Question:
Express each vector as a product of its length and direction.
[tex]\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k[/tex]
Answer:
[tex]\frac{1}{\sqrt{2}}[/tex] [tex](\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)[/tex]
Step-by-step explanation:
A vector v can be expressed as a product of its length and direction as follows;
v = |v| u
Where;
|v| = length/magnitude of v
u = unit vector in the direction of v
---------------------------------------------------------------------------------------
Let the given vector be v, i.e
[tex]v = \frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k[/tex]
(i) The length/magnitude |v| of vector v is therefore,
|v| = [tex]\sqrt{(\frac{1}{\sqrt{6}})^2 + (-\frac{1}{\sqrt{6}})^2 + (-\frac{1}{\sqrt{6}})^2[/tex]
|v| = [tex]\sqrt{(\frac{1}{6}) + (\frac{1}{6}) + (\frac{1}{6})[/tex]
|v| = [tex]\sqrt{(\frac{3}{6})[/tex]
|v| = [tex]\sqrt{(\frac{1}{2})[/tex]
|v| = [tex]\frac{1}{\sqrt{2}}[/tex]
(ii) The unit vector u in the direction of vector v, is therefore,
u = [tex]\frac{v}{|v|}[/tex]
[tex]u = \frac{\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k}{\frac{1}{\sqrt{2}}}[/tex]
[tex]u = \sqrt{2}(\frac{1}{\sqrt{6}}i - \frac{1}{\sqrt{6}}j - \frac{1}{\sqrt{6}}k)[/tex]
[tex]u = (\frac{\sqrt{2}}{\sqrt{6}}i - \frac{\sqrt{2}}{\sqrt{6}}j - \frac{\sqrt{2}}{\sqrt{6}}k)[/tex]
[tex]u = (\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)[/tex]
Therefore, the vector can be expressed as a product of its length and direction as:
|v| u = [tex]\frac{1}{\sqrt{2}}[/tex] [tex](\frac{1}{\sqrt{3}}i - \frac{1}{\sqrt{3}}j - \frac{1}{\sqrt{3}}k)[/tex]
10. Use the properties of exponents to simplify the expression:
[tex]\bigstar\:\boxed{\bf{\purple{x^{\frac{m}{n}}}=\orange{(\sqrt[n]{x})^m}}}[/tex]
Let's solve !
[tex]:\implies\sf\:25^{\frac{3}{2}}[/tex]
[tex]:\implies\sf\:(\sqrt[2]{25})^3[/tex]
[tex]:\implies\sf\:5^3[/tex]
[tex]:\implies\boxed{\bf{\red{125}}}[/tex]
Hence, Oprion-D is correct !
21. Chandra is retiling her bathroom floor. Each tile is in the shape of a
square, and is 6.5 inches long. How many square inches does one tile
cover? *
WILL MARK AS BRAINLIEST
Answer:
42.25 square inches
Step-by-step explanation:
the formula for area of a square is length x width
a square has four equal sides
so the length and width of the square are 6.5
so you would multiply 6.5 by itself: 6.5x6.5=42.25
so the tile overs 42.25 sq inch
to 5% - (8.1 + 5%).
What’s the answer
Answer:
rawr
Step-by-step explanation:
Answer:
Your correct answer is -81/10
Step-by-step explanation:
[tex]\frac{5}{100}- (8.1 + \frac{5}{100})[/tex]
= [tex]\frac{1}{20} - (8.1 + \frac{5}{100})[/tex]
= [tex]\frac{1}{20} - (8.1 + \frac{1}{20})[/tex]
= [tex]\frac{1}{20} -\frac{163}{20}[/tex]
[tex]=\frac{-81}{10}[/tex]
One year Hank had the lowest ERA (earned-run average, mean number of runs yielded per nine innings pitched) of any male pitcher at his school, with an ERA of
3.05. Also, Sally had the lowest ERA of any female pitcher at the school with an ERA of 2.96. For the males, the mean ERA was 3.848 and the standard deviation was
0.742. For the females, the mean ERA was 5.007 and the standard deviation was 0.722. Find their respective Z-scores. Which player had the better year relative to
their peers, Hank or Sally? (Note: In general, the lower the ERA, the better the pitcher.)
Tests
Hank had an ERA with a z-score of
Sally had an ERA with a z-score of
Answer:
Hank had an ERA with a z-score of 25.554
Step-by-step explanation:
solve for x: -2(x+3)= -2 - 6
0
3
all real numbers
no solution
Answer:
0
Step-by-step explanation:
-2 is multiply by x and 3 then from left the number are replace in right then like term are simplify.
