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3 years ago

Solve and share these questions

Mathematics

1 answer:

Ad libitum [116K]3 years ago

4 0

1. p ≤ 5
2. v < 9
3. g ≠ 8
4. d ≥ 6
5. t > 2

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What is k if : k!+48=48((k+1)^m)

lys-0071 [83]

Answer:

The value of k is greater than or equal to 0, i.e. k≥7.

Step-by-step explanation:

The given equation is

$k!+48=48((k+1)^m)$

The value of k must be a positive integer because k! is defined for k≥0, where k∈Z.

Subtract 48 from both the sides.

$k!=48((k+1)^m)-48$

$k!=48((k+1)^m-1)$

$k!=48(k+1-1)(\frac{(k+1)^m-1}{(k+1)-1})$

Using $[\frac{r^m-1}{r-1}=r^{m-1}+r^{m-2}+...+1]$ , we get

$k!=48k((k+1)^{m-1}+(k+1)^{m-2}+...+1)$

Divide both sides by 48k.

$\frac{k!}{48k}=(k+1)^{m-1}+(k+1)^{m-2}+...+1$

$\frac{k(k-1)!}{48k}=(k+1)^{m-1}+(k+1)^{m-2}+...+1$

$\frac{(k-1)!}{48}=(k+1)^{m-1}+(k+1)^{m-2}+...+1$

Note: The value of m can be 0 or 1.

The value of k is positive integer, so the right hand side of the above equation must be a positive integer.

Since RHS of the equation is positive integer, therefore (k-1)! is completely divisible by 48.

$k-1\geq 6$

Add 1 on both sides.

$k\geq 6+1$

$k\geq 7$

Therefore the value of k is greater than or equal to 0.

4 0

4 years ago

See attached image below.<br> Hi can anyone provide me with a solution to this question?

gladu [14]

Answer:

Insert equation into desmos (free online graphing calculator)

the two x intercepts are -0.33333 and 1.5

1.83333 is the answer

4 0

3 years ago

(b) A square has an area of 36 ft? What is the length of each side

chubhunter [2.5K]

The answer is 9 because 36 divided by 4 is 9.

Have a great day.

7 0

3 years ago

Read 2 more answers

How would you estimation to evaluate this expression:<br> 10.2 times(2time3.7)plus 8

Mamont248 [21]

Answer:

Step-by-step explanation:

10.2 × (2 × 3.7) + 8

≈ 10 × (2 × 4) + 8

= 10 × 8 + 8

= 80 + 8

= 88

6 0

4 years ago

Help please. It'd mean a whole lot.

svp [43]

So, the total area of the rectangle is just:

$(2x+11)(2x+6)=4x^2+12x+22x+66=4x^2+32x+66$

The area of the white rectangle is just 66 meters, so the area of the steel frame is $4x^2+32x$ , and we want it to be 28 meters so: $4x^2+32x-28=0 \impliesx= \frac{-32+\sqrt{1472}}{8} \approx .80 cm$

We don't have to consider the other root because it's obviously a negative.

3 0

4 years ago