Answer:
The smallest power of 10 that will exceed 
is 
.
Step-by-step explanation:
We can use the following approach to determine the smallest power of 10 that will exceed M. We can transform that number into scientific notation, which is of the form:
, 
Where:
- Integer part, formed by a digit, which is of the highest order.
- Decimal part, formed by a digit onwards.
- Power grade.
The smallest power of 10 that will exceed M is 
If 
, then, the power grade is number of spaces that dot must be moved leftwards. In this case, dot must be moved 5 spaces on the left. The integer part is 1 and the decimal part is 1852665902. Then, the value of in scientific notation is:
Then, the smallest power of 10 that will exceed is .
Well if rounding it to the tenths is 230 then you would round back down to 200
9514 1404 393
Answer:
470.16 cm²
Step-by-step explanation:
The apothem of the base is used for two purposes: to find the area of the base, and to find the slant height of each face.
The apothem of the base for side length s is ...
s/2 = a·tan(π/8)
a = s/(2·tan(π/8)) ≈ 7.24 cm
The slant height of a triangular face is found using the Pythagorean theorem. The apothem of the base and the height are legs of the right triangle whose hypotenuse is the slant height. For slant height x, we have ...
x² = 10² + a² = 100 +52.46
x ≈ √152.46 ≈ 12.35
__
The area of the 8 triangular faces will be ...
A = 1/2Px . . . . where P is the perimeter of the pyramid
The area of the base will be ...
A = 1/2Pa
So, the total surface area is ...
A = 1/2P(a + x) = (1/2)(8)(6 cm)(7.24 +12.35 cm) ≈ 470.16 cm²
1+tan^2(A) = sec^2(A) [Pythagorean Identities]
tan^2(A)cot(A) = tan(A)[tan(A)cot(A)] = tan(A)[1] = tan(A)
*see photo for complete solution*