Lena has $12 she bought a pack of craft paper for six dollars and a stapler for two dollars which expression correctly shows the money Lena has left
Answer:
6+2=8 12-8=4 so she has $4 left
Step-by-step explanation:
Answer:
12-6-2=4
or
6+2=8, 12-8=4
I need help please no one helps me
Answer:
the answer is A
bro please help mee
Step-by-step explanation:
if a gymnasium is 80 feet long and 60 feet wide, what will the distance be between opposite corners
Answer:
140
Step-by-step explanation:
Can someone help me understand this
First (Takeaway 4 from 46) Then (divide 6 and 2 and after THAT multipy it with 3) Finally only if needed (Multiply both answers to get the one you need)
Answer:
10
Step-by-step explanation:
46 - 4×(6÷2×3)= ⇒ solve parenthesis, division and multiplication have same priority so start from left to right46 - 4×(3×3) = ⇒ multiplication46 - 4×9 = ⇒ multiplication46 - 36 = ⇒ subtraction10 ⇒ answerWhat is .5 ( 5 repeating) in a fraction ?
Hey there! I'm happy to help!
Let's say that our fraction is x.
x=0.5555555...
Let's get rid of the repeating stuff. If you multiplied x by 10, the fraction would be equal to 5.5555555.....
x=0.55555555....
10x=5.5555555.....
What if we subtracted the first equation from the second? Then all of the repeating stuff would be gone!
9x=5
We divide both sides by 9.
x=5/9.
Have a wonderful day! :D
Find equations of the spheres with center(1, −1, 6)that touch the following planes.a) xy-planeb) yz-planec) xz-plane
Given :
Center of sphere , C( 1 , -1 , 6 ) .
To Find :
Find equations of the spheres with center (1, −1, 6) that touch the following planes.a) xy-plane b) yz-plane c) xz-plane .
Solution :
a)
Distance of the point from xy-plane is :
d = 6 units .
So , equation of circle with center C and radius 6 units is :
[tex](x-1)^2+(y-(-1))^2+(z-6)^2=6^2\\\\(x-1)^2+(y+1)^2+(z-6)^2=36[/tex]
b)
Distance of point from yz-plane is :
d = 1 unit .
So , equation of circle with center C and radius 1 units is :
[tex](x-1)^2+(x+1)^2+(z-6)^2=1^2\\\\(x-1)^2+(x+1)^2+(z-6)^2=1[/tex]
c)
Distance of point from xz-plane is :
d = 1 unit .
So , equation of circle with center C and radius 1 units is :
[tex](x-1)^2+(x+1)^2+(z-6)^2=1^2\\\\(x-1)^2+(x+1)^2+(z-6)^2=1[/tex]
Hence , this is the required solution .
Prove that root 7 is an irrational number.
Answer: Root 7 would equal 2.64575131106 and would go on forever.
Step-by-step explanation: It isn't one of the perfect squares. For example, the first 10 perfect square are 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.
Answer:
it is an irrational number and here is why
Step-by-step explanation:
So think of square root as it's answer is something that you you multiply its self by its self and you get that answer. Ex: 8 x 8 = 64 square root of 64 is 8. So in that case there is nothing you can exactly multiply by itself to get 7 so in that case it's a decimal or an irrational number.
HOPE THIS HELPS!
solve for n
8+8+n-4=3n-2n
Answer:
No solution
Step-by-step explanation:
8+8-4 = 12
12+ n = 3n-2n
3n-2n
12+n3n-2n
subtract n on both sides
12=0n
This makes it no solution
How many years old are you have lived 1 billion second
Wyatt owes $472.22 on his credit card. He returns two items, one for $49.63 and the other for $47.58.
Then he makes purchases of $39.57 and $32.21. What is the new balance on the card?
Answer:
Holy bloop you gotta learn
Step-by-step explanation:
you dumb
go to school
and learn
Solve for q in terms of m : m=2q−4/ q−5
Answer:
q = (4 - 5 m)/(2 - m)
Step-by-step explanation:
Solve for q:
m = (2 q - 4)/(q - 5)
Hint: | Reverse the equality in m = (2 q - 4)/(q - 5) in order to isolate q to the left hand side.
m = (2 q - 4)/(q - 5) is equivalent to (2 q - 4)/(q - 5) = m:
(2 q - 4)/(q - 5) = m
Hint: | Multiply both sides by a polynomial with respect to q to clear fractions.
Multiply both sides by q - 5:
2 q - 4 = m (q - 5)
Hint: | Write the linear polynomial on the right hand side in standard form.
Expand out terms of the right hand side:
2 q - 4 = m q - 5 m
Hint: | Isolate q to the left hand side.
Subtract m q - 4 from both sides:
q (2 - m) = 4 - 5 m
Hint: | Solve for q.
Divide both sides by 2 - m:
Answer: q = (4 - 5 m)/(2 - m)
Solve for x: 3x+2=11
Answer:
X= 3
Step-by-step explanation:
To solve this, you must first subtract 2 from 11, to get the 3x isolated.
You'll then have 3x=9, but the x is not alone, so you subtract the 3 from both sides. This leaves you with 3
the value of x will be 3 for the given function 3x+2=11.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
Given a function 3x+2=11
Simplifying the function:
=> 3x + 2 = 11
subtract by 2
=> 3x +2 - 2 = 11-2
=> 3x = 9
divide by 3 into both sides
=> x = 3
Therefore, the value of x will be 3 for the given function.
Learn more about function here:
https://brainly.com/question/29633660
#SPJ3
Nidhi is creating a rectangular garden in her back yard. The length of the garden is 10 feet. The perimeter of the garden must be at least 40 feet and no more than 76 feet. Write and solve a compound inequality to find the range of values for the width, w, of the garden.
