To find out the unit vector in the same direction of other vector, we can calculate the magnitude of its vector and then divide all coordinates by the magnitude, remember that the definition of a unit vector is that its magnitude is 1.
We can calculate the magnitude of a 2D vector as
[tex]\Large\displaystyle\text{$\begin{gathered}v = \left(x, y\right)\\ \\\|v\| = \sqrt{x^2 + y^2}\end{gathered}$}[/tex]
I'll call the vector (-4, 7) as v, so the magnitude of v is
[tex]\Large\displaystyle\text{$\begin{gathered}v = \left(-4, 7\right)\\ \\\|v\| = \sqrt{\left(-4\right)^2 + \left(7\right)^2}\\ \\\|v\| = \sqrt{65}\\ \\\end{gathered}$}[/tex]
So the unit vector that i'll call as v with an hat is
[tex]\Large\displaystyle\text{$\begin{gathered}\hat{v} = \frac{v}{\|v\|}\end{gathered}$}[/tex]
The vector divided by its magnitude, when we divide a vector by a scalar it's the same as divide all the coordinates, so
[tex]\Large\displaystyle\text{$\begin{gathered}\hat{v} = \frac{v}{\|v\|}\\ \\\hat{v} = \frac{v}{\sqrt{65}}\\ \\\hat{v} = \frac{\left(-4, 7\right)}{\sqrt{65}}\\ \\ \boxed{\hat{v} = \left(-\frac{4}{\sqrt{65}}, \frac{7}{\sqrt{65}}\right)}\end{gathered}$}[/tex]
We can also remove the square root from the denominator, then
[tex]\Large\displaystyle\text{$\begin{gathered}\hat{v} = \left(-\frac{4}{\sqrt{65}}, \frac{7}{\sqrt{65}}\right)\\ \\\hat{v} = \left(-\frac{4}{\sqrt{65}}\frac{\sqrt{65}}{\sqrt{65}}, \frac{7}{\sqrt{65}}\frac{\sqrt{65}}{\sqrt{65}}\right)\\ \\\hat{v} = \left(-\frac{4\sqrt{65}}{65}, \frac{7\sqrt{65}}{65}\right)\\ \\\end{gathered}$}[/tex]
Use what you prefer!
Hope you liked it
Questions? Ask me in the comments
solve the equation 6x-4 divided by 8 = 7 explain and provide the definition or property that justifies each step of the solution process
Hi! I'm happy to help!
We need to solve for x in this equation, we do this by isolating it on one side of the equation, and see what is on the other side (what it equals).
When we are isolating x, we are undoing the complication in the equation, so we are going to go backwards in the order of operations.
So, we will first write out our equation:
(6x-4)÷8=7,
Now, we need to get rid of that ÷8, we do this by multiplying both sides by 8:
(6x-4)÷8=7
×8 ×8
6x-4=56
Now, we have to add 4 to both sides to get rid of that "-4".
6x-4=56
+4 +4
6x=60
Now, to find what x is, we have to divide both sides by 6 (isolating x).
6x=60
÷6 ÷6
x=10
I hope this was helpful, keep learning! :D
What's the approximate length of an arc with radius 3 miles and central angle of 45
Length of the arc of a circle is given by,
Length of arc = [tex]\frac{\theta}{360^{\circ}}(2\pi r)[/tex]Here, θ is the central angle subtended by the arc
r = Radius of circle
By using this expression, approximate length of the arc with radius 3 miles will be 2.36 miles.
If the radius of circle = 3 miles
Central angle subtended by the arc = 45°
Therefore, length of the arc = [tex]\frac{45^{\circ}}{360^{\circ}}(2\pi )(3)[/tex]
= 2.36 miles
Length of the arc of the given circle will be 2.36 miles.
Learn more,
https://brainly.com/question/12566716
Find the distance between the points T(13, 1.6) and V(5.4.3.7).
Find the distance between the points t(13, 1.6)t(13, 1.6) and v(5.4, 3.7)v(5.4, 3.7).
