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
Arturiano [62]
2 years ago
7

Show whether or not y=x+3 is tangential to the curve y^2=x​

Mathematics
1 answer:
wolverine [178]2 years ago
3 0

The line y = x + 3 has slope 1, so we look for points on the curve where the tangent line, whose slope is dy/dx, is equal to 1.

y² = x

Take the derivative of both sides with respect to x, assuming y = y(x) :

2y dy/dx = 1

dy/dx = 1/(2y)

Solve for y when dy/dx = 1 :

1 = 1/(2y)

2y = 1

y = 1/2

When y = 1/2, we have x = y² = (1/2)² = 1/4. However, for the given line, when y = 1/2, we have x = y - 3 = 1/2 - 3 = -5/2.

This means the line y = x + 3 is not a tangent to the curve y² = x. In fact, the line never even touches y² = x :

x = y²   ⇒   y = y² + 3   ⇒   y² - y + 3 = 0

has no real solution for y.

You might be interested in
What is the equation of a line that contains the point (2,1) and is perpendicular to the line: y = 3x – 4?
irakobra [83]
There's  a website called desmos.com. That website can tell you the answer
7 0
3 years ago
Please help!! Which lists the sides of the triangle from least to greatest?
vredina [299]

Answer:

Scott Street, Park Street,Oak Street

Step-by-step explanation:

5 0
3 years ago
Factor the perfect square trinomial 25n² + 40np<br> + 16p^2
Nat2105 [25]

Answer:

(5n+4p)(5n+4p) or (5n+4p)^2

Step-by-step explanation:

i took the test :p

4 0
2 years ago
I’m having trouble with this question can anyone help me?
a_sh-v [17]
A: y= 10x+50
b: 120 C
5 0
3 years ago
A family of 2 adults and 3 children goes to a play Admission cost $8 per adult and $5 per child.What expression would show the t
alexdok [17]
[2x8]+[3x5]=31 that's the answer
7 0
3 years ago
Read 2 more answers
Other questions:
  • Which pair of triangles can be proven congruent by the HL theorem
    6·2 answers
  • Which number sentence is true? A. –7 + 10 = –3 B. –7 – (–10) = –17 C. 7 – 10 = 3 D. 7 – (–10) = 17
    12·2 answers
  • Growing up, Lisa lived in a tiny country village. When she left for college, the population was 840 people. Lisa recently heard
    10·2 answers
  • What is the area of a circle if it is 7ft
    13·2 answers
  • (CO 5) An advocacy group claims that the mean braking distance of a certain type of tire is 75 feet when the car is going 40 mil
    8·1 answer
  • Whatbis the missing numerator of [2]5/6=?/6
    8·1 answer
  • The solids are similar. Find the volume V of the red solid.
    12·2 answers
  • Word problem that represents 8 times -0.25
    6·1 answer
  • 3b - c +5 if c= - 4, b=2.
    5·1 answer
  • Please give me answer friend<br>​
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!