Plot the points on a graph. Connect the dots into a triangle. See that the height of the triangle is from y=5 down to y=1. So the height is 4 units.
Area of a triangle: A = (1/2)BH
You need to find the length of the base. Which is from point (-4,1) to (0,1). You can use the distance formula r just see from the graph that the base is 4 units.
A = (1/2)(4)(4)
A = 8
** Distance formula fyi
d² = (X-x)² + (Y-y)²
with points (X,Y) and (x,y)
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You can solve this problem two ways.
1. Divide 68g by 100 to get how many grams per pound and multiply that by 150. This is the hard way.
2. Multiply 68 by 1.5 to get your answer. This is possible because 150 is 1.5 of 100, so multiplying the amount for 100 by 1.5 gives you your answer.
Answer:
<em> 200cm²</em>
Step-by-step explanation:
Total surface area of the prism = bh + L(s1+s2+s3)
b is the base of the triangle = 15cm
h is the height of the triangle = 8cm
Perimeter of the triangular base = s1 + s2 + s3 = 8+17+15
Perimeter of the triangular base = 40cm
L is the lateral height = 2cm
Substitute the given values into the formula;
Total surface area of the prism = 15(8) + 2(40)
Total surface area of the prism = 120+80
Total surface area of the prism = 200cm²
<em>Hence the total surface area of the prism is 200cm²</em>
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:
