Answer:
 given that
 given that  and that
 and that  .
.
Step-by-step explanation:
The relation between the  and the
 and the  in this question is given by parametric equations (with
 in this question is given by parametric equations (with  as the parameter.)
 as the parameter.)
Make use of the fact that:
 .
.
 
Find  and
 and  as follows:
 as follows:
![\begin{aligned} \frac{dx}{dt} &= \frac{d}{dt} [a\, (\cos(t) + \sin(t))] \\ &= a\, (-\sin(t) + \cos(t)) \\ &= a\, (\cos(t) - \sin(t))\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20%5Cfrac%7Bdx%7D%7Bdt%7D%20%26%3D%20%5Cfrac%7Bd%7D%7Bdt%7D%20%5Ba%5C%2C%20%28%5Ccos%28t%29%20%2B%20%5Csin%28t%29%29%5D%20%5C%5C%20%26%3D%20a%5C%2C%20%28-%5Csin%28t%29%20%2B%20%5Ccos%28t%29%29%20%5C%5C%20%26%3D%20a%5C%2C%20%28%5Ccos%28t%29%20-%20%5Csin%28t%29%29%5Cend%7Baligned%7D) .
.
 as long as
 as long as  and
 and  .
.
![\begin{aligned} \frac{dy}{dt} &= \frac{d}{dt} [a\, (\sin(t) - \cos(t))] \\ &= a\, (\cos(t) - (-\sin(t))) \\ &= a\, (\cos(t) + \sin(t))\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20%5Cfrac%7Bdy%7D%7Bdt%7D%20%26%3D%20%5Cfrac%7Bd%7D%7Bdt%7D%20%5Ba%5C%2C%20%28%5Csin%28t%29%20-%20%5Ccos%28t%29%29%5D%20%5C%5C%20%26%3D%20a%5C%2C%20%28%5Ccos%28t%29%20-%20%28-%5Csin%28t%29%29%29%20%5C%5C%20%26%3D%20a%5C%2C%20%28%5Ccos%28t%29%20%2B%20%5Csin%28t%29%29%5Cend%7Baligned%7D) .
.
Calculate  using the fact that
 using the fact that  . Assume that
. Assume that  and
 and  :
:
 .
.
 
        
             
        
        
        
Step-by-step explanation:
Words	Decimal Representation	Scientific Notation
ten million	10,000,000	1 x 107
one hundred million	100,000,000	1 x 108
one billion	1,000,000,000	1 x 109
ten billion	10,000,000,000	1 x 1010
 
        
                    
             
        
        
        
The triangle that must appear to be obtuse mmust have one of its angle to be greater than 90 but less than 180 degrees:
<h3>What are obtuse triangles?</h3>
Obtuse triangles are triangles that has one of theor angles to greater than 90 degrees.
Most obtuse triangles has two acute angles (angles less than 90 degrees) and a obtuse angle (angles between  90 and 180 degrees)
Hence the triangle that must appear to be obtuse mmust have one of its angle to be greater than 90 but less than 180 degrees:
Learn more on obtuse triangle here: brainly.com/question/3250447
 
        
             
        
        
        
Answer:
Each term in Pattern A is one half the corresponding term in Pattern B.
Step-by-step explanation:
6 is half of 12 , 12 half 24, 18 half of 36, 24 half of 48 , 30 half of 60 etc.
 
        
                    
             
        
        
        
Your answer would be option (1) -3x² - 18x + 19.
To find this we need to substitute in the G and F expressions into G - 3F and see what the outcome is, as this will give us the answer.
First I’m going to multiply the F expression, 2x² + 6x - 5, by 3:
3 × (2x² + 6x - 5) = 3(2x²) + 3(6x) - 3(5) = 6x² + 18x - 15.
Now we need to subtract this expression from G, which is 3x² + 4, which I will do by term:
3x² - 6x² = -3x² 
0x - 18x = -18x
4 - -15 = 19
So therefore overall your answer is -3x² - 18x + 19.
I hope this helps! Let me know if you have any questions :)