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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)

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]

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;

https://brainly.com/question/10197594

Answer:

0.03

Step-by-step explanation:

calculator calculator calculator

Answer:

$608

Step-by-step explanation:

Turn the percentage into a decimal

$800(0.24) = 1$92

So you need to subtract 192 of 800

800 - 192 = $608

Hope this helps dude

Answer:

22

Step-by-step explanation:

8 times 10= 80 +8=88. now thats 11 packages. 11 times 2=22

Answer: The answers are x=y/3–4/3, and x=y/9–10/9.

Step-by-step explanation: You’ll need to isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

I can't help if I don't have enough to answer sorry

Step-by-step explanation:

Answer:

estimate, 3000. exact answer 3256

Step-by-step explanation:

hope this helps

Answer:

40%

Step-by-step explanation:

The line starts on 40%

Answer:

40%

Step-by-step explanation:

th line stars by the 40

Answer:

75.2

Step-by-step explanation:

Answer:

75.2 is the answer

Step-by-step explanation:

the answer is 75.2

Answer:

[tex] \frac{6}{9} [/tex]

or

[tex] \frac{2}{3} [/tex]

Step-by-step explanation:

There are nine in total and she has eaten 6, so the fraction would be 6/9.

If you need to simplify it it would be 2/3.

Answer:

A. 1mm = 5mi

Step-by-step explanation:

20 mi divided by 4 mm would simplify down to 5 mi per 1mm. If there is 4 mm then there is 5mi*4mm which equals out to 4 mm = 20 mi.

A scale of the map is the relationship between the distance on the map to the actual distance. The scale of the map is 1 mm: 5 miles (ml). Thus the option A is the correct option.

To find out the scale of the map, we have to know about scaling of map.

The scaling of map is the ratio or relationship between the distance of the map to the original distance.

Given information-

The distance of the two houses on the ground is 20 miles.

The distance of the two houses on the map is 4 mm.

Suppose the scale of the map is [tex]s[/tex].

As the 20 miles distance on the ground is same as the 4 mm distance on the map.

Thus the scale of the map can be given as,

[tex]s=\dfrac{4\rm mm}{20\rm miles} \\s=\dfrac{1\rm mm}{5\rm miles}[/tex]

Hence the scale of the map is 1 mm: 5 miles (ml). Thus the option A is the correct option.

Learn more about the scale of map here;

https://brainly.com/question/10283478

Answer:

15

Step-by-step explanation:

i guarantee you 100 percent this is correct

please give me brainliest

Answer:

can i help i need points

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Factorise: x*x-4*4

(x+4)(x-4)

so the answer is B.

Hope this helps

Merry Christmas!

Answer:

its 273 rounded but say 270

Step-by-step explanation:

The estimate is 270.

Answer:

its a function

slope form:y+5=-1.18·(x-3)

(-2.5,1.5)

Step-by-step explanation:

Answer:

x = 1, y = -1, z = 3

Step-by-step explanation:

x - 2y + 2z = 9

y + 2z = 5

z = 3

According to the last equation, z is equal to 3 so we can plug that in and our new 2 equations will be:

x - 2y + 6 = 9

y + 6 = 5

We can subtract 6 from both sides of the second equation to end up with:

y = -1

Now plugging this into the first equation, we have:

x + 2 + 6 = 9

x + 8 = 9

Subtract 8 from both sides

x = 1

C. They are similar by the definition of similarity in terms of a dilation.

The conclusion about the triangles is (c) they are similar by the definition of similarity in terms of a dilation.  

The coordinates are given as:

[tex]M = (1,3)[/tex]

[tex]N = (4,9)[/tex]

[tex]O = (7,3)[/tex]

[tex]P =(3,0)[/tex]

[tex]Q = (4,2)[/tex]

[tex]R = (5,0)[/tex]

Start by calculating the lengths of the triangles using the following distance formula

[tex]d = \sqrt{(x_1-x_2)^2 + (y_1 -y_2)^2}[/tex]

So, we have:

[tex]MN = \sqrt{(1 -4)^2 + (3 - 9)^2}[/tex]

[tex]MN = \sqrt{45}[/tex]

[tex]MO = \sqrt{(1 -7)^2 + (3 - 3)^2}[/tex]

[tex]MO = 6[/tex]

[tex]NO = \sqrt{(4 -7)^2 + (9 - 3)^2}[/tex]

[tex]NO = \sqrt{45}[/tex]

[tex]PQ = \sqrt{(3 -4)^2 + (0 - 2)^2}[/tex]

[tex]PQ = \sqrt{5}[/tex]

[tex]PR = \sqrt{(3 -5)^2 + (0 - 0)^2}[/tex]

[tex]PR = 2[/tex]

[tex]QR = \sqrt{(4 -5)^2 + (2 - 0)^2}[/tex]

[tex]QR = \sqrt{5}[/tex]

So, we have:

[tex]MN = \sqrt{45}[/tex]                  [tex]PQ = \sqrt{5}[/tex]

[tex]MO = 6[/tex]                       [tex]PR = 2[/tex]

[tex]NO = \sqrt{45}[/tex]                   [tex]QR = \sqrt{5}[/tex]

The above means that the triangles are not congruent.

So, we determine if they are similar by dividing the corresponding sides

[tex]k = \frac{MN}{PQ} = \sqrt{\frac{45}{5}} = 3[/tex]

[tex]k = \frac{MO}{PR} = \frac{6}{2} = 3[/tex]

[tex]k = \frac{NO}{QR} = \sqrt{\frac{45}{5}} = 3[/tex]

The scale factor is 3.

Hence, the triangles are similar

Read more about similar triangles at:

https://brainly.com/question/14285697

Answer:

yes it is correct tq

Step-by-step explanation:

my friend

Answer:

10 quarts.

Step-by-step explanation:

Work with amounts of pure acid.

There is 0.10*3 quarts of pure acid in the 10% solution.

3*0.10 + 0.75x = 0.60(x + 3)    where x is the number of quarts of 75% acid.

0.30 + 0.75x = 0.60x + 1.8

0.15x = 1.5

x = 10 .

Answer: v = B/y -1

B = yv + y = (v + 1)y

=> B/y = v + 1

⇔ [tex]v=\frac{B}{y}-1[/tex]

Step-by-step explanation:

Answer:

22 per hour

Step-by-step explanation:

8 divided by 176 lol Hope I did it right tho ;-;

Answer:

they can make 22 in one hour.

Answer:

thats a statement

Step-by-step explanation:

Answer:

D. 2.2m + 4.5

Step-by-step explanation: