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laiz [17]
3 years ago
6

3(4x-9)>=2x+12 >= is greater than equal to

Mathematics
2 answers:
ValentinkaMS [17]3 years ago
5 0
12x-27=2x+12
10x-27=12
10x=39
x=3.9
Dmitriy789 [7]3 years ago
5 0
3(4x-9) >= 2x + 12
12x-27 >= 2x + 12
12x >= 2x +39
10x >= 39
x >= 3.9
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3 years ago
Consider the parabola r​(t)equalsleft angle at squared plus 1 comma t right angle​, for minusinfinityless thantless thaninfinity
kodGreya [7K]

Given:-   r(t)=< at^2+1,t>  ; -\infty < t< \infty , where a is any positive real number.

Consider the helix parabolic equation :  

                                              r(t)=< at^2+1,t>

now, take the derivatives we get;

                                            r{}'(t)=

As, we know that two vectors are orthogonal if their dot product is zero.

Here,  r(t) and r{}'(t)  are orthogonal i.e,   r\cdot r{}'=0

Therefore, we have ,

                                  < at^2+1,t>\cdot < 2at,1>=0

< at^2+1,t>\cdot < 2at,1>=

                                              =2a^2t^3+2at+t

2a^2t^3+2at+t=0

take t common in above equation we get,

t\cdot \left (2a^2t^2+2a+1\right )=0

⇒t=0 or 2a^2t^2+2a+1=0

To find the solution for t;

take 2a^2t^2+2a+1=0

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The determinant D=0-4(2a^2)(2a+1)=-8a^2\cdot(2a+1)

Since, for any positive value of a determinant is negative.

Therefore, there is no solution.

The only solution, we have t=0.

Hence, we have only one points on the parabola  r(t)=< at^2+1,t> i.e <1,0>




                                               




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3 years ago
Find the distance between the pair of points.<br> (21,18) and (-20, -19)<br> The distance is
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Answer: answer in pic

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3 years ago
Which graph shows the solution to the system of linear inequalities?
V125BC [204]
<h2><u>Answer:</u></h2>

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On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 0) and (4, negative 2). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 2, 0) and (2, 2). Everything below the line is shaded.

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Step-by-step explanation:

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(80, 1), (40, 2), (20, 4), (10, 8), (16, 5)

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Usually the dimension are usually close, hence, the most sensible dimension a potholder with an area of 80 sq inch could have is 8 by 10 or vice-versa.

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