Answer:
- 5/13
Step-by-step explanation:
tans = 5/12 = height/base
Using Pythagoras, hypotenuse = √12² + 5² = 13
Therefore coss had to be 12/13
But since cos s < 0, cos s = - 12/13
Thus,
tanA = sinA/cosA
tanA cosA = sinA
(5/12)(- 12/13) = sinA
- 5/13 = sinA
Answer:
There are 23 dimes in the box
Step-by-step explanation:
Let nickels=n
Let dimes=(35-n)
Equation: 0.05n+0.10(35-n)=2.90
Multiply both sides by 100: 5n+10(35-n)=290
-5n+350=290
-5n=-60
n=12
35-12=23
Therefore, there are 23 dimes in the box
Answer:
15 ft.
Step-by-step explanation:
The tepee is a cone and its volume
= 1/3 pi r^2 h where r = radius and h = height.
The radius r = 1/2 * 10 = 5 ft.
So we have the equation:
393 = 1/3*3.14* 5^2 * h
h = 393 / (1/3*3.14*25)
= 15.02 ft.
Answer:
Amount of money Judy has in her account is
.
Amount of money Tommy has in his account is 
Step-by-step explanation:
To find : Amount of money in Judy account and amount of money in Tommy account:
Solution:
Given:
Judy has $7500 more than a number in her account.
Let the number be 'n'.
So we can say that;
Amount of money in Judy account is equal to 7500 plus number.
framing in equation form we get;
Amount of money in Judy account = 
Hence Amount of money Judy has in her account is
.
Now Given:
Tommy has 6 more than 3 times the amount of money in his bank account than Judy.
So we can say that;
Amount of money in Tommy account is equal to 3 multiplied by Amount of money in Judy account plus 6.
framing in equation form we get;
Amount of money in Tommy account = 
Hence Amount of money Tommy has in his account is
.
Answer:

Step-by-step explanation:
We are given that:

And we want to find F'(0).
First, find F(x):
![\displaystyle F'(x) = \frac{d}{dx}\left[ f(3x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20F%27%28x%29%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%5B%20f%283x%29%5D)
From the chain rule:
![\displaystyle \begin{aligned} F'(x) &= f'(3x) \cdot \frac{d}{dx} \left[ 3x\right] \\ \\ &= 3f'(3x)\end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbegin%7Baligned%7D%20F%27%28x%29%20%26%3D%20f%27%283x%29%20%5Ccdot%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cleft%5B%203x%5Cright%5D%20%5C%5C%20%5C%5C%20%26%3D%203f%27%283x%29%5Cend%7Baligned%7D)
Then:

In conclusion, F'(0) = 15.