Pls answer this is due in 30 minutes
1 answer:
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Answer: slope= 1
Step By Step: Slope, sometimes referred to as gradient in mathematics, is a number that measures the steepness and direction of a line, or a section of a line connecting two points, and is usually denoted by m. Generally, a line's steepness is measured by the absolute value of its slope, m. The larger the value is, the steeper the line. Given m, it is possible to determine the direction of the line that m describes based on its sign and value:
A line is increasing, and goes upwards from left to right when m > 0
A line is decreasing, and goes downwards from left to right when m < 0
A line has a constant slope, and is horizontal when m = 0
A vertical line has an undefined slope, since it would result in a fraction with 0 as the denominator. Refer to the equation provided below.
Slope is essentially change in height over change in horizontal distance, and is often referred to as "rise over run." It has applications in gradients in geography as well as civil engineering, such as the building of roads. In the case of a road the "rise" is the change in altitude, while the "run" is the difference in distance between two fixed points, as long as the distance for the measurement is not large enough that the earth's curvature should be considered as a factor. The slope is represented mathematically as:
m =
y2 - y1
x2 - x1
Answer:
Check the two conditions of Subspace.
Step-by-step explanation:
If W is a Subspace of a vector space, V then it should satisft the following conditions.
1) The zero element should be in W.
Zero element can be different for different vector spaces. For examples, zero vector in is (0, 0) whereas, zero element in
is (0, 0 ,0).
2) For any two vectors, and
in W,
should also be in W.
That is, it should be closed under addition.
3) For any vector in W and for any scalar,
in V,
should be in W.
That is it should be closed in scalar multiplication.
The conditions are mathematically represented as follows:
1) 0 W.
2) If then
.
3)
Here V = and W = Set of all (x, y, z) such that
We check for the conditions one by one.
1) The zero vector belongs to the subspace, W. Because (0, 0, 0) satisfies the given equation.
i.e., 0 - 2(0) + 5(0) = 0
2) Let us assume and
are in W.
That means: and
We should check if the vectors are closed under addition.
Adding the two vectors we get:
Rearranging these terms we get:
So, the equation becomes, 0 + 0 = 0
So, it s closed under addition.
3) Let k be any scalar in V. And
This means
Taking k common outside, we get:
The equation becomes k(0) = 0.
So, it is closed under scalar multiplication.
Hence, W is a subspace of .