Respuesta :
We have to compare diameters and arrange them in order smallest to greatest
We can see units for option A and B are in square inches so they represents area. So first we will find diameter from area using formula
[tex] A = \pi r^{2} [/tex]
so for choice (A) area is given as [tex] 4.375 \times 10^{7} [/tex]. So plug this in A place in formula and then solve for radius r
[tex] 4.375 \times 10^{7} = \pi r^{2} [/tex]
[tex] \frac{4.375 \times 10^{7}}{\pi} = \frac{\pi r^{2}}{\pi} [/tex]
[tex] 1.393 \times 10^{7} } = r^{2} [/tex]
[tex] \sqrt{1.393 \times 10^{7}} = \sqrt{r^{2}} [/tex]
3731.76 = r
So screw A will have
[tex] diameter = 2 \times r = 2 \times 3731.76 = 7463.52 [/tex] inches
Similarly for choice (E) area is [tex] 1.428 \times 10^{1} = 14.28 [/tex]
so again plug in formula
[tex] A = \pi r^{2} [/tex]
[tex] 14.28 = \pi r^{2} [/tex]
[tex] \frac{14.28}{\pi} = \frac{\pi r^{2}}{\pi} [/tex]
[tex] 4.5477 = r^{2} [/tex]
[tex] \sqrt{4.5477} = \sqrt{r^{2}} [/tex]
2.13201 = r
So screw E will have
[tex] diameter = 2 \times r = 2 \times 2.13201 = 4.26402 [/tex] inches
So diameters of all screws are as follows:
Screw A: 7463.52 inches
Screw B: 1.5 inches
Screw C: [tex] 1\frac{7}{8} = \frac{1\times 8+7}{8} = \frac{15}{8} = 1.875 [/tex] inches
Screw D: 0.25 inches
Screw E: 4.26402 inches
Comparing all numbers 7463.52, 1.5, 1.875, 0.25, 4.26402 we can see that smallest number is 0.25, then comes 1.5, then 1.875 and then 4.26402 and then 7463.52
So order from least to greatest will be screw D (0.25), B(1.5), C(1.875), E (4.26402), A (7463.52).
So thats the order D,B,C,E,A and the final answer
Answer: The order is D, B, C, E, A
Step-by-step explanation:
We need to order from least to greatest the numbers:
A: 4.375x10^7 in^2
B: 1.5 in^2
C: 1 and 7/8 in^2
D: 0.25 in^2
E: 1.428x10^1 in^2
The first thing we need to do is write all the numbers in the same notation, let's use standard notation
A: 4.375x10^7 in^2 = 4.375*10000000 in^2 = 43750000 in^2
B: 1.5 in^2
C: 1 and 7/8 in^2 = ( 1 + 7/8) in^2 = 15/8 in^2 = 1.875 in^2
D: 0.25 in^2
E: 1.428x10^1 in^2 = 1.428*10 in^2 = 14.28 in^2
Now you can see that the order from least to greatest is:
D, B, C, E, A