Part (a)
The resultant vector is the vector formed by adding the two vectors a and b. So we effectively add the corresponding components.
You can use the parallelogram law as a visual alternative.
Adding a and b leads to
a+b = (3i-2j) + (pi-2pj)
a+b = (3i+pi) + (-2j-2pj)
a+b = (3+p)i - (2+2p)j
Define vector d to be d = a+b so we can use it later below.
Recall that parallel vectors point in the same direction. This means the ratio of their components or coordinates are equal.
We can say the following
(x coord of d)/(x coord of c) = (y coord of d)/(y coord of c)
(3+p)/(2) = (-(2+2p))/(-3)
Let's solve for p
(3+p)/(2) = (-(2+2p))/(-3)
(3+p)/(2) = (2+2p)/3
3(3+p) = 2(2+2p) .... cross multiply
9+3p = 4+4p
4p+4 = 3p+9
4p-3p = 9-4
p = 5
Answer: p = 5========================================================
Part (b)
Since p = 5, from part (a), we can determine vector b
b = pi - 2pj
b = 5i - 2*5j
b = 5i - 10j
Then add vectors a and b to get
a+b = (3i-2j) + (5i - 10j)
a+b = (3i+5i) + (-2j - 10j)
a+b = (3+5)i - (2+10)j
a+b = 8i - 12j
Or we can say
a+b = (3+p)i - (2+2p)j .... from part (a)
a+b = (3+5)i - (2+2*5)j ... plugging in p = 5
a+b = 8i - 12j
Note the ratio of the components of vector d and vector c are such
(x coord of d)/(x coord of c) = (y coord of d)/(y coord of c)
8/2 = -12/(-3)
4 = 4
This helps confirm the answer
You could also graph the vectors c = 2i - 3j and d = 8i - 12j to note the two lines produce the same slope -3/2. We can see that -12/8 = -3/2. Lines of the same slope are parallel lines
Answer: 8i - 12ja.
The value of p is 5
Since vector a = 3i - 2j and vector b = pi - 2pj, the resultant of vectors a and b is R = a + b
= 3i - 2j + pi - 2pj
= (3 + p)i - 2(1 + p)j
Since R is aparallel to vector c = 2i - 3j, it implies that the cross product of R and c is zero.
The cross product of two vectors a and b is a × b = absinФ where a and b are the magnitudes of a and b and Ф is the angle between them.
So, R × c = [(3 + p)i - 2(1 + p)j] × [2i - 3j]
= (3 + p)i × 2i + (3 + p)i × (-3j) + (-2(1 + p)]j × 2i + (-2(1 + p)]j×(-3j)
= 0 - 3(3 + p)k - 4(1 + p)(-k) + 0
= -3(3 + p)k + 4(1 + p)k
= [-3(3 + p) + 4(1 + p)]k
= [-9 - 3p + 4 + 4p)]k
= [-9 + 4 - 3p + 4p)]k
= [-5 + p]k
[-5 + p]k = RcsinФ.
Since R and c are parallel, Ф = 0°
So, Rcsin0° = Rc × 0 = 0
So, [-5 + p]k = 0
-5 + p = 0
p = 5
The value of p is 5
b.
The resultant of vectors a and b is R = 8i - 12j
Since p = 5 and the resultant of vectors a and b is R = (3 + p)i - 2(1 + p)j
Substituting the value of p = 5 into r, we have
R = (3 + p)i - 2(1 + p)j
R = (3 + 5)i - 2(1 + 5)j
R = 8i - 2(6)j
R = 8i - 12j
So, the resultant of vectors a and b is R = 8i - 12j
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Slope of (2,8) and (2,6)
One tree can produce 175 avocados. The avocados are packed in boxes of 24. How many boxes are needed?
Answer:
8 boxes
Step-by-step explanation:
Divide 175 by 24 since you have 175 avocados and 24 can be put in each box. This gives you 7.29166666667. You have to round up to get 8.
Answer:
8 boxes would be needed
Step-by-step explanation:
175/24 = 7 with a remainder of 7 and you cannot just leave out those 7 avocados, they will be lonely so therefor you will need another box and 7+1=8
Sean adds up all the even integers from 2 to 500, inclusive. Julie adds up all the integers from 1 to 250, inclusive. What is Sean's sum divided by Julie's sum?
Answer:
Sean's sum divided by Julie's sum is 2.
Step-by-step explanation:
The sum of an arithmetic sequence is:
[tex]\frac{n}{2}(2a+(n-1)d)[/tex]
In Sean's sequence, a = 2, n = 250, and d = 2
In Julie's sequence, a = 1, n = 250, and d = 2
[tex]\frac{\frac{250}{2}(2(2)+(250-1)2)}{\frac{250}{2}(2(1)+(250-1)1)}\\= 2[/tex]
The Sean's sum divided by Julie's sum gives the 2.
What is arithmetic sequence?An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n+1)d, ...
Its nth term is ; T_n = a + (n-1)d
(for all positive integer values of n)
And thus, the common difference is T_{n+1} - T_n for all positive integer values of n
The sum of an arithmetic sequence is;
[tex]= \dfrac{n}{2}[2a + (n-1)d ][/tex]
In Sean's sequence, a = 2, n = 250, and d = 2
[tex]= \dfrac{250}{2}[2(2) + (250-1)2 ]\\[/tex]
In Julie's sequence, a = 1, n = 250, and d = 2 then;
[tex]= \dfrac{250}{2}[2(1) + (250-1)2 ]\\[/tex]
Therefore, the Sean's sum divided by Julie's sum gives the 2.
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HELP
The length of a rectangle is
[tex]18x ^{2} + 6x - 4[/tex]
and the width of the rectangle is
[tex]3x {}^{2} - 9x + 10[/tex]
what expression would represent the perimeter of the rectangle?
Answer:
21x^2+3x+12
Step-by-step explanation:
geometry question. please help
Answer:
The length of PQ is 18 feet.
The length of PR is 18 feet.
The length of QR is 24 feet.
Step-by-step explanation:
A way to set an equation up for this problem is:
[tex]\frac{4}{3}x+x+x=60[/tex]
where x is the three lengths of the isosceles triangle, but the base QR is 4/3 the length of the other two congruent sides, length PQ and PR. The 60 represents the total length of the perimeter.
Then, solve for x from the equation, and you’ll get x=18. But your not done yet. Since the variable x in the equation stands for the sides of the isosceles triangle, so plug 18 into the equation and it should look like this:
[tex]\frac{4}{3}(18)+18+18=60[/tex]
Don’t solve the whole equation, just solve the [tex]\frac{4}{3}(18)[/tex] part of the equation, which is equal to 24. So the final equation is this:
[tex]24+18+18=60[/tex]
Conclusion: 24 is the length of QR, and 18 is the length of PQ and PR. And they all equal 60, which is the perimeter. This is very true because the length of PQ and PR are the same (length 18), since it’s an isosceles triangle, and the length of QR is 4/3 the length of PQ and PR (4/3 of 18= 24).
Sorry for the long explanation.
But hope this helps and answers your question :)
What is the slope for 3y+6x=9
Answer:
The slope is -2!
Step-by-step explanation:
Lets Solve!
3y +6x = 9
First we subtract 6x from both sides
3y = -6x + 9
Next we divide by 3 from both sides.
y = -2x + 3
The slope is -2!
Determine if the ordered pair (-5, -1) is a
solution of 2x - y =-11.
Answer:(-5,-1) is not an ordered pair
Step-by-step explanation:
the ordered pair (-5,-1) is directly related to the variables (x,y) making -5=x and -1=y
so to figure out if the ordered pair is a solution you just plug in the number into their respective variable.
so the equation then becomes 2 (-5) - (-1) = -11
once you solve for the left part of the equation you are then left with -9 = -11 which we know is false.
A box of rice costs $2.99 for 62 oz. What is the unit cost for 1 oz?
Answer:
0.04
Step-by-step explanation:
set up a proportion!
sorry if its sloppy, i did this on my laptop :/
Answer:
.48 cents for 1 oz
Step-by-step explanation:
You first take the 2.99 and divide by 62 to get your amount for 1 oz
Randy, Sandy and Todd are my cousins and their combined age is 87 years. Randy is four times as old as Sandy, but Todd is actually 15 years older than Sandy. How old are each of my cousins
Answer:
Randy is 48 years old
Sandy is 12 years old
Todd is 27 years old
Step-by-step explanation:
Given
Represent their ages with the first letters of their names:
[tex]R + S + T = 87[/tex]
[tex]R = 4 * S[/tex]
[tex]T = 15 + S[/tex]
Required
Determine their individual ages
We'll solve the above equations using substitution method of simultaneous equations
Substitute 15 + S for T and 4 * S for R in [tex]R + S + T = 87[/tex]
This gives:
[tex]4 * S + S + 15 + S = 87[/tex]
[tex]4 S + S + 15 + S = 87[/tex]
Collect Like Terms
[tex]4 S + S + S = 87 - 15[/tex]
[tex]6S = 72[/tex]
Divide through by 6
[tex]S = 72/6[/tex]
[tex]S = 12[/tex]
This implies that Sandy is 12 years old
Substitute 12 for S in [tex]R = 4 * S[/tex] and [tex]T = 15 + S[/tex]
[tex]R = 4 * 12[/tex]
[tex]R = 48[/tex]
[tex]T = 15 + 12[/tex]
[tex]T = 27[/tex]
This implies that Randy is 48 years old and Todd is 27
The amount of money in my account went from being $5 to $8, what is the percent increase?
What is the binary number for 16
Answer:
Decimal Number 4-bit Binary Number Hexadecimal Number
14 1110 E
15 1111 F
16 0001 0000 10 (1+0)
17 0001 0001 11 (1+1
Step-by-step explanation:
hope this helped
The length of x 200 feet
Answer:
If the length of x is less than 200, then add <.
If the length of x is more than 200, then add >.
If the length of x is 200, then add =.
Step-by-step explanation:
HELPPPPPP PLSSSSSSSSSS ASP HELPPPPPPPPPPPPPPPPPPPPPP
Answer:
if it helps please mark brainliest!
Step-by-step explanation:
essays= x
quizzes=y
2x=60
x=30 1 essay per 30 days
4y=40
y=10 1 quiz every 10 days
120/30=4
120/10= 12
so 4 essays and 12 quizzes in 120 days
if it helps please mark brainliest!
how do you write 47,100 in scientific notations ?
Answer:
4.71 x 10^4
I did maf
Answer: It should be 4.71 x 104.
0.2(10-5c)=5c-16
solve the iniquality
What is the answer to The sum of 2 numbers is 19 and their difference is 3? And thank you brainly for helping. I need the answers correct because I play prodigy, a math game. Thank you!
Answer:
11 and 8
Step-by-step explanation:
11+8=19
11-8=3
Answer:
8 and 11
Step-by-step explanation:
PLEASE HELP ME WITH THESE QUESTIONS ASAP
Answer:
D.
Step-by-step explanation:
Answer:
the answer is d 64 because a rational number is a whole number not decimals.
Step-by-step explanation:
brainliest pls
i need help for this question. can someone help me
Answer:
the missing angle is 130
Step-by-step explanation:
180-50=130
Kyra observed that 85% of the students at a library liked reading mystery stories. If 30 students at the library did not like reading mystery stories, the number of students at the library who liked mystery stories was _____. (only put numeric values, no other symbols)
Answer:
The first thing we must do is find the percentage of students who do not like to read mystery stories.
We have then:
Then, to find the number of students who like to read mystery stories, we can make the following rule of three:
15% ----------------> 30 students
85% ----------------> x
From here, we clear the value of x.
We have then:
the number of students at the library who liked mystery stories was 170
On the coloring sheet find the ratio that is equivalent to 2/7
Answer:
Equivalent Ratios of 2 : 7
2 : 7 4 : 14 6 : 21 8 : 28 10 : 35 12 : 42 14 : 49 16 : 56 18 : 63 20 : 70 22 : 77 24 : 84 26 : 91 28 : 98 30 : 105 32 : 112 34 : 119 36 : 126 38 : 133 40 : 140 42 : 147 44 : 154 46 : 161 48 : 168 50 : 175 52 : 182 54 : 189 56 : 196 58 : 203 60 : 210
( Brainlyst helps my rank <3 )
The nth term of a different sequence is 10n^2+5 work out the 5th term of this sequence
Answer:
255
Step-by-step explanation:
10n^2+5
where n=5
10×5²+5
10×25+5
250+5
255
The 5th term of Sequence is 255.
What is Sequence?A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. Similar to a set, it has members (also called elements, or terms). The length of the series is the number of elements (potentially infinite).
Given:
10n² +5
Now for 5th term put n= 5 we get
10n² +5
= 10(5)² +5
= 10 x 25 + 5
= 250+ 5
= 255
hence, the 5th term is 255.
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what is the slope of the line?
plss answer now
Answer:
y= -3 I think but the next person will answer this for you
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Hint :
Slope of horizontal lines is
zero (( 0 )) .
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Thus ;
[tex]slope = 0[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
The average cost per unit c(x) to produce x units of lumber is given byc * (x) = 400/(x + 25) if the cost per unit is \$1.00 how many units have been produced if necessary round your answer to the nearest whole unit. the answer is 375
Answer:
The number of units of lumber that have been produced is 375
Step-by-step explanation:
From the question,
The average cost per unit c(x) to produce x units of lumber is given by
c(x) = 400/(x + 25).
Now, to determine how many units have been produced (that is, x) if the cost per unit is $1.00 (that is, c(x) = $1.00), we will put in the value into the given equation to determine x.
c(x) = 400/(x + 25)
c(x) = $1.00
∴ 1.00 = 400/(x + 25)
Then,
(x + 25) × 1.00 = 400
x + 25 = 400
x = 400 - 25
x = 375
Hence, the number of units of lumber that have been produced is 375.
Sandy charges each family that she babysits a flat fee of $10 for the night and an extra $5 per child. Which a y = 10x + 5 b y = 5x + 10 c y = -5x + 10 d y = -10x -5
Answer: B. y = 5x + 10
Step-by-step explanation:
Based on the scenario in the question, you didn't really say what you'll like to calculate but I guess you want to know the equation that can be used to represent the above information.
Let x = the number of children babysit
The amount charged by Sandy can then be written as:
y = 10 + 5(x)
y = 10 + 5x
y = 5x + 10
Therefore, the correct option is B.
HELP ME PLEASE!!!!!!!!!!!!
Answer: linear
Step-by-step explanation: cus when u connect the points it forms a straight line
A jar contains 12 caramels, 8 mints and 7 dark chocolates. What is the probability of selecting a mint? simplify if possible.
ME PUEDEN AYUDAR ES PARA HOY
Answer:
8/27
Step-by-step explanation:
ill give you'll brain list
Answer:
I can’t see. Pic is not readable
Step-by-step explanation:
A $136,000.00 home with 30yr mortgage with 1.1% fixed rate. 20% down down payment. How much is the down payment, the monthly payments, interest rate and the loan?
Answer:
down payment = home value x 20% = $136,000 x 20% = $27,200
loan = home value - down payment = $136,000 - $27,200 = $108,800
interest rate = 1.1% fixed (given) ≈ 0.09167% per month
duration of loan = 30 years or 360 months
monthly payment = present value of loan / PV annuity factor
PV annuity factor, 360 periods, 0.09167% = 306.5134 (I used an online annuity calculator)
monthly payment = $108,800 / 306.5134 = $354.96
help!!!!!!!!!!!!!!!!!
Answer:
5.2
Step-by-step explanation:
√27 = 5.1962 (5s.f.) = 5.2 (2s.f.)
Answer:
i hope 5.2 is the answer
Step-by-step explanation:
i m not sure
Find the equation of the line that contains the point ( - 1. - 4) and is parallel to the line 2x + 3y = 5
Answer:
Answer: 2x+3y=-14
Y needs to be changed in order to maintain parallelism
Good luck!