1
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The distance between any 2 points P(a,b) and Q(c,d) in the coordinate plane, is given by the formula:
Thus the distance between points t(13, 1.6) and v(5.4, 3.7) is found using the formula as:
The opposite of 50 feet below sea level
Answer:
50 ft above sea level.
Step-by-step explanation:
The exact opposite would just be 50 ft above the starting point.
Answer:
it will be 50 feet above the sea level
What is the distance between the points
Choose 1 answer:
Answer:
I believe it's B, 10
Step-by-step explanation:
well first you find where the points would meet. if you count over three, that's where they line up, and then you count up to the dot itself, which would be 7 more. 7+3 = 10 :D
At the gift shop they sell small grettong card and large greeting cards. The cost of small ones are 1.80 and the cost of large ones are 4.40. How much does it cost to get 5 small ones
Answer:
$9
Step-by-step explanation:
Since the question only asks for small ones, we only need to focus on 1.80 and 5. Multiple them. 1.80×5 and we get 9. 1.80×5=9
If someone could explain the error in depth and show step by step how to actually slove the problem that would be great.
Step-by-step explanation:
The first step is wrong. It claims that
[tex]\frac{9x^3}{2x^3+9}=\frac{9x^{\cancel 3}}{2x^{\cancel 3}+9}=\frac{9}{2+9}[/tex]
but it is not true. It is attempting to simplify the fraction by cancelling the x^3 terms from 9x^3 and 2x^3.
However, to perform this operation, all terms in the fraction must be divided by x^3. But this will mean
[tex]\frac{9x^3}{2x^3+9}=\frac{(9)(x^3)}{(2+\textcolor{red}{\frac{9}{x^3}})(x^3)}=\frac{9}{2+\textcolor{red}{\frac{9}{x^3}}}[/tex]
what integer best represents that the temperature outside increased by 12°F?
I WILL APPRECIATE
Answer:
-11.11*C
Step-by-step explanation:
12°F − 32) × 5/9 = -11.11*C
Select the choice that translates the following verbal phrase correctly to algebra:
the difference of m and 7 increased by 15
m − (7 + 15)
7m + 15
(m − 7) + 15
m − 7 ÷ 15
Easy question:
Two ends of a line have coordinates (-6,10) and (2,2). What are the coordinates of the midpoint of the line?
Answer:
midpoint = (-2 , 6)
Step-by-step explanation:
The midpoint can be found with the formula {(x1 + x2 )/2, (y1 + y2.) P1( x1 , y1 ), and P2 (x2 , y2 ) are the coordinates of two points, and the midpoint is a point lying equidistant and between these two points.
(2·4)+6÷2 need to know how to do this problem
seven subtracted from the product of four and a number is a most 26 use the variable C for the unknown number
A wall is 300 square feet. A gallon of paint covers 110 square feet. What is an appropriate conversion factor to help determine how many gallons of paint will be needed to paint the wall?
Answer:
2.723 gallons of paint is required to paint the wall.
Step-by-step explanation:
It is given that the area of the wall is 300 sq feet. A gallon of paint covers 110 sq feet. We are asked to determine how many gallons of paint will be needed to paint the wall.
The fraction of above statement is,
[tex]$\frac{110 f t^{2}}{300 f t^{2}}=\frac{1}{x}$[/tex]
[tex]$x=\frac{300}{110}$[/tex]
[tex]$x=2.723$[/tex]
Learn more about gallons refer:
https://brainly.com/question/19498153A nut-raisin mix costs $5.26 per pound. Rashid buys 15.5 pounds of the mix for a party. Rashid’s estimated cost of the nut-raisin mix is
$81.53 is the cost of nut-raisin mix
For which other positive integers a, less than 11, will the number (a^n) + (a^n+1) + (a^n+2) + (a^n+3) + (a^n+4) always be divisible?
Pls, Answer with the entire explanation.
If the number is supposed to be
[tex]a^n + a^{n+1} + a^{n+2} + a^{n+3} + a^{n+4}[/tex]
then it can be factorized as
[tex]a^n \left(1 + a + a^2 + a^3 + a^4\right)[/tex]
but there's not much to say about divisibility here without any more information about a.
If you meant
[tex]a^n + (a^n+1) + (a^n+2) + (a^n+3) + (a^n+4)[/tex]
simplifying gives
[tex]5a^n + 10 = 5 (a^n+2)[/tex]
which is clearly divisible by 5.
PLS HELP 20 POINTS- will give brainliest
Answer:
I thought I answered this before
-2
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
im taking algebra 2 and this was a question
PLS HELP
A certain stock's price, S (t), can be modeled by the polynomial function S (t) = t^4 – 12t^3 + 52t^2 – 96t + 64, where t represents the month in 2021. In which month will the price of the stock have a local maximum?
February
March
April
May
Answer:
April
Step-by-step explanation:
To solve, you find the maximum of the polynomial function. You can do this by either graphing or plugging in the values in a T chart.
I graphed the function, provided down below.
As you can see, the highest value in the graph is the middle most point, aka (4,1). Count down the months of the year to 4, and you'll find that April is the 4th month of the year.
Using derivative concepts, it is found that the function has a local maximum in March.
--------------------
A function S(t) has local maximums or minimums at points in which the derivative is 0.If the function goes from increasing(positive derivative) to decreasing(negative derivative), it has a local maximum.The function is:
[tex]S(t) = t^4 - 12t^3 + 52t^2 - 96t + 64[/tex]
Which has the following derivative:
[tex]S^{\prime}(t) = 4t^3 - 36t^2 + 104t - 96[/tex]
Now, for each month, it has to be tested the derivative, verifying if it's zero.--------------------
February is the 2nd month, thus, the derivative is:
[tex]S^{\prime}(2) = 4(2)^3 - 36(2)^2 + 104(2) - 96 = 0[/tex]
Now, we have to test a value less than 2, and one greater than two, to check if it goes from increasing to decreasing, that is, derivative goes from positive to negative.
[tex]S^{\prime}(1.5) = 4(1.5)^3 - 36(1.5)^2 + 104(1.5) - 96 = -7.5[/tex]
[tex]S^{\prime}(2.5) = 4(2.5)^3 - 36(2.5)^2 + 104(2.5) - 96 = 1.5[/tex]
From negative to positive, thus, a local minimum in February.
--------------------
March is the 3rd month, thus, the derivative is:
[tex]S^{\prime}(3) = 4(3)^3 - 36(3)^2 + 104(3) - 96 = 0[/tex]
Testing before and after:
[tex]S^{\prime}(2.5) = 4(2.5)^3 - 36(2.5)^2 + 104(2.5) - 96 = 1.5[/tex]
[tex]S^{\prime}(3.5) = 4(3.5)^3 - 36(3.5)^2 + 104(3.5) - 96 = -1.5[/tex]
From positive to negative, thus, it has a local maximum in March.
A similar problem is given at https://brainly.com/question/13539822
What is the image point of (4, - 7) after a translation right 4 units and up 5 units?
Answer:
( 8, - 2 )
Step-by-step explanation:
Annie borrowed $354 from her parents to buy a tablet. She plans to pay the money in 2 equal payments per month for the next 12 months. How much will each payment be?
Answer:
$354 divided by 12 equal payments equals $29.50 per month
Step-by-step explanation:
$354 divided by 12 months (also 12 equal payments) = $29.50 per month.
please help i will give extra points
Answer:
56
Step-by-step explanation:
solve expression using pemdas
(shown in image attached)
[tex]( - 8 \times - 6) - {4}^{2} \\ \\ - 77 - 16 \\ - 93[/tex]
Hope it help youGiven the list of numbers, 3, 2, 6, 3, 9, 5, 12, 7, if the pattern continues, what is the sum of the ninth and tenth numbers?
Answer:
Step-by-step explanation:
Every other one beginning with the first 3 adds 3 to the preceding number that has an odd position.
So the odd positions go up 3 6 9 12
And the next odd position is 15 which is the nineth term.
