Answer: 90°
Explanation: the sum of all the angles in a triangle = 180. So 70 + 30 = 90 and 180-90=90
Answer:
PQ = 134.9 feet
Step-by-step explanation:
sin 46 = 97/PQ
0.7193 = 97/PQ
PQ = 134.85 feet
Answer:
f(5) = 26.672 which is option D
Step-by-step explanation:
From question, f(1) = 2 and f'(x)=√(x^3 + 6)
f(5) = f(1) + (5,1)∫ f'(x) dx
Integrating using the boundary 5 and 1;
f(5) = 2 + (5,1)∫√(x^3 + 6) dx
f(5) = 2 + 24.672
So f(5) = 26.672
On a coordinate plane it is negetive 5
The tangent to 
through (1, 1, 1) must be perpendicular to the normal vectors to the surfaces 
and 
at that point.
Let 
. Then is the level curve 
. Recall that the gradient vector is perpendicular to level curves; we have
so that the gradient of 
at (1, 1, 1) is
For the surface , we have
so that 
. We can obtain a vector normal to by taking the cross product of the partial derivatives of 
, and evaluating that product for 
:
Now take the cross product of the two normal vectors to and :
The direction of vector (24, 8, -8) is the direction of the tangent line to at (1, 1, 1). We can capture all points on the line containing this vector by scaling it by 
. Then adding (1, 1, 1) shifts this line to the point of tangency on . So the tangent line has equation
