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3 years ago

The quotient of two numbers is 4, and the difference is 3. What are the two numbers

Mathematics

1 answer:

Pie3 years ago

6 0

Answer:

The numbers are 4 and 1

Step-by-step explanation:

Let x and y be the numbers

Quotient is division

x/y = 4

x-y =3

Taking the first equation and multiplying each side by y

x = 4y

Replacing into the second equation

4y -y = 3

3y = 3

Divide by 3

3y/3 = 3/3

y=1

Now we can find x

x -y =3

x-1 =3

Add 1 to each side

x= 4

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The ratio x : 8 is equivalent to the ratio 8 : x^2. What is the value of x?

dimulka [17.4K]

Answer:

x=1

Step-by-step explanation:

7 0

2 years ago

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Find the distance between the two points.<br> (-6, -7) and (154, - 43)

Vitek1552 [10]

Answer:

(160, 36)

Step-by-step explanation:

Distance is always positive because, well, you aren't -50 meters away from your house or something. You are just 50 meters away from your house. And 160 is the distance between -6 and 154, because there is one minus and one plus, you add them, because that is how far they are apart, and then-43 and -7 were easy just subtract them.

8 0

3 years ago

What is the simplified form of √144x^36

Nadusha1986 [10]

Answer:

The simplified form of $\sqrt{144x^{36}}$ is $12x^{18}$

Step-by-step explanation:

Given : $\sqrt{144x^{36}}$

We have to write the simplified form of $\sqrt{144x^{36}}$

Consider the given expression $\sqrt{144x^{36}}$

We know $\sqrt{144}=12$

and $\sqrt{x^{36}}=\sqrt{x^{18}\cdot x^{18}}$

Thus,

$\sqrt{144x^{36}}=\sqrt{12^2\cdot (x^{18})^2}$

Simplify, we have,

$=\sqrt{12^2\cdot (x^{18})^2}=12x^{18}$

Thus, The simplified form of $\sqrt{144x^{36}}$ is $12x^{18}$

6 0

3 years ago

Read 2 more answers

1. (5pts) Find the derivatives of the function using the definition of derivative.

andreyandreev [35.5K]

2.8.1

$f(x) = \dfrac4{\sqrt{3-x}}$

By definition of the derivative,

$f'(x) = \displaystyle \lim_{h\to0} \frac{f(x+h)-f(x)}{h}$

We have

$f(x+h) = \dfrac4{\sqrt{3-(x+h)}}$

and

$f(x+h)-f(x) = \dfrac4{\sqrt{3-(x+h)}} - \dfrac4{\sqrt{3-x}}$

Combine these fractions into one with a common denominator:

$f(x+h)-f(x) = \dfrac{4\sqrt{3-x} - 4\sqrt{3-(x+h)}}{\sqrt{3-x}\sqrt{3-(x+h)}}$

Rationalize the numerator by multiplying uniformly by the conjugate of the numerator, and simplify the result:

$f(x+h) - f(x) = \dfrac{\left(4\sqrt{3-x} - 4\sqrt{3-(x+h)}\right)\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{\left(4\sqrt{3-x}\right)^2 - \left(4\sqrt{3-(x+h)}\right)^2}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{16(3-x) - 16(3-(x+h))}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{16h}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)}$

Now divide this by <em>h</em> and take the limit as <em>h</em> approaches 0 :

$\dfrac{f(x+h)-f(x)}h = \dfrac{16}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ \displaystyle \lim_{h\to0}\frac{f(x+h)-f(x)}h = \dfrac{16}{\sqrt{3-x}\sqrt{3-x}\left(4\sqrt{3-x} + 4\sqrt{3-x}\right)} \\\\ \implies f'(x) = \dfrac{16}{4\left(\sqrt{3-x}\right)^3} = \boxed{\dfrac4{(3-x)^{3/2}}}$

3.1.1.

$f(x) = 4x^5 - \dfrac1{4x^2} + \sqrt[3]{x} - \pi^2 + 10e^3$

Differentiate one term at a time:

• power rule

$\left(4x^5\right)' = 4\left(x^5\right)' = 4\cdot5x^4 = 20x^4$

$\left(\dfrac1{4x^2}\right)' = \dfrac14\left(x^{-2}\right)' = \dfrac14\cdot-2x^{-3} = -\dfrac1{2x^3}$

$\left(\sqrt[3]{x}\right)' = \left(x^{1/3}\right)' = \dfrac13 x^{-2/3} = \dfrac1{3x^{2/3}}$

The last two terms are constant, so their derivatives are both zero.

So you end up with

$f'(x) = \boxed{20x^4 + \dfrac1{2x^3} + \dfrac1{3x^{2/3}}}$

8 0

2 years ago

8.35x - 1.5 = 71.98<br> (a) 8.6<br> (b) 8.8<br> (c) 9<br> (d) 10.3

prisoha [69]

<h3> Hola! :D ¡te invito a recibir ayuda de un latinoamericano puto!</h3><h2><u> _____________________________________ </u></h2><h2> 8.35x - 1.5 = 71.98</h2><h2> - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</h2>

<u>El -1,5 qlero pasaría al otro lado positivo</u>

<u>Ahora, se suma 71.98 + 1.5 = 73,48</u>

<u>El 8.35 qlero que está multiplicando, pasa al otro lado pero dividiendo</u>

<u>Dividimos</u>

<h3> x = 8,8</h3><h2> - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</h2><h2> <u>(b) 8,8</u> es la opción correcta</h2>

3 0

3 years ago