The right answer is -2/3
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Answer:
The measure of arc EF = 41°
Step-by-step explanation:
Given:
Arc DE = 73°
Now, we know from central angle theorem that the measure of central angle by an arc is twice that of the angle made by the same arc at the circumference. Therefore,
Now, we know that sum of all arcs on a circle is equal to 360°.
Therefore, arc DGF + arc DE + arc EF = 360°
Therefore, the measure of the arc EF is 41°.
d) You have a <u>difference of squares</u>:
49y² - 9 = (7y)² - 3²
Recall the identity,
a² - b² = (a - b) (a + b)
So,
49y² - 9 = (7y - 3) (7y + 3)
e) Pull out the common factor 3 from each term:
3x² - 3x - 90 = 3 (x² - x - 30)
Now use the <u>sum-product method</u>. Notice that we can write 30 = 5 • 6, and 5 - 6 = 1, so
3x² - 3x - 90 = 3 (x + 5) (x - 6)
f) Same as in (e), use the <u>sum-product method</u>. Notice that 42 = 7 • 6, and -7 - 6 = -13, so
x² - 13x + 42 = (x - 7) (x - 6)
Formula: V = (2/3) π r 3.
Radius is 3cm.
So, now we can plug it in to solve for the volume.
V = (2/3) π 3^3
First, let's multiply 3^3.
3^3 = 27
Then, 27 x π = 84.82
After, multiply by 2/3.
84.82 x 2/3 = 56.55
Lastly, round 56.55 to the nearest tenth of a cubic centimeter.
56.55 = 56.6
Therefore the volume of a hemisphere with a radius of 3cm is 56.6cm^3.
