5
(a)
Let u and v be non-zero vectors such that v is a unit vector. Show that |u•v|<|u|.When does
equality occur? Explain your reasoning.
[3]
(b)
Show that if x and y are non-zero parallel vectors, then X×Y=0.
[2]
(c)
Referred to the origin o, points A and B have position vectors a and b respectively. Let C be a
variable point with position vector 2(a - b). Show that the area of AABC is independent of 2. [2]
Answer:
5
(a)
Let u and v be non-zero vectors such that v is a unit vector. Show that |u•v|<|u|.When does
equality occur? Explain your reasoning.
[3]
(b)
Show that if x and y are non-zero parallel vectors, then X×Y=0.
[2]
(c)
Referred to the origin o, points A and B have position vectors a and b respectively. Let C be a
need some help!
help giving 10 points
Answer:
The remaining lenghts are [tex]x = 20.364\,cm[/tex] and [tex]y = 12.925\,cm[/tex].
Step-by-step explanation:
Given that there are two triangles opposite to each other and between two parallel lines, then both are similar, meaning than following relationships exist:
[tex]\frac{AC}{CD} = \frac{BC}{CE} = \frac{AB}{DE}[/tex] (1)
If we know that [tex]AC = 11\,cm[/tex], [tex]CD = 28\,cm[/tex], [tex]BC = 8\,cm[/tex] and [tex]DE = 32.9\,cm[/tex], then the missing lengths are, respectively:
[tex]\frac{11\,cm}{28\,cm} = \frac{8\,cm}{x}[/tex]
[tex]x = \frac{(28\,cm)\cdot (8\,cm)}{11\,cm}[/tex]
[tex]x = 20.364\,cm[/tex]
[tex]\frac{11\,cm}{28\,cm} = \frac{y}{32.9\,cm}[/tex]
[tex]y = \frac{(11\,cm)\cdot (32.9\,cm)}{28\,cm}[/tex]
[tex]y = 12.925\,cm[/tex]
The remaining lenghts are [tex]x = 20.364\,cm[/tex] and [tex]y = 12.925\,cm[/tex].
Please answer the question :)
Answer:
the lenght of the shortest side is 12
Step-by-step explanation:
So first add them all up becuase perimeter
3x+3x+5x-4+5x-4
You’ll get 16x-8
16x-8=56
16x=64
x=4
So then plug it in
3x=3*4=12
5x-4=5*4-4=16
so 12 is the shortest side
what does an amortization schedule show
Answer:
An amortization schedule is a complete table of periodic loan payments, showing the amount of principal and the amount of interest that comprise each payment until the loan is paid off at the end of its term.
Step-by-step explanation:
Answer:
Step-by-step explanation:
An amortization schedule is a complete table of periodic loan payments, showing the amount of principal and the amount of interest that comprise each payment until the loan is paid off at the end of its term\
Derivative of (x^7+2x-3)^3
Answer:
[tex]\displaystyle \frac{dy}{dx} = 3(7x^6 + 2)(x^7 + 2x - 3)^2[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = (x^7 + 2x - 3)^3[/tex]
Step 2: Differentiate
Basic Power Rule [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = 3(x^7 + 2x - 3)^2(x^7 + 2x - 3)'[/tex]Basic Power Rule [Derivative Properties]: [tex]\displaystyle y' = 3(7x^6 + 2)(x^7 + 2x - 3)^2[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!
show work
Rina’s recipe uses 2 cups of sugar to make 2 dozen cookies. Johan’s recipe uses 2 cups of sugar to make 3 dozen cookies. Which recipe uses more sugar for a dozen cookies? Why?
Answer:
Rita's recipe
Step-by-step explanation:
Use proportions and find it out. [Use s as sugar and c as cookies]
Rita's - 2s = 2c. would be 1 cup of sugar per dozen cookies.
Joahn's - 2s = 3c. would be 2/3 cup of sugar per batch of cookies
What is the missing reason in the proof?
Prove –(–y – x) – x = y
Statements Reasons
–(–y – x) – x = –[–y +(–x)] – x Definition of subtraction
–[–y +(–x)] – x = y + x – x Opposite of a sum property
y + x – x = y + x + (–x) Definition of subtraction
y + x + (–x) = y + [x + (–x)] Associative Property of Addition
y + [x + (–x)] = y + 0 Additive Inverse Property
y + 0 = y ________________________
Additive Identity Property
Opposite of a Sum Property
Additive Inverse Property
Symmetric Property
Answer: the answer is additive identity property i just took the test
Step-by-step explanation: i hope this helps
There are 17 more boys than girls at Juab Junior
High School. If there are a total of 981 students
there, how many students are boys?
claire is 120cm tall. her mum is 160cm tall. how much shorter is claire than her mum
If two different people are randomly selected from the 880 subjects, find the probability that they are both heavy smokers
Answer:
0.006795
Step-by-step explanation:
Note: The table of the question is attached as picture below
Total number of heavy smokers = 36+ 37 = 73
Total men and women = 880
We need to know the probability of selecting two DIFFERENT heavy smokers.
Probability of (First person selected is a heavy smoker) = 73/880
Discarding the first person, now you have 879 subjects left and 72 heavy smokers left.
So, Probability of Second person selected is a heavy smoker) = 72/879
Probability of 2 different people selected are heavy smokers) = 73/880 * 72/879
= 5256 / 773520
= 0.006795
The slope of the line below is -3. Use the coordinates of the labeled point to find a point-slope equation of the line. 10 -10 (5.-7) - 10+ O A. y-7 = 3(x + 5) B. y-73-3(x + 5) O C. y + 7 = 3(x - 5) D. y + 7 =-3(x-5)
Answer:
y + 7 = -3 ( x - 5 )
Step-by-step explanation:
Point slope is:
[tex]y-y_1=m(x-x_1)[/tex]
We are given the slope of -3 and the point of (5, -7).
Replace the variables with the appropriate values.
[tex]y-y_1=m(x-x_1)\rightarrow\boxed{y+7=-3(x-5)}[/tex]
The correct answer should be D.
Hope this helps.
Answer:
y + 7 = -3 ( x - 5 )
Step-by-step explanation:
A deck of cards contains 52 cards, of which 4 are aces. You are offered the following wager: Draw one card at random from the deck. You win $10 if the card drawn is an ace. Otherwise, you lose $1. If you make this wager very many times, what will be the mean amount you win?
Answer:
-$0.15
Step-by-step explanation:
We have been given win = $10, and loss = $-1
This deck of cards has 4 aces out of a total of 52 cards.
Then the probability can be explained as the number of favorable outcome/number of what is the possible outcome.
P(win) = number of favorable outcome/number of possible outcome
= 4/52
= 1/13
P(loss) = number of favorable outcome/number of possible outcome
= 48/52
= 12/13
Then we have
$10x1/13 + (-1)x12/13
= 10/13-12/13
= -2/13 dollars
= -$0.15
Using the principle of discrete probability, the expected value, which a measure of the mean amount after many plays is - 2/13
Calculating the required probabilities :
P(winning) = P(drawing an Ace) = 4/52 = 1/13
Hence, P(losing) = 1 - 1/13 = 12/13
X :____ 10 _____ - 1
P(X) : _ 1/13_____ 12/13
The expected value :
E(X) = 10 × (1/13) + - 1(12/13)
E(X) = 10/13 - 12/13
E(X) = - 2/13
Hence, the measure of the mean amount is -2/13.
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You and your friend get the same magazine. You spend $15 for twelve issues. Your
friend pays $1.50 per issue but gets the first two issues free. How many issues will your
friend get if he also spends $15?
Answer:
10 issues
Step-by-step explanation:
If my friend gets the first 2 issues free, then the remaining issues will be (12-2) = 10 issues .
for 12 issues my friend paid,
1 issue = $1.5
10 issues = 10 × $1.5 = $15
So, it matched which the question, which is $15 spent by my friend.
Answer = 10 issues
3.5 ÷ 2.29 round to nearest tenth
Answer:
1.5
Step-by-step explanation:
Thats rounded.
The perimeter of a rectangle is 98 feet. The ratio of its length to its width is 5:2.
Find the area of the rectangle.
Answer:
the area is 50
Step-by-step explanation:
value of the 5:2
The mean number of patients admitted per day to the emergency room of a small hospital is 3. If, on any given day, there are only 8 beds available for new patients, what is the probability that the hospital will not have enough beds to accommodate its newly admitted patients?
i think there are some mistakes in the question, Please check once again! :)
Pls help me with number 20 and you get 5 star and brainliest
Answer:
it is equal
Step-by-step explanation:
because they both have 90 86 and 84
Two lines that are perpendicular form what type of angles
I GIVE BRAINLIEST
Points A and B have opposite x-coordinates but the same y-coordinates.
On a coordinate plane, point A is 2 units to the left and 3 units up. Point B is 2 units to the right and 3 units up.
How many units away are each of the points from the y-axis?
Answer:2
Step-by-step explanation:toke the test
The number of units away from each of the points from the y-axis will be 2.
What is the distance between two points?It is the measure of distance between the two points and is known as length. The length is measured in meters generally.
Let one point be (x, y) and another point be (h, k).
Then the distance between the points will be
D² = (x - h)² + (y - k)²
The points are given below.
A(-2, 3) and B(2, 3)
The coordinate of the points that lie on the y-axis is (0, 3).
Then the distance from point A will be given as,
D² = (-2 + 0)² + (3 - 3)²
D² = 4
D = 2
Then the distance from point B will be given as,
D² = (2 + 0)² + (3 - 3)²
D² = 4
D = 2
The number of units away from each of the points from the y-axis will be 2.
Learn more about the distance between two points here:
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Convert to a 4/9 to a decimal?
Group of answer choices
4.9
0.49
0.444
0.494949
Answer:
0.444
Step-by-step explanation:
use the fraction bar as a division sign and solve the problem!
are the following lines parallel,perpendicular,neither
y =2x-1
y=-1/2x+3
Answer:
perpendicular
Step-by-step explanation:
The lines are not parallel because the slopes are not equal. However, they are perpendicular because perpendicular lines' slopes are opposite reciprocal. (×negative with the denominator and numerator switched.)
The expression 2.4x−3.9y−1.2x+ay is equivalent to 1.2x+1.2y.
What is the value of a?
The value of a from the given mathematical expression is 5.1.
Given the following data:
[tex]2.4x-3.9y-1.2x+ay[/tex][tex]1.2x+1.2y[/tex]To determine the value of a:
How to solve these mathematical expressions.In this exercise, you're required to solve for the value of a from the given mathematical expression. Since the two (2) mathematical expressions are equivalent (equal), we would go ahead to equate them as follows:
[tex]2.4x-3.9y-1.2x+ay = 1.2x+1.2y[/tex]
Simplifying the equation, we have:
[tex]2.4x-3.9y-1.2y+ay-1.2x-1.2x = 0 \\\\2.4x-5.1y+ay-2.4x = 0\\\\-5.1y+ay=0\\\\ay=5.1y[/tex]
a = 5.1
Read more on mathematical expressions here: https://brainly.com/question/13170908
Li is making beaded necklaces. for each necklace, she uses 25 spacers, plus 9 beads per inch of necklace length. write an equation to find how many beads Li needs for each necklace, where x is the length, in inches, of the necklace
Given that Li is making beaded necklaces for each necklace, she uses 27 spacers, plus 5 beads per inch of necklace length.
The equation to find how many beads Li needs for each necklace can be obtained as follows:
A. The input variable is the number of inches of the necklace length (x).
B. The output variable is the number of beads Li needs for each necklace (y).
C. The required equation is given by
y = 5x
PLEASE ANSWER QUICK!!! WILL MARK BRAINLIEST!!!
Answer:B A C
Step-by-step explanation:
true or false: a closed circle is used when a number is a not solution
plz answer my question
Answer:
The answer is below
Step-by-step explanation:
12m
Because you Multiply 6*2=12m
Hope this helps
BRAINLIEST
Which measurements could NOT represent the side lengths of a right triangle?
Answer:
c
Step-by-step explanation:
10 is to high compared to 6
can someone help me algebra 1
Help I will give a brainliest
Answer:
melting and freezing
Step-by-step explanation:
Graph the system below and write its solution.
y= 2x + 2.
x-2y=-7
Note that you can also answer "No solution" or "Infinitely many