I have to find an equation for a table
1 answer:
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The equation of the piecewise function is
On the graph, we have:
- y = 3 for all x values not more than -1
- y = -1 for all values greater than 2
Hence, the piecewise function is:
This is the set of input values
In (a), we have:
x ≤ -1 and x > 2
Hence, the domain is (∞, 3] u (2, ∞)
<h3>The range of the function</h3>This is the set of output values
In (a), we have:
f(x) = 3 and f(x) -1
Hence, the range is [3] u (-1)
Read more about piecewise function at:
#SPJ1
Given : In Right triangle ABC, AC=6 cm, BC=8 cm.Point M and N belong to AB so that AM:MN:NB=1:2.5:1.5.
To find : Area (ΔMNC)
Solution: In Δ ABC, right angled at C,
AC= 6 cm, BC= 8 cm
Using pythagoras theorem
AB² =AC²+ BC²
=6²+8²
= 36 + 64
→AB² =100
→AB² =10²
→AB =10
Also, AM:MN:NB=1:2.5:1.5
Then AM, MN, NB are k, 2.5 k, 1.5 k.
→2.5 k + k+1.5 k= 10
→ 5 k =10
Dividing both sides by 2, we get
→ k =2
MN=2.5×2=5 cm, NB=1.5×2=3 cm, AM=2 cm
As Δ ACB and ΔMNC are similar by SAS.
So when triangles are similar , their sides are proportional and ratio of their areas is equal to square of their corresponding sides.
But Area (ΔACB)=1/2×6×8= 24 cm²[ACB is a right angled triangle]
→ Area(ΔMNC)=24÷4
→Area(ΔMNC)=6 cm²
