Answer:
The unit vector in component form is [tex]\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)[/tex] or [tex]\hat{u} = \frac{2}{\sqrt{13}}\,i-\frac{3}{13}\,j[/tex].
Step-by-step explanation:
Let be [tex]\vec u = (2,-3)[/tex], its unit vector is determined by following expression:
[tex]\hat {u} = \frac{\vec u}{\|\vec u \|}[/tex]
Where [tex]\|\vec u \|[/tex] is the norm of [tex]\vec u[/tex], which is found by Pythagorean Theorem:
[tex]\|\vec u\|=\sqrt{2^{2}+(-3)^{2}}[/tex]
[tex]\|\vec u\| = \sqrt{13}[/tex]
Then, the unit vector is:
[tex]\hat{u} = \frac{1}{\sqrt{13}} \cdot (2,-3)[/tex]
[tex]\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)[/tex]
The unit vector in component form is [tex]\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)[/tex] or [tex]\hat{u} = \frac{2}{\sqrt{13}}\,i-\frac{3}{13}\,j[/tex].
Find the opposite of the given number. -18.6
Answer:
18.6
Step-by-step explanation:
Answer:
opposite of -18.6=18.6
what is formula to calculate the area of circle
Step-by-step explanation:
Area of circle
[tex] = \pi {r}^{2} [/tex]
r = radius of the circle
Answer:
[tex]\pi[/tex]r²
Step-by-step explanation:
A=[tex]\pi[/tex]r²
Write this number in standard form 70,000 + 5,000 + 20+3
Answer:
70,523
Step-by-step explanation:
This is standard form there no way to show.
Find the volume of the following solid figure. Use = 3.14.
V = 4/31r. A sphere has a radius of 4.5 inches.
Volume (to the nearest tenth) =
cubic inches
A. 56.5
B. 381.5
C. 84.8
Answer:
B. 381.5Step-by-step explanation:
[tex]r = 4.5\\\pi = 3.14\\\\V = ?\\\\Volume = \frac{4}{3} \pi r^3\\\\V= \frac{4}{3} \times 3.14 \times (4.5)^3\\\\V = \frac{4}{3} \times 286.1325\\\\V = \frac{1144.53}{3} \\\\V = 381.51\\\\Volume = 381.51 \: inches^3[/tex]
Sonia is walking 2.5 miles home from school. She leaves at 4:00 P.M., and gets home at 4:45 P.M. Graph the line that represents Sonia’s distance from school at a given time. Find and interpret the slope of the line.
Answer:
M = 1/18
Step-by-step explanation:
The slope is 1/18 mi/min, which means Sonia walks at a rate of 1 mile every 18 minutes.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
Given that, Sonia is walking 2.5 miles home from school.
She left at 4:00 pm and got home at 4:45 pm. She took 45 minutes to get there.
We can interpret the information as two points, the first one is (0,0) that represents the starting point. The second point is (45, 2.5), which represents the ending point when she arrived home. Let's graph these points and draw a line through them.
To find the slope, divide 2.5 miles by 45 minutes,
Thus, slope =2.5/45
m= 1/18 miles per minute
Therefore, the slope is 1/18 mi/min, which means Sonia walks at a rate of 1 mile every 18 minutes.
To learn more about the slope of a line visit:
https://brainly.com/question/14511992.
#SPJ2
Find the value of X Need help ASAP.
1. 4 inside angles must sum to 360:
X = 360-45-65-95 = 155
2. All the outside angles must sum
To 360:
