In the following diagram HI || JK.What is the measure of Angles are not necessarily drawn to scale.
1 answer:
ANSWER
xº = 52º
EXPLANATION
Since segments HI and JK are parallel, we can see segment AK as a transversal:
So angle JKA and angle HIA are <em>corresponding angles</em> and they are congruent.
Then we have triangle HAI, and we have two of the angle's measures. The sum of the measures of the interior angles of a triangle is 180º:
Solving for x:
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Answer:
A) Area as function of H ,
F'(a) = 2 +H
B) Area of triangle with height 6ft = 30 ft²
Step-by-step explanation:
Given as for a triangle ,
Let the height of triangle = H ft
And base = 4 ft + H ft
Now area of triangle = × height × base
F (a) = × H × ( 4ft + H ft)
Or, F (a) = × ( 4H + H² )
Now, here Area is function of height ,
So , F'(a) = (4 + 2H)
Hence Area as function of H ,
F'(a) = 2 +H
Now For height = 6 ft
Area of triangle = × height × base
= × H × ( 4ft + H ft)
= × ( 4H + H² )
= × ( 24 + 36 )
= × ( 60 )
= 30 ft²
Hence Area of triangle with height 6ft = 30 ft² Answer
The time for the village to dig the new well is about 7 1/2 years. At this time the population doubles from its current size.
<h3>How to graph a function?</h3>For a function f(x) = y, the steps to draw a graph for the given function are as follows:
- Consider certain values of x
- Substitute x values in the given function to obtain y values
- Plot the x and y values in the graph
- Join the points to know the variation.
It is given that,
f(x) = 200 ×
Village's population growing rate = 9.8%
Creating a table for x and f(x) values:
x: 0 2 4 6 8 10
f(x = 0) = f(0) = 200 × = 200
f(x = 2) = f(2) = 200 × = 241
f(x = 4) = f(4) = 200 × = 291
f(x = 6) = f(6) = 200 × = 350
f(x = 8) = f(8) = 200 × = 423
f(x = 10) = f(10) = 200 × = 509
So,
(x, f(x)): (0, 200) (2, 241) (4, 291) (6, 350) (8, 423) (10, 509)
Plotting these points in the graph and joining the points, the graph is shown below.
Finding the time for the village to dig a new well:
It is given that the population doubled from its current size, the village will need to dig new water well.
The current size of the village = 200
If it doubles for a certain time 't' = 400
So,
400 = 200 ×
⇒ = 2
⇒ log = log 2
⇒ t log(1.098) = 0.301
⇒ t × 0.04 = 0.301
∴ t = 7.525 years
Therefore, the village's population becomes double at the time 7 and half years from now. So, after 7 1/2 years, the village needs to dig a new well.
Learn more about the function and its graph here:
#SPJ1
