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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.

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4% of _____ days is 56 days
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Cross multiply:
4*? = 56*100
⇒ ? = 56*100/4
⇒ ?= 1,400

4% of 1,400 days is 56 days~
4 0
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Rudik [331]
C because median is all about the middle
5 0
3 years ago
Please help me solve the problem 3 \sqrt[5] 3\sqrt[100]
Advocard [28]
<span>3 X squareroot (10 X 100) = 3X (10) X squareroot (10) = [ where the squareroot of 100 is 10] 30 X squareroot (10) = 30 X squareroot (2 X 5) = [where the squareroot of 2 is 1.414] 30 X (1.414) X squareroot (5) = 94.85</span>
6 0
3 years ago
The area of a rectangle is 42 square inches and one side is 12 inches long find the perimeter of the rectangle show your work
uranmaximum [27]
So first of all we need to know that area is length times width
Area = L x W 
since we know the area is 42 and the length is 12 lets plug those in
42 = 12 x W 
now we dont know what W is yet but we can figure it out by dividing 42 by 12
42/12 = 3.5 
So W = 3.5!
but its asking for the perimeter and we know that perimeter is all of the sides of the rectangle added up. Heres a picture
   
       ___3.5___
      |                 |
      |                 |
 12 |                 |  12 
      |                 |
      ************
             3.5

see now we just add those all up together:)

12 + 12 + 3.5 + 3.5 = 31!!
so our perimeter is 31 inches:)
have a good one 
PICK ME BRAINLIEST!:D
5 0
2 years ago
You are designing a large rectangular fish tank for your tropical fish. The length will be 1 yard 3 inches, the width will be 1.
aliina [53]

Answer:

  A. 14040 cubic inches

  B. 61 gallons

Step-by-step explanation:

The volume of a cuboid is given by the formula ...

  V = LWH

__

<h3>A.</h3>

One yard is 36 inches, so 1 yard 3 inches is 36 +3 = 39 inches.

One foot is 12 inches, so 1.5 ft = 1.5×12 = 18 inches.

The volume of the fish tank is ...

  V = (39 in)(18 in)(20 in) = 14,040 in³

The volume is 14,040 cubic inches.

__

<h3>B.</h3>

One gallon is 16 cups, so 976 cups is 976/16 = 61 gallons.

976 cups equals 61 gallons.

_____

<em>Additional comment</em>

One gallon is 231 cubic inches, so the volume of the tank is actually about 972 cups, or 60.8 gallons.

8 0
1 year ago
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