Answer:
c.) aₙ = 5 × 4ⁿ⁻¹
Explanation:
Geometric sequence: aₙ = a(r)ⁿ⁻¹
where 'a' resembles first term of a sequence, 'r' is the common difference.
Here sequence: 5, 20, 80, 320,...
First term (a) = 5
Common difference (d) = second term ÷ first term = 20 ÷ 5 = 4
Hence putting into equation: aₙ = 5(4)ⁿ⁻¹
Answer:
the linearization is y = 1/4x +5/4
the linearization will produce <em>overestimates</em>
the values computed from this linearization are ...
f(3.98) ≈ 2.245
f(4.05) ≈ 2.2625
Step-by-step explanation:
Apparently, you have ...

from which you have correctly determined that ...

so that f(3) = 2 and f'(3) = 1/4. Putting these values into the point-slope form of the equation of a line, we get the linearization ...
g(x) = (1/4)(x -3) +2
g(x) = (1/4)x +5/4
__
The values from this linearization will be overestimates, as the curve f(x) is concave downward everywhere. The tangent (linearization) is necessarily above the curve everywhere.
__
At the given values, we find ...
g(3.98) = 2.245
g(4.05) = 2.2625
the second duckling is wandering by 2.6 units distance than the first duckling .
<u>Step-by-step explanation:</u>
Here we have , Two ducklings wander away from the nest while their mother is away. The first duckling's displacement (distance and direction) from the nest is (12,5) The second duckling's displacement is (13,-8) . We need to find How much farther did the second duckling wander than the first duckling. Let's find out:
Let a = (12,5) and b =(13,-8)
The distance each duckling wandered is the magnitude of its displacement vector. Therefore, the expression Distance second duck wandered is given by :
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
Therefore , the second duckling is wandering by 2.6 units distance than the first duckling .
The area covered by corn is x
The area covered by wheat is (x+480)
After 80% of wheat was collected, the new area was:
20/10(x+480)
=1/5(x+480)
After 25% of the corn was collected, the new area was:
75/100x
=3/4x
New area equation will be:
(3/4)x=1/5(x+480)+300
(3/4x)=(1/5)x+96+300
solving for x we get:
11/20x=396
x=720
thus the original area of corn was 720 acres
Original area of wheat was 720+480=1200 acres