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2 years ago

The number of dogs in a city is declining at a rate of about .08% each

Mathematics

1 answer:

MrRissso [65]2 years ago

6 0

Answer:

There will be 3472 cats in 10 years

Step-by-step explanation:

There were 3500 cats

The number of dogs in a city is declining at a rate of about 0.08% each year.

We are supposed to find the no. of cats in 10 years

Formula : $N(t)=N_0(1-r)^t$

Where N(t) = Remaining cats after t days

$N_0$ = Initial population

r = rate of depreciation

t=time

So, No. of cats remained after 10 years = $3500(1-\frac{0.08}{100})^{10}=3472.100$

Hence There will be 3472 cats in 10 years

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2 years ago

In the diagram below, AB is parallel to CD. What is the value of y?

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3 years ago

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8 months ago

Find the largest prime divisor of $15^6 - 7^6$<img src="https://tex.z-dn.net/?f=Find%20the%20largest%20prime%20divisor%20of%20%2

Novosadov [1.4K]

Answer:

Largest prime factor of the given expression is 379.

Step-by-step explanation:

Given the expression:

$15^6 - 7^6$

To find:

The largest prime factor of the given expression.

Solution:

First of all, let us factorize the given expression.

$15^6 - 7^6\\\Rightarrow (15^3)^2 - (7^3)^2\\\\\text{Using } x^{2} -y^2 = (x+y) (x-y)\\\\\Rightarrow (15^3+7^3)(15^3-7^3)$

Let us learn two formula:

$x^3+y^3 = (x+y)(x^2+y^2-xy)$

$x^3-y^3 = (x-y)(x^2+y^2+xy)$

Applying the above formula in the expression written above:

$(15^3+7^3) = (15+7)(15^2+7^2-15\times 7)\\\Rightarrow 22(225+49-105 ) = 2 \times 11 \times 169 \\\Rightarrow 2 \times 11\times 13\times 13\\\Rightarrow 2 \times 11\times 13^2$ ...... (1)

Similarly:

$(15^3-7^3) = (15-7)(15^2+7^2+15\times 7)\\\Rightarrow 8(225+49+105 ) = 2^3 \times 379$ ........ (2)

Multiplying the expressions from (1) and (2) to get the result:

$\therefore 15^6 - 7^6 = 2^4 \times 11 \times \underline{\bold{379}} \times 13 ^2$

So, largest prime factor of the given expression is 379.

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2 years ago

What expression is equivalent to 6 × 10^−4/2 × 10^3

Ksivusya [100]

The correct answer is: [A]: " 3 * 10 ⁻⁷ " .

_____________________

Explanation:

To solve:

Given:

 (6 * 10⁻⁴ )  = (6 ÷ 2) * 10⁽⁻⁴ ⁻³⁾ = 3 * 10 ⁻⁷ ; which is:

(2 * 10³ )

→ Answer choice: [A]: " 3 * 10 ⁻⁷ " .

_____________________

4 0

3 years ago