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2 years ago

PLEASE HELP WITH THIS

Mathematics

2 answers:

ArbitrLikvidat [17]2 years ago

8 0

Answer:

Step-by-step explanation:

The question can be written is

5^x = 75

Now take the log of both sides.

log(5x) = log(75) Bring the x outside the brackets

x log(5) = log(75) Divide by log 5

x = log(75)/log(5)

log 75 = 1.8751

log 5 = .8990

x = 1.8751/.8990 = 2.6826

marusya05 [52]2 years ago

7 0

Answer:

(b) 2.68

Step-by-step explanation:

Your question has a link to a suitable calculator. All you need to do is make use of it. It tells you log₅(75) ≈ 2.68.

Other ways to look at the problem

If you recall that a logarithm represents an exponent of the base, you can ask yourself, what power 5 must be raised to in order to get 75. You know that 5^2 = 25, and 5^3 = 125, so the power will have to be between 2 and 3. There is only one answer choice in that range: 2.68.

The rules of logarithms let you rewrite the given expression as ...

log₅(75) = log₅(3×5²) = log₅(3) +2·log₅(5) = log₅(3) +2

The log₅ of any number between 1 and 5 will be a positive fraction, so this sum must be between 2 and 3.

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Step-by-step explanation:

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3 years ago

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3 years ago

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3 years ago

A rock is thrown upward from a bridge that is 22 feet above a road. The rock reaches its maximum height above the road 0.69 seco

Flura [38]

Answer:

f(t) = -7.561(t + 1.15)(t - 2.53)

Explanation:

The hint is that the function f can be written in the form:

f(t) = c (t - t₁) (t - t₂)

It is a quadratic function, i.e. a parabola.

The maximum point, maximum height, of a parabola is its vertex.

And the x-coordinate of the vertex is at the midpoint between the two x-intercepts.

The time when the rock reaches the road is one x-intercept: t = 2.53 seconds: (2.53, 0).

The other x-intercept is sucht that (x + 2.53) / 2 = 0.69

(x + 2.53) / 2 = 0.69
x + 2.53 = 1.38
x = 1.38 - 2.53
x = -1.15

Thus, the equation is:

f(t) = c(t + 1.15) (t - 2.53).

You can find c by doing t = 0, because at t = 0 the height, f(t), is 22 feet:

f(0) = 22 = c (0 +1.15)(0 - 2.53)
22 = c(1.15)(-2.53)
22 = c (-2.9095)
c = - 22/(2.9095)
c = - 7.561

Then, the function can be written as:

f(t) = -7.561(t + 1.15) (t - 2.53) ← answer

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3 years ago