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Example Questions
Example Question #1 :Calculating The Length Of A Chord
The chord of acentral angle of a circle with areahas what length?
The radiusof a circle with areacan be found as follows:
The circle, the central angle, and the chord are shown below:
By way of the Isosceles Triangle Theorem,can be proved equilateral, so,正确的反应。
Example Question #2 :Calculating The Length Of A Chord
The chord of acentral angle of a circle with areahas what length?
The radiusof a circle with areacan be found as follows:
The circle, the central angle, and the chord are shown below, along with, which bisects isosceles
We concentrate on, a 30-60-90 triangle. By the 30-60-90 Theorem,
and
The chordhas length twice this, or
Example Question #1 :Calculating The Length Of A Chord
The chord of acentral angle of a circle with circumferencehas what length?
A circle with circumferencehas as its radius
.
The circle, the central angle, and the chord are shown below:
By way of the Isosceles Triangle Theorem,can be proved equilateral, so,正确的反应。
Example Question #1041 :Problem Solving Questions
What is the domain of?
all real numbers
all real numbers
The domain of the function specifies the values thatcan take. Here,is defined for every value of, so the domain is all real numbers.
Example Question #1 :How To Graph A Function
What is the domain of?
To find the domain, we need to decide which valuescan take. Theis under a square root sign, socannot be negative.can, however, be 0, because we can take the square root of zero. Therefore the domain is.
Example Question #211 :Advanced Geometry
What is the domain of the function?
To find the domain, we must find the interval on whichis defined. We know that the expression under the radical must be positive or 0, sois defined when. This occurs whenand. In interval notation, the domain is.
Example Question #4 :How To Graph A Function
Define the functionsandas follows:
What is the domain of the function?
The domain ofis the intersection of the domains ofand.andare each restricted to all values ofthat allow the radicandto be nonnegative - that is,
, or
Since the domains ofandare the same, the domain ofis also the same. In interval form the domain ofis
Example Question #5 :How To Graph A Function
Define
What is the natural domain of?
The radical in and of itself does not restrict the domain, since every real number has a real cube root. However, since the expressionis in a denominator, it cannot be equal to zero, so the domain excludes the value(s) for which
27 is the only number excluded from the domain.
Example Question #6 :How To Graph A Function
Define
What is the natural domain of?
Since the expressionis in a denominator, it cannot be equal to zero, so the domain excludes the value(s) for which. We solve forby factoring the polynomial, which we can do as follows:
Replacing the question marks with integers whose product isand whose sum is 3:
Therefore, the domain excludes these two values of.
Example Question #7 :How To Graph A Function
Define.
What is the natural domain of?
The only restriction on the domain ofis that the denominator cannot be 0. We set the denominator to 0 and solve forto find the excluded values:
The domain is the set of all real numbers except those two - that is,
.
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