The height of a building is 58.08 meters if the angle is 71 degree and the distance between A and B is 20 meters.
<h3>What is trigonometry?</h3>
Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
Angle = 71 degree
Distance between A and B = 20 meters
Let's suppose the height of the building is x meters.
From the right angle triangle applying the tan ratio:
tan71 = x/20
x = 58.08 meter
Thus, the height of a building is 58.08 meters if the angle is 71 degree and the distance between A and B is 20 meters.
Learn more about trigonometry here:
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Split
into two component segments,
and
, parameterized by
![\mathbf r_1(t)=(1-t)(0,0)+t(6,1)=(6t,t)](https://tex.z-dn.net/?f=%5Cmathbf%20r_1%28t%29%3D%281-t%29%280%2C0%29%2Bt%286%2C1%29%3D%286t%2Ct%29)
![\mathbf r_2(t)=(1-t)(6,1)+t(7,0)=(6+t,1-t)](https://tex.z-dn.net/?f=%5Cmathbf%20r_2%28t%29%3D%281-t%29%286%2C1%29%2Bt%287%2C0%29%3D%286%2Bt%2C1-t%29)
respectively, with
, where
.
We have
![\mathrm d\mathbf r_1=(6,1)\,\mathrm dt](https://tex.z-dn.net/?f=%5Cmathrm%20d%5Cmathbf%20r_1%3D%286%2C1%29%5C%2C%5Cmathrm%20dt)
![\mathrm d\mathbf r_2=(1,-1)\,\mathrm dt](https://tex.z-dn.net/?f=%5Cmathrm%20d%5Cmathbf%20r_2%3D%281%2C-1%29%5C%2C%5Cmathrm%20dt)
where ![\mathrm d\mathbf r_i=\left(\dfrac{\mathrm dx}{\mathrm dt},\dfrac{\mathrm dy}{\mathrm dt}\right)\,\mathrm dt](https://tex.z-dn.net/?f=%5Cmathrm%20d%5Cmathbf%20r_i%3D%5Cleft%28%5Cdfrac%7B%5Cmathrm%20dx%7D%7B%5Cmathrm%20dt%7D%2C%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dt%7D%5Cright%29%5C%2C%5Cmathrm%20dt)
so the line integral becomes
![\displaystyle\int_C(x+6y)\,\mathrm dx+x^2\,\mathrm dy=\left\{\int_{C_1}+\int_{C_2}\right\}(x+6y,x^2)\cdot(\mathrm dx,\mathrm dy)](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_C%28x%2B6y%29%5C%2C%5Cmathrm%20dx%2Bx%5E2%5C%2C%5Cmathrm%20dy%3D%5Cleft%5C%7B%5Cint_%7BC_1%7D%2B%5Cint_%7BC_2%7D%5Cright%5C%7D%28x%2B6y%2Cx%5E2%29%5Ccdot%28%5Cmathrm%20dx%2C%5Cmathrm%20dy%29)
![=\displaystyle\int_0^1(6t+6t,(6t)^2)\cdot(6,1)\,\mathrm dt+\int_0^1((6+t)+6(1-t),(6+t)^2)\cdot(1,-1)\,\mathrm dt](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%5Cint_0%5E1%286t%2B6t%2C%286t%29%5E2%29%5Ccdot%286%2C1%29%5C%2C%5Cmathrm%20dt%2B%5Cint_0%5E1%28%286%2Bt%29%2B6%281-t%29%2C%286%2Bt%29%5E2%29%5Ccdot%281%2C-1%29%5C%2C%5Cmathrm%20dt)
![=\displaystyle\int_0^1(35t^2+55t-24)\,\mathrm dt=\frac{91}6](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%5Cint_0%5E1%2835t%5E2%2B55t-24%29%5C%2C%5Cmathrm%20dt%3D%5Cfrac%7B91%7D6)
Answer:
0.2916, 0.1488, 0.0319
Step-by-step explanation:
Given that a sign on the pumps at a gas station encourages customers to have their oil checked, and claims that one out of 10 cars needs to have oil added.
Since each trial is independent there is a constant probability for any random car to need oil is 0.10
Let X be the number of cars that need oil
A) Here X is BIN(4,0.1)
![P(X=1) = 4C1(0.1)(0.9)^3 \\= 0.2916](https://tex.z-dn.net/?f=P%28X%3D1%29%20%3D%204C1%280.1%29%280.9%29%5E3%20%5C%5C%3D%200.2916)
B) Here X is Bin (8, 0.1)
![P(x=2) = 8C2 (0.1)^2 (0.9)^6\\\\=0.1488](https://tex.z-dn.net/?f=P%28x%3D2%29%20%3D%208C2%20%280.1%29%5E2%20%280.9%29%5E6%5C%5C%5C%5C%3D0.1488)
C) Here X is Bin (20,5)
![P(x=5) = 20C5 (0.1)^5 (0.9)^{15} \\=0.0319](https://tex.z-dn.net/?f=P%28x%3D5%29%20%3D%2020C5%20%280.1%29%5E5%20%280.9%29%5E%7B15%7D%20%5C%5C%3D0.0319)
Answer:
24%
Step-by-step explanation:
Answer:
T'(-1, 4), U'(8, 4) and V'(-1, 10)
Step-by-step explanation:
If we reflect the vertices of the given triangle VTU across a line y = 3,
Rule to followed for the image points,
Line of reflection will work as a mirror.
And distance of image points and original points will be same from the line of reflection.
Therefore, Coordinates of the vertices of the image triangle will be,
T'(-1, 4), U'(8, 4) and V'(-1, 10)