If a =5, 0, −1,find a vector b such that compab = 2.b = _______.
Answers
Answer:
[tex]b = (q,r , 5q-2\sqrt{26} )[/tex]
Step-by-step explanation:
From the question we are told that
The vector given is
[tex]a = (5,0,-1)[/tex]
Also [tex]comp_a b = 2[/tex]
Generally
[tex]comp_a b = \frac{a \cdot b}{|a|}[/tex]
Here [tex]|a|[/tex] is the magnitude of a which is mathematically represented as
[tex]|a| = \sqrt{5^2 + 0^2 +(-1)^2 }[/tex]
=> [tex]|a| = \sqrt{26}[/tex]
b is vector which we will assume to have the following parameters
[tex]b = (q , r , x)[/tex]
So
[tex]comp_a b = \frac{(5,0,-1) \cdot (q,r,x)}{\sqrt{26} } = 2[/tex]
=> [tex]\frac{5q + 0 -x}{\sqrt{26} } = 2[/tex]
=> [tex]x = 5q-2\sqrt{26}[/tex]
Hence the vector be can be mathematically represented as
[tex]b = (q,r , 5q-2\sqrt{26} )[/tex]
This means that the vector b is more than one value since it is made up of variable
This means that if
[tex]q = 1\\r=1\\x =1[/tex]
Then
[tex]b = (1,1,5-2\sqrt{26} )[/tex]
A quantity has magnitude but not position, that's why in this the vector [tex]b =(0,0, -2\sqrt{26}).[/tex]
Vector:If[tex]a =(5,0,-1)[/tex] Our goal is to determine a vector b that will allow comp to work properly [tex]_{a}b = 2.[/tex]
Allow the vector to flow naturally [tex]b =(x, y,z)[/tex]
Recalling
comp[tex]_{a}b =\frac{a.b}{|a|}[/tex]
Therefore,
comp [tex]_{a}b= 2 \\\\[/tex]
[tex]\to \frac{a.b}{|a|}= 2\\\\[/tex]
[tex]\to \frac{(5,0,-1)\cdot (x,y,z)}{ |(5,0,-1)|} =2\\\\\to \frac{5x+0-z}{5^2+0+(-1)^2}=2\\\\ \to \frac{5x-z}{\sqrt{26}}= 2 \\\\\to 5x-z = 2\sqrt{26}\\\\ \to z=5x-2\sqrt{26}\\\\[/tex]
As a result, the vector b can be expressed as,
[tex]\to b =(x,y,z) =(x, y, 5x-2\sqrt{26}) \\\\[/tex]
As a result, this aforementioned form can be found in an endless number of vectors.
One of them is [tex]b =(0,0, -2\sqrt{26}).[/tex]
Find out more about the vector here:
brainly.com/question/13322477
Related Questions
Solve LaTeX: \frac{-x}{3} \:-15 x > − 15 LaTeX: x\: \:-2
Answers
Answer:
The answer is option AStep-by-step explanation:
[tex] \frac{ - x}{3} < 5[/tex]First of all cross multiply
That's
[tex] - x < 5 \times 3 \\ - x < 15[/tex]Next divide both sides by - 1 to make x positive and change the sign from < to >
That's
[tex] \frac{ - x}{ - 1} < \frac{ 15}{ - 1} [/tex]We have the final answer as
[tex]x > - 15[/tex]Hope this helps you
Y=AB-8. Trying to learn how to solve for A.
Answers
Answer:
[tex]A=\frac{Y+8}{B}[/tex]
Step-by-step explanation:
So we have:
[tex]Y=AB-8\\[/tex]
First, add 8 to both sides. The right will cancel:
[tex]Y+8=AB[/tex]
Now, notice that A is multiplied to B. So, the isolate A, divide both sides by B. The right will cancel:
[tex]A=\frac{Y+8}{B}[/tex]
And we're done!
A rope 5 meters long was cut into 7 equal parts. What is the length of each part?
Answers
Answer:
5/7 meters
Step-by-step explanation:
Take the 5 meters and divide into 7 parts
5/7 = 5/7 meters
To find the length of each part, we can divide.
5 / 7 = 0.714...
We can just keep it as a fraction.
