The formula for slope is y=mx+b
so if you re arrange the equation from 8y-16x=12
to 8y=16x+12
the slope will be the coefficient of x =16
The total surface area of the remaining solid is 48(4+✓3) centimeters square.
<h3>How to calculate the surface area?</h3>
Through a regular hexagonal prism whose base edge is 8 cm and the height is 12 cm, a hole in the shape of a right prism.
The formula for the total surface area will be:
= Total surface area=2(area of the base)+ parameter of base × height
where,
Height= 8cm
Parameter of base=12(2) = 24
Area of the base= 6×✓3/4×4² = 64✓3/4
The surface area of the remaining solid will be:
= 2(64✓3/4) + 24 × 8
= 2(64✓3/4 + 192
With the hole is a rhombus prism with the following parameters:
diagonal 1 = 6, diagonal 2 = 8, height = 12
The volume is:
V1 =0.5 × d1 × d2 × h
V1 = 0.5 × 6 × 8 × 12
V1 = 96
The dimensions of the hexagonal prism are:
Base edge (a) = 8
Height (h) = 12
The volume is
V2 = (3✓(3)/2)a²h
V2 = (3✓3)/2) × 8² × 12
V2 = 1152✓3
The remaining volume is
V = V2 -V1
V = 1152✓3 - 96
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The answer is e, 3 3/4
if you add 3/4+3/4+3/4+3/4+3/4 (five times for the five batches), or did 3/4 * 5, you would get 15/4, which simplifies to 3.75, or 3 3/4
ITS MUltipling by 3 silly its 243
The geometric series is convergent and the value is 16.
<h3>How to illustrate the information?</h3>
Recall that the sum of an infinite geometric series, S, given first term, t_1, and common ratio, r, is given by:
S = t_1/(1 - r)
Note that:
3 = (4)(3/4)
9/4 = (3)(3/4)
27/16 = (9/4)(3/4)
So this a geometric series with t_1 = 4 and r = 3/4. Therefore:
4 + 3 + 9/4 + 27/16 + ... = 4/(1 - 3/4) = 4/(1/4) = 16
The correct option is 16.
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Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum
4+3+ 9/4 +27/16 +???
choices are
1. 3/4
2. 12
3. 4
4. divergent
5. 16
