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Amanda [17]
3 years ago
5

Suppose you need to know an equation of the tangent plane to a surface S at the point P(4, 1, 4). You don't have an equation for

S but you know that the curves r1(t) = 4 + 3t, 1 − t2, 4 − 5t + t2 r2(u) = 3 + u2, 2u3 − 1, 2u + 2 both lie on S. Find an equation of the tangent plane at P.
Mathematics
1 answer:
Alex777 [14]3 years ago
5 0

Answer:

15x-8y+9z=88

Step-by-step explanation:

We are given that

Equation of curves

r_1(t)=

r_2(u)=

Both curves lie on S.

We have to find the equation of tangent plane at P(4,1,4).

r'_1(t)=,r'_2(u)=

r_1(0)=, r_2(1)=

Hence, t=0 and u then it satisfied the given point.

Substitute the values in the derivatives

r'_1(0)=,r'_2(1)=

r'_1(0)\times r'_2(1)=\times =

The equation of tangent at point P(4,1,4) is given by

30(x-4)-16(y-1)+18(z-4)=0

30x-120-16y+16+18z-72=0

30x-16y+18z=176

15x-8y+9z=88

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FinnZ [79.3K]

Answer:

Bro.. is this even a question...???

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2 years ago
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Hello, can anyone help me by answering all these? Please
kompoz [17]

Answer: See step by step

Step-by-step explanation: For A my 15 statements are.

  1. It has 3 triangles inside it, ACD, ADC, and ABC
  2. It has 2 right triangles, and 1 isoceles
  3. AC≅AB
  4. CD≅DB
  5. D is midpoint of CB
  6. AD⊥CB
  7. Angle CDA=90 degrees
  8. Angle  BDA equal 90 degrees
  9. AD≅AD
  10. ΔCDA≅ΔBDA by any congruence theorem, (SSS, SSA,AAS,ASA, HL)
  11. AD^{2}+ DB^{2}=AB^{2}

 12.AD^{2}+ CD^{2}= AC^{2}

   13. Triangle ABC has a max of 180 degrees.

     14. We can rotate this triangle 180 degrees and it will coincide.

       15. We can reflect triangle ACD over vertical line ACD and it will be congruent to ABD.

 2.  We use pythagorean theorem since it has a right angle.

      AD^{2}+ DB^{2}=AB^{2} Let plug it in.

      40^{2}+b^{2}=45^{2}

        1600+ b^2=2025

      b^2=424

      sqr root of 425 is about 21. Now let find the perimeter.

      AB is 45, Since BD+DC=CB, and they are congruent they are equal so 21+21=42 and AC is congruent to AB so it is 45. So the perimeter is  132.

  For 3. Start at the orgin, then go up 5 on the y-axis so you should be at (0,5)

   Then use the rise over run method to graph it. go left -3 and and up 1. Keep doing that 2 more times then draw a straight line.  

Your 3 point should be

(0,5)

(1,2)

(2,1)

   

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How many different triangles can be constructed with three sides, each measuring 5 centimeters?
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Jan spent $48 for 5 movie tickets. Three kids’ tickets were $8 each. How much were the 2 adult tickets. Write an equation to mod
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Answer:

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