Part (a)
Lets say we had the two general vectors
u = (a,b)
v = (c,d)
The dot product is
u dot v = a*c + b*d
-------------------
Apply that rule to these specific vectors
u = (5, -2)
v = (0, 1)
So we get
u dot v = 5*0 + (-2)*1
u dot v = 0 - 2
u dot v = -2
Therefore,
(u dot v)*w = -2*(-1, -3)
(u dot v)*w = ( -2*(-1), -2(-3) )
(u dot v)*w = (2, 6)
Answer: (2, 6)
=============================================
Part (b)
u = (5, -2)
5u = 5*(5, -2)
5u = (5*5, 5*(-2))
5u = (25, -10)
5u dot v = (25, -10) dot (0,1)
5u dot v = 25*0 + (-10)*1
5u dot v = 0 - 10
5u dot v = -10
Answer: -10
14. The diagram in Fig. 1.34 shows a uniform metre rule
weighing 100 gf, pivoted at its centre 0. Two weights
150 gf and 250 gf hang from the points A and B
respectively of the metre rule such that OA = 40 cm
and OB = 20 cm. Calculate : (i) the total anticlockwise
moment about O, (ii) the total clockwise moment about
O, (iii) the difference of anticlockwise and clockwise
moments, and (iv) the distance from O where a 100 gf
weight should be placed to balance the metre rule.
7-20 cm
А
승
B
40 cm
)
150 gf
Fig. 1.34
250 gf
Answer:
(i) The total anticlockwise moment about O, is 6000 + 50 × OD
(ii) The total clockwise moment about O, is 5000 + 50 × OC
(iii) The difference between the anticlockwise and the clockwise moment is 1000 N·cm
(iv) The distance from O where a 100 gf force should be placed to balance the meter rule is 10 cm to the right of the point O on the meter rule
Step-by-step explanation:
The given parameters are;
The mass of the uniform meter rule = 100 gf
The center of the meter rule = O
The mass of the weight at point A = 150 gf
The mass of the weight at point B = 250 gf
The distance of the point A from the point O = OA = 40 cm
The distance of the point B from the point O = OB = 20 cm
(i) Whereby the point A is on the left of the meter rule, and taking the mass of half the meter rule as acting on the center, of the midspan from the left edge to the center, O, which is the point, D we have;
The total anticlockwise moment, Mₐ = 150 × 40 + 50 × OD = 6000 + 50 × OD
(ii) The total clockwise moment about O, is given similarly as follows;
The total clockwise moment, [tex]M_c[/tex] = 250 × 20 + 50 × OC = 5000 + 50 × OC
(iii) The difference between the anticlockwise and the clockwise moment = Mₐ - [tex]M_c[/tex] = 6000 + 50 × OD - 5000 + 50 × OC
Where, OD = OC, we have;
Mₐ - [tex]M_c[/tex] = 6000 + 50 × OD - 5000 + 50 × OD = 1,000
Mₐ - [tex]M_c[/tex] = 1000 N·cm
Therefore, Mₐ > [tex]M_c[/tex]
(iv) The distance from O where a 100 g force should be placed to balance the meter rule should give a 1000 N·cm clockwise moment as follows;
Let the 100 gf load be placed at the point E, to the right of the point O, therefore;
100 gf × OE = 1000 N·cm
OE = 1000/(100) = 10
OE = 10 cm
Therefore, the 100 gf should be placed 10 cm to the right of the point O.
You pay 6% tax on a $30 portable speaker. What is the amount of tax?
Answer:
31.80 is the total 1.80 is the amount of tax
Step-by-step explanation:
Answer:
$1.80
Step-by-step explanation:
6% is equal to 0.06
Multiply 30 by 0.06 and that equals 1.8
$1.80 is your answer
what’s the height of the triangle
in a survey of 3,200 people who owned a certain type of car, 1,760 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
Answer:
The percent would be 54.69%
Rounded up to whole percent would be 55%
Step-by-step explanation:
Sharad went to his friend's place on a motorcycle. When he started, the reading was 19,235 km. When he reached his friend's place it was 19,301 km. How many km did sharad travel ?
Answer:
the number of km did sharad travel is 66 km
Step-by-step explanation:
The computation of the number of km did sharad travel is as follows:
= The km at his friend place - km when he started
= 19,301 km - 19,235 km
= 66 km
Hence, the number of km did sharad travel is 66 km
So, the same is to be considered by applying the given formula so that the correct distance could come
I will give brainliest
Answer: 16 quarts of blue paint
Step-by-step explanation:
i divided 3 by 24 to see how many quarts there was then took the answer which is 8 and multiplied it by 2.... i dont know if its right but i tried
Please find X! plspls
Answer:
16.8
Step-by-step explanation:
you get this by taking the ratio of 12:30 and applying it to 42
you get 30 by taking the total of 12 + 18
you then divide 12 / 30 which equals 0.4
you then multiply 0.4 * 42 which gives you 16.8
if you were to solve for the other ratio you would divide 18 / 30
and then take the answer of that, 0.6 and multiply it by 0.6 * 42
then you have the other part of the ratio.
Bfksksbckdnxjmcbssoxonxnf
Answer:
The LCM of 4 and 7 is 28
Step-by-step explanation:
LCM is the lowest common multiple of two or more numbers.
To find it do that:
List the multiples of each numberFind the first common multiple of them, it will be the LCMLet us find the lowest common multiple of 4 and 7
→ List the multiples of 4
∵ The multiples of 4 are, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, .......
→ List the multiples of 7
∵ The multiples of 7 are, 7, 14, 21, 28, 35, 42, 49, .........
→ Find the first common multiple of 4 and 7
∵ 28 is the first common multiple of 4 and 7
∴ The lowest common multiple of 4 and 7 is 28
∴ The LCM of 4 and 7 is 28
Answer:
28
Step-by-step explanation:
have a wonderful day!!!!
Ellen needs to make b batches of blueberry scones this weekend for her family's brunch party. She needs 2 cartons of blueberries for each batch, and each carton costs $4. Pick all the expressions that represent how much Ellen will spend on blueberries.
Answer:
Ellen will spend
$4(2b) on blueberries
Where b = number of batches of Blueberry scones she wants to make
Step-by-step explanation:
From the above question:.
Ellen needs to make b batches of blueberry scones this weekend for her family's brunch party.
Since she needs 2 cartons of blueberries for each batch, and each carton costs $4
1 batch = 2 cartons of blueberries
b batches =
Cross Multiply
b × 2 cartons
= 2b cartons of blueberries.
We also know that:
1 carton blueberries = $4
2b cartons of blueberries = x
Cross Multiply
x = 2b × $4
Therefore, Ellen will spend :
$4(2b) on blueberries
k/5 = 9/15 plz help mee
Answer:
k = 3
Step-by-step explanation:
Reduce the right side of the equation by 3 to get 3/5. Since both denominators now are even you should get 3 which is k as your answer.
Please helpp!!
A model car is for sale online. The owner discounts the price by 5% each day until it sells. On the third day, the car sells. If the original price of the model car was $40, how much did the car sell for to the nearest cent? What percent discount does this represent from the original price? Round to the nearest whole percent.
Answer:
2
Step-by-step explanation:
The middle-school camera club sold 240 tulip bulbs and 360 daffodil bulbs. Students divided the bulbs into 100 bags to sell at the school fair. Write an expression to show how many bulbs went into each of the 100 bags if students put the same total number of bulbs in each bag.
There would be 600 bulbs in all, that makes. 6 in each of the 100 bags. An expression could be: 600 = 100x.
MOM PLSSSS COME ONLINE
Find the slope of a line parallel to 3y - 6x = 9
A. 2
B. 6
C.9
D.-6
answer this, please !!!
Answer:
C or R
Step-by-step explanation:
Carol observes that all of the juniors are taking physics this year. She concludes that when she is a junior, she will take physics for her science class. What kind of reasoning is Carol using to from her conjecture?
A.) Deductive Reasoning
B.) Inductive Reasoning
Answer:
The answer is B.) Inductive Reasoning
Step-by-step explanation:
Deductive reasoning requires one to start with a few general ideas, called premises, and apply them to a specific situation. Recognized rules, laws, theories, and other widely accepted truths are used to prove that a conclusion is right.
Answer:
Inductive Reasoning
Step-by-step explanation:
Carol’s conjecture is based on her observations.
identifying angles
Answer:
The angles 3 and 9 are corresponding.
To be a member of the choir, you must go to an audition. Henry's cousin is a member of the choir. What conjecture can you make about Henry's cousin?
A.) Henry’s cousin practices with the choir
B.) Henry is in the choir
C.) Henry’s cousin went to an audition
Answer:
b
Step-by-step explanation:
Answer:
Henry's cousin went to an audition.
Step-by-step explanation:
i need the equation in slope intercept in fraction form.
(-3,18),(3,2)
Pls help me ASAP I have other homework to do and I don’t have time for this. It also detects if it’s right or wrong:(
Answer:
5 hours
Step-by-step explanation:
(450-200)÷50=5
write an equivalent expression using exponents “abaab”
Answer: a to the 3rd power and b to the 2nd power.
Step-by-step explanation:
You could do a*a*a and b*b.
Either way it's a3b2
Answer:
[tex]abaab = a^3b^2[/tex]
.
Step-by-step explanation:
[tex]a^n \times a^m = a^{n + m}[/tex]
Kylie drove 406 miles in 7 hours, how far would she travel in 19 hours
Answer:
1102
Step-by-step explanation:
5,680÷80=
WITH REMAINDER
NO CALCULATOR IT WILL NOT WORK
Answer:
71
Step-by-step explanation:
i used my calculator :D
pls help
due at 11:59
Answer:
C. E.
Step-by-step explanation:
A zoologist is recording the loss of wolves in her state. She notes the number of wolves, w, in the state on January 1. One year later, there were 84 wolves in the state, which is 23 fewer wolves than were in the state a year earlier. What is the number of wolves in the state on January 1?
Which equation can be used to find the number of wolves in the state on January 1?
w + 23 = 84
w−23=84
w−84=−23
23−w=84
Answer:
w+23=84 is the answer for that problem because in order to find the answer u need to do the opposite of subtraction
Answer:
w - 23 = 84
Step-by-step explanation:
W is the amount of wolves they had in the state for the first year. If 84 wolves is 23 less than what they had originally you would be subtracting that amount to get 84.
Hope this helps
(-9,-11) , (6,3) helppppppp
And.. what about the cordnaites?
hihi! can you help me please? Giving brainleist to the best/correct awnser :))
Solve for x
9(3−2x)=2(10−8x)
Answer:
x= 2/7
Step-by-step explanation:
i think that's the answer jdmsmzmsms
Answer:
Step-by-step explanation:
x=7/2
the half life of radium is 1690 years. if 100 grams are present now, when will there be 20% of the original amount
In triangle ABC, AB= 10cm, AC=9cm and angle B=60 degrees. Let BC=x cm. Use cosine rule to show that x is a solution of x^2-10x+19=0
Answer:
Step-by-step explanation:
what is 0.000 002 in standard form
Answer:
[tex] 0.000 002 = 2 \times {10}^{ - 6} [/tex]
Step-by-step explanation:
It is already in standard form and can be expressed in scientific form as:
[tex]0.000 002 = 2 \times {10}^{ - 6} [/tex]
Answer:
0.000 002 in standard form is NaN x 100^0
Step-by-step explanation:
Beth was working at the grocery store, in the quick check-out line. A customer bought cereal for $3.29 and milk for $3.45. The customer paid with $10.00. How much change does Beth need to give the customer?
$3.36
$3.26
$6.74
None of these is correct.
Answer:
3.26
Step-by-step explanation:
first subtract $10.00 bye $3.26 witch equals $6.75
then subtract $6.76 bye $3.45 witch equals $3.26