A trapezoid with a right angle and an area greater than 40 square inches
1 answer:
Answer:
see the attached figure.
Step-by-step explanation:
We need to draw a trapezoid with a right angle and an area greater than 40 square inches
See the attached figure
The area of the trapezoid = 0.5 ( base_1 + base_2 ) * height
So, as shown ABCD is a trapezoid with a right angle at A
base_1 = 14 inches , base_2 = 10 inches and the height = 5 inches
So, the area = 0.5 ( 14 + 10 ) * 5 = 0.5 * 24 * 5 = 60 square inches > 40
Note: we can use any numbers other than 5 , 10 , 14
for example: 5 , 8 , 12 in this case the area = 0.5 * (8+12) * 5 = 50 > 40
<u>The point is choose any numbers which gives area > 40</u>
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Answer:
Area = 32/3
Step-by-step explanation:
x = u ²
y = uv
z = 12v ²
0 ≤ u ≤ 2
0 ≤ v ≤ 1
Since ru = <2u, v, 0> and rv = <0, u, 24v>, we have
Where ru is the differentiation of x, y, z with respect to u and rv is the differentiation of x, y, z wit respect to v.
we find the cross product of ru and rv
ru × rv = 24v²i - 48uv²j + 2u²k
absolute value of ru × rv = 2u² + 24v²
We can now find the area
∫₀² du ∫₀¹ dv (2u² + 24v²) = ∫₀² du [2u²v + 8v³]₀¹ = 32/3
Detailed description can be found in the attachment
Answer:
a) f(x) = x² -9
function is an even function
b) g(x) = |x -3|
function is an even function
c) f(x)= x / x²-1
function is odd function
d) g(x) = x + x²
Given function is not an even not odd function
This function is neither even or odd
Step-by-step explanation:
<u><em>Explanation</em></u>:-
a) Given f(x) = x² -9
<u><em>Even function </em></u>
If f(-x) = f(x) , then the function is even function.
f(-x) = (-x)² -9
= x² -9
= f(x)
f(-x) = f(x)
∴ Given function is an even function
b)
Given g(x) = |x -3|
<u><em>Even function </em></u>
If g(-x) = g(x) , then the function is even function.
g(-x) = |-(x-3)|
= |x-3|
g(-x) = g(x)
∴ Given function is an even function
c)
<u><em>odd function</em></u>
If f(-x) =- f(x) , then the function is odd function.
f(-x) =
= -f(x)
f(-x) = -f(x)
∴ Given function is odd function
d)
If g(-x) = g(x) , then the function is even function.
g(x) = x + x²
g(-x) = -x + (-x)²
= - (x - x²)
This is not either even or odd function
∴ Given function is neither function