All categories

2 years ago

Please simplify the expression.

Mathematics

1 answer:

Dafna1 [17]2 years ago

7 0

Answer:The answer can be simplify by the following steps;

Step-by-step explanation:

You might be interested in

36 is 25% of what number?

DedPeter [7]

Answer:

36 is 25% of 144

Step-by-step explanation:

25% means 25/100 or 1/4. Thus, 36 is 1/4 of 36*4 = 144

4 0

3 years ago

Read 2 more answers

Determine whether the given vectors are orthogonal, parallel or neither. (a) u=[-3,9,6], v=[4,-12,-8,], (b) u=[1,-1,2] v=[2,-1,1

nevsk [136]

Answer:

a) $u v= (-3)*(4) + (9)*(-12)+ (6)*(-8)=-168$

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

$|u|= \sqrt{(-3)^2 +(9)^2 +(6)^2}=\sqrt{126}$

$|v| =\sqrt{(4)^2 +(-12)^2 +(-8)^2}=\sqrt{224}$

$cos \theta = \frac{uv}{|u| |v|}$

$\theta = cos^{-1} (\frac{uv}{|u| |v|})$

If we replace we got:

$\theta = cos^{-1} (\frac{-168}{\sqrt{126} \sqrt{224}})=cos^{-1} (-1) = \pi$

Since the angle between the two vectors is 180 degrees we can conclude that are parallel

b) $u v= (1)*(2) + (-1)*(-1)+ (2)*(1)=5$

$|u|= \sqrt{(1)^2 +(-1)^2 +(2)^2}=\sqrt{6}$

$|v| =\sqrt{(2)^2 +(-1)^2 +(1)^2}=\sqrt{6}$

$cos \theta = \frac{uv}{|u| |v|}$

$\theta = cos^{-1} (\frac{uv}{|u| |v|})$

$\theta = cos^{-1} (\frac{5}{\sqrt{6} \sqrt{6}})=cos^{-1} (\frac{5}{6}) = 33.557$

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

c) $u v= (a)*(-b) + (b)*(a)+ (c)*(0)=-ab +ba +0 = -ab+ab =0$

Since the dot product is equal to zero then the two vectors are orthogonal.

Step-by-step explanation:

For each 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.

Part a

u=[-3,9,6], v=[4,-12,-8,]

The dot product on this case is:

$u v= (-3)*(4) + (9)*(-12)+ (6)*(-8)=-168$

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:

$|u|= \sqrt{(-3)^2 +(9)^2 +(6)^2}=\sqrt{126}$

$|v| =\sqrt{(4)^2 +(-12)^2 +(-8)^2}=\sqrt{224}$

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

$cos \theta = \frac{uv}{|u| |v|}$

And the angle is given by:

$\theta = cos^{-1} (\frac{uv}{|u| |v|})$

If we replace we got:

$\theta = cos^{-1} (\frac{-168}{\sqrt{126} \sqrt{224}})=cos^{-1} (-1) = \pi$

Since the angle between the two vectors is 180 degrees we can conclude that are parallel

Part b

u=[1,-1,2] v=[2,-1,1]

The dot product on this case is:

$u v= (1)*(2) + (-1)*(-1)+ (2)*(1)=5$

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:

$|u|= \sqrt{(1)^2 +(-1)^2 +(2)^2}=\sqrt{6}$

$|v| =\sqrt{(2)^2 +(-1)^2 +(1)^2}=\sqrt{6}$

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

$cos \theta = \frac{uv}{|u| |v|}$

And the angle is given by:

$\theta = cos^{-1} (\frac{uv}{|u| |v|})$

If we replace we got:

$\theta = cos^{-1} (\frac{5}{\sqrt{6} \sqrt{6}})=cos^{-1} (\frac{5}{6}) = 33.557$

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

Part c

u=[a,b,c] v=[-b,a,0]

The dot product on this case is:

$u v= (a)*(-b) + (b)*(a)+ (c)*(0)=-ab +ba +0 = -ab+ab =0$

Since the dot product is equal to zero then the two vectors are orthogonal.

5 0

3 years ago

Read 2 more answers

Modern car company has come out with a new car model. Market analysts predict that 4,600 cars will be sold in the first month an

Arte-miy333 [17]

The first five terms of the sequence are; 4,600, 4,550, 4,500, 4,450, 4,400 and the total predicted number of sold cars for the first year is 51,900 cars

<h3>Arithmetic sequence</h3>

First month, a = 4,600 cars
Common difference, d = -50 cars

First five terms;

a = 4,600

a + d = 4600 + (-50)

= 4600 - 50

= 4,550

a + 2d

= 4600 + 2(-50)

= 4600 - 100

= 4,500

a + 3d

= 4,600 + 3(-50)

= 4,600 - 150

= 4,450

a + 4d

= 4600 + 4(-50)

= 4,600 - 200

= 4,400

cars predicted for the twelfth month.

a + 11d

= 4600 + 11(-50)

= 4600 + 550

= 4,050

Total predicted number of sold cars for the first year:

Sn = n/2{2a + (n - 1)d }

= 12/2{2×4600 + (12-1)-50}

= 6{9200 + 11(-50)}

= 6(9,200 - 550)

= 6(8,650)

= 51,900 cars

Learn more about arithmetic sequence:

brainly.com/question/6561461

#SPJ1

7 0

2 years ago

Find the x-intercepts of the parabola with vertex (1, -9) and y intercept at (0, -6).

liberstina [14]

1,0
I think that would be it

5 0

3 years ago

Read 2 more answers

4x+5y=-5 and what is it graphed

viva [34]

Answer:

go to m a t h w a y . c o m but dont add the spaces and it will give you the answer just type it exactly how you did on here

Step-by-step explanation:

3 0

3 years ago