It's hard to tell what the even ones are doing. It could be anything just about. I'm guessing its a 9. So the tenth term is 9.
The sum of 9 and 15 = 24
If someone gives you a more consistent answer, take it.
(3.0x10^-1)-(1.4x10^-3)
Answer:
.2986
Step-by-step explanation:
( .3 ) - ( . 0014 ) = .2986
Answer:
here u go
Step-by-step explanation:
0.2986x
In which quadrant is the point (-2, -3) located?
Quadrant II
Quadrant TV
Quadrant II
Quadrant l
The point (-2 , -3) is located in the 3rd quadrant.
[tex] \boxed{ \boxed{ \mathrm{lll \: \: quadrant}}}[/tex]
Please solve these questions with the equations. Will give 80 points and mark brainliest to the person with the answers.
1]
[tex]8(x-7)=128 \ \ /:8\\\\x-7=16 \ \ /+7\\\\\huge\boxed{x=23}[/tex]
2]
[tex]16=2(x+7) \ \ /:2\\\\x+7=8 \ \ /-7\\\\\huge\boxed{x=1}[/tex]
3]
[tex]\frac{7y}{7}=20\\\\\huge\boxed{y=20}[/tex]
4]
[tex]2x-1=9 \ \ /+1\\\\2x=10 \ \ /:2\\\\\huge\boxed{x=5}[/tex]
5]
[tex]2(x-8)=20 \ \ /:2\\\\x-8=10 \ \ /+8\\\\\huge\boxed{x=18}[/tex]
The y-Int and the slope of C=7n+20
If you can show the formula
Someone answer this please
Answer:
[tex] →\frac{8xy}{24y} = \frac{8}{24} . \frac{xy}{y} = \frac{1}{3}. x = \boxed{ \frac{x}{3} }✓ \\ [/tex]
x/3 is the right answer.The mean length of 7 planks of wood is 1.35m. When an extra plank of wood is added, the mean length of a plank of wood increase to 1.4m. the length of the extra plank of wood that was added is Select one a. 2. 4 b. 1 C. 1.25 d. 1.75V
Answer: Hello There!................
Mean = Sum of observation / total number of observation
Mean = 1.35m
1.35 = Sum of length of 7 wood planks/ 7
1.35*7 = Sum of the length of 7 wood planks
9.45 = Sum of the length of 7 wood planks
Let the length of extra added wood plank = x
So,
(Sum of the length of 7 wood planks + x) / 8 = 1.4m
(9.45 + x) / 8 = 1.4
9.45 + x = 1.4 * 8
9.45 + x = 11.2
x = 11.2- 9.45
= 1.75
So,
The length of extra added wood plank = 1.75m
Step-by-step explanation:
Mark me brainest please. Hope this helps. Anna ♥
-3x + 6y = 18
-3x = 6y+14
a) What is the slope of the 1st equation?
b) What is the slope of the 2nd equation?
c) Are they parallel, perpendicular, or neither?
Step-by-step explanation:
-3x + 6y = 18
-3x = 6y+14
a) the slope of the 1st equation = -(-3)/6 = ½
b) the slope of the 1st equation = -3/6 = -½
c) they are niether parallel nor perpendicular
#1
-3x+6y=18-x+2y=62y=x+6y=x/2+3slope=1/2
#2
-3x=6y+146y=-3x-14y=-1/2x-7/3slope=-1/2
#3
Neither
Please answer correctly this time answer ASAP please due soon
Step-by-step explanation:
Down 2 units : we will move the point 2 units to the down direction of the vertical line (y-axis)
which means (x ,y-2) = (-2,1)
right 3 units = we will move the point 3 units to the right direction of the horizontal line (x axis )
(x+3,y)= (1,3)
up 1 unit and left 4 units : we will move the point 1 unit in the up direction of the vertical line (y-axis)
and move it 4 units in the left direction of the horizontal line (x axis )
(x-4,y+1l. = (-6,4)
which figure is the odd one out?
Answer:
I'm pretty sure its A cuz it looks different than the others
