Answer:
15
Step-by-step explanation:
since 3d is multiplying, it would be set up as 3*5=15
Answer:1,230.5
Reason: just learn how to divide
Answer:
Equation of tangent plane to given parametric equation is:

Step-by-step explanation:
Given equation
---(1)
Normal vector tangent to plane is:


Normal vector tangent to plane is given by:
![r_{u} \times r_{v} =det\left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\cos(v)&sin(v)&0\\-usin(v)&ucos(v)&1\end{array}\right]](https://tex.z-dn.net/?f=r_%7Bu%7D%20%5Ctimes%20r_%7Bv%7D%20%3Ddet%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Chat%7Bi%7D%26%5Chat%7Bj%7D%26%5Chat%7Bk%7D%5C%5Ccos%28v%29%26sin%28v%29%260%5C%5C-usin%28v%29%26ucos%28v%29%261%5Cend%7Barray%7D%5Cright%5D)
Expanding with first row

at u=5, v =π/3
---(2)
at u=5, v =π/3 (1) becomes,



From above eq coordinates of r₀ can be found as:

From (2) coordinates of normal vector can be found as
Equation of tangent line can be found as:

Answer:
Step-by-step explanation:
<u>Given equation:</u>
- x² + y² + 8x - 4y - 7 = 0
<u>Convert this to standard form by completing the square:</u>
- (x - h)² + (y - k)² = r², where (h, k) - center, r - radius
- x² + 2*4x + 4² + y² - 2*2y + 2² - 16 - 4 - 7 = 0
- (x + 4)² + (y - 2)² - 27 = 0
- (x + 4)² + (y - 2)² = 27
- (x + 4)² + (y - 2)² = (√27)²
The center is (- 4, 2) and the radius is √27
Answer:
(g ○ f)(- 5) = 4
Step-by-step explanation:
evaluate f(- 5) then substitute the value obtained into g(x)
f(- 5) = (- 5)² + 6(- 5) + 3 = 25 - 30 + 3 = - 2 , then
g(- 2) = 2(- 2) + 8 = - 4 + 8 = 4
(g ○ f)(- 5) = 4