Answer:
The simplified expression is
20x^2 - 33x - 27
Step-by-step explanation:
(6x - 9 - 2x)(8 + 5x - 5)
We must first rewrite the expression as a product of two binomials.
This can be done by adding like terms
(6x - 9 - 2x)(8 + 5x - 5)
We have,
(4x-9)(5x+3)
Multiplying the resulting binomial expression
(4x-9)(5x+3)
(20x^2+12x-45x-27)
Add the like terms
20x^2-33x-27
The simplified expression is
20x^2 - 33x - 27
Twenty x squared minus thirty-three x minus twenty-seven
Answer:
Differentiation will give you the gradient for the tangent at any point, and you use the product rule whenever a function can be thought of as two functions multiplied together.
If
f
(
x
)
=
g
(
x
)
×
h
(
x
)
then
f
'
(
x
)
=
g
'
(
x
)
h
(
x
)
+
g
(
x
)
h
'
(
x
)
so if
y
=
x
×
sin
x
then
d
y
d
x
=
1
×
sin
x
+
x
×
cos
x
=
sin
x
+
x
cos
x
We know that
x
=
π
2
, so the gradient is
m
=
sin
(
π
2
)
+
π
2
cos
(
π
2
)
=
1
+
π
2
×
0
=
1
Therefore, we can say that
y
=
m
x
+
c
y
=
(
1
)
x
+
c
y
=
x
+
c
So all we really need to find now is the value for
c
, the
y
intercept. We do this by working out a point
(
x
,
y
)
on the graph. We are already given that
x
=
π
2
, so
y
=
x
sin
x
=
π
2
sin
(
π
2
)
=
π
2
×
1
=
π
2
∴
(
x
,
y
)
=
(
π
2
,
π
2
)
Now we substitute this into the equation we already have for the tangent,
y
=
x
+
c
,
(
x
,
y
)
=
(
π
2
,
π
2
)
π
2
=
π
2
+
c
c
=
π
2
−
π
2
=
0
∴
y
=
x
+
c
=
x
+
(
0
)
=
x
which means the tangent to the curve
y
=
x
sin
x
at
(
π
2
,
π
2
)
is simply
y
=
x
.
The equation that represents the <em>sinusoidal</em> function is ![x(t) = -8 + 6.5 \cdot \sin \left[\left(\frac{2}{3} \pm \frac{4\cdot i}{3}\right)\cdot t + \left(\frac{2\pi}{3} \pm \frac{7\pi \cdot i}{3} \right)\right]](https://tex.z-dn.net/?f=x%28t%29%20%3D%20-8%20%2B%206.5%20%5Ccdot%20%5Csin%20%5Cleft%5B%5Cleft%28%5Cfrac%7B2%7D%7B3%7D%20%5Cpm%20%5Cfrac%7B4%5Ccdot%20i%7D%7B3%7D%5Cright%29%5Ccdot%20t%20%2B%20%5Cleft%28%5Cfrac%7B2%5Cpi%7D%7B3%7D%20%5Cpm%20%5Cfrac%7B7%5Cpi%20%5Ccdot%20i%7D%7B3%7D%20%20%5Cright%29%5Cright%5D)
, 
.
<h3>Procedure - Determination of an appropriate function based on given information</h3>
In this question we must find an appropriate model for a <em>periodic</em> function based on the information from statement. <em>Sinusoidal</em> functions are the most typical functions which intersects a midline (
) and has both a maximum (
) and a minimum (
).
Sinusoidal functions have in most cases the following form:
(1)
Where:
- Angular frequency
- Angular phase, in radians.
If we know that 
, 
, 
, 
and 
, then the sinusoidal function is:
(2)
(3)
The resulting system is:
(2b)
(3b)
By applying <em>inverse trigonometric </em>functions we have that:
, 
(2c)
, (3c)
And we proceed to solve this system:
, 
By (2c):
The equation that represents the <em>sinusoidal</em> function is , .
To learn more on functions, we kindly invite to check this verified question: brainly.com/question/5245372
Answer:
t = - 1/8
Step-by-step explanation:
t ÷ 5/12 = - 3/10
t × 12 ÷ 5 = - 3/10
12t/5 = - 3/10
12t × 10 = -3 × 5
120t = - 15
t = - 15/120
t = - 1/8
Thus, t divided 5/12 = - 3/10 => -1/8
<u>-TheUnknown</u><u>S</u><u>c</u><u>ientist</u>
Answer:
-12+18x
Step-by-step explanation:
-3(4-6x)=-12+18x
