f(x)=lnx
y=f(x)
dy/dx= 1/x
tangent at (x,y) has slope 1/x
eqn of tangent is y = mx + c
since the tangent passes through origin, c=0
substitute y = lnx and m= 1/x to above eqn
lnx = 1
x=e
y=lne=1
Vertex: 0,4.92
focus: 0,4.8575
axis of symmetry: x = 0
directrix: y = 4.9825
Answer:
Point H does lie on the graph y = 4.6x - 7
Step-by-step explanation:
Step 1: Define
y = 4.6x - 7
H(0, -7)
Step 2: Substitute, Evaluate, and Check
-7 = 4.6(0) - 7
-7 = 0 - 7
-7 = -7
Answer:
y = 3/5x + 5
Step-by-step explanation:
Slope-intercept form is y = mx + b where m is the slope (rise / run of the line) and b is y-intercept (y value of where the line intersects with the y-axis.
The line is rising up 3 and run to the right 5 and so it's slope is 3/5. The line intersects with the y-axis at a y value of 5 and so it's y-intercept is 5.
Therefore, your answer in slope-intercept form is y = 3/5x + 5.
Answer:
1. 15 - 5n where n>=1
2. n² where n>=1
Step-by-step explanation:
1. {10, 5, 0, -5, -10} is an Arithmetic Progression
nth term is a + (n - 1)d
where a = first term, n= nth term, d= common difference.
a = 10, d = -5 (5-10, 0-5, -5-0, -10-(-5))
Therefore, nth(General) term of the sequence:
= 10 + (n - 1)-5
= 10 + (-5n) + 5
= 10 + 5 - 5n
= 15 - 5n
Test:
if n = 1; 15 - 5(1) = 10
if n = 2; 15 - 5(2) = 5
if n = 3; 15 - 5(3) = 0 and so on.
2. {1, 4, 9, 16, 25}
The general term of the sequence is n²
Test:
if n = 1; 1² = 1
if n = 2; 2² = 4
if n = 3; 3² = 9 and so on.
