Answer:
13.96units
Step-by-step explanation:
To get the length of CD, we will use the cosine rule as shown:
CD² = DE²+CE²-2(DE)(CE)cos m<E
Substitute the given values
CD² = 14²+9²-2(14)(9)cos71
CD² = 196 + 81 - 252cos71
CD² =277 - 252cos71
CD² = 277 - 82.0431
CD² = 194.95682
CD = √194.95682
CD = 13.96 units
Hence the length of CD of 13.96units
Answer:
-30(x-4) + 29 (y-1) -12(z-3) = 0
Step-by-step explanation:
You can find the perpendicular vector to both curves using the cross product between them, and that will give you all the information you need to find the equation of the tangent plane to the surface S.
Let's find the parameter of each curve for the specific point.
For the first curve notice that
And for the second curve notice that
Thus for the first curve we reach our point at and for the second curve we reach our point at
Then we compute the tangent vector to our curves, and it would be given by the derivative so
and at we have that
Similarly
The the cross product between the two vectors would be
Since (-30,29,-12) would be the perpendicular vector to the tangent plane and (4,1,3) would be a point of the tangent then we would have that the equation of the tangent plane is given by
-30(x-4) + 29 (y-1) -12(z-3) = 0
Answer:
Length of diagonal line from 1 to 2 =17.3 cm
Mass= 124.57 grams =0.12457 kg
Weight=1.22 Newton
Step-by-step explanation:
Sides of cube = s=10cm
First take the bottom of cube we can get right angle triangle
And using Pythagoras theorem
By solving
Now taking the triangle formed between point 1 and 2 we get
=17.3
Density=2.1 gram per cubic inch
Density = mass/volume
As sides=10 cm=3.9 inch
Volume of cube ==59.3 cubic inch
Mass=Density X Volume
Mass= 2.1 X 59.3=124.57 grams =0.12457 kg
Weight = mass X g
As
Weight = 0.12457 X 9.8 =1.22 Newton