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ANTONII [103]
2 years ago
5

Find the exponential function that passes through the points (2,80) and (5,5120)​

Mathematics
1 answer:
juin [17]2 years ago
3 0

Answer:

  y = 5·4^x

Step-by-step explanation:

If you have two points, (x1, y1) and (x2, y2), whose relationship can be described by the exponential function ...

  y = a·b^x

you can find the values of 'a' and 'b' as follows.

Substitute the given points:

  y1 = a·b^(x1)

  y2 = a·b^(x1)

Divide the second equation by the first:

  y2/y1 = ((ab^(x2))/(ab^(x1)) = b^(x2 -x1)

Take the inverse power (root):

  (y2/y1)^(1/(x2 -x1) = b

Use this value of 'b' to find 'a'. Here, we have solved the first equation for 'a'.

  a = y1/(b^(x1))

In summary:

  • b = (y2/y1)^(1/(x2 -x1))
  • a = y1·b^(-x1)

__

For the problem at hand, (x1, y1) = (2, 80) and (x2, y2) = (5, 5120).

  b = (5120/80)^(1/(5-2)) = ∛64 = 4

  a = 80·4^(-2) = 80/16 = 5

The exponential function is ...

  y = 5·4^x

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What four factors were used to create this product game board 9,15,18,21,30,35,36,42,49
IgorLugansk [536]
To see what are the factors use, we write each of the numbers, as product of prime factors:

9= 3 \cdot 3\\\\
15=3 \cdot 5\\\\
18= 2 \cdot 9 = 2 \cdot 3 \cdot3\\\\21= 3\cdot 7\\\\30=3 \cdot10=3 \cdot 2 \cdot 5\\\\35=5 \cdot7\\\\36=6\cdot6=2\cdot3\cdot2\cdot3\\\\42=6\cdot7=2\cdot3\cdot7\\\\49=7\cdot7


As we can see, the 4 factors used to produce the numbers in the list are {2, 3, 5, 7}


Answer:  {2, 3, 5, 7}
5 0
3 years ago
Read 2 more answers
Let P(x) = 3x³-ax+b. If P(1) = P(-1) and P(2)=16, find the values of a and b
kozerog [31]

P(1) = P(-1)

P(1) = 3 - a + b
P(-1) = -3 + a + b

-> 3 - a + b = -3 + a + b
-> 3 - a + b + 3 - a - b = 0
-> 6 - 2a = 0
-> a = 3.

P(2) = 24 - 2a + b -> 24 - (2a - b) = 16 -> 2a - b = 8
-> 6 - b = 8
b = -2.

So, a = 3 and b = -2

Recheck : P(1) = 3 - 3 + (-2) = -2
P(-1) = -3 + 3 + (-2) = -2 => P(1) = P(-1) (true)

P(2) = 24 - 6 + (-2) = 16.

6 0
2 years ago
Using the sine rule, calculate the length y. Give your answer to 2 s.f.​
Tpy6a [65]

Answer:

y = 9.84 mm

Step-by-step explanation:

<h2>Sine rule:</h2>

Law of sine:

   \sf \boxed{\bf \dfrac{a}{Sin \ A}=\dfrac{b}{Sin \ B}= \dfrac{c}{Sin \ C}}

    a = y

    A = 31°

   b  = 17 mm

    B = 117°

\sf \dfrac{y}{Sin \ 31^\circ}=\dfrac{17}{Sin \ 117^\circ}\\\\

          \sf y = \dfrac{17}{Sin \ 117^\circ}*Sin \ 31^\circ\\\\  y = \dfrac{17}{0.89}*0.515\\\\y = 9.84 \ mm

8 0
2 years ago
Nhich pairs of triangles appear to be congruent? Check all that apply.
Fiesta28 [93]

Answer:

Answer is B and C Triangles 1, 3 and 4 appear to be congruent

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