A diagonal of a cube measures StartRoot 294 EndRoot cm. The diagonal of a face measures 14 cm. What is the length of an edge of
1 answer:
The side of the edge of the cube is 9. 9cm
<h3>How to determine the length</h3>
Given that the diagonal of a cube measures the square root of 294cm and the diagonal of a face measures 14cm
To find the edge of the face, we know that the face of the cube is a square
Formula for diagonal of a square =
Where is the side of the square
We then have,
Make 'a' the subject
a =
Simplify the surd
a = ×
a =
a =
a = 9. 9cm
Therefore, the side of the edge of the cube is 9. 9cm
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Answer:
Step-by-step explanation:
f(x) = x2 + 2x - 2 should be rewritten using " ^ " to indicate exponentiation:
f(x) = x^2 + 2x - 2.
We find a couple of key points and use the fact that this parabola is symmetric about the line
-2
x = ----------- = -1. When x = -1, y = f(-1) = (-1)^2 + 2(-1) - 2, or 1 - 2 -2, or -3.
2(1)
Thus the vertex is at (-1, -3). The y-intercept is found by letting x = 0: y = -2. The axis of symmetry is x = -1.
Graph x = -1 and then reflect this y-intercept (0, -2) about the line x = -1, obtaining (-2, -2). If necessary, find 1 or two more points (such as the x-intercepts).
To find the roots (x-intercepts), set f(x) = x^2 + 2x - 2 = 0 and solve for x.
Completing the square, we obtain x^2 + 2x + 1 - 2 = + 1, or (x + 1)^2 = 3.
Taking the square root of both sides yields x + 1 = ±√3. One of the two roots is x = 1.732 - 1, or 0.732, so one of the two x-intercepts is (0.732, 0).
Answer:
Step-by-step explanation:
For the surface area we need to add up all the areas in the pyramid:
- area of the base
- area of the triangle sides (there are 4 triangles)
Area of the base:
the base is a square, and the area of a square is given by:
where is the length of the side:
, thus:
Area of the triangles:
one triangle has the area given by the formula:
where is the base of the triangle:
and is the height of the triangle:
, thus we have the following:
the expression that represents the surface area of the pyramid is:
substituting our values:
which is option B