Answer:
10<=w<=33
Step-by-step explanation:
length is 10 so width can only add up to 20 less than those
40-20=20
20/2=10
76-20=66
66/2=33
p.s. <= is greater than or equal to oops
The Cobb family’s natural gas bill was 85.50 for 95 cubic feet of gas, What is the unit rate? (Cost per cubic foot of gas?)
Answer:
I will not tell you
Step-by-step explanation:
Not telling
The tree was 60 inches tall to use later it was 105 inches tall what is the percentage increase to the nearest hundredth of the height of the tree
Answer:
[tex]\%\ increase = 75\%[/tex]
Step-by-step explanation:
Initial Height = 60 inches
Final Height = 105 inches
Required
Determine the percentage increase
Percentage increase is calculated as thus;
[tex]\%\ increase = \frac{Final\ Height - Initial\ Height}{Initial\ Height}[/tex]
Substitute values for the final and the initial height
[tex]\%\ increase = \frac{105 - 60}{60}[/tex]
[tex]\%\ increase = \frac{45}{60}[/tex]
[tex]\%\ increase = 0.75[/tex]
Convert to percentage
[tex]\%\ increase = 75\%[/tex]
The height of the tree increased by 75%.
Given that the tree was 60 inches tall, and later it was 105 inches tall, to determine what is the percentage increase to the nearest hundredth of the height of the tree, the following cross multiplication must be performed:
60 = 100 105 = X 105 x 100/60 = X 10500/60 = X 175 = X 175 - 100 = 75Therefore, the height of the tree increased by 75%.
Learn more in https://brainly.com/question/9897756
Angel took a 2-year lease on a new car and after 4 months of driving, he’d put 5,600 miles on it. The lease allows 10,000 miles per year. If his driving habits stay consistent, will he stay under the allotted mileage for years? By how much?
Answer:
Step-by-step explanation:
Lease years = 2 years
Allowed mileage per year = 10,000 miles
After 4 months of driving ; 5600 miles on car
If driving habit stays consistent, Angel won't stay under the alloted mileage for years,
If 4 months = 5600 miles
Average miles driven per month :
5600 / 4 = 1400 miles / month
After two years ; ( 2 × 12) = 24 months
Total miles driven :
1400 miles × 24 = 33600 miles
Total alloted miles for 2 years:
10,000 × 2 = 20,000 Miles
Excess miles driven;
20,000
x+2/2×>1/2 in rational in equalities
Hi there!
~
[tex]x + \frac{2}{2} (\frac{1}{2} )[/tex]
= [tex]x + \frac{1}{2}[/tex]
Hope this helped you!
Which term has a degree of 8? a.) 9xy^8 b.)-2x^3y^5 c.) 3x^2y^4 d.) 8xy
Answer:
A
Step-by-step explanation:
I honestly guessed,but i just took the test and got it right.
Answer:
-2x^3y^5
Step-by-step explanation:
malik's solution to the equation [tex]\frac{2}{5}[/tex]×-4y=10
Answer:
10
Step-by-step explanation:
you put the answer on the board
Part a: A deli receives a large order for sandwiches for a company picnic. The company wants one club sandwich and two regular sandwiches for each person. The company also wants an extra Dagwood sandwich. A club sandwich has $3$ slices of bread. A regular sandwich has $2$ slices. A Dagwood has $5$ slices. If there are $n$ people going to the company picnic, how many slices of bread does the deli need to make this order? Write your answer as a fully simplified expression. Your answer should have the variable $n$ in it exactly once. Part b: Given that the deli ends up using $110$ slices of bread, how many people are going to the company picnic?
Answer:
Um...
I know the answer to Part A, but not to Part B.
Step-by-step explanation:
The answer for Part A is 7n + 5. Hope this helps!
please me asap :)) will give 40 points
i only need 4-101
x = -3
y = 5
x = -2
y = 0
x = -1
y = -3
x = 0
y = -4
x = 1
y = -4
x = 2
y = 0
x = 3
y = 5
What is the image point of (-1, 1) after a translation left 2 units and down 2 units?
Submit Answer
attempt 1 out of 2
Answer:
(-3,-1)
Step-by-step explanation:
What is the value of x & y?
Answer:
x = 16, y = 9
Step-by-step explanation:
The 2 triangles are similar by the AA postulate, thus the ratios of corresponding sides are equal, that is
[tex]\frac{x}{24}[/tex] = [tex]\frac{12}{18}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )
3x = 48 ( divide both sides by 3 )
x = 16
----------------------------------------------------
[tex]\frac{y}{6}[/tex] = [tex]\frac{18}{12}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )
2y = 18 ( divide both sides by 2 )
y = 9
What part of 20 is 25?
Answer:
80%
Step-by-step explanation:
just look it up on google thyats what i did
5000 Vbucks for who ever answers first
Answer:
;_(
Step-by-step explanation:
Answer:
4453r plss im soo poor in fortnite honour64 pls gift me skins
Step-by-step explanation: