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1 year ago

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A number m is formed by writing all the prime numbers between 0 and 10 in ascending order. another number n is formed by writing

all the square numbers between 0 and 10 in descending order: a)find m -n b)express(m-n) as a product of its prime factors

1 answer:

Brums [2.3K]1 year ago

3 0

Answer:

(a) 1416

(b) 2 × 2 × 2 × 3 × 59

Step-by-step explanation:

The prime numbers between 0 and 10 are 2, 3, 5,7 (1 is not considered prime)
Therefore m = 2357

The square numbers between 0 and 10 are 1, 4, 9 and in descending order 9,4.1so n = 941

m - n = 2357 - 941 = 1416

Unique prime factors of 1416 are 2,3,59

1416 as a product of prime factors = 2 × 2 × 2 × 3 × 59

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1. The company has agreed on a 9- character password format, comprised of uppercase letters, lower case letters, and digits (0-9

pochemuha

Answer: a) 1977060966, b) 146581344.

Step-by-step explanation:

Since we have given that

There are 10 numbers,

There are 26 lower case letters,

There are 26 upper case letters,

Since the first 3 characters have to be digits and next 6 can be upper or lower.

So, a) repetitions are allowed:

$10^3\times (26+26)^6\\\\=10^3\times 52^6\\\\=1977060966$

b) repetitions are not allowed:

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Hence, a) 1977060966, b) 146581344.

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2 years ago

Write this expression in simplified form.<br> -5x^6*9x^5

masya89 [10]

Answer:

-45x^11

Step-by-step explanation:

-5x^6 * 9x^5

Multiply -5x and 9x together:

-45x

Remember when multiplying powers, you add them together, which leaves you with:

-45x^11

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2 years ago

Consider the polynomial equation x(x - 3)(x + 6) (x-7) -0. Which of the following are zoros of the

Black_prince [1.1K]

Answer:

The zeros are : 0, 3, -6, 7.

Step-by-step explanation:

Zeros of a polynomial is the values at which the polynomial becomes zero. They are also called the roots of the polynomial.

When (x - a)(x - b) = 0, we can say that either (x - a) = 0 or (x - b) = 0. At least one zero renders the whole equation to be zero.

Now, we are given that: x. (x - 3). (x + 6). (x - 7) = 0

⇒ To make the equation zero, at least one of the following should be true:

x = 0

x - 3 = 0 ⇒ x = 3

x + 6 = 0 ⇒ x = -6

x - 7 = 0 ⇒ x = 7

Therefore, x can take any one of the above values and that would make the polynomial zero.

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2 years ago

The back of a dog house is composed of a square and a triangle . How much wood wood is needed for the back of the dog house to t

Anastaziya [24]

Answer:

68

Step-by-step explanation:

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2 years ago

The surface area of a right circular cone of radius r and height h is S = πr√ r 2 + h 2 , and its volume is V = 1 3 πr2h. What i

kirill115 [55]

Answer:

Required largest volume is 0.407114 unit.

Step-by-step explanation:

Given surface area of a right circular cone of radious r and height h is,

$S=\pi r\sqrt{r^2+h^2}$

and volume,

$V=\frac{1}{3}\pi r^2 h$

To find the largest volume if the surface area is S=8 (say), then applying Lagranges multipliers,

$f(r,h)=\frac{1}{3}\pi r^2 h$

subject to,

$g(r,h)=\pi r\sqrt{r^2+h^2}=8\hfill (1)$

We know for maximum volume $r\neq 0$ . So let $\lambda$ be the Lagranges multipliers be such that,

$f_r=\lambda g_r$

$\implies \frac{2}{3}\pi r h=\lambda (\pi \sqrt{r^2+h^2}+\frac{\pi r^2}{\sqrt{r^2+h^2}})$

$\implies \frac{2}{3}r h= \lambda (\sqrt{r^2+h^2}+\frac{ r^2}{\sqrt{r^2+h^2}})\hfill (2)$

And,

$f_h=\lambda g_h$

$\implies \frac{1}{3}\pi r^2=\lambda \frac{\pi rh}{\sqrt{r^2+h^2}}$

$\implies \lambda=\frac{r\sqrt{r^2+h^2}}{3h}\hfill (3)$

Substitute (3) in (2) we get,

$\frac{2}{3}rh=\frac{r\sqrt{R^2+h^2}}{3h}(\sqrt{R^2+h^2+}+\frac{r^2}{\sqrt{r^2+h^2}})$

$\implies \frac{2}{3}rh=\frac{r}{3h}(2r^2+h^2)$

$\implies h^2=2r^2$

Substitute this value in (1) we get,

$\pi r\sqrt{h^2+r^2}=8$

$\implies \pi r \sqrt{2r^2+r^2}=8$

$\implies r=\sqrt{\frac{8}{\pi\sqrt{3}}}\equiv 1.21252$

Then,

$h=\sqrt{2}(1.21252)\equiv 1.71476$

Hence largest volume,

$V=\frac{1}{3}\times \pi \times\frac{\pi}{8\sqrt{3}}\times 1.71476=0.407114$

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2 years ago