What is the length of the diagonal, ddd, of the rectangular prism shown below?
1 answer:
Answer:
≈ 9.6 units
Step-by-step explanation:
<em>Refer to attachment</em>
The diagonal d is the hypotenuse of right triangle with sides of 5 and a
The line a is the hypotenuse of the right triangle with the sides of 2 and 8.
<u>So, as per Pythagorean theorem:</u>
- d² = 5² + a²
- d²= 5² + 2²+ 8² = 25 + 4 + 64 = 93
- d² = 93
- d = √93
- d ≈ 9.6 units (rounded to the nearest tenth)
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Answer as a compound inequality:
Answer in interval notation: [-4, 2)
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Explanation:
The range is the set of all possible y outputs of a function. When dealing with a graph like this, we just look at the highest and lowest points to determine which y values are possible.
The lowest point occurs when y = -4. We include this value. So far we have which is the same as
The upper ceiling for the y value is y = 2. We can't actually reach this value because of the open hole at (-3,2). So we say that
Combine and
to get the compound inequality
This says y is between -4 and 2, including -4 but excluding 2.
To convert this to interval notation, we write [-4, 2) where the square bracket says to include the endpoint and the curved parenthesis says to exclude the endpoint.