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aivan3 [116]
3 years ago
12

Maria works in a factory that produces new cars. She is having trouble with one of the machines. In order to work properly, the

two gears in the machine must be perpendicular. Maria makes some adjustments and wants to know if the two gear shifts are aligned correctly. The new directional vectors of the gears are:g1= 5i -j+2k g2=I-3j-4k
Mathematics
1 answer:
Dovator [93]3 years ago
3 0

Answer:

Maria did her job properly. Both gears are perpendicular.

Step-by-step explanation:

Recall that given vectors a and b, they are perpendicular if and only if a\cdot b =0. If a=(a_1,a_2),b=(b_1,b_2). Then a\cdot b = a_1b1_+a_2b_2.

IN our case a=(5,-1,2) and b) (1,-3,-4). So,

a\cdot b = 5\cdot 1 + (-1)\cdot(-3) + 2\cdot(-4) = 5+3-8 =0

So both gears are perpendicular.

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When writing a set of hypotheses for a situation, which of the following is true?
Andre45 [30]

Answer:

The Null hypothesis is a claim the researcher is trying to disprove. (I think)

Step-by-step explanation:

The null hypothesis states that there is no relationship between the two variables being studied (one variable does not affect the other). It states results are due to chance and are not significant in terms of supporting the idea being investigated.

4 0
3 years ago
Read 2 more answers
Simplify the ratio of<br> 35 : 14
Ne4ueva [31]

Answer:

5:2

Step-by-step explanation:

divide both numbers by 7

hope this helps...

3 0
2 years ago
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Simon caught 5 striped fish. Each one weighed the same number of pounds.Then he caught another fish that weighted 7 pounds. Writ
nekit [7.7K]
5x + 7 

5x represents the weight of the 5 striped fish. 

7 represents the fish that weighs 7 pounds. 
8 0
3 years ago
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The third term of an arithmetic sequence is 14 and the 9th term is -1. Find the first four terms of the sequence.​
Liula [17]

Answer:

The first four terms of the sequence are :  19, 16.5 , 14 , 11.5

Step-by-step explanation:

In the given sequence:

a(3) =  14, a(9)  = -1

The general term of a sequence in Arithmetic Progression is:

a(n) = a + (n-1)d

a(3) = a + (3 -1) d = a + 2 d

and a(9) = a + (9- 1 ) d = a  + 8 d

⇒   a + 2 d =  14      .........  (1)

and a + 8 d  = -1    ...........  (2)

Now, solving the given system of equation, we get:

From (1), a  = 14 - 2 d

Put in (2), we get:

a + 8 d  = -1                ⇒   14 - 2 d + 8d = -1

⇒  14 +   6d   = -1  

or,  6d = -1 -14 = -15

⇒  d = -15/6 = -2.5

or, d  = -2.5

Then a  = 14 - 2 d = 14 - 2(-2.5)  =14 + 5  = 19, or a  = 19

Now, first four terms of the sequence is:

a = 19

a(2) = a + 4 = 19 - 2.5 = 16.5

a(3) = a + 2d = 19 + 2(-2.5) = 19 - 5 = 14

a(4) = a  + 3d = 19 + 3(-2.5)  = 19  - 7.5  = 11.5

Hence, the first four terms of the sequence are :  19, 16.5 , 14 , 11.5

4 0
3 years ago
Which equation is equivalent to StartRoot x EndRoot + 11 = 15?
Lerok [7]

The equivalent expression of \sqrt x + 11 = 15 is \sqrt x = 15 - 11

<h3>How to determine the equivalent expression?</h3>

The complete question is in the attached image

The expression is given as:

\sqrt x + 11 = 15

Subtract 11 from both sides of the equation

\sqrt x + 11 - 11= 15 - 11

This gives

\sqrt x = 15 - 11

Hence, the equivalent expression of \sqrt x + 11 = 15 is \sqrt x = 15 - 11

Read more about equivalent expression at:

brainly.com/question/4344214

#SPJ1

5 0
2 years ago
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