Answer:
[tex]T(ln2)[/tex][tex]= <\sqrt{145} , \frac{6\sqrt{2} }{\sqrt{145} } , \frac{6\sqrt{2} }{\sqrt{145} } >[/tex]
Step-by-step explanation:
Given : [tex]r(t)=<7-\sqrt{e^t}, 3e^t,3e^t > .........(i)[/tex]
We first have to differentiate of equation [tex](i)[/tex]
[tex]r'(t) = < \frac{\sqrt{e^t} }{2} , 3e^t,3e^t> ..........(ii)[/tex]
Now to get a unit tangent vector at the given value of [tex]t[/tex], we put [tex]t = ln2[/tex] in equation [tex](ii)[/tex]
[tex]r'(ln2) = < \frac{\sqrt{e^{ln2}} }{2} , 3e^{ln2},3e^{ln2}>[/tex]
[tex]= <\frac{1}{\sqrt{2} } ,6,6>[/tex] [∵[tex]e^{lna}=a[/tex]]
Now to get a unit tangent vector , we will divide our vector [tex]r'(ln2)[/tex] by its magnitude. So let's first find the magnitude.
[tex]|r'(ln2)|=\sqrt{(\frac{1}{\sqrt{2} } )^2 +6^2+6^2}[/tex]
[tex]= \sqrt{\frac{1}{2}+36+36 }[/tex]
[tex]= \sqrt{\frac{145}{2} }[/tex]
Now we can find the our unit tangents vector.
[tex]T(ln2)=\frac{r'(ln2)}{|r'(ln2)|}[/tex]
[tex]= \frac{<\frac{1}{\sqrt{2}} ,6,6> }{\sqrt{\frac{145}{2}} }[/tex]
[tex]= <\frac{\frac{1}{\sqrt{2} } }{\sqrt{\frac{145}{2}} } ,\frac{6}{{\sqrt{\frac{145}{2}} }}, \frac{6}{{\sqrt{\frac{145}{2}} }} >[/tex]
[tex]= <\sqrt{145} , \frac{6\sqrt{2} }{\sqrt{145} } , \frac{6\sqrt{2} }{\sqrt{145} } >[/tex]
Hence, [tex]T(ln2)[/tex] [tex]= <\sqrt{145} , \frac{6\sqrt{2} }{\sqrt{145} } , \frac{6\sqrt{2} }{\sqrt{145} } >[/tex]
Can somebody help me thank you.
Rani bought 9 similar notebooks. She gave the cashier $10 and received change of $5.05. What was the cost of 1 notebook?
Answer: the anwer is 0.55
Step-by-step explanation: if he received 5.05$ change that wasnt the cost. to find real cost subtract 5.05 from ten then divide 4.95 by 9 which equels 0.55
pls give brainest award
First try was incorrect
Simplify: 4(-3 - 2x) simplify
-12-8x is the answer your looking for :)
the art students are using clay. Each student needs 9/10
Answer:
ok mam yes mam going to do my clay
GUYS PLS HELP 25 POINTS + BRAINLIEST IF CORRECT ANSWER
Answer:
B) 50º
Step-by-step explanation:
first we need to find angle MPL. to do this we do 180 - 70 - 60 = 50º. angle KPN is the smae as angle MPL. so angle KPN is 50º.
Answer:
C
Step-by-step explanation:
your answer is C because when you solve the answer question you get 60 degrees .What I did to get the answer is that I solve each solution answer and that is how I got 60 degrees
Hope this helps:)
Pls mark brainlist
x2 - 2x + 1 = 0? Please answer fast I need it now
Answer:
1
Step-by-step explanation:
x2 - x2 = 0
+1 = 1
Find the value of N
9 : 10 = 54 : N
Answer:
I think Value of N is 60
Step-by-step explanation:
because 9 ×6 =54
therefore, 10×6=60
hope its correct and hope ti helps..
Evaluate the expression P(6,1)
Answer:
p(6,3)=120
Step-by-step explanation:
In the pic is how to do it
The value of the permutation expression P(6, 1) will be 6.
What are permutation and combination?A permutation is an act of arranging items or elements in the correct order. Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.
Evaluate the expression P(6, 1).
We know that the formula for the permutation is given as,
ⁿPₓ = n! / (n - x)!
From the above, the value of n is 6 and the value of x is 1. Then we have
⁶P₁ = 6! / (6 - 1)!
⁶P₁ = 6! / 5!
⁶P₁ = 6 x 5! / 5!
⁶P₁ = 6
The value of the permutation expression P(6, 1) will be 6.
More about the permutation and the combination link is given below.
https://brainly.com/question/11732255
#SPJ5
20 to the power of 3 divided by 2
Answer:
4000
Step-by-step explanation:
20 to the power of 3 is 8000 and 8000/2 is 4000
What is the solution to the system? x + y = 4 x+y=1
Given :
x + y = 4x + y = 1To Find :
The value of x and y.Answer :
x + y = 4 ....[Equation (i)]x + y = 1......[Equation (ii)]Adding eqⁿ (ii) and eqⁿ (i) we get :
→ x + y + x - y = 4 + 1
→ 2x = 5
→ x = 5/2
→ x = 2.5
Now, put the value of x = 5/2 in eqⁿ (i) we get :
→ x + y = 4
→ 5/2 + y = 4
→ y = 4 - 5/2
→ y = 1.5
Elena and Noah used different methods to compute 0.23 x 1.5. Both calculations were correct. Analyze the 2 methods.
Answer:
i have this same question. im sorry but i don't get it either. sorry..
Step-by-step explanation:
A store has clearance items that have been marked down by 60%. They are having a sale, advertising an additional 45% off clearance items. What percent of the original price do you end up paying
Answer:
You end up paying 22% of the original price.
Step-by-step explanation:
The statement indicates that a store has clearance items that have been marked down by 60% and this means that you have to pay 40% of the price as:
100%-60%=40%
Now, the statement says that the are advertising an additional 45% off clearance items which means that you will have a 45% discount on the 40% of the original price. So, you have to calculate 45% of 40 and subtract that from 40 to find the percentage that you will end up paying:
40*45%=18
40-18=22
According to this, the answer is that you end up paying 22% of the original price.
If each of the numbers in the following data set were multiplied by 17, what
would be the median of the data set?
28, 58, 20, 14, 18, 71, 36
A. 986
B. 1207
C. 476
D. 612
Answer:
B
Step-by-step explanation:
Jug A holds 1800ml Jug B hold 3/10 more. How much does jug B hold?
Answer:
Jug B can hold 2340 ml.
Step-by-step explanation:
Given
The amount in Jug A = 1800ml
To determine
How much does jug B hold?
Give that the Jug B holds 3/10 more, i.e.
[tex]\frac{3}{10}\times \:1800=540[/tex]
Thus,
The total amount in Jug B = 540+1800
= 2340 ml
Therefore, Jug B can hold 2340 ml.
Answer:
get into it
Step-by-step explana tion:
What is 1 infinity plus 1 infinity equal.
Answer:
infinity
Step-by-step explanation:
lol
I have 6 fish. 3 of them drowned. How many fish do I have left?
Answer:
6
Step-by-step explanation:
because fish don't drown
Someone please help me
Answer:
1. X: 0, -3
2. Y: 1, -1
3. Z: 4, -4
4. M: -4, 1
5. N: -2, 2
6. P: 2, 4
7. Q: 2, 0
8. R: -3, -1
Answer:
1. (0,-3)
2. (1,-1)
3. (4,-4)
4. (-4,1)
5. (-2,2)
6. (2,4)
7. (2,0)
8. (-3,-1)
9-17: first photo
18a: second photo
18b. A pentagon. When you connect the points, the shape has 5 sides
Step-by-step explanation:
What is the length of side EF in the triangle? Please give a step by step explanation, I'm having lots of trouble finding the solution. Thank you!
