Answer:
Domain : {x | all real numbers} ; Range: {y | y > 0}
Step-by-step explanation:
The function can be written as :
![f(x)=\sqrt[\frac{2}{3}]{108^{2\cdot x}}\\\\\implies f(x)=(108)^{(\frac{3}{2})^{2\cdot x}}](https://tex.z-dn.net/?f=f%28x%29%3D%5Csqrt%5B%5Cfrac%7B2%7D%7B3%7D%5D%7B108%5E%7B2%5Ccdot%20x%7D%7D%5C%5C%5C%5C%5Cimplies%20f%28x%29%3D%28108%29%5E%7B%28%5Cfrac%7B3%7D%7B2%7D%29%5E%7B2%5Ccdot%20x%7D%7D)
Now, since x is exponent so it can take any real values. So, its domain of f(x) is all real numbers
But value of f(x) can not be less than 1 because for x = 0 the value of f(x) is 1 and also for any values of x, the value of f(x) can never be less than 1
So, Range of f(x) is all real numbers greater than 0
Hence, Domain and Range of f(x) is given by :
Domain : {x | all real numbers} ;
Range: {y | y > 0}
Wheres the table?
once you get it I would be glad to help!
r
sin
θ
=
−
3
Explanation:
Imagine we have a point
P
with Rectangular (also called Cartesian) coordinates
(
x
,
y
)
and Polar coordinates
(
r
,
θ
)
.
The following diagram will help us visualise the situation better:
https://keisan.casio.com/exec/system/1223526375
https://keisan.casio.com/exec/system/1223526375
We can see that a right triangle is formed with sides
x
,
y
and
r
, as well as an angle
θ
.
We have to find the relation between the Cartesian and Polar coordinates, respectively.
By Pythagora's theorem, we get the result
r
2
=
x
2
+
y
2
The only properties we can say about
θ
are its trigonometric functions:
sin
θ
=
y
/
r
⇒
y
=
r
sin
θ
cos
θ
=
x
/
r
⇒
x
=
r
cos
θ
So we have the following relations:
⎧
⎪
⎨
⎪
⎩
r
2
=
x
2
+
y
2
y
=
r
sin
θ
x
=
r
cos
θ
Now, we can see that saying
y
=
−
3
in the Rectangular system is equivalent to say
r
sin
θ
=
−
3
Answer link
Jim G.
May 19, 2018
r
=
−
3
sin
θ
Explanation:
to convert from
cartesian to polar
∙
x
x
=
r
cos
θ
and
y
=
r
sin
θ
⇒
r
sin
θ
=
−
3
⇒
r
=
−
3
sin
θ
this can be turned into an equation to be solved more easily. so the amount of bananas can be x. there are 17 peaches. So the equation would be:
(17 - 3) ÷ 2 = x
you begin with what's inside the parenthesis
17 - 3 = 14.
14 ÷2 = 7
x = 7
there are 7 bananas in the bag of bananas