2x + 70+ 86 + 9 = 2x + 248
2x = 360-248
2x = 112
X = 112/2 = 56
3. Sum of interior angles for 6 sides figure = 720.
X = 720 - 90-120-130-140-150
X = 90
4. Exterior angles sum to 360
4x +x + 98 + 162 = 360
5x + 260 = 360
5x = 100
X = 100/5
X = 20
( 5n 3 + n 4 - 5 ) - ( -5 - 6n 3 - 4n 4 ) A) 5n 4 + 11n 3 B) 5n 4 + 11n 3 + 2 C) 4n 4 + 11n 3 + 2 D) 4n 4 + 19n 3 + 2
Answer:
i got 53 n
Step-by-step explanation:
could be wrong but try lol
Help! Please what’s the answer
Answer:
837 sq. ft
Step-by-step explanation:
area of garden = area of rectangle + area of semicircle
area of rectangle = 20 X 34 = 680 sq. ft
area of semicircle = 1/2 X 3.14 X 100 = 157 sq.ft
area of garden = 837 sq. ft
i am 1 brainly away from virtuoso, your help would be appreciated
What is the simplified form of the expression below? (6 + 7b) + 14
Answer: 20+7b
Step-by-step explanation:
Given
(6+7b)+14
Take off parentheses
=6+7b+14
Move like terms together (Commutative property)
=6+14+7b
Combine like terms
=20+7b
Hope this helps!! :)
Please let me know if you have any question
Answer:
[tex]\huge\boxed{ answer}[/tex]
[tex]\blue\star[/tex]6 + 7b + 14 = 0
[tex]\blue\star[/tex]7b + 20 = 0
[tex]\blue\star[/tex]7b = - 20
[tex]\blue\star[/tex]b = -20\7
[tex]\star[/tex]simplified form
[tex]\blue\star[/tex](6 + 7b) +14
firstly remove the brackets.
[tex]\blue\star[/tex]6 + 7b +14
seprate terms and variables
[tex]\blue\star[/tex] 7b +20
[tex]\huge\boxed{7b + 20}[/tex]
Hope it helps..
find the derivative of f(x)=x+1/x-1 using first principal
f ' ( x ) = 1 ( x + 1 ) 2
Explanation:
differentiating from first principles
f ' ( x ) = lim h → 0
f ( x + h ) − f ( x ) h
f ' ( x ) = lim h → 0
x + h x + h + 1 − x x + 1 h
the aim now is to eliminate h from the denominator
f ' ( x ) = lim h =0
( x + h ) ( x + 1 )− x ( x + h + 1) h ( x + 1 ) ( x + h + 1 )
f ' ( x ) = lim h → 0
x 2 + h x + x + h − x 2 − h x − x h ( x + 1 ) ( x+h + 1 )
f ' ( x ) = lim h → 0
h 1 h 1 ( x + 1 ) ( x + h +1 )
f ' ( x ) = 1 ( x + 1 ) 2
Richard has 3 times as many music CDs as Benny does.
If Richard has y CDs, the number of CDs Benny has is given by the expression
. If Richard has 30 CDs, Benny has
CDs.
Answer:
y = 10 CDs
Step-by-step explanation:
30 divided by 3 equals 10
10 times 3 equals 30
Answer:
first blank is y/3
second blank is 10
Step-by-step explanation:
What are integers between -8 and 2 not inclusive?? Please help me
All numbers between -8 and 2 are integers except 0
All the integers between - 8 and 2 are,
{- 7, - 6, - 5, - 4, - 3, - 2, - 1, 1 }.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The numbers is,
⇒ - 8 and 2
Now, All the numbers between - 8 and 2 are,
⇒ - 7, - 6, - 5, - 4, - 3, - 2, - 1, 1
Thus, All the integers between - 8 and 2 are,
{- 7, - 6, - 5, - 4, - 3, - 2, - 1, 1 }.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ2
What is the simplest form of this expression? -b^3 (3b + 1) – 2b^4
Answer:
-5b^4 - b^3
Step-by-step explanation:
-b^3 (3b + 1) – 2b^4
Distribute
-3b^4 - b^3 -2b^4
Combine like terms
-5b^4 - b^3
A snail travels 820 mm in 0.75 minutes. What was his speed in m/s?
Answer:
speed in m/s=0.01822 metre/s
Step-by-step explanation:
Conversation rate of mm to m is
1000 mm = 1 metre
820 mm= 820/1000
829 mm= 0.82 metres
Conversation rate of minutes to second
I minute = 60 seconds
0.75 minute = 60*0.75 seconds
0.75 minute= 45 seconds
speed in m/s= 0.82 metres/45 seconds
speed in m/s= 0.82/45
speed in m/s=0.01822 metre/s
Brainliest!