The answer is 5/7m
Best of Luck!
Please help I will give out brainliest
Answers
Hey There!! ~
The answer to this is: the upper bound for the length is [tex]21.5cm.[/tex] Lower and Upper Bounds
The lower bound is the smallest value that will round up to the approximate value.
The upper bound is the smallest value that will round up to the next approximate value.
Ex:- a mass of 70 kg, rounded to the nearest 10 kg, The upper bound is 75 kg, because 75 kg is the smallest mass that would round up to 80kg.
Here , A length is measured as 21cm correct to 2 significant figures. We need to find what is the upper bound for the length . let's find out:
As discussed above , upper bound for any number will be the smallest value in decimals which will round up to next integer value . So , for 21 :
⇒ [tex]21.5cm.[/tex]
21.5 cm on rounding off will give 22 cm . So , the upper bound for the length is [tex]21.5cm.[/tex]
Hope It Helped!~
[tex]ItsNobody[/tex]~
Solve −5x = 30 a.) 6 b.) -6 c.) 25 d.) 35
Answers
What number groups does 15 classify into? Counting numbers, whole numbers, integers, rational numbers, real numbers?
Answers
Answer:
Hey, I think you've done this already!
Step-by-step explanation:
Answer:
brainliest
Step-by-step explanation:
The federal tax code allows some items used for business purposes to be depreciated. That is, their taxable value decreases over time. A new van used in your delivery business has a taxable value of $22,000. The tax code allows you to depreciate this van by $1900 per year. Find a formula that gives the taxable value T, in dollars, of the van after n years of depreciation.
Answers
Answer: T = 22,000 - 1,900n
Step-by-step explanation:
Taxable value is $22,000
The tax code allows for the depreciation of this van by $1,900 per year.
After n years therefore the total depreciation is;
= 1,900 * n
This depreciation will need to be removed from the taxable value of $22,000 to find out the taxable value left.
Formula is therefore;
T = 22,000 - 1,900n
Seven times the sum of 4 and some number is 42
Answers
Answer:
[tex]x=2[/tex]
Step-by-step explanation:
[tex]7\times{(4+x)}=42[/tex]
Divide both sides by 7:
[tex]4+x=42\div{7}\\4+x=6[/tex]
Subtract 4 from both sides:
[tex]x=6-4\\x=2[/tex]
Solve : 3x – 4 = 2(x-1)
Answers
Answer:
Step-by-step explanation:
Answer:
x=2
Step-by-step explanation:
3x-4=2(x-1)
=>3x-4=2x-2
=>3x-2x=-2+4
=>x=2
The question is 108 divided by -0.9
Answers
Answer:
your answer will be -120
Answer:
you're answer would be -120
Step-by-step explanation:
108/(-0.9)=(-120)
Madelyn was baking cookies for her classmates. Each batch of cookies calls
for 1/2 a cup of sugar. If she is making 8 batches, how many cups of sugar will she need?
Answers
Answer:
4 cups
Step-by-step explanation:
In the Atlanta metropolitan area, 723 new cases of invasive cancer of the cervix occurred among white women between 1975 and 1984, inclusive. An estimated 620,000 white women lived in this area on average during this time period. What is the average annual incidence rate of invasive cervical cancer in this population?
Answers
Answer:
1.166 per 1000 of population
Step-by-step explanation:
Given the following :
Newly recorded cases of invasive cervical cancer = 723
Period of time = 1975 - 1984 ( inclusive)
Estimated average Population of white women in the area at the time = 620,000
Average annual. Incidence rate invasive of cervical cancer in the population.
Incidence rate = (new cases / total population) × 10^n
Incidence rate = (723/620000) × 10^n
= 0.0011661
= 1.166 per 1000 of population
what is the anwer of 40+678
Answers
Answer:
718
Step-by-step explanation:
just add the two numbers
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{718}}}}}[/tex]
Step-by-step explanation:
( see attached picture )
Hope I helped!
Best regards!
On one map of a town , the scale from the town to the map is 12mi to 3 cm. the school is 2.5cm from the grocery store on this map. on a different map of the same town ,the scale from the town to the map is 12mi to 2cm .the school is 1.5cm from the library on that map. is the grocery store or library closer to the school?
