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
mr_godi [17]
4 years ago
5

The curve with the equation given below is called a kampyle of Eudoxus. Find the equation of the tangent line to this curve at t

he point (-1, 2). y2 = 5x4 − x2
Mathematics
1 answer:
Nesterboy [21]4 years ago
6 0

Answer:

y= (-9/2)*x-5/2  or  2y+9x+5=0

Step-by-step explanation:

given the following equation

y² = 5*x⁴ - x²

we can take the derivative with respect to x in both sides to get the slope of the tangent line , and knowing that y=f(x) we can apply the chain rule , therefore

d(y²)/dx = d(5*x⁴ - x²)/dx

2*y*dy/dx = 5*4*x³ - 2*x

dy/dx = (10*x³-x)/y

replacing values (x=-1,y=2)

m=dy/dx = (10*(-1)³-(-1))/2 = -9/2

now from the equation of the line

y= m*x+h

we know that (x=-1,y=2) belongs also to the line since it is tangent to the curve, thus

2= (-9/2)*(-1) + h

h = 2 - 9/2 = (-5/2)

thus

y= (-9/2)*x-5/2

or

2y+9x+5=0

You might be interested in
Tammy learns in science class that water freezes when its temperature is
Oksanka [162]

The required number line that shows all of the possible

temperatures is option A.

<h3>Inequalities and number line</h3>

From the given question, we have that water freezes when its temperature is no more than 32 °F

The statement no more than 32 °F shows that the temperature cannot be greater than 32 but less than or equal to 32. This is written mathematically as;

t ≤ 32.

We are to select the number line that shows all of the possible temperatures. The required number line that shows all of the possible

temperatures is option A.

Learn more on number lines here: brainly.com/question/24644930

7 0
3 years ago
ill in the missing numbers along the sides of the triangle so that it contains each of the numbers from through exactly once. ​
mihalych1998 [28]

Each side of the triangle should contain four numbers whose sum is 28.

3+5+9+11=28

3+10+8+7=28

11+6+9+7=28

The pain of numbers that can be used for A and B is [5,9] The pain of numbers that can be used for C and D is [10,8] and the pain of numbers that can be used for E and f is [6,4].

<h3>What are the 3 sides of a triangle?</h3>

The hypotenuse of a right triangle is its longest side; its "opposite" side is the one that faces the angle in question; and its "adjacent" side is the one that faces it. We use special terminology to define the sides of right triangles.

We use special terminology to define the sides of right triangles.

The side opposite the right angle is always the hypotenuse of a right triangle. It is the longest side in a right triangle.

The opposing and neighboring sides are the other two sides. The labels on these sides relate to an angle.

One side is across from another at a particular angle.

To learn more about sides of a triangle visit:

brainly.com/question/9449776

#SPJ4

5 0
2 years ago
The Best Theme Park sold 130 tickets in an hour and made $5,300 from ticket sales. An adult ticket sells for $50.00. A child tic
lilavasa [31]
The solution to the system is (90,40)....x = adults and y = child's...so x = 90 (there were 90 adult tickers) and y = 40 (there were 40 child tickets)...u already had the answer right in front of you
8 0
3 years ago
Read 2 more answers
Sara ran 10km in 2.5 hours. Katerina ran 7.5 km in 2 hours. Candice ran 9.5 km in 2.25 hours. Who had the fastest average speed?
Arisa [49]

10 km ÷ 2.5 hours = 4 km/h — This is Sara's record

7.5 km ÷ 2 hours = 3.75 km/h — This is Katerina's record

9.5 km ÷ 2.25 hours = 4.2 km/h — This is Candice's record

Therefore, the answer is Candice had the fastest average speed.

6 0
4 years ago
Can someone answer #10 please?
n200080 [17]
Not sure of the question...1 missing vs 8 found
or 1 missing vs 9 piece puzzle

8 0
3 years ago
Other questions:
  • CAN SOMEONE HELP (AND HELP ME UNDERSTAND)
    15·1 answer
  • Using your answers from parts b and c, what are the ages of the brother and sister, respectively?
    12·1 answer
  • Sam went 300 feet below sea level. Ken is at an elevation of 100 feet. Write an inequality to compare their location
    15·1 answer
  • If the selling price is $75.50 and includes the cost plus 5% of the cost, then what is the cost?
    14·2 answers
  • Janet is collecting coins. She starts with 6 coins. The next week she has 10 coins. In two weeks she has 14 coins. If this patte
    12·1 answer
  • Factor the equation 4x^2-20x=1
    10·1 answer
  • In the case of normally distributed classes, discriminant functions are linear (straight lines, planes, and hyperplanes for two-
    8·1 answer
  • Help!!! 10 points dhdhdhhhshmsmhsm
    13·1 answer
  • Can someone please help me with this question?
    12·2 answers
  • 6A./25% घाटामा बेचिएको कुनै सामानलाई रु. 21,000 बढीमा बेच्न सकिएको भए 10% नाफा
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!