1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
elena55 [62]
3 years ago
7

A curve passes through the point (0, 5) and has the property that the slope of the curve at every point P is twice the y-coordin

ate of P. What is the equation of the curve? (Use x as the independent variable.)
Mathematics
1 answer:
Bess [88]3 years ago
5 0

Answer:

y =5e^{2x}

Step-by-step explanation:

Given that a curve passes through the point (0, 5) and has the property that the slope of the curve at every point P is twice the y-coordinate of P.

Let y =f(x) be the equation of the curve

Since slope = 2y

we have

\frac{dy}{dx}= 2y\\\\y'     = 2dx\\ln y = 2x+C\\y = Ae^{2x}

To find A

It passes through (0,5)

Substitute x=0 and y=5

5=A

SO equation is

y =5e^{2x}

You might be interested in
Please answer this question.
Kaylis [27]
Combine the like terms
-x-x^2+7
4 0
3 years ago
Sales Daria sells televisions. She earns a fixed amount for each television and an additional $25 if the buyer gets an extended
aliina [53]
Answer: Daria earns a fixed amount of $55 for each​ television.
Step-by-step explanation:
Let a represent the fixed amount that Daria earns for each​ television.
Daria earns a fixed amount for each television and an additional $25 if the buyer gets an extended warranty. This means that if she sells b televisions with extended warranties, the total amount that she would earn is
ab + 25b
If Daria sells 14 televisions with extended warranties,she earns $1,120. Therefore,
14a + 14 × 25 = 1120
14a + 350 = 1120
14a = 1120 - 350
14a = 770
a = 770/14
a = 55
5 0
3 years ago
Anna would like to purchase a new bike that costs $205. She already has $31 saved. If she saves a maximum of $12 a week, the fol
Dmitrij [34]

Answer:

It will take at least 15 weeks

Step-by-step explanation:

12w+31 ≥ 205

Subtract 31 from each side

12w+31-31 ≥ 205-31

12w ≥ 174

Divide each side by 12

12w/12 ≥ 174/12

w ≥ 14.5

Rounding up to the nearest integer

w ≥ 15

It will take at least 15 weeks

5 0
3 years ago
Read 2 more answers
Alice’s backyard is a rectangular piece of property that is twice as long as it is wide. The total area of her yard is 1,000 m2.
irina [24]
The approximate width of Alice's backyard is 22.36 in.

Let l be the length of the rectangle and w be the width.
l = 2w
A = 1000 m2 = l*w
1000 m2 = 2w *w
500 m2 = w^2
√500 m2 = √w^2
w = <span>22.360679775 in or 22.36 in</span>

Thank you for posting your question. I hope you found what you were after. Please feel free to ask me more.

<span> </span>


8 0
3 years ago
Read 2 more answers
At Mr. Hynd's ranch, there are 35 chickens and 20 cows. What is the ratio of the number of cows to the
Anton [14]
7/4 because you simplify
5 0
3 years ago
Other questions:
  • Determine whether the given point (-6,2) is a solution of the equation y = -2x - 1
    13·2 answers
  • Please help it would be appreciated!
    5·1 answer
  • Find the average value of the function i = 15(1 - e1/2t) from t = 0 to t = 4. A. 7.5(1 + e-2) B. 7.5(2 - e-2) C. 7.5(2 + e-2) D.
    7·1 answer
  • The equation y=-7x-5 and the solution of (-2,9)
    6·1 answer
  • suppose you deposit $1000 in an account paying 4.6% annual interest compounded continuously. How long will it take for the money
    12·1 answer
  • What is the surface area of this square pyramid?
    8·1 answer
  • Find the area of this shape. The area of this shape is _______ square centimeters.
    5·2 answers
  • If 2 of the angles of a triangle are 30 and 70 degrees, the third angle measures ...
    8·1 answer
  • Which ordered pair is in the solution set of y&gt; 2x + 3?
    8·2 answers
  • You are starting a lawn mowing business to earn
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!