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]
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14) The value of y varies directly with x, and y = 3.6 when x = 6. Find y when x= 48.
Please and thank you. I needed now. Please help
Answer: y = 28.8
Step-by-step explanation:
By using ratios
if the values vary with each other, then they will increase the same amount. 6x8 is 48. So 3.6 x 8 is your answer, 28.8
Lucy rides her bicycles 240 feet. A wheel of her bicycle turns 40 times as the bicycle travels this distance. What is the diameter of the wheel?
Find the degree measure of the angle with the given radian measure. (Round your answer to one decimal place.)
Answer:
108 degrees
Step-by-step explanation:
Since we are not given the radian measure. Let the radian measure be 3π/5 rad;
Using the conversion;
πrad = 180°
3π/5 rad = x
Cross mulriply;
π * x = 180 * 3π/5
x = 180 * 3/5
x = 36 * 3
x = 108 degrees
Hence the degree measure is 108 degrees
Note that the same conversion can be used to convert other values in radians
bölenin 8,bölümün 68 olduğu bir bölme işleminde bölünen sayı en fazla kaç olur
Cevap:
68 bölü 8, bundan çıkardığım şey, yanılıyorsam cevabımı sil. Ancak 68 bölü 8 = 8,5
Verify experimentally that the angle opposite to the longer side is greater than
the angle opposite to the shorter side in any triangle (at least two figures are
necessary)
Answer:
If two sides of a triangle are unequal, the angle opposite to the longer side is larger (or greater). You may prove this theorem by taking a point P on BC such that CA = CP.
Step-by-step explanation:
That's how you can prove which side is bigger
Pls help 2 and 3!!!!!!!!!
Answer:
2)
d. -1 1/2
3)
c. 21 1/2
Step-by-step explanation:
Write an equation for the n th term of the arithmetic sequence 56, 48, 40, 32, ....
Answer:
-8n+64
Step-by-step explanation:
What is the simple interest earned when the principal is $500 at a rate of 10% held in the ban for 8 months?
S.I= PRT /100
where,
P = price $500
R = rate 10%
T = time =8months
= $500*10*8/100
= $40,000/100
S.I = $400
CAN SOMEONE PLEASE ANSWER THIS QUESTION ASAP!!
Please give me the correct answer
Answer:
i dont think so.
Step-by-step explanation:
I don't get this find all missing angles what does it mean how do I do it
First, you can find angle 1 by using the triangle angle formula, stating that all angles add up to 180 deg. Thus, angle 1 is equal to 180-72-57= 51 deg.
Next, you can find angle 2 by using the right angle shown. This means that angle 2 plus 72 deg = 90 deg. Thus, angle 2 is equal to 90-72= 18 deg.
For angle 3, notice that it is bordering the other angle on a straight line. A straight line is equal to 180 deg. This means that angle 3 + 57 deg = 180 deg. Thus, angle 3 is equal to 180-57= 123 deg.
Angle 4 can be found by using the triangle angle formula used for angle 1. In this case, angle 2+3+4 will equal 180 deg. Thus, angle 4 is equal to 180-18-123= 29 deg.
Answer:
1= 51
2= 18
3= 123
4= 39
Step-by-step explanation:
First you must know that all triangles equal 180. From there you can add and subtract the known numbers to get your answers. For example with angle 1, because you are give 72 and 57 you must add them together to get 129 then subtract that from 180 to get 51. You can do similar steps for all the angles to receive the answers.
Which expression is equal to 2xx−2−x+3x+5?
Answer:
It's the fourth one
Following are the solution to the given expression:
Given:
[tex]\bold{\frac{2x}{x-2}- \frac{x+3}{x+5}}[/tex]
To find:
Expression =?
Solution:
[tex]\to \bold{\frac{2x}{x-2}- \frac{x+3}{x+5}}\\\\\to \bold{\frac{2x(x+5) -(x+3) (x-2)}{(x-2)(x+5)}}\\\\\to \bold{\frac{2x^2+10x -(x^2 -2x+ 3x-6)}{(x-2)(x+5)}}\\\\\to \bold{\frac{2x^2+10x -(x^2 +x-6)}{(x-2)(x+5)}}\\\\\to \bold{\frac{2x^2+10x -x^2 -x+6)}{(x-2)(x+5)}}\\\\\to \bold{\frac{x^2+9x+6}{(x-2)(x+5)}}\\\\[/tex]
Therefore, the answer is "last choice".
