Which equation represents the proportional relationship?

Mathematics

1 answer:

elena-14-01-66 [18.8K]3 years ago

6 0

Proportional = goes through point of origin (0,0) and is linear.

D. Represents a proportional relationship

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Derivative of these questions<br>

shtirl [24]

Answer: $\bold{y'=\dfrac{1}{2(a-b)^2}\bigg(\dfrac{1}{\sqrt{x+a}}+\dfrac{1}{\sqrt{x+b}}\bigg)}$

<u>Step-by-step explanation:</u>

$y=\dfrac{1}{\sqrt{x+a}-\sqrt{x+b}}\\\\\\\text{Rationalize the denominator:}\\y=\dfrac{1}{\sqrt{x+a}-\sqrt{x+b}}\bigg(\dfrac{\sqrt{x+a}+\sqrt{x+b}}{\sqrt{x+a}+\sqrt{x+b}}\bigg)\\\\\\y=\dfrac{\sqrt{x+a}+\sqrt{x+b}}{x+a-x-b}\\\\\\y=\dfrac{\sqrt{x+a}+\sqrt{x+b}}{a-b}\\\\\\\text{Apply the derivative (derivative of the numerator (top) divided by the}\\\text{denominator (bottom) squared).}$

$\text{Derivative of }\sqrt{x+a}\quad \rightarrow \quad (x+a)^{\frac{1}{2}}\quad = \quad \dfrac{1}{2}(x + a)^{-\frac{1}{2}}\\\\\text{Derivative of }\sqrt{x+b}\quad \rightarrow \quad (x+b)^{\frac{1}{2}}\quad = \quad \dfrac{1}{2}(x + b)^{-\frac{1}{2}}\\\\\\\text{Derivative of}\ \dfrac{\sqrt{x+a}+\sqrt{x+b}}{a-b}:\\\\= \dfrac{\dfrac{1}{2}(x + a)^{-\frac{1}{2}}+\dfrac{1}{2}(x + b)^{-\frac{1}{2}}}{(a-b)^2}$

$\text{Factor out }\dfrac{1}{2}\ \text{from the numerator:}\\\\\dfrac{(x+a)^{-\frac{1}{2}}+(x+b)^{-\frac{1}{2}}}{2(a-b)^2}\\\\\\\text{Move the terms with negative exponents to the denominator:}\\\\=\dfrac{1}{2(a-b)^2}\bigg(\dfrac{1}{\sqrt{x+a}}+\dfrac{1}{\sqrt{x+b}}\bigg)$

3 0

3 years ago

HOW CAN YOU USE SUBTRACTION TO DESCRIBE DIVISION? GIMME AN EXAMPLE PLS :(

nadya68 [22]

Answer:

By repeated subtraction.

Step-by-step explanation:

It is pretty much the same thing as division, but in subtraction. Since, Dividing and Subtraction are a like, repeated subtraction is a great example to use for this example

Hope this helps. :)

5 0

4 years ago

Read 2 more answers

Mika and her two best friends are all dressing up as superheroes for Halloween this year. Their costumes are almost ready, but e

Sever21 [200]

Answer:

4yards

Step-by-step explanation:

4ft×3=12ft

1yrd=3ft

12ft÷3ft=4yards