Divide
18198
--------
27
A.518
B.608
C.674
D.689
Answer:C
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
27)18198(674
162
-
--------
199
189
-
---------
108
108
-
------
0
------
Translate the English phrase into an algebraic expression: the sum of 17y² and 19.
Answer:
17y^2+19
Step-by-step explanation:
sum means add
Answer:
19+ 17y²
Step-by-step explanation:
write as an equation: 1/3 of a shipment of books weights 28 pounds
Answer:
x=28 (pounds) * 1/3
Step-by-step explanation:
28/3 gives you 1/3 of the shipment weight.
Which set of data is displayed in the box plot below?
Answer:
It would tske to long for me to break it down but my best bet is B
Step-by-step explanation:
is the number 10,104 divisible by 4?
Step-by-step explanation:
A no. is divisible by four if the last two digits is a multiple of 4
04 is a multiple of four
The no. 10,104 is divisible by 4Point S is on line segment \overline{RT}
RT
. Given ST=5x-7,ST=5x−7, RT=4x+9,RT=4x+9, and RS=2x+7,RS=2x+7, determine the numerical length of \overline{ST}.
ST
.
The value of ST is 8.
What is equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.
Given:
ST=5x-7, RT=4x+9, RS=2x+7
So,
RS + ST = RT
2x +7 + 5x -7 = 4x+9
7x = 4x +9
3x= 9
x=3
So,
ST= 5x-7 = 5*3 -7= 15-7= 8
Learn more about equation here:
https://brainly.com/question/10413253
#SPJ2
An agribusiness performed a regression of wheat yield (bushels per acre) using observations on 26 test plots with four predictors (rainfall, fertilizer, soil acidity, hours of sun). The standard error was 1.29 bushels.
(a) Find the approximate width of a 95% prediction interval for wheat yield. (Round your answer to 2 decimal places.)
yˆi ±
(b) Find the approximate width using the quick rule. (Round your answer to 2 decimal places.)
yˆi ±
(c) The quick rule gives a similar result.
a. Yes
b. No
Answer:
A)y ± [tex]t_{21}[/tex] ( 1.29 )
B) y ± 2.58
C ) yes
Step-by-step explanation:
standard error = 1.29 bushels
approximate width of 95% prediction interval for an individual can be represented as ; [tex]y[/tex] ± [tex]t_{n-k-1}[/tex] ( SE )
[tex]t_{n-k-1} = critical value of t at n-k-1[/tex] degree of freedom
n = 26
k = 4
a) Approximate width of a 95% prediction interval for wheat yield
[tex]y[/tex] ± [tex]t_{n-k-1}[/tex] ( SE )
Insert the values into the equation
n - k -1 = 26 - 4 - 1 = 21
y ± [tex]t_{21}[/tex] ( 1.29 ) you can get the value of [tex]t_{21}[/tex] from the t table for 21 degrees at 0.05 significance level
B) The approximate width using the quick rule
y ± 2SE
y ± 2(1.29) = y ± 2.58
C) The quick rule gives a similar result = yes
A certain antihistamine is often prescribed for allergies. A typical dose for a 100-pound person is 19mg every six hours. Complete parts (a) and (b) below. Following this dosage, how many 13.2mg chewable tablets would be taken in a week? A 100-pound person could take ____ tablets in a week. (Round to the nearest whole number as needed.)
Answer:
40 tablets
Step-by-step explanation:
What we want to do is find how many mg of antihistamine you can take in a week.
If you can take 19mg in 6 hours, that means you can take [tex]19\cdot4=76[/tex]mg per day (because [tex]24\div6=4[/tex], so you can take 19mg every 6 hours 4 times in a day.)
There are 7 days in a week, so you can take [tex]76\cdot7=532[/tex] mg per week.
Now, we know how many mg of antihistamine you can take per week. If we take antihistamine in increments of 13.2mg, then the total amount of tablets we can take per week is going to be [tex]532\div13.2[/tex], which is approximately equal to 40.
