Answer:
30
Step-by-step explanation:
Answer:I believe its 30
Step-by-step explanation:
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
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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What is the x- intercept of the line?
Answer:
-1
Step-by-step explanation:
Answer: -1
Step-by-step explanation: though I can't see the numbers, the x intercept is the number that the line hits when it's on the x axis. Assuming that every unit is one, then your answer is -1
Would someone like to help me with my math homework and the math is College for Readiness?
I will mark you BRAINLIEST
Answer:
can i help i need points
Step-by-step explanation:
My house is 20 miles from yours, but on the map it is only 4 mm away.
What is the scale of the map?
A. 1 mm = 5 mi
B. 1 mm = 20 mi
C. 1 mi= 20 mm
D. 20 mm = 4 mi
E. 5 mi = 4 mm
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.
What is the 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
What was the battery’s charging level when the charging began?
Answer:
40%
Step-by-step explanation:
The line starts on 40%
Answer:
40%
Step-by-step explanation:
th line stars by the 40
Click the photo to find the value of x
Ronda has 34.27 in her checking account. She deposits $25.00 into her account and then writes a check for $59.99. What is Ronda's account balance now?
solve the simultaneous equations
5x + 6y = 3
2x - 3y = 12
Answer: x =3; y = -2
[tex]\left \{ {{5x+6y=3} \atop {2x-3y=12}} \right.\\\\<=>\left \{ {{x=\frac{3-6y}{5} } \atop {2x-3y=12}} \right.\\\\<=>\left \{ {{x=\frac{3-6y}{5} } \atop {2.\frac{3-6y}{5}-3y =12}} \right.\\\\<=>\left \{ {{x=\frac{3-6y}{5} } \atop {6-12y-15y=12.5}} \right.\\\\<=>\left \{ {{x=\frac{3-6y}{5} } \atop {17y=6-60=-54}} \right.\\\\<=>\left \{ {{x=\frac{3-6y}{5} } \atop {y=-54/27}} \right.\\\\\\ <=>\left \{ {{x=\frac{3-6y}{5} } \atop {y=-2}} \right.\\\\<=>\left \{ {{x=3} \atop {y=-2}} \right.[/tex]
Step-by-step explanation:
Answer:
x = 3, y = -2.
Step-by-step explanation:
5x + 6y = 3
2x - 3y = 12 Multiply this by 2:
4x - 6y = 24 Now add this to the first equation:
9x = 27
x = 3.
Substitute x = 3 in the second equation:
2(3) - 3y = 12
-3y = 12 - 6 = 6
y = 6 / -3
y = -2.
help please !!!! my brain hurts
Answer:
the answer id d.
Step-by-step explanation:
The vertices of ΔMNO are M (1, 3), N (4, 9), and O (7, 3). The vertices of ΔPQR are P (3, 0), Q (4, 2), and R (5, 0). Which conclusion is true about the triangles?
The ratio of their corresponding sides is 1:2.
The ratio of their corresponding angles is 1:2.
They are similar by the definition of similarity in terms of a dilation.
They are congruent by the definition of congruence in terms of rigid motions.
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:
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[tex]4 - \frac{2}{3} x = \frac{x - 6 }{5} [/tex]
Answer:
Step-by-step explanation:
60-10x=3x-18
78=13x
x=6
Dave worked 30 hours this week. He makes $15 per hour. What is Dave’s gross pay?
Answer:
$450 of gross pay
Answer:
450
Step-by-step explanation:
160% of what number is 47
Answer:
75.2
Step-by-step explanation:
Answer:
75.2 is the answer
Step-by-step explanation:
the answer is 75.2
Lauren opened a lemonade stand on her street. It costs her $8.00 to buy the supplies each day, and she sells lemonade for $2.50 a cup. If she wants to make at least $175.00 in profits (sales - expenses) each day, what is the minimum number of cups of lemonade Lauren needs to sell? Input your answer as a whole number.
Determine the coordinate of the point shown. It’s on a (3,-5) (1,-2) (1.5, -2.5) (-2.5, 1.5)
Answer:
its a function
slope form:y+5=-1.18·(x-3)
(-2.5,1.5)
Step-by-step explanation:
Need answer quick small information
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!
how many quarts of a 75% acid solution must be mixed with 3 quarts of a 10% acid solution to make a 60% acid solution
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 .
a(-1, 1)b(1, -2)c(0, -4) rotated 270 degrees by the origin
Which letter has rotational symmetry?
E
B
Z
V
Answer:
V
Step-by-step explanation:
A tv is on sale for 24% off. If the original price was $800, find the sales price?
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
Factor the expression. x2-x-6
Answer:
(x+2)⋅(x−3)
Step-by-step explanation:
Answer:
[tex](x-3)(x+2)[/tex]
Step-by-step explanation:
[tex]x^2-x-6\\=x^2-3x+2x-6\\=x(x-3)+2(x-3)\\=(x-3)(x+2)[/tex]
What is the product of 3.4 x 10-14 and 1.8 x 10287
O6.12 x 1014
O9.4x 1014
O5.2 x 1042
O6.12 x 1042
What’s 41/12 I need some explanation
Simplify the following expression: 2(c-8)
Answer:
2c-16
Step-by-step explanation:
Multiply what is inside the parentheses by 2.
Estimate the quotient for 5,738 divided by 21
Answer:
its 273 rounded but say 270
Step-by-step explanation:
The estimate is 270.
Circle A has a radius of 4 cm and Circle B has a radius of 3 cm. What scale factor would alter circle B to become the size of Circle A? Round your answer to the nearest whole number and only enter the numeric value.
Answer:
B
Step-by-step explanation:
Solve the system for X:
y=3x +4
у=х+8 x +10
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.
Find the sum. Write your answer as a decimal.
-5.74 + 5.5 =
Answer:
-0.24
Step-by-step explanation:
Math is math i just know it in my head i do nt know how tpo explain itSolve the formula for the indicated variable.
B=yv+y, for v
The solution is v=?
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:
2of 5
The ratio of boys to girls in a class is 7:5. There are 36students in the class. How many
students are girls?
Answer:
15
Step-by-step explanation:
i guarantee you 100 percent this is correct
please give me brainliest