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kondor19780726 [428]

3 years ago

9

An n-digit number is a positive number with exactly n digits. Nine hundred distinct n digit numbers are to be formed using only

three digit 5, 7, 9. The smallest value of n for which this is possible is :
(A) 6
(B)7
(C)8
(D)9

1 answer:

kolbaska11 [484]3 years ago

5 0

$\underbrace{3\cdot3\cdot3\cdot\ldots}_{n}\geq900\\\\
3^n\geq900\\\\
\log_3 3^n\geq \log_3900\\\\
n\geq \log_3900\\\\
n\geq\dfrac{\ln 900}{\ln 3}(\approx6.2)$

So, the least $n$ is 7.

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A triangle has vertices at (-1,5), (4,2), and (0,0). What is the perimeter of the triangle

yan [13]

The perimeter of the triangle is 15.4 units.

<u>Step-by-step explanation:</u>

The triangle has vertices at (-1,5), (4,2), and (0,0).

To find the perimeter of the triangle, you need to find the distance of the three points which is the length of the three sides of the triangle.

Let us consider the points as A (-1,5) and B (4,2) and C (0,0).

<u>The distance formula is given by :</u>

⇒ $\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }$

<u>Distance of AB :</u>

A (-1,5) ⇒ (x1,y1)

B (4,2) ⇒ (x2,y2)

⇒ $\sqrt{(4+1)^{2}+(2-5)^{2} }$

⇒ $\sqrt{5^{2}+-3^{2} }$

⇒ $\sqrt{25+9}$

⇒ $\sqrt{34}$

⇒ 5.8

∴ The length of the side AB of the triangle is 5.8 units.

<u>Distance of BC :</u>

B (4,2) ⇒ (x1,y1)

C (0,0) ⇒ (x2,y2)

⇒ $\sqrt{(0-4)^{2}+(0-2)^{2} }$

⇒ $\sqrt{16+4 }$

⇒ $\sqrt{20}$

⇒ 4.5

∴ The length of the side BC of the triangle is 4.5 units.

<u>Distance of CA :</u>

C (0,0) ⇒ (x1,y1)

A (-1,5) ⇒ (x2,y2)

⇒ $\sqrt{(-1-0)^{2}+(5-0)^{2} }$

⇒ $\sqrt{1+25}$

⇒ $\sqrt{26}$

⇒ 5.1

∴ The length of the side CA of the triangle is 5.1 units.

Now, the perimeter of the triangle is given by :

Perimeter = Sum of the lengths of all three sides of the triangle.

⇒ 5.8 + 4.5 + 5.1

⇒ 15.4 units.

∴ The perimeter of the triangle is 15.4 units.

4 0

3 years ago

What is the distance between these two points

irakobra [83]

Answer:

pretty sure it is 11

7 0

3 years ago

The amount of fertilizer needed for a lawn varies directly with the area of the lawn Mr. Dundee lawn is a rectangular shape and

FrozenT [24]

Answer:

39 pounds is needed

Step-by-step explanation:

Given

Lawn Dimension: 78' by 93'

4 pounds fertilizer for 750ft² area

Required

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First, we need to calculate the area of the lawn

$Area = 78' * 93'$

' means feet

So:

$Area = 78ft * 93ft$

$Area = 7254 ft^2$

Let the amount of fertilizer need be x

So, we have:

4 pounds = 750ft²

and

x = 7254ft²

Cross Multiply:

$x * 750 = 4 * 7254$

$x * 750 = 29016$

Solve for x

$x = 29016/750$

$x = 38.688$

<em></em> $x = 39$ <em> (approximated)</em>

4 0

3 years ago

Find the value of 8!.

skelet666 [1.2K]

Answer:

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Step-by-step explanation:

! means take that number and multiply all the numbers down to 1

8! means

8*7*6*5*4*3*2*1 =40320

5 0

3 years ago

Read 2 more answers

Simplify the expressions.<br><br> i32 = <br><br> i25 = <br><br> i86 = <br><br> i51 =

maw [93]

Simplify the expression using the definition of an imaginary number i = sqrt -1

i32 = 1

i25 = i

i86 = -1

i51 = -i

3 0

3 years ago