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3 years ago

find the greatest possible length which can be used to measure exactly the lengths 4m 95cm; 9m and 16m 65cm?

Mathematics

1 answer:

san4es73 [151]3 years ago

7 0

Answer: H.C.F. = 32 x 5 = 45. Hence, required length = 45 cm

Step-by-step explanation:

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A company has fixed monthly costs of $130,000 and production costs on its product of $32 per unit. The company sells its product

Svet_ta [14]

Answer:

The cost function is $C(x)=32x+130000$ .

The revenue function is $R(x)=66x$ .

The profit function is $P(x)=34x-130000$ .

Step-by-step explanation:

We have the following definitions:

The cost function is a mathematical formula that gives the total cost to produce a certain number of units. It consists of variable costs and fixed costs and is given by

$C(x)=(fixed \:cost)+x\cdot (variable \:cost)$

If $x$ units are sold and the price per unit is $p(x)$ , then the total revenue is

$R(x)=x\cdot p(x)$

and $R(x)$ is called the revenue function.

If $x$ units are sold, then the total profit is

$P(x)=R(x)-C(x)$

and $P(x)$ is called the profit function.

Applying the above definitions we get that:

We know that the company has fixed monthly costs of $130,000 and production costs on its product of $32 per unit.

Therefore,

The cost function is $C(x)=32x+130000$ .

We know that the company sells its product for $66 per unit.

Therefore,

The revenue function is $R(x)=66x$ .

The profit function is

$P(x)=R(x)-C(x)\\P(x)=66x-(32x+130000)\\P(x)=34x-130000$

4 0

3 years ago

Factor:

nekit [7.7K]

Answer:

a) $(7\cdot m^{6}+4)\cdot (7\cdot m^{6}-4)$

b) $(7\cdot a\cdot b^{8}+1)\cdot (7\cdot a\cdot b^{8}-1)$

c) $a = 0.7\cdot t^{9}$

d) There are two possible answers only considering real coefficients:

(i) $16\cdot x^{2}-81 = (4\cdot x +9)\cdot (4\cdot x - 9)$

(ii) $14\cdot x^{2}-81 =(\sqrt{14}\cdot x+9)\cdot (\sqrt{14}\cdot x - 9)$

e) $(a^{3}+4)\cdot (a^{3}-4)$

Step-by-step explanation:

Now we proceed to solve each algebraic equation:

a) Factor $49\cdot m^{12}-16$

This binomial is of the form $a^{2}-b^{2} = (a+b)\cdot (a-b)$ . In this case, we can rewrite and factor the equation below:

$49\cdot m ^{12}-16$

$(7\cdot m^{6})^ 2-4^{2}$

$(7\cdot m^{6}+4)\cdot (7\cdot m^{6}-4)$

b) Factor $49\cdot a^{2}\cdot b^{16}-1$

This binomial is of the form $a^{2}-b^{2} = (a+b)\cdot (a-b)$ . In this case, we can rewrite and factor the equation below:

$49\cdot a^{2}\cdot b^{16}-1$

$(7\cdot a\cdot b^{8})^{2}-1^{2}$

$(7\cdot a\cdot b^{8}+1)\cdot (7\cdot a\cdot b^{8}-1)$

c) Nicole is factoring $0.49\cdot t^{18}-25$ by using the rule $a^{2}-b^{2} = (a+b)\cdot (a-b)$ . What will she use for the value of $a$ ?

From this rule we find that $a^{2} = 0.49\cdot t^{18}$ , that is:

$a^{2} = 0.49\cdot t^{18}$

$a^{2} = \frac{49}{100}\cdot t^{18}$

$a = \frac{7}{10}\cdot t^{9}$

$a = 0.7\cdot t^{9}$

d) Which binomial is a difference of squares?

A binomial is a difference of square if and only if $a^{2}-b^{2} = (a+b)\cdot (a-b)$ . There are two possible answers only considering real coefficients:

(i) $16\cdot x^{2}-81 = (4\cdot x +9)\cdot (4\cdot x - 9)$

(ii) $14\cdot x^{2}-81 =(\sqrt{14}\cdot x+9)\cdot (\sqrt{14}\cdot x - 9)$

e) Factor $a^{6}-16$

This binomial is of the form $a^{2}-b^{2} = (a+b)\cdot (a-b)$ . In this case, we can rewrite and factor the equation below:

$a^{6}-16$

$(a^{3})^{2}-4^{2}$

$(a^{3}+4)\cdot (a^{3}-4)$

6 0

3 years ago

find the greatest possible length which can be used to measure exactly the lengths 4m 95cm; 9m and 16m 65cm?​

find the greatest possible length which can be used to measure exactly the lengths 4m 95cm; 9m and 16m 65cm?