Answer:
Step-by-step exExplanation:
Solve:
3
x
2
−
4
x
−
5
=
0
is a quadratic equation in standard form:
a
x
2
+
b
x
+
c
,
where:
a
=
3
,
b
=
−
4
,
c
=
−
5
Quadratic formula
x
=
−
b
±
√
b
2
−
4
a
c
2
a
Plug in the known values.
x
=
−
(
−
4
)
±
√
(
−
4
)
2
−
4
⋅
3
⋅
−
5
2
⋅
3
Simplify.
x
=
4
±
√
76
6
Prime factorize
76
.
x
=
4
±
√
2
2
×
19
6
Apply rule:
√
a
2
=
a
x
=
4
±
2
√
19
6
Simplify.
x
=
2
±
√
19
3
Solutions for
x
.
x
=
2
+
√
19
3
,
2
−
√
19
3
Related questions
How do you know how many solutions
2
x
2
+
5
x
−
7
=
0
has?
What is the Quadratic Formula?
planation:
RemarkIf you don't start exactly the right way, you can get into all kinds of trouble. This is just one of those cases. I think the best way to start is to divide both terms by x^(1/2)
Step OneDivide both terms in the numerator by x^(1/2)
y= 6x^(1/2) + 3x^(5/2 - 1/2)
y =6x^(1/2) + 3x^(4/2)
y = 6x^(1/2) + 3x^2 Now differentiate that. It should be much easier.
Step TwoDifferentiate the y in the last step.
y' = 6(1/2) x^(- 1/2) + 3*2 x^(2 - 1)
y' = 3x^(-1/2) + 6x I wonder if there's anything else you can do to this. If there is, I don't see it.
I suppose this is possible.
y' = 3/x^(1/2) + 6x
y' =

Frankly I like the first answer better, but you have a choice of both.
Answer:
Step-by-step explanation:
wefasv
Answer:
First one: 5x3(0.75)2t
and fourth one: 0.05x500(0.005)t
Step-by-step explanation:
In order to have an exponencial decay, the rate of the exponencial function needs to be lesser than 1.
The rate is the value between parenthesis, so in the first equation, the rate is 0.75, so this is an exponencial decay.
The second equation has rate = 2.4, so this is not an exponencial decay.
The third equation has rate = 1.04, so this is not an exponencial decay.
The fourth equation has rate = 0.005, so this is an exponencial decay.