Answer:
B. 152 cm²
Step-by-step explanation:
To find the surface area using a net, do this:
Take apart the figure. We see that there are three rectangles and two triangles. Find the area of each (
) and then add the values together:
The first rectangle on the left is the same as the one on the right.
Two measures are 40 cm².
The middle rectangle is:
48 cm²
The formula for the area of a triangle is 
:
The area of the two triangles is 12 cm².
Now add the values:
The area of the figure is 152 cm².
:Done
Answer:
9 feet
Step-by-step explanation:
Given:
The border of the garden is a right angled triangle.
Two lengths are given as 12 ft and 15 ft.
Let the length of the shortest timber be 'x' feet.
Now, in a right angled triangle, the longest length is called the hypotenuse.
As 15 feet is the largest length, it is the hypotenuse of the triangle. Now, applying Pythagoras theorem, we get:
The negative value is neglected as length can never be negative.
Therefore, the length of the shortest timber is 9 feet.
As usual, draw a diagram. You can easily see that if you are x away from the wall,
<span>the angle of elevation of the bottom of the screen (A) is </span>
<span>cotA = x/3 </span>
<span>A = arccot(x/3) </span>
<span>angle B to the top is </span>
<span>cotB = x/10 </span>
<span>B = arccot(x/10) </span>
<span>So, since θ = B-A </span>
<span>dθ/dt = dB/dt - dA/dt </span>
<span>= -3/(x^2+9) + 10/(x^2+100) </span>
<span>= 7(x^2-30)/((x^2+9)(x^2+100)) </span>
<span>so, at x=30 </span>
<span>dθ/dt = 203/30300</span>
