Those are all lines...
So the x interval is from -2 to 3, because of x=-2 and x=3
The upper line is y(u)=4x and the lower line is y(l)=x-5
So the area between the two lines is:
A=⌠y(u)-y(l) dx
A=⌠4x-x+5 dx
A=⌠3x+5 dx
A=[3x^2/2+5x]
A=[(3x^2+10x)/2], x=[-2,3]
A=(1/2)(27+30-(12-20))
A=(1/2)(57+8)
A=(1/2)(65)
A=32.5 u^2
Answer:
140 ft
Step-by-step explanation:
Given data
Area= 14 square feet
Height a = 1/5 ft
Base b=????
We know that the area of a triangle is given as
Area= (1/2)B*H
substitute
14= 1/2* B* 1/5
14= B/10
cross multiply
B= 140
Hence the base is 140 ft
The horizontal distance until the plan flies over the island is 2687.05 feet approximately.
<u>Solution:</u>
Given that, A plane at an altitude of 7000 ft is flying in the direction of an island
An angle of depression is 21 degree from the plane to the island
We have to find what is the horizontal distance until the plan flies over the island
The diagram is attached below
Assume as shown in the diagram
, now we can use the right angle triangle property




Hence, the distance between plane and point above island is 2687.05 feet approximately.
Using the slope concept, it is found that the angle between the ladder and the floor will be of 33.69º.
<h3>What is a slope?</h3>
The slope is given by the <u>vertical change divided by the horizontal change</u>, and it's also the tangent of the angle of depression.
In this problem, we have that:
- The vertical distance is the height of h.
- The horizontal distance is of 3m.
Hence:
tan(45º) = h/3.
1 = h/3.
h = 3 m.
If the ladder slides 1 m down, the height will be of 2m, hence the angle will be given as follows:



More can be learned about the slope concept at brainly.com/question/18090623
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