Formula:
![y = p\% \times x](https://tex.z-dn.net/?f=y%20%3D%20p%5C%25%20%5Ctimes%20x)
![p = 37\% \div 100 = 0.37](https://tex.z-dn.net/?f=p%20%3D%2037%5C%25%20%5Cdiv%20100%20%3D%200.37)
![y = 0.37 \times 1500 = 555](https://tex.z-dn.net/?f=y%20%3D%200.37%20%5Ctimes%201500%20%3D%20555)
so there are 555 woman working.
![1500 - 555 = 945](https://tex.z-dn.net/?f=1500%20-%20555%20%3D%20945)
there are 945 men working
Please find the attached diagram for a better understanding of the solution provided here.
In the attached diagram, OP is the height of the tree.
Rest of the diagram should be sufficiently self explanatory.
In
,
![tan(30^0)=\frac{OP}{x}](https://tex.z-dn.net/?f=%20tan%2830%5E0%29%3D%5Cfrac%7BOP%7D%7Bx%7D%20%20)
.........................Equation #1
Again, in
,
![tan(20^0)=\frac{OP}{PH+HL}=\frac{OP}{x+50}](https://tex.z-dn.net/?f=%20tan%2820%5E0%29%3D%5Cfrac%7BOP%7D%7BPH%2BHL%7D%3D%5Cfrac%7BOP%7D%7Bx%2B50%7D%20%20%20)
.........................Equation #2
Thus, equating the equations Equation #1 and Equation #2, we have:
![\frac{OP}{tan(30^0)}=\frac{OP}{tan(20^0)}-50](https://tex.z-dn.net/?f=%20%5Cfrac%7BOP%7D%7Btan%2830%5E0%29%7D%3D%5Cfrac%7BOP%7D%7Btan%2820%5E0%29%7D-50%20%20%20%20)
Evaluating we get:
![1.732(OP)=2.747(OP)-50](https://tex.z-dn.net/?f=%201.732%28OP%29%3D2.747%28OP%29-50%20)
![1.015(OP)=50](https://tex.z-dn.net/?f=%201.015%28OP%29%3D50%20)
![\therefore OP=\frac{50}{1.015}\approx49.26 ft](https://tex.z-dn.net/?f=%20%5Ctherefore%20OP%3D%5Cfrac%7B50%7D%7B1.015%7D%5Capprox49.26%20ft%20%20)
Thus the height of the tree is approximately 49.26 feet
Answer:
Step-by-step explanation:
The standard form of a parabola is
![y=ax^2+bx+c](https://tex.z-dn.net/?f=y%3Dax%5E2%2Bbx%2Bc)
If we know the y intercept is (0, 400), that means that when x = 0, y = 400. That allows us to begin by finding c:
and c = 400.
Now to find a and b. Using the fact that the vertex is (1, 405), we know that h is 1 and k is 405. If
and h = 1, then
and
2a = -b so
b = -2a. Save that for a minute or two.
If
and k = 405, then
and
and
405 = 400 - 4a and
5 = -4a so
![a=-\frac{5}{4}](https://tex.z-dn.net/?f=a%3D-%5Cfrac%7B5%7D%7B4%7D)
We will use that a value now to find the value of b. If b = -2a, then
and
![b=\frac{10}{4}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7B10%7D%7B4%7D)
Writing our parabolic equation now:
![y=-\frac{5}{4}x^2+\frac{10}{4}x+400](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B5%7D%7B4%7Dx%5E2%2B%5Cfrac%7B10%7D%7B4%7Dx%2B400)
Finding the x-intercepts is just another way of saying "factor this quadratic" so we will begin that by setting the quadratic equal to 0:
and who hates all those fractions more than I do? Probably nobody, so we are going to get rid of them by multiplying everything by 4 to get
Assuming you can throw that into the quadratic formula to solve for the 2 values of x where y = 0, you'll find that the x-intercepts are
x = -16.91647287 and 18.91647287
Answer: C= 10
Step-by-step explanation:
Answer:
associative property
Step-by-step explanation:
This is the associative property. The numbers and signs on both sides of the equation stay IN THE SAME ORDER, this is a big hint!