(c) The line with equation y = 2x +k is a tangent to curve y = 3x² +4. Find the value of k.
1 answer:
Answer:
k = 11/3
Step-by-step explanation:
If the line is tangent to the curve, then Δ = 0.
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Remembering:
Δ>0 two different points of intersection x' x''
Δ=0 one point of intersection x' = x''
Δ<0 two different points of intersection in the complex plan x' and -x'
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As the line and the curve have one point of intersection, which is (x, y), we can make a equality between them:
2x + k = 3x² + 4
0 = 3x² - 2x + (4 - k)
Now we can use the Δ=0 (Δ= b² - 4ac)
Δ = 0 = (-2)² - 4.3.(4-k)
0 = 4 - 48 + 12k
12k = 44
k = 44/12 = 2 . 22 /3. 2.2 = 22/3.2 = 11/3
k = 11/3
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Answer:
No
Step-by-step explanation:
For a proportional relationship :
y = kx
Where , k = constant of proportionality
Taking the first set of data:
x = 50 ; y = 10
10 = 50k
k = 10/ 50 = 1/5
Hence, the proportional equation or relation is :
y = 1/5x
Check if this is true for other data points on the data :
Taking the second data point :
x = 85 ; check if y will be 20
From :
y = 1/5x
y = 1/5*85
y = 85/5
y = 17
Since ;
y value from the equation isn't the same as that in the table, then the table does not show a proportional relationship.
