Answer:
The measure of the complement =
= 80°
The measure of the supplement=
= 170°
Step-by-step explanation:
Let
90-x equal the degree measure of its complement
180-x equal the degree measure of its supplement.
We are told in the question that: the supplement of a given angle is 10 degrees more than twice its complement.
Hence, the Equation is;
(180 - x) = 10° + 2(90 - x)
180 - x = 10 + 180 - 2x
Collect like terms
-x + 2x = 10 + 180 - 180
x = 10°
Hence,
The measure of the complement =
90 - x
= 90 - 10
= 80°
The measure of the supplement=
180 - x
= 180 - 10
= 170°
Answer:
![\frac{6x^2+3}{2x^3+3x}](https://tex.z-dn.net/?f=%5Cfrac%7B6x%5E2%2B3%7D%7B2x%5E3%2B3x%7D)
Step-by-step explanation:
You need to apply the chain rule here.
There are few other requirements:
You will need to know how to differentiate
.
You will need to know how to differentiate polynomials as well.
So here are some rules we will be applying:
Assume ![u=u(x) \text{ and } v=v(x)](https://tex.z-dn.net/?f=u%3Du%28x%29%20%5Ctext%7B%20and%20%7D%20v%3Dv%28x%29)
![\frac{d}{dx}\ln(u)=\frac{1}{u} \cdot \frac{du}{dx}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Cln%28u%29%3D%5Cfrac%7B1%7D%7Bu%7D%20%5Ccdot%20%5Cfrac%7Bdu%7D%7Bdx%7D)
![\text{ power rule } \frac{d}{dx}x^n=nx^{n-1}](https://tex.z-dn.net/?f=%5Ctext%7B%20power%20rule%20%7D%20%5Cfrac%7Bd%7D%7Bdx%7Dx%5En%3Dnx%5E%7Bn-1%7D)
![\text{ constant multiply rule } \frac{d}{dx}c\cdot u=c \cdot \frac{du}{dx}](https://tex.z-dn.net/?f=%5Ctext%7B%20constant%20multiply%20rule%20%7D%20%5Cfrac%7Bd%7D%7Bdx%7Dc%5Ccdot%20u%3Dc%20%5Ccdot%20%5Cfrac%7Bdu%7D%7Bdx%7D)
![\text{ sum/difference rule } \frac{d}{dx}(u \pm v)=\frac{du}{dx} \pm \frac{dv}{dx}](https://tex.z-dn.net/?f=%5Ctext%7B%20sum%2Fdifference%20rule%20%7D%20%5Cfrac%7Bd%7D%7Bdx%7D%28u%20%5Cpm%20v%29%3D%5Cfrac%7Bdu%7D%7Bdx%7D%20%5Cpm%20%5Cfrac%7Bdv%7D%7Bdx%7D)
Those appear to be really all we need.
Let's do it:
![\frac{d}{dx}\ln(2x^3+3x)=\frac{1}{2x^3+3x} \cdot \frac{d}{dx}(2x^3+3x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Cln%282x%5E3%2B3x%29%3D%5Cfrac%7B1%7D%7B2x%5E3%2B3x%7D%20%5Ccdot%20%5Cfrac%7Bd%7D%7Bdx%7D%282x%5E3%2B3x%29)
![\frac{d}{dx}(\ln(2x^3+3x)=\frac{1}{2x^3+3x} \cdot (\frac{d}{dx}(2x^3)+\frac{d}{dx}(3x))](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%28%5Cln%282x%5E3%2B3x%29%3D%5Cfrac%7B1%7D%7B2x%5E3%2B3x%7D%20%5Ccdot%20%28%5Cfrac%7Bd%7D%7Bdx%7D%282x%5E3%29%2B%5Cfrac%7Bd%7D%7Bdx%7D%283x%29%29)
![\frac{d}{dx}(\ln(2x^3+3x)=\frac{1}{2x^3+3x} \cdot (2 \cdot \frac{dx^3}{dx}+3 \cdot \frac{dx}{dx})](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%28%5Cln%282x%5E3%2B3x%29%3D%5Cfrac%7B1%7D%7B2x%5E3%2B3x%7D%20%5Ccdot%20%282%20%5Ccdot%20%5Cfrac%7Bdx%5E3%7D%7Bdx%7D%2B3%20%5Ccdot%20%5Cfrac%7Bdx%7D%7Bdx%7D%29)
![\frac{d}{dx}(\ln(2x^3+3x)=\frac{1}{2x^3+3x} \cdot (2 \cdot 3x^2+3(1))](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%28%5Cln%282x%5E3%2B3x%29%3D%5Cfrac%7B1%7D%7B2x%5E3%2B3x%7D%20%5Ccdot%20%282%20%5Ccdot%203x%5E2%2B3%281%29%29)
![\frac{d}{dx}(\ln(2x^3+3x)=\frac{1}{2x^3+3x} \cdot (6x^2+3)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%28%5Cln%282x%5E3%2B3x%29%3D%5Cfrac%7B1%7D%7B2x%5E3%2B3x%7D%20%5Ccdot%20%286x%5E2%2B3%29)
![\frac{d}{dx}(\ln(2x^3+3x)=\frac{6x^2+3}{2x^3+3x}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%28%5Cln%282x%5E3%2B3x%29%3D%5Cfrac%7B6x%5E2%2B3%7D%7B2x%5E3%2B3x%7D)
I tried to be very clear of how I used the rules I mentioned but all you have to do for derivative of natural log is derivative of inside over the inside.
Your answer is
.
Answer:
what it literally means I don't understand
Answer:
$5.91 for the t-shirt. $8.24 for the skirt
Step-by-step explanation:
It's correct don't worry. The problem is I cant explain but it's correct, also if you can please give brainliest