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2 years ago

Could someone help me on this

Mathematics

1 answer:

allochka39001 [22]2 years ago

8 0

Answer:

13.) 314.2 in²

15.) 181.5 ft²

Step-by-step explanation:

The area of a circle is found using the equation:

A = πr²

In this equation, "π" represents the number pi (3.14....) and "r" represents the radius (half the diameter).

For 13.), you have been given the radius. Thus, you can substitute it into the equation and solve for "A".

A = πr²

A = π(10)²

A = π x (100)

A = 314.2 in²

For 15.), you have been given the diameter. To find the radius, you need to divide this value by 2. Once you find the radius, you can plug it into the equation and simplify like above.

diameter = 15.2 ft
radius = 7.6 ft

A = πr²

A = π(7.6)²

A = π x (57.76)

A = 181.5 ft²

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A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has i

goldfiish [28.3K]

Answer:

P(t) = 100·2.3^t
529 after 2 hours
441 per hour, rate of growth at 2 hours
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Step-by-step explanation:

It often works well to write an exponential expression as ...

value = (initial value)×(growth factor)^(t/(growth period))

(a) Here, the growth factor for the bacteria is given as 230/100 = 2.3 in a period of 1 hour. The initial number is 100, so we can write the pupulation function as ...

P(t) = 100·2.3^t

(b) P(2) = 100·2.3^2 = 529 . . . number after 2 hours

(c) P'(t) = ln(2.3)P(t) ≈ 83.2909·2.3^t

P'(2) = 83.2909·2.3^2 ≈ 441 . . . bacteria per hour

(d) We want to find t such that ...

P(t) = 10000

100·2.3^t = 10000 . . . substitute for P(t)

2.3^t = 100 . . . . . . . . divide by 100

t·log(2.3) = log(100)

t = 2/log(2.3) ≈ 5.5 . . . hours until the population reaches 10,000

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4 years ago

I need help with number 4 I can’t get an answer

Alecsey [184]

Answer:

14.93

Step-by-step explanation:

For this problem you need to know distance formula, which is

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3 years ago

Which inequality is shown in the graph?

sergij07 [2.7K]

Answer:

The answer to your question is: letter C

Step-by-step explanation:

Data

Find the Parabola's equation and express the equation as an inequality.

Vertex = (0, -5)

Equation

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x² = y + 5

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But, we need the area upper the parabola, then

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3 years ago

For which function is f(x) equal to f^1(x) ( answer choices in picture )

Sonja [21]

Answer:

C. $f(x)=\frac{x+1}{x-1}$

Step-by-step explanation:

Let's find the inverse of each of the given options.

Option A:

$f(x)=\frac{x+6}{x-6}\\y=\frac{x+6}{x-6}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+6}{y-6}$

Rewrite in terms of 'y'. This gives,

$x(y-6)=y+6\\xy-6x=y+6\\xy-y=6x+6\\y=\frac{6x+6}{x-1}$

The given function $y=\frac{6x+6}{x-1}\ne y=\frac{x+6}{x-6}$

So, option A is incorrect.

Option B:

$f(x)=\frac{x+2}{x-2}\\y=\frac{x+2}{x-2}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+2}{y-2}$

Rewrite in terms of 'y'. This gives,

$x(y-2)=y+2\\xy-2x=y+2\\xy-y=2x+2\\y=\frac{2x+2}{x-1}$

The given function $y=\frac{2x+2}{x-1}\ne y=\frac{x+2}{x-2}$

So, option B is incorrect.

Option C:

$f(x)=\frac{x+1}{x-1}\\y=\frac{x+1}{x-1}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+1}{y-1}$

Rewrite in terms of 'y'. This gives,

$x(y-1)=y+1\\xy-x=y+1\\xy-y=x+1\\y=\frac{x+1}{x-1}$

The given function $y=\frac{x+1}{x-1}\ equals\ y=\frac{x+1}{x-1}$

So, option C is correct.

Option D:

$f(x)=\frac{x+5}{x-5}\\y=\frac{x+5}{x-5}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+5}{y-5}$

Rewrite in terms of 'y'. This gives,

$x(y-5)=y+5\\xy-5x=y+5\\xy-y=5x+5\\y=\frac{5x+5}{x-1}$

The given function $y=\frac{5x+5}{x-1}\ne y=\frac{x+6}{x-6}$

So, option D is incorrect.

Therefore, only option C is correct.

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3 years ago

If cos x=1/2 and 90°

Talja [164]

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3 years ago