The magnitude of the Pennsylvania earthquake is 4.
<h3>What is a logarithm function?</h3>
An exponent is a logarithm. You may convert any exponential expression to logarithmic form. As an illustration, if 8 = 23, the base is 2, the exponent is 3, and the outcome is 8. This may be represented as 3 = log2 8 in logarithmic notation.
The equation y=logb(x+h)+k shifts the logarithmic function, y=logbx, by k units vertically and h units horizontally.
Using the formula,
log I₁ / I₂ = M₁ - M₂
M₁ = 7.7, I₁ / I₂ = 4900
log 4900 = 7.7 - M₂
log 4900 ≈ 3.69
On calculating,
M₂ ≈ 4
The magnitude of the Pennsylvania earthquake is 4.
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See below for the proof of the equation
<h3>How to prove the equation?</h3>
The equation is given as:
Take the LCM
Expand
Evaluate the like terms
Rewrite as:
Factorize the numerator
Divide
2(a - b)= 2(a - b)
Both sides are equal
Hence, the equation has been proved
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9514 1404 393
Answer:
y = 1/4x^1 -x -4
Step-by-step explanation:
Same question as previous parts. The working is identical, using different numbers.
Focus-vertex distance is (y-difference) p = -4-(-5) = 1. Vertex is (h, k) = (2, -5). Putting these values into the vertex form and expanding to standard form, you get ...
y = (1/(4p))(x -h)^2 +k
y = 1/4(x -2)^2 -5 . . . . . . . . fill in the values for p, h, k
y = 1/4(x^2 -4x +4) -5 . . . . expand the square
y = 1/4x^2 -x +1 -5 . . . . . . . use the distributive property to eliminate parens
y = 1/4x^1 -x -4 . . . . . . . . . collect terms
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Answer:
Step-by-step explanation:
We want to for a polynomial function whose real zeros are -2 with multiplicity 2 and 4 with multiplicity 1.
If -2 is a zero of a polynomial, then by the factor theorem, x+2 is a factor.
Since -2 has multiplicity 2, (x+2)² is a factor.
Also 4 is a zero which means x-4 is a factor.
We write the polynomial in factored form as:
We expand to get:
We expand further to get: