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3 years ago

Find the distance between the points. (-3,5) and (1,5)

Mathematics

2 answers:

Ksju [112]3 years ago

8 0

Answer:

4 units

Step-by-step explanation:

Citrus2011 [14]3 years ago

8 0

Answer:

4 units

Step-by-step explanation:

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Can somebody explain to me stem and leaf diagrams please?

aev [14]

They are a method for showing the frequency of a data plot in a much more compact and numerical way.

1[2 3
2[1 7
3[3 4 5 7
4[ 0 0 1

Key 1[2= 12

meaning that 3[5 is 35 and 4[0 is 40 and so and so forth

5 0

3 years ago

Slove for P. 5/7=p+4/7

Sever21 [200]

p= 1/7
Alright, so first, you need to flip the equation.It will turn into p+4/7=5/7
Next, you want to get the variable by itself so you need to subtract 4/7 from both sides. 5/7-4/7=1/7
p=1/7

5 0

3 years ago

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

4 years ago

Read 2 more answers

Joe paid $14 for a board game. this is 70% of the original price. what was the original price?

tino4ka555 [31]

Step-by-step explanation:

It is given that Joe paid 14.00 for a board game this is 70% of the original price what is the original price.

Let the original price of board game be

x * 70/100 = 14

x * 7/10 = 14

Multiply both sides by 10.

7x = 140

Divide both sides by 7.

x = 20

4 0

2 years ago

Here is another one I need help with

aksik [14]

Answer:

Step-by-step explanation:

Surface area of objects with flat surfaces like this is simply the area of each surface added together, so let's get to work.

Both have 6 faces, so we will be adding six values together for each.

Container A:

Hopefully you can imagine the six different faces. It's kinda like a cereal box.

The front and back of a cereal box have the same area, as do the two sides and the top and bottom, so that makes it a little easier.

Front and Back: 28 * 36 = 1008

Sides: 36*6 = 216

Top and Bottom: 6*28 = 168

Let me know if you don't understand how I did any of that. Anyway, since there is a matching face for each we add them all together twice.

1008*2 + 216*2 + 168*2 = 2784 in^2

Container B has a similar setup, I won't write out everything like I did unless you want me to work it out with you.

2(16*12+16*22+22*12) = 1616 in^2

So since Container A has a surface area of 2784 and Container B has a surface area of 1616 it's obvious container A has a larger surface area

4 0

3 years ago