Step-by-step explanation:
second one because
only x+2y=8 passes through the point (2,3)
the proof is 2+2*3=2+6=8
if we replace the given point to the other equations we will take wrong results for example
first equation
x+2y=4. 2+2*3=2+6=8 that is not equal to 4
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Volume of a cone = (1/3) pi x r^2 x h
Volume of a cylinder = pi x r^2 x h
Volume of the cylinder = pi x 2^2 x 3 = 37.68 cubic inches
Now set the volume for the cone to the volume of the cylinder and solve for the height.
37.68 = (1/3) x pi x r^2 x h
37.68 = (1/3) x pi x 3^2 x h
37.68 = (1/3) x pi x 9 x h
37.68 = 9.42 x h
h = 37.68 / 9.42
h = 4
The height of the cone is 4 cm.
Answer:
B=23.19
Step-by-step explanation:
First, find the last side of the triangle using the Pythagorean theorem.
![a^{2} +b^{2} =c^{2} \\21^{2} +9^{2} =c^{2} \\441+81=c^{2} \\\sqrt[3]{58}=c](https://tex.z-dn.net/?f=a%5E%7B2%7D%20%2Bb%5E%7B2%7D%20%3Dc%5E%7B2%7D%20%5C%5C21%5E%7B2%7D%20%2B9%5E%7B2%7D%20%3Dc%5E%7B2%7D%20%5C%5C441%2B81%3Dc%5E%7B2%7D%20%5C%5C%5Csqrt%5B3%5D%7B58%7D%3Dc)
Then, find the missing angle, lets name it B.
The angle B can be found using the inverse sine function.
B=arcsin(opp/hyp)
![B=arcsin(\frac{9}{\sqrt[3]{58} } )\\B=23.19](https://tex.z-dn.net/?f=B%3Darcsin%28%5Cfrac%7B9%7D%7B%5Csqrt%5B3%5D%7B58%7D%20%7D%20%29%5C%5CB%3D23.19)
Answer:
Note that orthogonal to the plane means perpendicular to the plane.
Step-by-step explanation:
-1x+3y-3z=1 can also be written as -1x+3y-3z=0
The direction vector of the plane -1x+3y-3z-1=0 is (-1,3,-3).
Let us find a point on this line for which the vector from this point to (0,0,5) is perpendicular to the given line. The point is x-0,y-0 and z-0 respectively
Therefore, the vector equation is given as:
-1(x-0) + 3(y-0) + -3(z-5) = 0
-x + 3y + (-3z+15) = 0
-x + 3y -3z + 15 = 0
Multiply through by - to get a positive x coordinate to give
x - 3y + 3z - 15 = 0
