The value of n given the form of the function is (b) positive odd number
<h3>How to interpret the graph?</h3>
The form of the graph is given as:
f(x) = a(x + k)^1/n + c
For the given graph, we have the following features:
a > 0 --- a is positive
k > 0 --- k is positive
c < 0 --- c is negative
If n is an even number, the function would be undefined because the even root of a number is undefined
However, the function is defined if n is an odd number,
Hence, the value of n given the form of the function is a positive odd number
Read more about functions at:
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Answer:
See Explanation
Step-by-step explanation:
![A+B= 45 \degree \\ \\ assuming \: \tan \: on \: both \: sides \\ \\\implies \: \tan( A+B)= \tan 45 \degree \\ \\ \implies \: \tan( A+B)= 1 \: \: \\ ( \because \: \tan 45 \degree = 1) \\ \\ \implies \: \frac{\tan \: A +\tan \: B }{1 - \tan \: A .\tan \: B } = 1 \\ \\ \implies \: \tan \: A +\tan \: B = 1 - \tan \: A .\tan \: B \\ \\ \purple{ \implies }\: \orange{ \bold{\tan \: A +\tan \: B + \tan \: A .\tan \: B= 1 }} \\ \\ thus \: proved](https://tex.z-dn.net/?f=A%2BB%3D%2045%20%5Cdegree%20%5C%5C%20%20%5C%5C%20assuming%20%20%5C%3A%20%20%5Ctan%20%5C%3A%20on%20%5C%3A%20both%20%5C%3A%20sides%20%5C%5C%20%20%5C%5C%5Cimplies%20%5C%3A%20%5Ctan%28%20A%2BB%29%3D%20%20%5Ctan%2045%20%5Cdegree%20%5C%5C%20%20%5C%5C%20%20%5Cimplies%20%5C%3A%20%5Ctan%28%20A%2BB%29%3D%20%201%20%5C%3A%20%20%5C%3A%20%5C%5C%20%20%28%20%20%5Cbecause%20%5C%3A%20%5Ctan%2045%20%5Cdegree%20%3D%201%29%20%5C%5C%20%20%5C%5C%20%5Cimplies%20%5C%3A%20%20%5Cfrac%7B%5Ctan%20%5C%3A%20A%20%2B%5Ctan%20%5C%3A%20B%20%7D%7B1%20-%20%5Ctan%20%5C%3A%20A%20.%5Ctan%20%5C%3A%20B%20%7D%20%20%3D%201%20%5C%5C%20%20%5C%5C%20%5Cimplies%20%5C%3A%20%5Ctan%20%5C%3A%20A%20%2B%5Ctan%20%5C%3A%20B%20%3D%201%20-%20%5Ctan%20%5C%3A%20A%20.%5Ctan%20%5C%3A%20B%20%5C%5C%20%20%5C%5C%20%5Cpurple%7B%20%5Cimplies%20%7D%5C%3A%20%20%5Corange%7B%20%5Cbold%7B%5Ctan%20%5C%3A%20A%20%2B%5Ctan%20%5C%3A%20B%20%20%2B%20%5Ctan%20%5C%3A%20A%20.%5Ctan%20%5C%3A%20B%3D%201%20%7D%7D%20%5C%5C%20%20%5C%5C%20thus%20%5C%3A%20proved)
Answer:
a) Q(-2,1) is false
b) Q(-5,2) is false
c)Q(3,8) is true
d)Q(9,10) is true
Step-by-step explanation:
Given data is
is predicate that
then
. where
are rational numbers.
a)
when ![x=-2, y=1](https://tex.z-dn.net/?f=x%3D-2%2C%20y%3D1)
Here
that is
satisfied. Then
![(-2)^{2}](https://tex.z-dn.net/?f=%28-2%29%5E%7B2%7D%3C1%5E%7B2%7D)
this is wrong. since ![4>1](https://tex.z-dn.net/?f=4%3E1)
That is ![x^{2}](https://tex.z-dn.net/?f=x%5E%7B2%7D)
Thus
is false.
b)
Assume
.
That is ![x=-5, y=2](https://tex.z-dn.net/?f=x%3D-5%2C%20y%3D2)
Here
that is
this condition is satisfied.
Then
![(-5)^{2}](https://tex.z-dn.net/?f=%28-5%29%5E%7B2%7D%3C2%5E%7B2%7D)
this is not true. since
.
This is similar to the truth value of part (a).
Since in both
satisfied and
for both the points.
c)
if
that is
and
Here
this satisfies the condition
.
Then ![3^{2}](https://tex.z-dn.net/?f=3%5E%7B2%7D%20%3C8%5E%7B2%7D)
This also satisfies the condition
.
Hence
exists and it is true.
d)
Assume ![Q(x,y)=Q(9,10)](https://tex.z-dn.net/?f=Q%28x%2Cy%29%3DQ%289%2C10%29)
Here
satisfies the condition ![x](https://tex.z-dn.net/?f=x%3Cy)
Then ![9^{2}](https://tex.z-dn.net/?f=9%5E%7B2%7D%3C10%5E%7B2%7D)
satisfies the condition
.
Thus,
point exists and it is true. This satisfies the same values as in part (c)
Answer:
29.42 units
Step-by-step explanation:
<u>1) Find the perimeter around the semi-circle</u>
To do this, we find the circumference of the circle using the given diameter:
where d is the diameter
Plug in 6 as the diameter
![C=\pi (6)\\C=6\pi](https://tex.z-dn.net/?f=C%3D%5Cpi%20%286%29%5C%5CC%3D6%5Cpi)
Divide the circumference by 2
![\frac{6\pi }{2} \\= 3\pi](https://tex.z-dn.net/?f=%5Cfrac%7B6%5Cpi%20%7D%7B2%7D%20%5C%5C%3D%203%5Cpi)
Therefore, the perimeter around the semi-circle is 3π units.
<u>2) Find the perimeter around the rest of the shape</u>
Although it's impossible to determine the lengths of the varied sides on the right side of the shape, we know that all of those <em>vertical</em> sides facing the right add up to 6. We also know that all of those <em>horizontal </em>sides facing up add up to 7. Please refer to the attached images.
Therefore, we add the following:
7+6+7
= 20
Therefore, the perimeter around that area of the shape is 20 units.
<u>3) Add the perimeter around the semi-circle and the perimeter around the rest of the shape</u>
![20+3\pi \\= 20+9.42\\= 29.42](https://tex.z-dn.net/?f=20%2B3%5Cpi%20%5C%5C%3D%2020%2B9.42%5C%5C%3D%2029.42)
Therefore, the perimeter of the shape is approximately 29.42 units.
I hope this helps!