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dmitriy555 [2]
3 years ago
11

A curve passes through the point ( 0 , 7 ) (0,7) and has the property that the slope of the curve at every point P P is twice th

e y y -coordinate of P P . What is the equation of the curve
Mathematics
1 answer:
STatiana [176]3 years ago
6 0

Answer:

The equation for the curve is:

f(x) = 7*e^{2*x}

Step-by-step explanation:

We know that for a curve defined as:

y = f(x)

The slope of the curve at the point x is:

y = f'(x)

where f'(x) = df(x)/dx

Here we know that we have a function that passes through the point (0, 7)

We also know that the slope of the curve at every point is twice the value of the y-coordinate. (remember that the y-coordinate is given by f(x))

Then we have two equations:

f(0) = 7

f'(x) = 2*f(x)

From the shape of the equation, we can assume than this is an exponential equation like:

f(x) = A*e^{k*x}

Replacing that in the second equation, we get:

k*A*e^{k*x} = 2*A*e^{k*x}

From that equation, we can conclude that k = 2

Then:

f(x) = A*e^{2*x}

Now we can use the first equation:

f(0) = 7

With this, we can find the value of A.

f(0) = 7 =  A*e^{2*0}\\7 = A*e^0 = A*1\\7 = A

Then we can conclude that the equation for the curve is:

f(x) = 7*e^{2*x}

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What is the average rate of change for the sequence shown below?​
statuscvo [17]

Answer:

-1/2

Step-by-step explanation:

If you connected the dots here you would have a straight line.  The average rate of change for a straight line is also known as the slope.  Slope, by definition, is rise over run (although rise doesn't necessarily mean "up"; it could also mean down, as it does here).  From one point to the next in our graph, we go down 1 unit (-1) and to the right 2 units (+2).  Therefore, the slope of the line is -1/2.

6 0
3 years ago
What is 52,437 rounded to the nearest 100
Liono4ka [1.6K]

Answer:

52400

Step-by-step explanation:

52437

52400

Answer:  52400

4 0
3 years ago
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If 75 people attend a concert and tickets for adults cost $2.75 while tickets for children cost $2.25 and
Serhud [2]

Answer:

Adult = 39

Children = 36

Step-by-step explanation:

The total number of people = 75

Cost of adult ticket = $2.75

Cost of children ticket = $2.25

Total receipts = $188.25

Let the number of adult = x

Let the number of children = y

X + y = 75 ......equation (i)

(X × 2.75) + (y × 2.25) = 188.25

2.75x + 2.25y = 188.25.......equation (ii)

To find the numbe of adult and children that attended, we'll have to solve equation (i) and (ii) simultaneously.

From equation 1,

X + y = 75

X = 75 - y......equation(iii)

Put equation (iii) into equation (ii)

2.75*(75 - y) + 2.25y = 188.25

206.25 - 2.75y + 2.25y = 188.25

206.25 - 0.5y = 188.25

Collect liketerms

0.5y = 206.25 - 188.25

0.5y = 18

Y = 18 / 0.5

Y = 36

Put y = 36 into equation (i)

X + 36 = 75

X = 39

Therefore the number of adult is 39 while that of children is 36.

4 0
3 years ago
10.)A child-sized swimming pool can be modeled by a cylinder. The pool has a diameter of 6 1/2 feet and a height of 12 inches. T
Luba_88 [7]

Answer:

165.47≈165 Gallons of Water

Step-by-step explanation:

According To the Question,

  • Given, A child-sized swimming pool can be modeled by a cylinder. The pool has a diameter of 6 1/2 feet (or) 6.5 feet (radius is 3.25 feet) and a height of 12 inches(1 feet).

The pool is filled with water to 2/3 of its height (H= 2/3 feet) .

Volume of Cylinder = π×R²×H , now put values, we get

Volume = 3.14×3.25²×2/3

Volume = 22.122 foot³ .

And, One cubic foot equals 7.48 gallons of water

Thus, 22.122 cubic foot equals to 165.47≈165 gallons of water .

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Answer:

A and F.

Explaination:

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