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2 years ago

Find a ⋅ b. a = 6i - 6j, b = 4i + 2j

Mathematics

2 answers:

Marat540 [252]2 years ago

7 0

You multiply the two vectors to get an answer of 12.

ivann1987 [24]2 years ago

3 0

Answer:

The value of $a \cdot b =12$

Step-by-step explanation:

Given : $a = 6i-6j, b = 4i + 2j$

To find : The value of a ⋅ b?

Solution :

We know that, The dot product of two vectors in form

$v=ai+bj$ and $w=ci+dj$

Then, $v \cdot w = ac + bd$

Applying the same in the given situation,

a=6 ,b=-6 ,c =4 ,d=2 and v=a , w=b

Substitute in the formula,

$a \cdot b = (6)(4) + (-6)(2)$

$a \cdot b =24-12$

$a \cdot b =12$

Therefore, The value of $a \cdot b =12$

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1 year ago

From home, Mary’s work is two thirds along the way to training. Training is 2.5km from work. Mary normally goes to work, then tr

polet [3.4K]

First thing to do is to illustrate the problem, Since it was mentioned that work was along the way to training, the order is shown in the picture. Mary's home and workplace are nearer compared to her training center. It is also mentioned that the distance between work and home, denoted as x, is 2/3 of the total distance from home to training. The total distance is (x + 2.5). Thus,

x = 2/3(x+2.5)
x = 2/3 x + 5/3
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Thus, the distance from home to work is 5 km. This means that Mary has to walk this distance twice to return home to get her shoes. Then, she will travel again the total distance of 5+2.5 = 7.5 km to get to her training center. So,

Total distance = 2(5km) + 7.5 km
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1 year ago

Eva left her home and drove for 4.3 hours due north at a rate of 60 miles per hour. After visiting a beach, she drove due south

Inessa05 [86]

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1 year ago

6. Problems and Applications Q6 Consider an economy that produces only chocolate bars. In year 1, the quantity produced is 3 bar

natulia [17]

Answer:

Year 1 GDP Deflator is 100%

Year 2 GDP Deflator is 30%

Year 3 GDP Deflator is 14.29%

Inflation Rate between year 2 and year 3 is 50%

The Real GDP growth Rate for Year 2 and year 3 is 110%

Step-by-step explanation:

Year 1

Price of chocolate bar is $2 and 3 bars are sold that year so the real GDP is 3 x $2=$6 which we are also given that this year is the nominal base year so the nominal GDP is also $6. GDP is the sum of all market value produced products in an economy. Therefore that’s why we calculated as the price of a chocolate multiplied the number produced. To calculate the GDP Deflator will be as follows:

GDP Deflator= (nominal GDP/Real GDP) x 100

= ($6/$6) x 100

= 100%

Year 2

Price of chocolate bars is $4 per bar and 5 bars were produced therefore Real GDP =$4 x 5 = $20, now we will calculate the GDP deflator as we have been told that year is the nominal year therefore nominal GDP is $6.

GDP Deflator= (nominal GDP/Real GDP) x 100

= ($6/$20) x100

= 30%

Year 3

Price of chocolate bars is $6 per bar and 7 bars were produced therefore Real GDP =$6 x 7 =$42, now we calculate the GDP deflator as we have been told that year 1 is the nominal year therefore nominal GDP is $6.

GDP Deflator = (nominal GDP/ Real GDP) x 100

= ($6/$42)

=14.29%

Now we calculate the inflation rate between year 2 and year 3.we use the CPI (consumer price index to get the inflation rate for year 2 ad 3)

Consumer Price Index = (Current price of bar/previous price of bar) x 100 formula for CPI

= ($6/$4) x 100= 150%-100%

= 50% is the inflation rate as the consumer price gave us a positive value.

Now we compute the real GDP growth rate between year 2 and year 3

Real GDP growth rate = [ (current Real GDP- Previous Real GDP)/Previous Real GDP] x 100

= ($42-$20)/$20

= 110% so real GDP grew by 110% from year 2 to year 3.

8 0

2 years ago

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yawa3891 [41]

we will find number of non-zero elements on each rows

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First row: