To the nearest square inch, what is the area of the figure?
309
118
64
49
Answer:
309in²
Step-by-step explanation:
Area of an octagon is expressed as;
A=2(1+√2)a²
a is the side length of the octagon
Given
a = 8
Substitute into the formula
A = 2(1+√2)(8)²
A = 2(1+√2)(64)
Expand
A = 2(64+64√2)
A = 128+128√2
A = 128+128(1.414)
A = 128+181.01
A = 309in²
Hence the area of the octagon is 309in²
B.$5607.42
C.$4846.84
D.$22,429.68
Answer:
Angelica's gross income from the two jobs last year is $22,429.68
Step-by-step explanation:
Angelica had two jobs last year, and she received two W-2 forms.
On the first W-2 form, the figure in box 1 was $13,638.26,
while on the second W-2 form, the figure in box 1 was $8791.42.
Income from first job is $13,638.26
Income from second job is $8791.42
Total income = first job income + second job income
=13638.26 + 8791.42 = 22,429.68
Angelica's gross income from the two jobs last year is $22,429.68
To convert the ratio 9 yards to 48 feet into a fraction in simplest form, we need to first convert 9 yards into feet, which is 27 feet. Then, we express this ratio as a fraction, 27/48. To simplify this fraction, we divide both numerator and denominator by their GCD, which is 3, resulting in 9/16.
The student has asked to express the ratio 9 yards to 48 feet as a fraction in simplest form. Given that 1 yard equals 3 feet, we first need to convert 9 yards to feet. So, 9 yards * 3 feet/1 yard = 27 feet.
Now, let's express 27 feet to 48 feet as a fraction. The ratio is 27:48, and we can write this as the fraction 27/48. However, this is not the simplest form. We simplify a fraction by dividing both the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD). The GCD of 27 and 48 is 3. Therefore, we divide 27 and 48 by 3 to get 9/16. So, the fraction in simplest form is 9/16.
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The volume generated by rotating the region in the first quadrant bounded by y = ex and the x-axis from x = 0 to x = ln(3) about the y-axis is (πln(3)3)/3.
To find the volume generated by rotating the region in the first quadrant bounded by y = ex and the x-axis from x = 0 to x = ln(3) about the y-axis, we can use the disk method. The disk method involves slicing the region into thin disks and adding up their volumes.
The volume of each disk is πr2h, where r is the radius of the disk and h is the thickness of the disk. In this case, the radius of each disk is x and the thickness is dx.
So, the volume of the region is:
V = ∫0ln(3)πx2dx
We can use the power rule for integration to solve this integral:
V = π∫0ln(3)x2dx = π[(x3)/3]0ln(3) = π[(ln(3)3)/3 - (03)/3] = (πln(3)3)/3
Therefore, the volume generated by rotating the region in the first quadrant bounded by y = ex and the x-axis from x = 0 to x = ln(3) about the y-axis is (πln(3)3)/3. This is the exact form of the volume.
To know more about disk method refer here:
brainly.com/question/28184352#
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21x>2 should be the answer