Sin x = 0.5
sin x = 1/2
sin x = opp/hyp
therefore the ratio of opp/hyp = 1/2, (opp = 1, hyp = 2)
Find the opp side
1² + x² = 2²
1 + x² = 4
x² = 4 -1
x² = 3
x =√3
The opp side is √3
cos x = opp/hyp = √3/2 = 0.87 (round to the nearest hundredths)
Answer:
g(x) = ![9(\frac{1}{3})^x](https://tex.z-dn.net/?f=9%28%5Cfrac%7B1%7D%7B3%7D%29%5Ex)
Step-by-step explanation:
Exponential function 'g' that can be written as g(x) = a.bˣ
From the graph attached,
Graph of the function passes through two points (0, 9) and (1, 3)
g(0) = a.b⁰
9 = a
Similarly, g(1) = a.b¹
3 = a.b
3 = 9(b)
b = ![\frac{3}{9}=\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B9%7D%3D%5Cfrac%7B1%7D%7B3%7D)
Therefore function will be,
g(x) = ![9(\frac{1}{3})^x](https://tex.z-dn.net/?f=9%28%5Cfrac%7B1%7D%7B3%7D%29%5Ex)
Answer:
I think it is A≈225.77
Step-by-step explanation:
Answer:
x-intercepts: (1,0), (2,0), (5,0)
y-intercepts: (0,-10)
Step-by-step explanation:
One factor of the function
is ![(x-5).](https://tex.z-dn.net/?f=%28x-5%29.)
Factor the polynomial in the following way:
![x^3-8x^2 + 17x-10\\ \\=x^3-5x^2-3x^2+15x+2x-10\\ \\=x^2(x-5)-3x(x-5)+2(x-5)\\ \\=(x-5)(x^2-3x+2)](https://tex.z-dn.net/?f=x%5E3-8x%5E2%20%2B%2017x-10%5C%5C%20%5C%5C%3Dx%5E3-5x%5E2-3x%5E2%2B15x%2B2x-10%5C%5C%20%5C%5C%3Dx%5E2%28x-5%29-3x%28x-5%29%2B2%28x-5%29%5C%5C%20%5C%5C%3D%28x-5%29%28x%5E2-3x%2B2%29)
Now factor the quadratic in brackets:
![x^2-3x+2\\ \\=x^2-2x-x+2\\ \\=x(x-2)-(x-2)\\ \\=(x-2)(x-1)](https://tex.z-dn.net/?f=x%5E2-3x%2B2%5C%5C%20%5C%5C%3Dx%5E2-2x-x%2B2%5C%5C%20%5C%5C%3Dx%28x-2%29-%28x-2%29%5C%5C%20%5C%5C%3D%28x-2%29%28x-1%29)
Hence,
![f(x)=(x-5)(x-2)(x-1)](https://tex.z-dn.net/?f=f%28x%29%3D%28x-5%29%28x-2%29%28x-1%29)
The x-intercepts are points at which y = 0, so
![(x-5)(x-2)(x-1)=0\\ \\x-5=0\ \text{or}\ x-2=0\ \text{or}\ x-1=0\\ \\x=5\ \text{or}\ x=2\ \text{or}\ x=1](https://tex.z-dn.net/?f=%28x-5%29%28x-2%29%28x-1%29%3D0%5C%5C%20%5C%5Cx-5%3D0%5C%20%5Ctext%7Bor%7D%5C%20x-2%3D0%5C%20%5Ctext%7Bor%7D%5C%20x-1%3D0%5C%5C%20%5C%5Cx%3D5%5C%20%5Ctext%7Bor%7D%5C%20x%3D2%5C%20%5Ctext%7Bor%7D%5C%20x%3D1)
The y-intercepts are points at which x = 0, so
![y=0^3-8\cdot 0^2+17\cdot 0-10=-10](https://tex.z-dn.net/?f=y%3D0%5E3-8%5Ccdot%200%5E2%2B17%5Ccdot%200-10%3D-10)