}}\huge\checkmark[/tex]

[tex]\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\dfrac{\frak{LoveYourselfFirst}}{:)}[/tex]

Answer:

c

Step-by-step explanation:

because I said so " But rearle you cant start a sentence with because"

ok then, The answer is C because I said so

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