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Alexandra [31]
3 years ago
5

Find a unit vector that has the same direction as the vector a and the opposite direction of the vector

Mathematics
1 answer:
nasty-shy [4]3 years ago
5 0
The unit vector is given by the following formula:
 a '= (a) / (lal)
 Where,
 a: vector a
 lal: Vector module a
 We are looking for the module:
 lal = root ((- 15) ^ 2 + (8) ^ 2)
 lal = 17
 Same direction:
 a = -15i + 8j
 The unit vector is:
 a '= (1/17) * (- 15i + 8j)
 Opposite direction:
 a = 15i - 8j
 The unit vector is:
 a '= (1/17) * (15i - 8j)
 Answer:
 
a unit vector that has the same direction as the vector a is:
 
a '= (1/17) * (- 15i + 8j)
 
a unit vector that has the opposite direction of the vector a is:
 
a '= (1/17) * (15i - 8j)
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Use the distributive property to write an equivalent expression.<br> 9(9x+2y-6)
Marizza181 [45]

Step-by-step explanation:

Multiply the number outside the brackets to the numbers inside:

So,

9 * 9x = 81x

9 * 2y = 18y

9 x -6 = -54

So the simplified or equivalent expression is:

81x + 18y - 54

4 0
2 years ago
The volume of the cone shown below is 108pie cm^3. What is the value of H?
saw5 [17]

Answer:

h = 4cm

Step-by-step explanation:

Diameter = 18cm

Radius = Diameter/2 = 18/2 = 9cm

V = 1/3*pi*r^2*h

We know that the volume is 108pi cm^3. We can just plug in 108pi cm^3 for V and we also know that our Radius (r) is 2.

So,

108 pi = 1/3*pi*9^2*h

108 pi = (81pi*h)/3

multiply 3 from both side

108pi*3 = (81pi*h)/3 *3

324pi = 81pi*h

Now divide the 81pi from both side

324pi/81pi = (81pi*h)/81pi

4 = h

So the height is 4cm

3 0
2 years ago
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Find the average rate of change.<br><br> p(x) = 6x + 7 on [2, 2 + h] , h ≠ 0
siniylev [52]

Answer:

6.

Step-by-step explanation:

This is [p(2+h))  - p(2) ] /  ((2 + h - 2)

= [ 6(2) + h) + 7 - (6(2) + 7)] / h

=  (  12 + 6h + 7 - 12 - 7) / h

=  6h / h

= 6.

4 0
3 years ago
There are 450 vehicles in a car lot. Select the correct value for the umber of vehicles of each type that are in the lot. Hybrid
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5 0
3 years ago
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Which of the following expressions illustrates the commutative property of addition? 3 + (-7) = (-7) + 3 -4(5) = 5(-4) 4 + (1 +
umka2103 [35]
By definition, we have to:

 In mathematics, the commutative property or commutativity is a fundamental property that has some operations according to which the result of operating two elements does not depend on the order in which they are taken.

 This is fulfilled in ordinary addition and multiplication: the order of the addends does not alter the sum, or the order of the factors does not alter the product.

 We have then, that the commutative property of the addition is:
 3 + (-7) = (-7) + 3

 Answer:
 
An expression that illustrates the commutative property of addition is:
 
3 + (-7) = (-7) + 3
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