Answer:
Look below.
Step-by-step explanation:
![2 (cotx)^{2} + 2 = 7 + 3 cot x\\let \\ u=cotx\\2u^2+2=7+3u\\2u^2-3u-5=0\\](https://tex.z-dn.net/?f=2%20%28cotx%29%5E%7B2%7D%20%20%20%2B%202%20%3D%207%20%2B%203%20cot%20x%5C%5Clet%20%5C%5C%20u%3Dcotx%5C%5C2u%5E2%2B2%3D7%2B3u%5C%5C2u%5E2-3u-5%3D0%5C%5C)
![x=\frac{-(-3)+\sqrt{9-4(2)(-5))} }{2(2)} \\x=\frac{-(-3)-\sqrt{9-4(2)(-5))} }{2(2)} \\x={11/4}\\x=-1\\\\u=cotx\\x=arccotu\\x_{1}=arccot(-1) \\x_{2}=arccot(11/4)\\](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-%28-3%29%2B%5Csqrt%7B9-4%282%29%28-5%29%29%7D%20%7D%7B2%282%29%7D%20%5C%5Cx%3D%5Cfrac%7B-%28-3%29-%5Csqrt%7B9-4%282%29%28-5%29%29%7D%20%7D%7B2%282%29%7D%20%5C%5Cx%3D%7B11%2F4%7D%5C%5Cx%3D-1%5C%5C%5C%5Cu%3Dcotx%5C%5Cx%3Darccotu%5C%5Cx_%7B1%7D%3Darccot%28-1%29%20%5C%5Cx_%7B2%7D%3Darccot%2811%2F4%29%5C%5C)
Calculate x1 and x2 in calculator. Check for domain.
Answer:
Height, base(4,1) to A(4,3)
Step-by-step explanation:
The height that is shown is incorrect as it is showing the distance between A and B, which is not the height of the triangle, and simply a side. We need to find the altitude(height) which is a line perpendicular to the base. If we draw a line that is perpendicular to the base that intersects the highest point of the triangle, A, we get the point of intersection of that line and the base at (4,1)
Answer:
3x³ + 12x
Step-by-step explanation:
→ Multiply 3x by x²
3x³
→ Multiply 3x by 4
12x
13 units.
Since both are negative, and they’re just asking for distance between, you can just subtract 12 from 25 to get 13.
Answer:
only for ![3x+4\in [0, \infty)](https://tex.z-dn.net/?f=3x%2B4%5Cin%20%5B0%2C%20%5Cinfty%29)
Step-by-step explanation:
Key formulas used:
Given
,
We can use the first formula on the left side of the equation.
In this case, for
,
, we have:
![\sqrt{3x+4}^2=|3x+4|](https://tex.z-dn.net/?f=%5Csqrt%7B3x%2B4%7D%5E2%3D%7C3x%2B4%7C)
Similarly, we can use the second formula on the right side of the equation.
In this case, for
,
, we have:
![(1+\sqrt{3x-11})^2=1^2+2\cdot 1\cdot \sqrt{3x-11}+\sqrt{3x-11}^2,\\=1+2\sqrt{3x-11}+3x-11,\\=3x+2\sqrt{3x-11}-10](https://tex.z-dn.net/?f=%281%2B%5Csqrt%7B3x-11%7D%29%5E2%3D1%5E2%2B2%5Ccdot%201%5Ccdot%20%5Csqrt%7B3x-11%7D%2B%5Csqrt%7B3x-11%7D%5E2%2C%5C%5C%3D1%2B2%5Csqrt%7B3x-11%7D%2B3x-11%2C%5C%5C%3D3x%2B2%5Csqrt%7B3x-11%7D-10)
Therefore, when you square both sides of the equation, you get:
![\boxed{\text{B. }3x+4=3x+2\sqrt{3x-11}-10}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Ctext%7BB.%20%7D3x%2B4%3D3x%2B2%5Csqrt%7B3x-11%7D-10%7D)
*Important:
This answer choice is actually only correct if
, because of the first formula we used. If
(negative), then
. Graphically, you can show this since the line
is not equal to
but instead
.
and
only overlap if you restrict the domain to
(positive numbers), hence
only for
.