What is the rational exponent expression of 6 square root of f
1 answer:
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*see attachment for the diagram
Answer:
A. 178 units²
Step-by-step explanation:
Surface area of the figure = (surface area of the square pyramid + surface area of the square prism) - 2(base area of the square pyramid)
✔️Surface area of the square pyramid = s² + 2*s*l
Where,
s = side length of square base (w) = 6 units
l = slant height = ?
Use Pythagorean theorem to find l
l = √((w/2)² + y²)
l = √((6/2)² + 5²) = √(9 + 25)
l = √34
l ≈ 5.8 units
Surface area of the square pyramid = 6² + 2*6*5.8 = 105.6 units²
✔️Surface area of square prism:
SA = 2a² + 4ah
Where,
a = w = 6 units
h = x = 3 units
Substitute
SA = 2(6²) + 4*6*3
= 72 + 72
= 144 units²
✔️base area of the square pyramid = s²
s = w
Base area = 6²
Base area = 36 units²
✅Surface area of the figure = (surface area of the square pyramid + surface area of the square prism) - 2(base area of the square pyramid)
Surface area of the figure = (105.6 + 144) - 2(36)
= 249.6 - 72
= 177.6
≈ 178 units²
The two possible positions of point P are:
(3, -5) and (0.6, 5.8)
<h3>How to find the two possible positions of point P?</h3>
We know that point P lies on the line:
y = 4 - 3*x
And that the distance between P and the origin is √34, then if the coordinates of point P are (x, y), we have that:
Now, we can replace "y" in the distance equation by the linear equation, and also remove the square roots:
Now we can solve the quadratic equation for x:
The solutions are:
So the two solutions are:
x = (24 + 36)/20 = 3
x = (24 - 36)/20 = -0.6
To get the points, we need to evaluate y on these values:
y = 4 - 3*3 = -5 So we have P = (3, -5)
y = 4 - 3*(-0.6) = 2.2 So we have the point (0.6, 5.8)
There are the two possible positions of point P.
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