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seropon [69]
2 years ago
14

Let $$\mathbf { u } , \mathbf { v } , \text { and } \mathbf { w }$$ be vectors. Which of the following make sense, and which do

not? Give reasons for your answers. $$
a.( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { w }\quad
b. \mathbf { u } \times ( \mathbf { v } \cdot \mathbf { w } )\ quad
c. \mathbf { u } \times ( \mathbf { v } \times \mathbf { w } )\quad
d. \mathbf { u } \cdot ( \mathbf { v } \cdot \mathbf { w } ).$$
Mathematics
1 answer:
Daniel [21]2 years ago
5 0

(<em>u</em> × <em>v</em>) • <em>w</em> makes sense, since <em>u</em> × <em>v</em> is another vector, and so (<em>u</em> × <em>v</em>) • <em>w</em> is a scalar.

<em>u</em> × (<em>v</em> • <em>w</em>) does not make sense, since <em>v</em> • <em>w</em> is a scalar, and the cross product is not defined between a vector and a scalar.

(<em>u</em> × <em>v</em>) × <em>w</em> makes sense, since <em>u</em> × <em>v</em> is a vector and so is <em>w</em>.

<em>u</em> • (<em>v</em> • <em>w</em>) does not make sense, since <em>v</em> • <em>w</em> is scalar, and the dot product is not defined between a vector and a scalar.

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A rocket is launched from a tower. The height of the rocket, y in feet, is related to the
devlian [24]

Answer:

The rocket will reach its maximum height after 6.13 seconds

Step-by-step explanation:

To find the time of the maximum height of the rocket differentiate the equation of the height with respect to the time and then equate the differentiation by 0 to find the time of the maximum height

∵ y is the height of the rocket after launch, x seconds

∵ y = -16x² + 196x + 126

- Differentiate y with respect to x

∴ y' = -16(2)x + 196

∴ y' = -32x + 196

- Equate y' by 0

∴ 0 = -32x + 196

- Add 32x to both sides

∴ 32x = 196

- Divide both sides by 32

∴ x = 6.125 seconds

- Round it to the nearest hundredth

∴ x = 6.13 seconds

∴ The rocket will reach its maximum height after 6.13 seconds

There is another solution you can find the vertex point (h , k) of the graph of the quadratic equation y = ax² + bx + c, where h = -\frac{b}{2a} and k is the value of y at x = h and k is the maximum/minimum value

∵ a = -16 , b = 196

∴ h=-\frac{196}{2(-16)}

∴ h = 6.125

∵ h is the value of x at the maximum height

∴ x = 6.125 seconds

- Round it to the nearest hundredth

∴ x = 6.13 seconds

4 0
3 years ago
There are four steps in the manufacturing process of a stuffed toy: cutting, stuffing, sealing, and packaging. There are two emp
Anit [1.1K]

Answer:

(a) 2min/15units

(b) 1min/20units

(c) The bottleneck stage is cutting. The process capacity is 450units/hour

(d) The capacity of the new employee should be 1unit/2sec. The process capacity will increase four times

Step-by-step explanation:

(a) Cycle time for stage cutting for 2 employees = 16sec/2units × 1min/60sec = 2min/15units

(b) Cycle time for stage sealing for 1 employee = 3sec/1unit × 1min/60sec = 1min/20units

(c) Process capacity of stage cutting = 15units/2min × 60min/1hour = 450units/hour

(d) If the capacity of the new employee is 1unit/2sec, the process capacity = 1unit/2sec × 3600sec/1hour = 1800units/hour. The process capacity increases 4 times (1800/450 = 4)

7 0
3 years ago
a piece of ribbon that is 2/3 of a yard long is to be cut into 1/12 yard pieces. How many pieces will there be?
Darina [25.2K]
Length of the original ribbon = 2/3 yard
Length of the ribbon in which the actual ribbon has to be cut = 1/12 yards
The above information's are already given in the question. It is required to find the number of pieces that the ribbon can be cut with the length that is already mentioned.
Then
Number of pieces that will be there = (2/3)/(1/12)
                                                         = (2 * 12)/3
                                                         = 24/3
                                                         = 8
So the actual ribbon can be cut into 8 pieces and each piece will have a length of 1/12 yards. Hopefully the procedure for doing this problem is clear to you. this is the easiest method for attempting these kind of problems.
3 0
3 years ago
Cristiano is saving money to buy a bike that costs $189. He saved $99 so far. He plans on saving $10 each week. In how many week
Jlenok [28]

Answer:

189-99=90 (What he needs left)

90/10= 9

so the answer is 9 weeks.

6 0
3 years ago
Ayso has 18 8th grade boys teams this year but this is a 28% decrease from the prior year. How many 8th grade teams were there l
NikAS [45]

Answer:

23pupils

Step-by-step explanation:

Given parameters:

Number of 18th grade boys this year = 18

Percentage decrease  = 28%

Unknown:

How many 8th grade teams were there last year  = ?

Solution:

Since this is a percentage decrease, ;

     Number of pupils this year  = Number of pupils last year - (28% x 18 )

                  18 + (28% x 18 ) = Number of pupils last year

         Number of pupils last year = 23pupils

4 0
3 years ago
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