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azamat
2 years ago
10

-

Mathematics
1 answer:
bixtya [17]2 years ago
7 0

Using an exponential function, it is found that f(5.5) = 19.8.

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

An exponential function is a function in which the growth rate is a percentage, modeled by:

y = ab^x

In which:

  • a is the initial value.
  • b is the rate of change.

f(3.5) = 25 means that:

ab^{3.5} = 25

a = \frac{25}{b^{3.5}}

f(8.5) = 14 means that:

ab^{8.5} = 14

Hence:

\frac{25}{b^{3.5}} \times b^{8.5} = 14

25b^5 = 14

b = \sqrt[5]{\frac{14}{25}}

b = 0.89

a = \frac{25}{0.89^{3.5}} = 37.59

Hence, the function is given by:

y = 37.59(0.89)^x

Then, when x = 5.5:

f(5.5) = 37.59(0.89)^{5.5} = 19.8

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

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Write each power as a product of the same factor then find the value of 10 power 6
swat32

Answer:

1,000,000

Step-by-step explanation: I just know

7 0
3 years ago
Fill in the blank. In the triangle below, zº =
lianna [129]

Answer:

38^{\circ}

Step-by-step explanation:

In a given triangle, the sum of every angle is always 180^{\circ}. Here, we are given a right angle (90^{\circ}), as well as another 52^{\circ} angle. Simply subtracting from 180 will give us the answer.

z^{\circ}=180^{\circ}-90^{\circ}-52^{\circ} \\z^{\circ}=90^{\circ}-52^{\circ} \\z^{\circ}=38^{\circ}

5 0
3 years ago
Read 2 more answers
G(x) = 60(1 - 0.5)^x, g(4) *<br><br><br> Please do answer step by step
Flura [38]

Answer:

3.75

Step-by-step explanation:

g(x)=60(1-0.5)^x, g(4)

g(4)=60(1-0.5)^4

g(4)=60(.5)^4

g(4)=60(0.0625)

g(4)=3.75

7 0
3 years ago
Find an equation of the line containing the centers of the two circles whose equations are given below.
Anna35 [415]

Answer:

<h2><em>3y+x = -5</em></h2>

Step-by-step explanation:

The general equation of a circle is expressed as x²+y²+2gx+2fy+c = 0 with centre at C (-g, -f).

Given the equation of the circles x²+y²−2x+4y+1  =0  and x²+y²+4x+2y+4  =0, to  get the centre of both circles,<em> we will compare both equations with the general form of the equation above as shown;</em>

For the circle with equation x²+y²−2x+4y+1  =0:

2gx = -2x

2g = -2

Divide both sides by 2:

2g/2 = -2/2

g = -1

Also, 2fy = 4y

2f = 4

f = 2

The centre of the circle is (-(-1), -2) = (1, -2)

For the circle with equation x²+y²+4x+2y+4  =0:

2gx = 4x

2g = 4

Divide both sides by 2:

2g/2 = 4/2

g = 2

Also, 2fy = 2y

2f = 2

f = 1

The centre of the circle is (-2, -1)

Next is to find the equation of a line containing the two centres (1, -2) and (-2.-1).

The standard equation of a line is expressed as y = mx+c where;

m is the slope

c is the intercept

Slope m = Δy/Δx = y₂-y₁/x₂-x₁

from both centres, x₁= 1, y₁= -2, x₂ = -2 and y₂ = -1

m = -1-(-2)/-2-1

m = -1+2/-3

m = -1/3

The slope of the line is -1/3

To get the intercept c, we will substitute any of the points and the slope into the equation of the line above.

Substituting the point (-2, -1) and slope of -1/3 into the equation y = mx+c

-1 = -1/3(-2)+c

-1 = 2/3+c

c = -1-2/3

c = -5/3

Finally, we will substitute m = -1/3 and c = 05/3 into the equation y = mx+c.

y = -1/3 x + (-5/3)

y = -x/3-5/3

Multiply through by 3

3y = -x-5

3y+x = -5

<em>Hence the equation of the line containing the centers of the two circles is 3y+x = -5</em>

5 0
3 years ago
Help me please. I don't understand this.
navik [9.2K]

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

Apparently, you're being asked to identify the sequence of steps you would use to compute the volume of the pyramid.

It seems to be a good idea to start with the formula for the volume.

Then, recognize that you need to compute B, so make that computation. The area of the base (B) is the product of the base dimensions (14)(12).

Once you have the value of B, then you can put that, along with the value of h, into the original volume formula.

Evaluating it gives the volume in cubic units.

_____

<em>Additional comment</em>

If you're familiar with the pyramid volume formula, you know that you must compute B before you can make use of the formula. That makes the sequence be B=14(12); B=168; V=1/3Bh; V=1/3(168)(7).

However, if you're starting from scratch, it is probably good to begin with the volume formula. That is what tells you that you need to find B in the first place. This is the sequence we show below.

6 0
3 years ago
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