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]
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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Don’t mod this look at picture
plz help asap i will do brainliest!!! A car takes 4 hours to reach a destination travelling at the speed of 63 km/h. How long will it take to cover the same distance if the car travells at the speed of 56 km/h? Do these quantities (time and speed) vary directly or inversely? Find the constant of variation.
Answer:
A car takes 4 hours to reach a destination travelling at the speed of 63 km/h.
Speed = distance / time
Distance = speed × time
Distance it took the car, travelling for 4 hours to a destination at a speed of 63 kilometers per hour would be
4 × 63 = 252 kilometers.
if the car travels at a different speed of 56 kilometers per hour and the distance remains 252 kilometers, the time it takes will be
Time = distance / speed
= 252/56 = 4.5 hours
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
s varies inversely with t
Introducing constant of inverse variation k, it becomes
s = k/t
When s = 56, t = 4.5
56 = k/4.5
k = 4.5 × 56 =252
This is the distance
Step-by-step explanation:
Find how many solutions there are to the given equation that satisfy the given condition.
y1 +y2+y3+y4=27, each yi is a nonnegative integer.
Answer:
17550 solutions
Step-by-step explanation:
Given that:
y1 +y2+y3+y4=27
where;
(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.
i.e
[tex]\bigg(^{27}_{4} \bigg)[/tex]
∴
The number of nonnegative integer solution is [tex]\bigg(^{27}_{4} \bigg)[/tex]
[tex]= \dfrac{27!}{4!(27-4)!}[/tex]
[tex]= \dfrac{27!}{4!(23)!}[/tex]
[tex]= \dfrac{27\times 26\times 25\times 24 \times 23 !}{4\times 3\times 2\times 1(23)!}[/tex]
[tex]= \dfrac{27\times 26\times 25\times 24 }{4\times 3\times 2\times 1}[/tex]
[tex]= \dfrac{421200}{24}[/tex]
= 17550 solutions
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.
The vectors point in opposite directions.
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 :)
the averages of the squared differences between the data values and the mean is known as
Problem ID: PRABJVTY
Answer:
I'm confused too I'm sorry
What’s x, and y ? Show work.
Y = 6x + 11
2x - 3y = 7
can someone please help ?
Please help me please
Answer:
To be honest I don't know I just need some points 1+1=2
Step-by-step explanation:
25 POINTSSSS PLEASE HELP ME I NEED HELP!!! PLZZZ
Which exponential function has the greatest average rate of change over the interval [0, 2]?
Answer:
I think its A
Step-by-step explanation:
what is the area of a rectangle with a length of 142 cm and a width of 23 cm?
Answer:
3,266
Step-by-step explanation:
Answer:
3266cm²
Step-by-step explanation:
try it it healps
what is the slope of the line containing (2,-9) and (-5,-3)
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
[tex] - \frac{6}{7} \\ [/tex]
Hope this helps you
Connections Academy Geometry10A semester exam. Does anyone have the answers im 1% away from passing.
Answer:
probably not, but if you were to post the questions without it saying on it that its an exam (because those get deleted all the time) people could help you through it. :)
Step-by-step explanation:
PLZ HELPPPPPPPPPPPPP GIVING BRAINLIST Match each expression to its value.
1. -1 + 2
1
2. 1 + (-2)
-3
3. -1 - 2
3
4. 1 - (-2)
-1
Answer:
1 and 3, 2 and 4.
Step-by-step explanation:
1. -1.66666666667
2. 1
3. -1.66666666667
4. -1
The scale on a map is 1 inch = 60 miles. If two cities are 2 3/4 inches apart on the map, how many miles are they apart?
Answer:
120.75 miles apart
Step-by-step explanation:
PLEASE HELP ME ITS DUE TODAY!!
PLS SHOW WORK OR EXPLAIN!!
Answer:
(-3, -0.5)
first put the points, then just draw the line that goes throw that row of dots.
Step-by-step explanation:
so this isnt very complicated, you need to put the points on the coordinate plane (the grid) and find where they meet coordinates (written starting with the x and ending with the y are written like this: (x,y))
go to the bottom line (x axis) and find the number in the x row on the page, then take the vertical line and go until the two ends meet,repeat that until there are no more coordinates to graph on the left box draw a straight line for all of the coordinates do the same with the other box drawing a line whre the other coordinates. if done right the lines should intersect, and the intersecting point is the answer
what is the value of the expression below (81^2)^1/8
[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
Measure the distance between lines c and d and the lengths of did”, ee”, ff “
72 638 rounded to the nearest
is 72 600.
Answer:
hundreth
Step-by-step explanation:
कम्प्युटरको गति मापन गर्ने एकाइहरूलाई वर्णन गर्नुहोस् ।
Answer:
मापनको एकाईलाई हर्ट्ज (हर्ट्ज) भनिन्छ, जुन प्रति सेकंड टेक्निकली एक चक्र हो, घडीको गति मापन गर्न प्रयोग हुन्छ। ... कम्प्युटरको घडी गति सामान्यतया मेगाहेर्ट्झ (मेगाहर्ट्ज) वा गिगाहर्ट्ज (GHz) मा मापन गरिएको छ। एक मेगाहेर्ट्ज प्रति सेकेन्ड १० लाख टिक्स बराबर हुन्छ, र एक गिगाहर्ट्ज बराबर एक सेकेन्ड टिक टिक प्रति सेकेन्ड।
Marcus is a car salesman and he earned an 8% commission on his monthly sales last month his sales total was $95,342 how much commission was he paid
Answer:
7627.36
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.
$833.75
B.
$616.25
C.
$108.75
D.
$10.88
Step-by-step explanation:
Can someone please explain to me how to tell if a number it's prime or not
Answer:
A prime number is a number that can only be divided by 1 and itself.
three times the difference of two times m and five is equal to eight times m to the second power increased by four
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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What's the length of the diameter of the ferris wheel?
If a is half b , and b is twice c , then a:c=
Answer: a/c = 1
a/b = 1/2 => a = 1/2 .b
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".
For more about fractions,
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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?
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.
The following histogram shows the height of basketball players what would be the best estimate of average height ?
A. 75in
B. 82in
C. 85in
D. 80in
Answer:
D
Step-by-step explanation:
please give answer please!!!!!!!!!!!!
All of them produce an angle of 90 degrees, therefore
90 degrees x 4 = 360 degrees
Which of the following numbers
does NOT have the same value as
one quarter?
X
-2
-1
0
1
2
у
N
3
4
5
6
Answer:
can you round it up? what is the question and what are we solving for?
Need ASAP plz plz plz
Answer:
12/7
Step-by-step explanation: