8 multiplied by 9.6 equals

find the angle between the vectors. (first find the exact expression and then approximate to the nearest degree. ) a=[1,2,-2]. B

SashulF [63]

Answer:

$\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190$

Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel

And the anfle is approximately $\theta \approx 48$

Step-by-step explanation:

For this case first we need to calculate the dot product of the vectors, and after this if the dot product is not equal to 0 we can calculate the angle between the two vectors in order to see if there are parallel or not.

a=[1,2,-2], b=[4,0,-3,]

The dot product on this case is:

$a b= (1)*(4) + (2)*(0)+ (-2)*(-3)=10$

Since the dot product is not equal to zero then the two vectors are not orthogonal.

Now we can calculate the magnitude of each vector like this:

$|a|= \sqrt{(1)^2 +(2)^2 +(-2)^2}=\sqrt{9} =3$

$|b| =\sqrt{(4)^2 +(0)^2 +(-3)^2}=\sqrt{25}= 5$

And finally we can calculate the angle between the vectors like this:

$cos \theta = \frac{ab}{|a| |b|}$

And the angle is given by:

$\theta = cos^{-1} (\frac{ab}{|a| |b|})$

If we replace we got:

$\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190$

Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel

And the anfle is approximately $\theta \approx 48$

3 0

3 years ago

The Royal Fruit Company produces two types of fruit drinks. The first type is 55% pure fruit juice, and the second type is 80% p

Stolb23 [73]

Answer:

First type of fruit drinks: 48 pints

Second type of fruit drinks: 32 pints

Step-by-step explanation:

Let's call A the amount of first type of fruit drinks. 55% pure fruit juice

Let's call B the amount of second type of fruit drinks. 80% pure fruit juice

The resulting mixture should have 65% pure fruit juice and 80 pints.

Then we know that the total amount of mixture will be:

$A + B = 80$

Then the total amount of pure fruit juice in the mixture will be:

$0.55A + 0.8B = 0.65 * 80$

$0.55A + 0.8B = 52$

Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.8 and add it to the second equation:

$-0.8A -0.8B = -0.8*80$

$-0.8A -0.8B = -64$

+

$0.55A + 0.8B = 52$

--------------------------------------

$-0.25A = -12$

$A = \frac{-12}{-0.25}$

$A = 48\ pints$

We substitute the value of A into one of the two equations and solve for B.

$48 + B = 80$

$B = 32\ pints$

6 0

3 years ago

Which group of numbers even or odd include more prime numbers? Why?

serg [7]

The First group i.e 1-10 include more prime numbers .(2,3,5,7,1)

Because it has the basic inputs of every number
Like 15 consists of 3×5

7 0

3 years ago

Read 2 more answers

Help? haha<br> solve the equation below:)<br> 3x - 5 = 10 + 2x

Setler [38]

Step-by-step explanation:

3x-2x=5+10 [taking variables on one side and constant on other]

x=15

soln:

3x-5= 2x+10

3x -5+5=2x+10+5 [ adding 5 on both side]

3x=2x+15

3x-2x=2x+15-2x [subtracting 2x on both side]

x=15

Ans=15

8 0

3 years ago

Read 2 more answers

Twelve percent of the population is left handed. Approximate the probability that there are at least 20 left-handers in a school

DochEvi [55]

Answer:

Step-by-step explanation:

We would assume a binomial distribution for the handedness of the population. Let x be a random variable representing the type of handedness in the population. The probability of success, p is that a randomly chosen person is left handed only. Then probability of failure is that a chosen person is not left handed only(right handed only or both).

p = 12/100 = 0.12

number of success, x = 20

n = 200

the probability that there are at least 20 left-handers is expressed as P(x ≥ 20)

From the binomial probability calculator,

P(x ≥ 20) = 0.84

8 0

4 years ago