Answer: the answer is base of triangle, height of triangle
got it wrong because of that other guy answers was wrong
Answer:
perimeter of square
Step-by-step explanation:
9
B.
18
C.
36
D.
54
Answer:
The LCM of the numbers 3, 6, and 9, is 18.
Step-by-step explanation:
The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.
The required, there is no part of the sphere x² + y² + z² = 16 that lies above the cone z = x² + y², where z > x² + y².
To find the part of the sphere x² + y² + z² = 16 that lies above the cone z = x² + y², where z > x² + y², we can use spherical coordinates. In spherical coordinates, the equations for the sphere and the cone are simpler.
Spherical coordinates are represented as (ρ, θ, φ), where ρ is the radial distance, θ is the azimuthal angle (measured from the positive x-axis in the xy-plane), and φ is the polar angle (measured from the positive z-axis).
For the sphere x² + y² + z² = 16, the spherical representation is:
ρ = 4 (since ρ² = x² + y² + z² = 16)
For the cone z = x² + y², the spherical representation is:
ρ = ρ (since ρ^2 = x² + y²)
Now, to find the part of the sphere that lies above the cone (z > x² + y^2), we need to restrict the values of φ.
When z > x² + y², we have z = ρ cos(φ) > ρ².
Since ρ = 4, we get 4 cos(φ) > 4², which simplifies to cos(φ) > 4.
However, the range of φ in spherical coordinates is 0 ≤ φ ≤ π, which means that the values of φ that satisfy cos(φ) > 4 are not within the valid range.
Therefore, there is no part of the sphere x² + y² + z² = 16 that lies above the cone z = x² + y², where z > x² + y².
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We use the given equations of the sphere and cone and express them in spherical coordinates. The sphere lies on or above the cone when z's value in the sphere equation is greater or equal than z's value in the cone equation. One method is to use spherical coordinates and represent the radius and polar angle in terms of u and v.
The question involves spherical and rectangular coordinates and the relationship between the two. We are given the sphere's equation as x^2 + y^2 + z^2 = 16 and the cone's equation as z = x^2 + y^2. Here's one way to think of the part of the sphere that lies on or above the cone. If we view z=x^2 + y^2 as a function of x and y, the sphere lies above this cone when z's value in the equation of the sphere is greater or equal to the value of z in the cone's equation. To express x, y, and z in terms of u and/or v, you can use a method such as spherical coordinates.
In spherical coordinates, the relationship between spherical and rectangular coordinates can be represented as:
Here r, θ, and φ are the radius, polar, and azimuthal angles respectively, which we can let u and v represent. One potential assignment is to let r=u and θ=v, assuming we want only two parameters.
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1/4
1/8
1/10
1/6
Answer:
x < 3
Step-by-step explanation:
Divide both sides by 2.
(2x)/2 < 6/2
x < 3
_____
An inequality is solved the same way an equation is solved, with one exception. If an operation is performed that changes ordering, then the comparison symbol is reversed. The usual case is multiplication or division by a negative number:
2 > 1
-2 < -1 . . . . both sides multiplied by -1
Answer: A (Vertical Lines)
Step-by-step explanation:
The slope of a line passing through points (7,-4) and (7,0) is undefined. This is because a line with the same x-coordinate for two different y-coordinates implies a vertical line, which has an undefined slope. Therefore, the correct answer is A. Undefined (vertical line).
The slope of a line passing through two points (x1,y1) and (x2,y2) is defined by the formula slope = (y2 - y1) / (x2 - x1). Given the two points are (7,-4) and (7,0), we use the formula and get slope = (0 - (-4)) / (7 - 7). This results in 0/0 which is undefined mathematically. Furthermore, when a line has the same x-coordinate for two different y-coordinates, it implies the line is vertical. Thus, we can decide that the line passing through those points is indeed a vertical line, and the slope is undefined; as vertical lines have undefined slopes.
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