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ch4aika [34]
3 years ago
14

Write an exponential function y = ab" whose graph passes through (2,12) and (5,96).

Mathematics
1 answer:
motikmotik3 years ago
3 0

Answer:

y = 3(2)^{x}

Step-by-step explanation:

Substitute the given points into the function and solve for a and b

Using (2, 12)

12 = ab² → (1)

Using (5, 96)

96 = ab^{5} → (2)

Divide (2) by (1)

\frac{ab^5}{ab^2} = \frac{96}{12} , that is

b³ = 8 ( take the cube root of both sides )

b = \sqrt[3]{8} = 2

Substitute b = 2 into (1) and solve for a

12 = a2² = 4a ( divide both sides by 4 )

3 = a

Thus

y = 3(2)^{x} ← is the exponential function

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son4ous [18]
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6 0
3 years ago
You throw a ball up and its height h can be tracked using the equation h=2x^2-12x+20.
postnew [5]

<em><u>This problem seems to be wrong because no minimum point was found and no point of landing exists</u></em>

Answer:

1) There is no maximum height

2) The ball will never land

Step-by-step explanation:

<u>Derivatives</u>

Sometimes we need to find the maximum or minimum value of a function in a given interval. The derivative is a very handy tool for this task. We only have to compute the first derivative f' and have it equal to 0. That will give us the critical points.

Then, compute the second derivative f'' and evaluate the critical points in there. The criteria establish that

If f''(a) is positive, then x=a is a minimum

If f''(a) is negative, then x=a is a maximum

1)

The function provided in the question is

h(x)=2x^2-12x+20

Let's find the first derivative

h'(x)=4x-12

solving h'=0:

4x-12=0

x=3

Computing h''

h''(x)=4

It means that no matter the value of x, the second derivative is always positive, so x=3 is a minimum. The function doesn't have a local maximum or the ball will never reach a maximum height

2)

To find when will the ball land, we set h=0

2x^2-12x+20=0

Simplifying by 2

x^2-6x+10=0

Completing squares

x^2-6x+9+10-9=0

Factoring and rearranging

(x-3)^2=-1

There is no real value of x to solve the above equation, so the ball will never land.

This problem seems to be wrong because no minimum point was found and no point of landing exists

3 0
3 years ago
How do i do segment measures
Eduardwww [97]

Asimply measure its length. What else could you measure? After all, length is the only feature a segment has. You’ve got your short, your medium, and your long segments.

Step-by-step explanation:

length

7 0
3 years ago
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bija089 [108]

Answer:

<h3>m% of n</h3><h3>m/100 . n</h3>

<h3>mn/100</h3>

Step-by-step explanation:

<h3>I hope it helps ❤❤</h3>
8 0
2 years ago
7x2 +11x-6/7x2 - 10x + 3
velikii [3]

Answer:

Final result :

 x + 2

 —————

 x - 1

Step-by-step explanation:

Step-1 : Multiply the coefficient of the first term by the constant   7 • 3 = 21  

Step-2 : Find two factors of  21  whose sum equals the coefficient of the middle term, which is   -10 .

     -21    +    -1    =    -22  

     -7    +    -3    =    -10    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -7  and  -3  

                    7x2 - 7x - 3x - 3

Step-4 : Add up the first 2 terms, pulling out like factors :

                   7x • (x-1)

             Add up the last 2 terms, pulling out common factors :

                   3 • (x-1)

Step-5 : Add up the four terms of step 4 :

                   (7x-3)  •  (x-1)

            Which is the desired factorization

Please mark brainliest and have a great day!

3 0
3 years ago
Read 2 more answers
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