Answer:
EF = 8.8 cm
Step-by-step explanation:
In the given right angled ΔDEF, DE is the hypotenuse while EF and DF are adjacent sides. So that applying the Pythagoras theorem, we have;
[tex]/hyp/^{2}[/tex] = [tex]/adj1/^{2}[/tex] + [tex]/adj2/^{2}[/tex]
[tex]/DE/^{2}[/tex] = [tex]/EF/^{2}[/tex] + [tex]/DF/^{2}[/tex]
[tex]/16.2/^{2}[/tex] = [tex]/EF/^{2}[/tex] + [tex]/13.6/^{2}[/tex]
262.44 = [tex]/EF/^{2}[/tex] + 184.96
[tex]/EF/^{2}[/tex] = 262.44 - 184.96
= 77.48
EF = [tex]\sqrt{77.48}[/tex]
= 8.8023
EF = 8.8 cm
The length of side EF is 8.8 cm.
What is
12а + 7x - За – 2х
Answer:
=12a-3a+7x-2x
=9a+5x
This is the answer.
Hope it helps you..
Answer
=12a+7x-3a-2x
=9a+7x-2x
=9a+5x
Explanation
This is the ans. hope you like it....
The length of a room is 7.25 feet longer than the width, x, of the room. Which expression represents the perimeter of the room?
Answer:
P = 14.5+4x
Step-by-step explanation:
Let the width of the room is x.
Length = 7.25 feet longer than the width = 7.25 +x
We need to find an expression the represents the perimeter of the room.
Perimeter = sum of all sides
P = 2(l+b)
l is length and b is width
P = 2(7.25 +x+x)
=2(7.25 +2x)
=14.5+4x
Hence, the required expression for the perimeter is 14.5+4x.
3 There are 5 times as many boys as girls in a school.
Together the school has 810 pupils.
How many boys are there?
Answer:
Number of boys = 675
Step-by-step explanation:
Given that:
There are 5 times as many boys as girls in a school.
Number of pupils in school = 810
Let,
x be the number of girls
y be the number of boys
According to given statement;
x+y=810 Eqn 1
y = 5x Eqn 2
Putting y=5x in the Eqn 1
x+5x=810
6x=810
Dividing both sides by 6
[tex]\frac{6x}{6}=\frac{810}{6}\\x=135[/tex]
Putting x=135 in Eqn 2
y = 5(135)
y = 675
Hence,
Number of boys = 675
Is the given value a solution of the inequality?
Answer:
I don't think so
Step-by-step explanation:
if the s has to be more than or equal to then s would have to equal 8 or more
6.5(6.24-1.69)=?
pls help
Answer:
29.575
Step-by-step explanation:
6.5(6.24-1.69)= 6.5(4.55) = 29.575
Answer:
[tex]6.5(6.24 - 1.69) \\ = 6.5 \times 4.55 \\ = 29.575[/tex]
29.575 is the right answer.Mrs. Poster's class is divided into three groups of students. Each group has 3 girls and 2 boys, Which expression could she use to find the total number of students in the class?
O 3+(2+3)
(3 X 2) + 3
O 3x (2+3)
(32)
Answer:
3 X (2+3)
Step-by-step explanation:
If we have five students (3 girls and 2 boys), and three groups, we can use the expression 3 X (2+3), which concludes three groups times five students (in each group), which will give us our total of 15 students.
What are the names of these polygons?
Answer:
1)Quidrilateral
2)Pentagon
Need help please ???????
Answer:
5pm
Step-by-step explanation:
5 x 4= 20 miles
4 x 5= 20 miles
What is the area of the figure to the nearest hundredth 14m and 4 m
Answer: I believe its 56
Step-by-step explanation:
A pizzeria charges $2 per slice of pizza, plus an additional $0.75 per topping. If
Erica has at most $12.50 to spend on her pizza, how
many toppings could she get
on ONE slice of pizza? Write an inequality expression that represents the
situation and solve! Explain your reasoning (no work, no points)! You can
copy/paste the following symbols as needed: 2s<>
Your answer
Answer:
Maximum amount of toppings is 14 inequality is t <=14
Step-by-step explanation:
let t be the amount of toppings on the pizza
0.75t + 2 <= 12.50
0.75t <= 10.50
t <= 14
What is 1/2 percentage of a whole number (show work if u can) HELP IM DUM
Answer:
50%?
Step-by-step explanation:
Hello! :)
Please help me solve this + explain your answer :)
I will indeed give you Brainlst <3
Answer: the triangles are congruent
Step-by-step explanation: if u add up all the angles u get 180 so all angles are congruent