Danny has a rectangular rose garden that measures 8m by 12.5m. One bag of fertilizer can cover 16m2. How many bags will he need
to cover the entire garden?
1 answer:
Answer:
do your work and ask a teacher or parent for help to solve it and stop asking random strangers for the answer and learn how to do it. <3
Step-by-step explanation:
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False. The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.
Answer:
See explanation
Step-by-step explanation:
Given the equation:
![2x\sin (2y)dx-(x^2+12)\cos ydy=0](https://tex.z-dn.net/?f=2x%5Csin%20%282y%29dx-%28x%5E2%2B12%29%5Ccos%20ydy%3D0)
Separate variables
and
:
![2x\sin (2y)dx=(x^2+12)\cos y dy\\ \\\dfrac{2x\sin (2y)dx}{x^2+12}=\cos ydy\ [\text{Divided by non-zero expression }x^2+12]\\ \\\dfrac{2x}{x^2+12}dx=\dfrac{\cos y}{\sin (2y)}dy\ [\text{Divided by }\sin (2y)]\\ \\\dfrac{2x}{x^2+12}dx=\dfrac{\cos y}{2\sin y\cos y}dy\ [\text{Use formula }\sin (2y)=2\sin y\cos y]\\ \\\dfrac{2x}{x^2+12}dx=\dfrac{1}{2\sin y}dy\ [\text{Simplify when }\cos y\neq 0]](https://tex.z-dn.net/?f=2x%5Csin%20%282y%29dx%3D%28x%5E2%2B12%29%5Ccos%20y%20dy%5C%5C%20%5C%5C%5Cdfrac%7B2x%5Csin%20%282y%29dx%7D%7Bx%5E2%2B12%7D%3D%5Ccos%20ydy%5C%20%5B%5Ctext%7BDivided%20by%20non-zero%20expression%20%7Dx%5E2%2B12%5D%5C%5C%20%5C%5C%5Cdfrac%7B2x%7D%7Bx%5E2%2B12%7Ddx%3D%5Cdfrac%7B%5Ccos%20y%7D%7B%5Csin%20%282y%29%7Ddy%5C%20%5B%5Ctext%7BDivided%20by%20%7D%5Csin%20%282y%29%5D%5C%5C%20%5C%5C%5Cdfrac%7B2x%7D%7Bx%5E2%2B12%7Ddx%3D%5Cdfrac%7B%5Ccos%20y%7D%7B2%5Csin%20y%5Ccos%20y%7Ddy%5C%20%5B%5Ctext%7BUse%20formula%20%7D%5Csin%20%282y%29%3D2%5Csin%20y%5Ccos%20y%5D%5C%5C%20%5C%5C%5Cdfrac%7B2x%7D%7Bx%5E2%2B12%7Ddx%3D%5Cdfrac%7B1%7D%7B2%5Csin%20y%7Ddy%5C%20%5B%5Ctext%7BSimplify%20when%20%7D%5Ccos%20y%5Cneq%200%5D)
Now,
![\int \dfrac{2x}{x^2+12}dx=\int \dfrac{1}{2\sin y}dy\\ \\\int \dfrac{d(x^2)}{x^2+12}=\dfrac{1}{2}\int \dfrac{\sin y}{\sin^2 y}dy\\ \\\int \dfrac{d(x^2+12)}{x^2+12}=-\dfrac{1}{2}\int \dfrac{d(\cos y)}{1-\cos^2 y}\\ \\\ln (x^2+12)+C=-\dfrac{1}{2}\int \left(\dfrac{1}{2(1-\cos y)}+\dfrac{1}{2(1+\cos y)}\right)d(\cos y)\\ \\\ln (x^2+12)+C=-\dfrac{1}{4}\int \dfrac{d(\cos y)}{1-\cos y}-\dfrac{1}{4}\int \dfrac{d(\cos y)}{1+\cos y}\\ \\\ln (x^2+12)+C=\dfrac{1}{4}\ln (1-\cos y)-\dfrac{1}{4}\ln (1+\cos y)](https://tex.z-dn.net/?f=%5Cint%20%5Cdfrac%7B2x%7D%7Bx%5E2%2B12%7Ddx%3D%5Cint%20%5Cdfrac%7B1%7D%7B2%5Csin%20y%7Ddy%5C%5C%20%5C%5C%5Cint%20%5Cdfrac%7Bd%28x%5E2%29%7D%7Bx%5E2%2B12%7D%3D%5Cdfrac%7B1%7D%7B2%7D%5Cint%20%5Cdfrac%7B%5Csin%20y%7D%7B%5Csin%5E2%20y%7Ddy%5C%5C%20%5C%5C%5Cint%20%5Cdfrac%7Bd%28x%5E2%2B12%29%7D%7Bx%5E2%2B12%7D%3D-%5Cdfrac%7B1%7D%7B2%7D%5Cint%20%5Cdfrac%7Bd%28%5Ccos%20y%29%7D%7B1-%5Ccos%5E2%20y%7D%5C%5C%20%5C%5C%5Cln%20%28x%5E2%2B12%29%2BC%3D-%5Cdfrac%7B1%7D%7B2%7D%5Cint%20%5Cleft%28%5Cdfrac%7B1%7D%7B2%281-%5Ccos%20y%29%7D%2B%5Cdfrac%7B1%7D%7B2%281%2B%5Ccos%20y%29%7D%5Cright%29d%28%5Ccos%20y%29%5C%5C%20%5C%5C%5Cln%20%28x%5E2%2B12%29%2BC%3D-%5Cdfrac%7B1%7D%7B4%7D%5Cint%20%5Cdfrac%7Bd%28%5Ccos%20y%29%7D%7B1-%5Ccos%20y%7D-%5Cdfrac%7B1%7D%7B4%7D%5Cint%20%5Cdfrac%7Bd%28%5Ccos%20y%29%7D%7B1%2B%5Ccos%20y%7D%5C%5C%20%5C%5C%5Cln%20%28x%5E2%2B12%29%2BC%3D%5Cdfrac%7B1%7D%7B4%7D%5Cln%20%281-%5Ccos%20y%29-%5Cdfrac%7B1%7D%7B4%7D%5Cln%20%281%2B%5Ccos%20y%29)
![\ln (x^2+12)+C=\dfrac{1}{4}\ln \dfrac{1-\cos y}{1+\cos y}](https://tex.z-dn.net/?f=%5Cln%20%28x%5E2%2B12%29%2BC%3D%5Cdfrac%7B1%7D%7B4%7D%5Cln%20%5Cdfrac%7B1-%5Ccos%20y%7D%7B1%2B%5Ccos%20y%7D)
Find the constant solutions, if any, that were lost in the solution of the differential equation:
When
![\cos y=0,](https://tex.z-dn.net/?f=%5Ccos%20y%3D0%2C)
then
![y=\dfrac{\pi }{2}+\pi k,\ k\in Z](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B%5Cpi%20%7D%7B2%7D%2B%5Cpi%20k%2C%5C%20k%5Cin%20Z)
Y = x-4
2x + y = 5
2x + (x-4) = 5
3x - 4 = 5
3x = 9
x = 3
Answer: $153.17
Step-by-step explanation:
85+85=$170
15% of $170 is $25.50.
170-25.50= $144.50
6% of 144.50=$8.67
144.50+8.67= $153.17
So, the answer is (B)-$153.17
Correct, c and e. they are the only ones that make sense