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What is the slope of a line represented by 3x-14y=28
Answer:
3/14
Step-by-step explanation:
3x-14y=28
solve
add -3 both sides
3x−14y+−3x=28+−3x
−14y=−3x+28
divide both sides by -14
y= 3 /14 x−2
y=mx+b
so 3/14 is the slope
6. Lars walks his dog 4 times farther than Michelle
walks her dog. Michelle walks her dog 0.23 mile.
How far does Lars walk his dog?
Answer:
0.92
Step-by-step explanation:
PLEASE HELP ME!
100 POINTS!
A cylinder has a volume of 20x®y4 units cubed. If the base of the cylinder has an area of
5x"y2 units squared, which of the following expressions represent the height of the cylinder?
(Hint: V = Bh)
O 100x®y
O 15wy?
o 4x®y?
O 4xy?
Answer:
100xy
Step-by-step explanation:
The height of the cylinder is 4x³y² unit.
The correct option is A.
What is a cylinder?A cylinder is a 3D solid form made up of two bases that are parallel and identical and are connected by a curving surface. These bases resemble spherical disks. The axis of the cylinder form is a line drawn through the center or connecting the centers of two circular bases.
Given:
A cylinder has a volume of 20x⁶y⁴ units cubed.
The base of the cylinder has an area of 5x³y² units squared.
And the volume of the cylinder V = Base area x height.
So, 20x⁶y⁴ = 5x³y² (height).
The height of the cylinder = 20x⁶y⁴/ 5x³y²
The height of the cylinder = 4x³y²
Therefore, 4x³y² is the height of the cylinder.
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The complete question is given in the attached image.
Please helpp I’ll give brainleist
Answer:
87 for lo and om is 56
Step-by-step explanation:
Answer:
<LON= 98 Degrees
Step-by-step explanation:
180-55(2)=70
70+28=98
Acellus help slope intercept
Greetings.
The answer is y = 2x + 7.
Explanation:
If you are an expert in graph then you are able to find the slope without calculating. (Rise over Run by looking at the graph.)
We can also find the slope by calculating m-value.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] ---> Rise Over Run
But how are we gonna calculate if we don't have any two given ordered pairs?
The answer is, we can just pick two ordered pairs that are part of the graph, or rather say that the graph passes through.
The graph passes through (-3,1) and (-2,3).
Then we can calculate the slope by using rise/run.
[tex]m=\frac{3-1}{-2-(-3)}\\m=\frac{2}{-2+3}\\m=\frac{2}{1}\\m=2[/tex]
Thus, the slope is m = 2.
However, we are not done yet. We just only found out the slope. We need to find the y-intercept too.
From Linear Function - [tex]y=mx+b[/tex]
Where m = slope and b = y-intercept.
Since b = y-intercept, we don't need to calculate/substitute x = 0. We simply find which number the graph has y-intercept at.
Which is (0,7), the y-intercept.
Then we substitute b = 7 as y-intercept.
Thus the answer is [tex]y=2x+7[/tex]
Robert is collecting books to donate to the library.
The number of books he collects, nn, is defined by n=14d+21 where d is the number
of days he spends collecting books.
What does 14 represent in the context of Robert's book collecting?
A represents the number of books per day that are collected.
B represents the number of books per week that are collected.
C represents the number of books per month that are collected.
D represents the number of books per year that are collected.
Number 6 btw
The answer is c because it makes sense that it would be months.
Answer:
is A because basically in my EXAM is just have the first option
Two pounds of cashews cost $19, and 8 pounds cost $76.
Number of pounds 2 3 8
Cost ($) 19 28.50 76
Is the relationship between the cost and the number of pounds of cashews a proportional relationship? Explain.
How can you use your equation to find the cost of 6 pounds of cashews?
Would it be possible to prove this is proportional or not proportional without the table? Explain how you know.
Please reply quickly thanks : )
Answer:
Yes there is a proportinal relationship because when I did 19 divided by 2 I got 9.5 and when I do 76 divided by 8 I got 9.5 so its proportinal. Yes I can find how much money 6 pounds is its 57. And yes I can do it without a table because all you have to do is divide the 19 and 2 and the other 2 numbers and if there the same then its proportinal.
Step-by-step explanation:
BRAINLIEST MAYBE???
Find the inverse: f(x) = -3 -4/3 x
Answer:
3+4/3x
Step-by-step explanation:
Seth has 2 ¾ candy bars to give away. If he gives each person ⅛ of a candy bar, how many people will get candy?
