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3 years ago

How many distinct permutations of the word ADDRESSEE are there?

Mathematics

1 answer:

kaheart [24]3 years ago

3 0

Answer: There are 15120 distinct permutations.

Step-by-step explanation:

Since we have given that

ADDRESSEE

Here, 1 A,

2 D

2 S

3 E

Total number of letters in this word = 9

So, Number of permutations would be

$\dfrac{9!}{3!\times 2!\times 2!}\\\\=15120$

Hence, there are 15120 distinct permutations.

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The first hole of a golf course is 250 metres long. A golfer hits her drive exactly 250 m,

Serga [27]

Answer: A golfer finds himself in two different situations on different holes. On the second hole he is 120 m from the green and wants to hit the ball 90 m

Step-by-step explanation:

7 0

1 year ago

(p²-pq + q²) ( 3p+ 3q)

RUDIKE [14]

Answer:

3p^3 + qp^2 - pq^2 + 3q^3

Step-by-step explanation:

(p²-pq + q²) ( 3p+ 3q)

3p^3 + 3qp^2 - 3qp^2 - 3pq^2 + 3pq^2 + 3q^3

3p^3 + qp^2 - pq^2 + 3q^3

3 0

2 years ago

Help out please thank you

Helga [31]

Answer:

x = 26

Step-by-step explanation:

The three angles form a straight line, so they will sum to 180

4x - 8 + 34 + 76- x = 180

Combine like terms

3x+ 102 = 180

Subtract 102 from each side

3x+102-102 = 180-102

3x= 78

Divide each side by 3

3x/3 = 78/3

x = 26

3 0

3 years ago

What is the answer to <br>|5 + -4|

luda_lava [24]

$|a|=\left\{\begin{array}{ccc}a&if&a\geq0\\-a&if&a < 0\end{array}\right\\\\|5+(-4)|=|5-4|=|1|=1$

3 0

3 years ago

3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k

Andreas93 [3]

a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

$\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt$

Evaluate the integral to solve for y :

$\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt$

$\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x$

$\displaystyle y = x^3+2x^2+kx - 2$

Use the other known value, f(2) = 18, to solve for k :

$18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}$

Then the curve C has equation

$\boxed{y = x^3 + 2x^2 + 2x - 2}$

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

$\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2$

The slope of the given tangent line $y=x-2$ is 1. Solve for a :

$3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1$

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).

Decide which of these points is correct:

$x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1$

So, the point of contact between the tangent line and C is (-1, -3).

7 0

2 years ago