So you can take 40 tablets in a week if you are 100 pounds.
Hope this helped!
Answer:
Step-by-step explanation:
b. A 100-pound person could take
enter your response here mL in a week.
(Round to the nearest whole number as needed.)
One environmental hazard recently identified is overexposure to airborne asbestos. In a sample of 10 public buildings over 20 years old, three were found to be insulated with materials that produced an excess number of airborne asbestos bodies. what is the approximate probability that another buitding of this rype will have this problem? What method are you using to assign this probability?
Answer:
1. 0.3
2. Relative frequency
Step-by-step explanation:
We would be calculating for p(A) which is the probability of A. With A being that public buildings would be found to be insulated with same materials that causes same issues
n = sample space of public buildings = 10
F = frequency = 3
P(A) = 3/10 = 0.3
Therefore 0.3 is the approximate probability of another building having same issues
Question 2 says we should find method used to assign probability
The method used is relative frequency method and it is determined by:
P(A) = frequency(f)/total number of data values(n).
Donte is planning on repairing bikes and skateboards to save up money for
college. He can repair up to 2 bikes per day and 4 skateboards per day. If b
represents the number of bikes and s represents the number of
skateboards, write the expression that represents the total number of
things Donte can repair in a single day. *
Answer:
y=2b+4s
Step-by-step explanation:
Determine whether set B is a subset of A.
7. A = {2, 3, 5, 7, 11}
B = {3, 5, 7, 9, 11)
Answer:
Set B is not a subset of A.
Step-by-step explanation:
If there are sets, A and B with some elements, then B can be called subset of A, if every element of B is present in set A.
Example.
Example
A is set of integers
B is set of natural numbers
we know set of integers is all the negative numbers, 0 and all the positive discrete numbers like
A = {......-3,-2,-1,0,1,2,3,4........}
B is set of positive discrete numbers from 1 to infinity)
B = {1,2,3,4........}
Thus, we see every element of B is present in A . Hence B is subset of A
___________________________________________
Given
A = {2, 3, 5, 7, 11}
B = {3, 5, 7, 9, 11)
Here,
In set B . elements 3,5,7,11 are present in set A, but
Element 9 from set B is missing Set A.
Since, every element of Set B is not present in set A hence
Set B is not a subset of A.
Point F bisects segment GH. Find GH if GF = 14 1/2 feet.
Answer:
Segment GH = 29 ft
Step-by-step explanation:
Point F bisects segment GH means that the segment GH is being divided into two by point F.
If GF = 14 1/2 feet
Since point F divides GH into two, multiplying GF by two will give segment GH
GH= 2GF
GH= 2(14 1/2
GH= 2(29/2)
GH= 29 ft
Segment GH = 29 ft
I need this quick, anyone got the answer?
Answer:
C
Step-by-step explanation:
So we have a cylinder with a hole the shape of a rectangular prism through it.
Therefore, our total volume would be the cylinder minus the volume of the rectangular prism.
The volume of a cylinder is given by the formula:
[tex]V=\pi r^2h[/tex]
Use 3.14 for π, 10 for radius, and 15 for the height. Thus:
[tex]V=(3.14)(10)^2(15)\\V=4710[/tex]
So the volume of the cylinder is 4710 cubic feet.
Now, find the volume of the rectangular prism.
The formula for the volume of a rectangular prism is given by:
[tex]V=lwh[/tex]
The length is 5, width is 3, and height is 15. Thus:
[tex]V=(5)(3)(15)\\V=225[/tex]
So, the total volume is:
[tex]V_{\text{Total}}=V_{\text{Cylinder}}-V_{\text{Rectangle}}\\V_{\text{Total}}=4710-225=4485\text{ feet}^3[/tex]
Our answer is C
What type of number is -44.1?
Answer:
-44.1 is a real and complex number
Step-by-step explanation:
What is the area of this figure? 3 ft 15 ft 20 ft 17 ft 5 ft 20 ft square feet
Answer:
45
Step-by-step explanation:
what are the orders pairs for this figure