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Anastasy [175]
2 years ago
13

What is the equation of the exponential graph shown?

Mathematics
1 answer:
Evgesh-ka [11]2 years ago
7 0

Answer:

  • f(x) = 100*(1/2)ˣ

Step-by-step explanation:

<u>Exponential function is:</u>

  • f(x) = a*bˣ

<u>Use two points on the graph to determine the value of a and b:</u>

  • (0, 100), (1, 50)

<u>Find the values of a and b:</u>

  • f(0) = a*b⁰ = a = 100
  • f(1) = a*b¹ = ab = 100b = 50 ⇒ b = 50/100 = 1/2

<u>The function is:</u>

  • f(x) = 100*(1/2)ˣ
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The diagram shows the cross-section of a wall of a cinema. It has to be painted. Work out the area that needs to be painted.
mestny [16]

Answer:

Area = 370 m²

Cost to paint = £105

Step-by-step explanation:

Area of the wall of a cinema hall = Area of a trapezoid (1)+ Area of a rectangle (2) + Area of a trapezoid (3)

Area of a trapezoid = \frac{1}{2}(b_1+b_2)h

where b_1 and b_2 are the parallel sides and h is the distance between these sides.

Area of trapezoid (1) = \frac{1}{2}(11+12)\times 6

                                  = 69 m²

Area of the rectangle (2) = Length × Width

                                         = 12 × 15

                                         = 180 m²

Area of the trapezoid (3) = \frac{1}{2}(12+10)\times 11

                                         = 121 m²

Now area of the wall = 69 + 180 + 121

                                   = 370 m²

One tin covers the area = 25 m²

Number of tins required to paint the wall = \frac{\text{Total area}}{\text{Area covered by one tin}}

= \frac{370}{25}

= 14.8

Therefore, number of tins to be purchased = 15

Cost to paint the complete wall = 15 × £7

                                                       = £105

8 0
3 years ago
Factor 2a2b3 - 14ab + 16a
zhuklara [117]

Answer:

2a(b^3 - 7b + 8)

Step-by-step explanation:

I'm assuming that 2a2b3 is 2a2b^2. If not, this answer isn't correct.

Look at the whole numbers. Is there a number that divides into them evenly? Yes, 2, so you pull 2 from the problem and divide each number by 2. Do the same for each variable.

2a2b3 - 14ab + 16a

2(ab^3 - 7ab +8a)

2a(b^3 - 7b + 8)

6 0
3 years ago
A store pays $3 for a magazine.The markup price is 5%
Andrew [12]
$3.00 x .05 = 15 cents

$3.00+ .15= $3.15

3.15 final answer
4 0
3 years ago
Use the Newton-Raphson method to find the root of the equation f(x) = In(3x) + 5x2, using an initial guess of x = 0.5 and a stop
xxMikexx [17]

Answer with explanation:

The equation which we have to solve by Newton-Raphson Method is,

 f(x)=log (3 x) +5 x²

f'(x)=\frac{1}{3x}+10 x

Initial Guess =0.5

Formula to find Iteration by Newton-Raphson method

  x_{n+1}=x_{n}-\frac{f(x_{n})}{f'(x_{n})}\\\\x_{1}=x_{0}-\frac{f(x_{0})}{f'(x_{0})}\\\\ x_{1}=0.5-\frac{\log(1.5)+1.25}{\frac{1}{1.5}+10 \times 0.5}\\\\x_{1}=0.5- \frac{0.1760+1.25}{0.67+5}\\\\x_{1}=0.5-\frac{1.426}{5.67}\\\\x_{1}=0.5-0.25149\\\\x_{1}=0.248

x_{2}=0.248-\frac{\log(0.744)+0.30752}{\frac{1}{0.744}+10 \times 0.248}\\\\x_{2}=0.248- \frac{-0.128+0.30752}{1.35+2.48}\\\\x_{2}=0.248-\frac{0.17952}{3.83}\\\\x_{2}=0.248-0.0468\\\\x_{2}=0.2012

x_{3}=0.2012-\frac{\log(0.6036)+0.2024072}{\frac{1}{0.6036}+10 \times 0.2012}\\\\x_{3}=0.2012- \frac{-0.2192+0.2025}{1.6567+2.012}\\\\x_{3}=0.2012-\frac{-0.0167}{3.6687}\\\\x_{3}=0.2012+0.0045\\\\x_{3}=0.2057

x_{4}=0.2057-\frac{\log(0.6171)+0.21156}{\frac{1}{0.6171}+10 \times 0.2057}\\\\x_{4}=0.2057- \frac{-0.2096+0.21156}{1.6204+2.057}\\\\x_{4}=0.2057-\frac{0.0019}{3.6774}\\\\x_{4}=0.2057-0.0005\\\\x_{4}=0.2052

So, root of the equation =0.205 (Approx)

Approximate relative error

                =\frac{\text{Actual value}}{\text{Given Value}}\\\\=\frac{0.205}{0.5}\\\\=0.41

 Approximate relative error in terms of Percentage

   =0.41 × 100

   = 41 %

7 0
3 years ago
There is an alien machine which produces seven aliens every two seconds. At this rate how many aliens will produces in one hour?
lyudmila [28]
Well, there are 60 minutes in 1 hour, and there are 60 seconds in 1 minute, so in 60 minutes, there are 60 * 60 seconds, or 3600 seconds in 60 minutes, or 1 hour, therefore, in 1 hour there are 3600 seconds.

the machine makes 7 aliens in 2 seconds, how many will it make in 3600 seconds?

\bf \begin{array}{ccll}&#10;aliens&seconds\\&#10;\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\&#10;7&2\\&#10;a&3600&#10;\end{array}\implies \cfrac{7}{a}=\cfrac{2}{3600}\implies \cfrac{7\cdot 3600}{2}=a

that many.
3 0
3 years ago
Read 2 more answers
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