Answer is: a= -4
STEP
1
:
1
Simplify —————
a + 3
Equation at the end of step
1
:
a 3 1
(————————+—————)-——— = 0
((a2)-9) (a-3) a+3
STEP
2
:
3
Simplify —————
a - 3
Equation at the end of step
2
:
a 3 1
(————————+———)-——— = 0
((a2)-9) a-3 a+3
STEP
3
:
a
Simplify ——————
a2 - 9
Equation at the end of step
3
:
a 3 1
(————————————————— + —————) - ————— = 0
(a + 3) • (a - 3) a - 3 a + 3
Equation at the end of step
4
:
(4a + 9) 1
————————————————— - ————— = 0
(a + 3) • (a - 3) a + 3
Pull out like factors :
3a + 12 = 3 • (a + 4)
Equation at the end of step
6
:
3 • (a + 4)
————————————————— = 0
(a + 3) • (a - 3)
3•(a+4)
——————————— • (a+3)•(a-3) = 0 • (a+3)•(a-3)
(a+3)•(a-3)
a+4 = 0
Subtract 4 from both sides of the equation :
a = -4
Answer:
Total Amount in Barista's tip jar = $ 10 + $ 0.50n
Step-by-step explanation:
Barista makes an average of $ 0.50 from each customer
So, for n more customers, She will be having following amount in her tip jar:
Additional tip amount = $ 0.50 x n
Here the word "additional" is used, because she already had an amount of $ 10 in her tip jar.
Adding this amount to her additional tip amount, we will get following expression:
Total Amount in Barista's tip jar = $ 10 + ($ 0.50 x n)
Its looks like there is no question here. Find x maybe?
the shaded part is a right triangle so we can use Pythagorean theorem
c² = a² + b²
c is the longest side of the or hypotenuse
so I can write it as m² + m² = 9²
m² + m² = 81
2m² = 81
/2 /2
m² = 40.5
√ √
m = √40.5 (well its actually = or - but since it really measurement its +)
~ 6.39
since x is to ms its 2 x 6.39
Answer:
Fs = 15 Hz > 12.7322 Hz
Hence, Nyquist theorem is NOT violated
Step-by-step explanation:
Given that;
a signal given by 15cos(20t) + 20sin(40t)
sampled at a rate of 15 Hz
Is the Nyquist theorem violated?
so;
from 15cos(20t) + 20sin(40t)
Freq F1 = 20/2π Hz
F1 = 3.1830 Hz
and
Freq F2 = 40/2π
F2 = 6.3661 Hz
Now, Nyquist's rate FN ≥ 2 × F_max
FN ≥ 2 × 6.3661
FN ≥ 12.7322 Hz
Now our given signal was sampled at a rate of 15 Hz
so, Fs = 15 Hz > 12.7322 Hz
Hence, Nyquist theorem is NOT violated