Answer:
<h2>√126</h2>Option D is the right option.
solution,
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A large teepee has slanted sides that measure 10 feet each. The bottom of the teepee measures 4 feet across. What is the height
1 answer:
The height of the teepee is 9.1651 feet.
Step-by-step explanation:
Step 1:
A right-angled triangle can be formed using the given information.
The length of the slanted sides represents the hypotenuse of the triangle. One of the other sides of this right-angled triangle measures 4 feet.
According to the Pythagorean theorem, the square of the hypotenuse is the sum of the squares of the other two sides.
Assume the other side measures a length of x feet.
Step 2:
According to the Pythagorean theorem,
The height of the teepee is 9.1651 feet.
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Step-by-step explanation:
The absolute value function is a well known piecewise function (a function defined by multiple subfunctions) that is described mathematically as
.
This definition of the absolute function can be explained geometrically to be similar to the straight line , however, when the value of x is negative, the range of the function remains positive. In other words, the segment of the line
where
(shown as the orange dotted line), the segment of the line is reflected across the <em>x</em>-axis.
First, we simplify the expression.
.
We, now, can simply visualise the straight line, , as a line having its y-intercept at the point
and its <em>x</em>-intercept at the point
. Then, imagine that the segment of the line where
to be reflected along the <em>x</em>-axis, and you get the graph of the absolute function
.
Consider the inequality
,
this statement can actually be conceptualise as the question
.
Algebraically, we can solve this inequality by breaking the function into two different subfunctions (according to the definition above).
- Case 1 (when
)
- Case 2 (when
)
*remember to flip the inequality sign when multiplying or dividing by
negative numbers on both sides of the statement.
Therefore, the values of <em>x</em> that satisfy this inequality lie within the interval
.
Similarly, on the real number line, the interval is shown below.
The use of open circles (as in the graph) indicates that the interval highlighted on the number line does not include its boundary value (-4 and 2) since the inequality is expressed as "less than", but not "less than or equal to". Contrastingly, close circles (circles that are coloured) show the inclusivity of the boundary values of the inequality.
