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Kamila [148]
3 years ago
8

If x is an acute angle and tan x = 5,

Mathematics
1 answer:
lyudmila [28]3 years ago
4 0
We have that
tan x=5

we know that
tan x =sin x/ cos x
sin x/ cos x=5------> squaring-----> sin² x/cos² x=25
remember that
sin² x+cos² x=1-----> cos² x=1-sin² x
substitute
sin² x/[1-sin² x]=25
sin² x=25-25*sin² x
26*sin² x=25
sin² x=25/26
sin x=5/√26

cos² x=1-(5/√26)²----> 1-(25/26)----> 1/26
cos x=1/√26

the answers are
sin x=5/√26
cos x=1/√26

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4 years ago
A group of yeast cells grows by 75% every 3hrs. At 9am, there are 200 yeast cells [9 marks].
vodomira [7]

a) The exponential function that models the number of cells is: A(t) = 200(1.75)^{\frac{t}{3}}

b) There will be 1292 cells after 10 hours.

<h3>What is an exponential function?</h3>

An increasing exponential function is modeled by:

A(t) = A(0)(1 + r)^{\frac{t}{n}}

In which:

  • A(t) is the amount after t hours.
  • A(0) is the initial amount.
  • r is the rate of change, as a decimal.
  • n is the time it takes to change.

For this problem, the parameters are:

A(0) = 200, r = 0.75, n = 3.

Hence the equation is:

A(t) = A(0)(1 + r)^{\frac{t}{n}}

A(t) = 200(1 + 0.75)^{\frac{t}{3}}

A(t) = 200(1.75)^{\frac{t}{3}}

The number of cells after 10 hours is:

A(t) = 200(1.75)^{\frac{t}{3}}

A(10) = 200(1.75)^{\frac{10}{3}}

A(10) = 1292.

More can be learned about exponential functions at brainly.com/question/25537936

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7 0
2 years ago
What is the square root of 33
larisa [96]

Answer and Explanation: The square root of 33, √33, equals approximately 5.74456. The easiest way to start is to consider the factors of 33. 1, 3, 11, etc.

3 0
3 years ago
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Find the slope of the line that passes through the pair of points (6,-2) and (5,-4).
wel

Answer:

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<u>Step-by-step explanation:</u>

co-ordinates = (6,-2) (5,-4)

slope = (y² - y¹) / (x² - x¹)

slope = (-4 - 6) / (5 - (-2))

slope = (-10) / (5+2)

slope = (-10) / 7

slope = -10 / 7

6 0
3 years ago
Read 2 more answers
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You should use photo math it helps a lot
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3 years ago
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