Answers
Answer:
Step-by-step explanation:
Grocery Store
12 mi / 3 cm = x / 2.5 cm Cross multiply
12 * 2.5 = 3 * x Multiply
30 = 3x Divide by 3
30/3 = x
x = 10 miles
Library
12 mi / 2 cm = x / 1.5 Cross multiply
12 * 1.5 = 2x
18 = 2x Divide by 2
18/2 = x
9 miles
The library is closer than the grocery store.
What is 2.1 with 1repeating as a mixed number
Answers
Answer:
2 1/10. is the answer i think105,159 to nearest hundred thousands place
Answers
The answer is 100,000.
solve for x. x - 1
2 = 4
Answers
Answer:
x = 16
Step-by-step explanation:
x - 12 = 4
+ 12 = +12
x = 16
Answer:
16
Step-by-step explanation:
y< 4 3 x+3 y≤−2x−1 Which graph represents the system of inequalities?
Answers
Answer:
Don't see any graphs
Step-by-step explanation:
Answer:
its A
Step-by-step explanation:
Evaluate the expression when c=-6.
c2 +6c+5
Answers
Answer:
the evaluation gives 5 as the result
Step-by-step explanation:
We just replace -6 instead of "c" in the expression and perform the appropriate operations:
[tex]c^2+6\,c+5\\(-6)^{2} +6\,(-6)+5\\36-36+5\\5[/tex]
Answer: NEGATIVE 1
Step-by-step explanation:
I got the answer wrong and it told me the right answer was -1 so lol
Solve for y.
4y2 = 7y+2
If there is more than one solution, separate them with commas.
If there is no solution, click on "No solution."
Answers
Answer:
y=-1/4, 2.
Step-by-step explanation:
4y^2=7y+2
4y^2-7y-2=0
factor,
(4y+1)(y-2)=0
zero property,
4y+1=0, y-2=0,
4y=0-1=-1,
y=-1/4,
y=0+2=2.
A rectangle’s base is 6 cm longer than its height. The rectangle’s area is 135 cm2. Find this rectangle’s dimensions. You must include units with your answers
Answers
Area of a rectangle = length x height
Area = 135
Height = X
Lenght = x +6
135 = x * x+6
Simplify:
135 = x^2 +6x
Subtract 135 from both sides:
x^2 + 6x - 135 = 0
Solve:
2 numbers when added need to equal 6 and when multiplied equal -135
x = 9 and x = -15
The height can't be a negative number so the height is 9
Length = 9 +6 = 15
Height = 9cm, Length = 15 cm
Which of the named angles is not an angle found in the picture?
Answers
Answer:c
Step-by-step explanation:
cccccccccc
What are the coordinates of G, H, and I after a rotation about (0,0) by 90 degrees clockwise? Thank you.
Answers
Answer:
Ok, when we have a point (x, y) and we do a rotation of 90° the new points will actually depend on the quadrant where we are, but it will always change the order to (y, x) but this does not end here, because depending on the quadrant where the point ends, the signs will change as follows.
1st quad (+y, +x)
2nd quad (-y, +x)
3rd quad (-y, -x)
4th quad (+y, -x)
So if we are in the second quadrant, the transformed point will be in the first quadrant
Now, we have that the points G and H are:
G = (-1, 3)
This point is in the second quadrant, so it moves to the first quadrant (where bot values must be positive).
The new point will be:
G´ = (3, 1)
And the other point is:
H = (-4, 0)
It also rotates to the first quadrant, so the new point will be:
H' = (0, 4)
Answer:
Because the person above already explained I’ll just give the answers.
Step-by-step explanation:
G = (-1,3) H = (-4,0) I = (3,-2)
it's easy it's called Two-way tables please help
Answers
Answer: The filled out table is shown below in the attached image
===========================================================
Explanation:
The letters A through J are one way to fill out the table. Though there are other possible orders.
Start at letter A, which is from the fact we have 40 people total
Then move to letter B. This is the total number who like pasta (26)
We have C = A-B = 40-26 = 14 people who don't like pasta
--------------
Now move to cell D. This is the total who don't like netball, which is 21 people. There are E = A-D = 40-21 = 19 people who do like netball.
F = 4 is the number of people who don't like either thing (netball or pasta). So G = D-F = 21-4 = 17 people like pasta but don't like netball.
Of those people who like netball (E = 19), we have 9 who also like pasta. This is in cell H in the upper left corner. This means J = E-H = 19-9 = 10 people like netball but don't like pasta.
----------------
So we have these values
A = 40B = 26C = 14D = 21E = 19F = 4G = 17H = 9 J = 10Please assist me with these problems and show the work: Part 2 6. The angle of elevation of the sun is 68° when a tree casts a shadow 14.3 m long. How tall is the tree, to the nearest tenth of a metre? 7. A wheelchair ramp is 4.2 m long. It rises 0.7 m. What is its angle of inclination to the nearest degree?
Answers
Answer: 6) 35 meters 7) Ф = 10°
Step-by-step explanation:
[tex]6.\quad \tan\ 68^o=\dfrac{x}{14.3}\\\\\\.\quad 14.3 \tan\ 68^o=x\\\\.\quad 35\ meters =x[/tex]
[tex]7.\quad \sin \theta =\dfrac{0.7}{4.2}\\\\\\.\qquad \quad \theta=\sin ^{-1}\bigg(\dfrac{1}{6}\bigg)\\\\\\,\qquad \quad \theta =10^o[/tex]
Question 6:
tan 68 = x/14.3
14.3tan(68) = x
35m = x
Question 7:
sinθ = 0.7/4.2
θ = sin^-1(1/6)
θ = 10
Best of Luck!
Which is the value of g(-5) if g() = 3.46 - 8?
Answers
Steps to solve:
g() = 3.46 - 8?
~Subtract
g() = -4.54
Best of Luck!
What is the most simplified expression for 4 c squared d + 3 d c minus 2 (d c squared + c d) + 6 c squared d squared?
Answers
Answer:
[tex] \boxed{ \bold{ {\boxed{ \sf{6 {c}^{2} {d}^{2} + 2 {c}^{2} d + cd}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{4 {c}^{2} d + 3dc - 2(d {c}^{2} + cd) + 6 {c}^{2} {d}^{2} }[/tex]
Distribute 2 through the parentheses
[tex] \dashrightarrow{ \sf{4 {c}^{2} d + 3dc - 2d {c}^{2} - 2cd + 6 {c}^{2} {d}^{2} }}[/tex]
Collect like terms
[tex] \dashrightarrow{ \sf{6 {c}^{2} {d}^{2} + 4 {c}^{2} d - 2d {c}^{2} + 3dc - 2cd}}[/tex]
[tex] \dashrightarrow{ \sf{6 {c}^{2} {d}^{2} + 2 {c}^{2}d + cd }}[/tex]
Hope I helped !
Best regards! :D
the answer is a on engenuity
Please help ASAP I will make you brainliest
Answers
Answer:
9 miles
Step-by-step explanation:
First 3 miles 10$
Every additional miles 4$
So 34$ minus 10$ is 24$
24$ divided by 4$ and that is 6 miles
6 + 3 is 9 miles
Solve for x: 3/2 + 1/2x=2x
Answers
1. Explain how measurements taken by standard rulers and scales are limited,
2. Include two to three examples to demonstrate these limitations. Include at least one limitation of using
a ruler and at least one limitation of using a scale,
3. Make sure to write your answer using five to ten complete sentences,
Answers
Answer:
Please find the answer in the explanation
Step-by-step explanation:
RULER
measurements taken by ruler can be limited due to absolute errors, zero error and uncertainties.
1.) If the end of the ruler is worn out giving rise to a zero error
2.) The calibration of the ruler may give rise to another systematic error if the makings are incorrect.
3.) If the object to be measured is not on the same level as graduated surface of the ruler, the angle at which the scale is viewed will affect the result. This is known as parallax error.
SCALE
Systematic error can occur in a scale when the scale is wrongly calibrated.
Also, reading a scale from different angles introduces a variable parallax error.
random uncertainty could be a parallax error caused by taking readings from different angles. This can be reduced by the use of a mirror behind the scale and viewing normally.