The spider's movement is an illustration of a parabola.
- The equation of a parabola is:
- The focus of a parabola is: (40,-30)
- The axis of symmetry is:
- The directrix is:
<u>(a) The equation</u>
The spider passes through the origin.
So, we have:
The spider jumps to a maximum height of 10mm, midway 80mm.
So, the vertex is:
The equation of a parabola is:
So, we have:
Subtract 10 from both sides
Solve for a
Substitute and in
<u>(b) The focus, directrix and the axis of symmetry</u>
The focus of a parabola is:
Where:
So, we have:
So, we have:
The axis of symmetry is:
So, we have:
The directrix is:
Read more about parabolas at:
brainly.com/question/25237745
Exact form : 5/3
decimal form : 1.6 repeating
mixed number form : 1 2/3
A 54,311.87
It moves the decimal places to the left by two.
The sequence is an arithmetic sequence with
a₁ = -4
d = a₂ - a₁
d = -1 - (-4)
d = -1 + 4
d = 3
an = x
Sn = 437
General formula in arithmetic sequence
Formula to find nth term
an = a₁ + d(n - 1)
Formula to find sum of sequence (sn)
Sn = n/2 (a₁ + an)
We have to make an equation system based on the problem
plug the numbers into the formula
First equation
an = a₁ + d(n - 1)
x = -4 + 3(n - 1)
x = -4 + 3n - 3
x = 3n - 7
Second equation
Sn = n/2 (a₁ + an)
n/2 (a₁ + an) = 437
n/2 (-4 + x) = 437
n(x - 4) = 874
xn - 4n = 874
Solve the equation system by subtitution method
Subtitute x with 3n - 7 in the second equation
xn - 4n = 874
(3n - 7)n - 4n = 874
3n² - 7n - 4n = 874
3n² - 11n - 874 = 0
(3n + 46)(n - 19) = 0
n = -46/3 or n = 19
Because the number of terms shouldn't be negative, -46/3 isn't required, so the value of n is 19.
Solve for x, back to the first equatin
x = 3n - 7
x = 3(19) - 7
x = 57 - 7
x = 50
The solution is 50
Answer:
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