Answer:
n must be greater than 5 for the product to be greater than 10.
Step-by-step explanation:
10 times 2/5 = 4 (no)
10 times 6/5 = 12 (yes)
10 times 5/5 = 10 (no)
Answer:
f(x) = 1.5x - 0.5x
Step-by-step explanation:
The function of the pattern represented by the pentagonal numbers is the sum of three triangular numbers.
The triangular number general formula
x (x + 1) / 2
For example,
The sequence
1, 3, 6, 10
*
* * *
* * * * * *
* , * *, * * *, * * * *
_____________________________
The pentagonal numbers
The sequence:
1, 5, 12, 22, 35
As shown in the picture can be divided into three triangles
Triangle 2
x (x + 1) / 2
Triangle 1 and 3 (they are triangles one unit smaller than 2)
n (n + 1) / 2
n= x-1
Replacing n
(x-1) ((x-1) + 1) / 2
(x-1) (x) / 2
(x-1) x / 2
______________
Function represents the pattern
Triangle 2 + (Triangle 1 + Triangle 3)
Triangle 1 = Triangle 3
So then,
Triangle 2 + 2* Triangle 1
x (x +1) /2 + 2* (x -1) x/2
Rearranging
0.5 x (x +1) + x(x -1)
0.5x^2 + 0.5x + x^2 -x
(0.5 x^2 + x^2) + (0.5x -x )
1.5 x^2 - 0.5 x
______
Answer:
Step-by-step explanation:
The cross section will have the same shape as the base of the pentagonal prism; the dimensions will be proportionally smaller.
Answer:
ksh 140
Step-by-step explanation:
When a watch is sold for ksh 126 a loss of x% is made, that is( 100 - x)%
Hence, the loss amount = (126 X 100)/(100 - x)
When the same watch is sold for ksh 154 a profit of x% is made, that is (100 + x)%
Hence, the profit amout = (154 X 100)/(100 + x)
Therefore, (126 X 100)/(100 - x) = (154 X 100)/(100 + x)
12600(100 + x) = 15400(100 - x)
1260000 + 12600x = 1540000 - 15400x
28000x = 280000
x = 10%
In that case for a watch sold for ksh 126 a loss 10% is made, that is( 100 - 10)%
Hence, loss amount = (126 X 100)/90 = ksh 140
∴ the buying price is ksh 140
9514 1404 393
Answer:
- 113.0 cm²
- 2464.0 in²
- 95.0 ft²
Step-by-step explanation:
1. The area of a circle is given by the formula ...
A = πr² . . . . . where r is the radius
The radius is shown as 6 cm, so the area is ...
A = (3.14)(6 cm)² = 113.0 cm²
__
2. The radius is shown as 28 in. We note that this is a number divisible by 7, so we choose 22/7 for π.
A = (22/7)(28 in)² = 2464 in² . . . . see comment
__
3. The radius is half the diameter, so is 11/2 = 5.5 ft. Then the area is ...
A = (3.14)(5.5 ft)² = 95.0 ft²
_____
<em>Additional comment</em>
If you use a more exact value of π for problem 2, the area is 2463.0 in². If you use 3.14 as the value of π, the area rounds to 2461.8 in². For these values of pi (3.14 or 22/7), the answer is only good to about 3 significant digits. 2464 has more significant digits, so digits beyond the first 3 may be in error.
