ANSWER:
Let the smallest integer = x
x + x + 1 = 3 ( x + 2 ) - 17
2x + 1 = 3x + 6 - 17
2x - 3x = 6 - 17 - 1
- x = - 12
x = 12
FINAL ANSWER:
Therefore, the smallest integer is 12.
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Option (C) -: The hotel floors are parallel to each other, and the elevator moves in a path that is perpendicular to them both.
<h3>What is parallel and perpendicular ?</h3>
In geometry two lines are parallel to each other when they have no intersecting point and the distance between them is constant.
Two lines are perpendicular if they have an intersecting point and they intersect each other at at 90°.
From the given figure we can observe the distance between the floor ceiling of 3rd and 6th floor is constant therefore they are parallel to each other.Now if we imagine the elevator going up and down an imaginary line (meeting line of two elevator doors) would intersect them at an angle of 90°.
∴The hotel floors are parallel to each other, and the elevator moves in a path that is perpendicular to them both.
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Answer:
C(t)=5000 -10t
Step-by-step explanation:
There are many examples in the real world of relationships that are functions.
For example, imagine a tank full of water with a capacity of 5000 liters, this tank has a small hole, by which 10 liters of water are lost every hour.
If we call C the amount of water in the tank as a function of time, then we can write the following equation for C:
Where:
C (t): Amount of water in the tank as a function of time
: Initial amount of water in the tank at time t = 0
a: amount of water lost per hour
t: time in hours
Then the equation is:
The graph of C (t) is a line of negative slope. This relation is a function since for each value of t there is a single value of C.
Its domain is the set of all positive real numbers t between [0,500]
Because the time count starts at t = 0 when the tank is full and ends at t = 500 when empty
Its Range is the set of all positive real numbers C between [0,5000] Because the amount of water in the tank can never be less than zero or greater than 5000Litres
Step-by-step explanation:
The answer is OPTION C
Find the Inverse of a 3x3 Matrix.
First
Find the Determinant of A(The coefficients of e
Proceed towards finding the CO FACTOR of the 3x3 Matrix.
+. - +
A= [ 1 -1 -1 ]
[ -1 2 3 ]
[ 1 1 4 ]
The determinant of this is 1.
Find the co factor
| 2 3 | |-1 3 | |-1 2 |
| 1. 4. | |1 4 | |1. 1 |
|-1. -1 | |1 -1 | |1 -1
| 1. 4 | |1. 4| |1 1|
|-1. -1 | |1 -1 | |1. -1
|2. 3| |-1. 3| |-1 2|
After Evaluating The Determinant of each 2x 2 Matrix
You'll have
[ 5 7 -3]
[3 5 -2 ]
[-1 -2 1]
Reflect this along the diagonal( Keep 5,5 -2)
Then switching positions of other value
No need of Multiplying by the determinant because its value is 1 from calculation.
After this
Our Inverse Matrix Would be
[ 5 3 -1 ]
[7 5 -2 ]
[ -3 -2 1]
THIS IS OUR INVERSE.
SO
OPTION C
Answer:
-sqrt(3)/2
Step-by-step explanation:
Use double angle identity for sin(2x)
sin(2x)=2sin(x)cos(x)
We are given sin(x)=-1/2 so we already have so far that:
sin(2x)=2(-1/2)cos(x)
sin(2x)=-1*cos(x)
We just need to find cos(x).
x is in the fourth quadrant so cosine will be positive there
knowing the unit circle we should know that if sin(x)=-1/2 then cos(x)=sqrt(3)/2 while in 4th quadrant.
So the answer is sin(2x)=-1*sqrt(3)/2=-sqrt(3)/2
