A pizza slice is in the shape of a circular sector OAB, with the central angle 0 = 50 deg and a radius of 7cm. 0 A B В Find the
perimeter of the pizza slice. (no answer)
1 answer:
Answer:
<em>The perimeter of the pizza slice is 20.1 cm</em>
Step-by-step explanation:
<u>Perimeter of a Sector of a Circle</u>
The arc length of a sector of a circle of radius r and angle θ is given by:
L = rθ
The angle must be expressed in radians.
The total perimeter of the circular sector, including the two radii, is:
P = rθ + 2r
The pizza slice has a radius of r=7 cm and a central angle of θ=50°
Converting to radians:
The perimeter is:
Calculating:
P = 20.1 cm
The perimeter of the pizza slice is 20.1 cm
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We have that
triangle ABC coordinates
A (0,2) B(2,4) C(0,0)
triangle DEF coordinates
D (2,0) E ( 4,4) F (4,2)
using a graph tool
see the attached figure
therefore
Line 1<span> Segment AC equals 2. Segment FE equals 2. Segment AC is congruent to segment FE
</span>so
Segment AC equals 2-------> is correct
Segment FE equals 2-----> is correct
Segment AC is congruent to segment FE------> is correct
<span>Line 2 ∠A ≅ ∠F------> is correct
</span>
<span>Line 3 Length of segment AB. A (0, 2) B (2, 4) d equals square root of quantity x sub 2 minus x sub 1 squared plus quantity y sub 2 minus y sub 1 squared, d equals square root of quantity 0 minus 2 all squared plus quantity 2 minus 4 all squared, d equals square root of negative 2 squared plus negative 2 squared, d equals square root of 4 plus 4, d equals square root of 8 segment AB = 2.83
</span>
find the distance AB
d=√[(4-2)²+(2-0)²]--------> d=√[4+4]-----> d=√8-----> d=2.83
AB=2.83
so
Line 3 is correct
<span>Line 4 Length of segment DE. D (2, 0) E (4, 4) d equals square root of quantity x sub 2 minus x sub 1 squared plus quantity y sub 2 minus y sub squared, d equals square root of quantity 2 minus 4 all squared plus quantity 0 minus 4 all squared, d equals square root of negative 2 squared plus negative 4 squared, d equals square root of 4 plus 16, then d equals square root of 20 segment DE = 4.47
</span>
find the distance DE
d=√[(4-0)²+(4-2)²]--------> d=√[16+4]-----> d=√20-----> d=4.47
DE=4.47
so
Line 4------> is correct
<span>Line 5 segment AB is congruent with segment DE
AB is not congruent with DE
so
Line 5 is not correct
therefore
the answer is
</span><span>the student make the first mistake in line 5</span><span>
</span>
triangle ABC coordinates
A (0,2) B(2,4) C(0,0)
triangle DEF coordinates
D (2,0) E ( 4,4) F (4,2)
using a graph tool
see the attached figure
therefore
Line 1<span> Segment AC equals 2. Segment FE equals 2. Segment AC is congruent to segment FE
</span>so
Segment AC equals 2-------> is correct
Segment FE equals 2-----> is correct
Segment AC is congruent to segment FE------> is correct
<span>Line 2 ∠A ≅ ∠F------> is correct
</span>
<span>Line 3 Length of segment AB. A (0, 2) B (2, 4) d equals square root of quantity x sub 2 minus x sub 1 squared plus quantity y sub 2 minus y sub 1 squared, d equals square root of quantity 0 minus 2 all squared plus quantity 2 minus 4 all squared, d equals square root of negative 2 squared plus negative 2 squared, d equals square root of 4 plus 4, d equals square root of 8 segment AB = 2.83
</span>
find the distance AB
d=√[(4-2)²+(2-0)²]--------> d=√[4+4]-----> d=√8-----> d=2.83
AB=2.83
so
Line 3 is correct
<span>Line 4 Length of segment DE. D (2, 0) E (4, 4) d equals square root of quantity x sub 2 minus x sub 1 squared plus quantity y sub 2 minus y sub squared, d equals square root of quantity 2 minus 4 all squared plus quantity 0 minus 4 all squared, d equals square root of negative 2 squared plus negative 4 squared, d equals square root of 4 plus 16, then d equals square root of 20 segment DE = 4.47
</span>
find the distance DE
d=√[(4-0)²+(4-2)²]--------> d=√[16+4]-----> d=√20-----> d=4.47
DE=4.47
so
Line 4------> is correct
<span>Line 5 segment AB is congruent with segment DE
AB is not congruent with DE
so
Line 5 is not correct
therefore
the answer is
</span><span>the student make the first mistake in line 5</span><span>
</span>
To solve this equation , we need to write it in quadratic form
To get the equation in quadratic form we replace x^2 with u
can be written as
, Replace u for x^2
So equation becomes
Now we factor the left hand side
-16 and -1 are the two factors whose product is +16 and sum is -17
(u-16) (u-1) = 0
u -16 = 0 so u=16
u-1 =0 so u=1
WE assume u = x^2, Now we replace u with x^2
Now take square root on both sides , x= +4 and x=-4
Now take square root on both sides , x= +1 and x=-1
So zeros of the function are -4, -1, 1, 4