Answer:
given that 
and that 
.
Step-by-step explanation:
The relation between the 
and the 
in this question is given by parametric equations (with 
as the parameter.)
Make use of the fact that:
.
Find 
and 
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 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 
. Assume that 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 :)