Answer:
22 people
Step-by-step explanation:
Change 2 3/4 into a fraction, 11/4.
Then divide by 1/8
11/4 x 8/1 = 22
pls help me it would mean a lot <3
Answer:
The equation of the line will be:
[tex]y\:=\:\frac{2}{5}x[/tex]Step-by-step explanation:
We know the slope-intercept of a line equation is
[tex]y = mx+b[/tex]
where m is the slope and b is the y-intercept
Given two points on a line graph
(0, 0)(25, 10)Finding the slope between two points
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(0,\:0\right),\:\left(x_2,\:y_2\right)=\left(25,\:10\right)[/tex]
[tex]m=\frac{10-0}{25-0}[/tex]
[tex]m=\frac{2}{5}[/tex]
We know that the y-intercept on a line graph can be observed by setting x=0 and checking the corresponding value of y.
From the graph, it is clear
at x = 0, y = 0
Thus, the y-intercept = b = 0
Now, substituting b = 0, and m = 2/5 in the slope-intercept form
[tex]y = mx+b[/tex]
[tex]y\:=\:\frac{2}{5}x+0[/tex]
[tex]y\:=\:\frac{2}{5}x[/tex]
Therefore, the equation of the line will be:
[tex]y\:=\:\frac{2}{5}x[/tex]HELP!!! The probability that a male’s foot is between 10 and 12.5 inches is__
p(10
Answer:
I suggest you use Socratic, it solves questions like this.
Step-by-step explanation:
given: 2c=d-2b, c=a-b, d=a+b prove: a=b
Answer:
D
Step-by-step explanation:
A store is offering a discount on shorts of 23.4%.The original price of the shirt is $13.24.how much will you have to pay the clerk
Answer:
Step-by-step explanation:
Hi
Answer:
13.24
Step-by-step explanation:
Your buying a shirt not shorts
What is the first step to solving the division problem below?
Divide 15 into 82 to get 5.
Divide 15 into 82 to get 6.
Multiply 15 by 5 to get 75.
Multiply 15 by 6 to get 80.
Answer:
divide 15 into 82 to get 5 is the first step
Step-by-step explanation:
Answer:
The answer is A, ¨Divide 15 into 82 to get 5.¨
Step-by-step explanation:
Please make as brainliest! Thanks and i hope it is right!!! Pls say if wrong. Bye
Find the value of the power 6 to the -4th
Answer:
6 to the -4th is 7.716 x 10^-4
Step-by-step explanation:
Which measure is not the area of a circle with radius 20 mm?
Answer:
C
Step-by-step explanation:
Answer:
thank you
Step-by-step explanation:
WILL MARK BRAINLIEST PLS HELP
choose all of the points that are solutions to the equation y = x2 - 3x - 4
-4,0
-1, 0
0, -4
1, -6
1, 0
3, -7
pls
Answer:
-1,0
0,-4
1,-6
Step-by-step explanation:
plug in the first number into x and it gets you the second number
(-1, 0), (0, -4), (1, -6) points are solutions of the given quadratic equation.
What is a quadratic equation?A quadratic equation is an equation where the variable has the highest power of 2.
Given equation is y = x² - 3x - 4
1. For (-4, 0), L.H.S = 0, R.HS = (- 4)² - 3(- 4) - 4 = 24.
Hence, (-4, 0) is not a solution of the given equation.
2. For (-1, 0), L.H.S = 0, R.HS = (- 1)² - 3(- 1) - 4 = 0.
Hence, (-1, 0) is a solution of the given equation.
3. For (0, -4), L.H.S = -4, R.HS = (0)² - 3( 0) - 4 = - 4
Hence, (0, -4) is a solution of the given equation.
4. For (1, -6), L.H.S = -6, R.HS = (1)² - 3(1) - 4 = -6.
Hence, (1, -6) is a solution of the given equation.
5. For (1, 0), L.H.S = 0, R.HS = (1)² - 3(1) - 4 = -6.
Hence, (1, 0) is not a solution of the given equation.
6. For (3, -7), L.H.S = -7, R.HS = (3)² - 3(3) - 4 = -4.
Hence, (3, -7) is not a solution of the given equation.
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Simplify 8x + 9d + 3x -5d
Please Do Show Your Work Explanation
Answer:
The answer is =4d+11x
Step-by-step explanation:
8x + 9d + 3x -5d
=9d-5d+8x+3x
=4d+11x
Answer:
putting in arranged and sum the like terms
8x+3x+9d-5d
11x+4d
