Find the inner product for (3,1,4)*(2,8,2) and state whether the vectors are perpendicular.
2 answers:
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Answer:
The values for Fx(1,2) and Fy(1,2) are 5 and 2 respectively.
Approximation at points (1.1,1.9) is 0.7
Step-by-step explanation:
Given:
Tangent plane to a surface z=5x+2y-10 as the function at point (1,2)
To find :
f(x,y) at (1,2)
partial derivatives of function w.r.t. (x and y) and value of that function at given points.
Solution:(refer the attachment also)
Now we know that
the equation of tangent plane at given points to the surface is given by,
f(x1,y1,z1) and z=f(x,y)
z-z1=Fx(x1,y1)*(x-x1)+Fy(x1,y1)*(y-y1)
here Fx(x1,y1) and Fy(x1,y1) are the partial derivatives of x and y.
now
taking partial derivative w.r.t. x we get
Fx(x1`,y1)=
=5.
Then w.r.t y we get
Fy(x1,y1)=
=2.
The values for Fx(1,2) and Fy(1,2) are 5 and 2 respectively.
Using the Linearization or linear approximation we get
L(x,y)=f(x1,y1)+Fx(x,y)*(x-x1)+Fy(x,y)(y-y1)
=-1+5(x-1)+2(y-2)
=5x+2y-10
Approximation at F(1.1,1.9)
=5(1.1)+2(1.9)-10
=5.5+3.8-10
=0.7
Approximation at points (1.1,1.9) is 0.7
<h2>Greetings!</h2>
<h2>Hope this helps! </h2>
Answer:
B)
Step-by-step explanation:
Y intercept:
Simply substitute all the x values with 0:
When x = 0:
3(0) - 2y = 18
Move the - 2y over to the other side making it a +2y:
0 = 18 + 2y
Move the +18 over to the other side making it a -18:
-18 = 2y
Divide both sides by 2:
-9 = y
So y intercept is:
<h3> (0 , -9)</h3>X - intercept:
Simply substitute all the Y's with 0:
3x - 3(0) = 18
3x = 18
Divide both sides by 3:
x = 6
So the X intercept is:
<h3>(6 , 0)</h3>This means that your guess of B is correct.
<h2>Hope this helps! </h2>