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Georgia [21]
3 years ago
7

Write the equation in slope intercept form through: (1,5), perp. to y=-1/2x - 4

Mathematics
1 answer:
Softa [21]3 years ago
5 0
--------------------------------------------------------------
Slope :
--------------------------------------------------------------
Slope = 2  (negative reciprocal of the perpendicular line)

--------------------------------------------------------------
Y-intercept :
--------------------------------------------------------------
at (1, 5)
5 = 2(1) + b
5 = 2 + b 
b = 3

--------------------------------------------------------------
Equation : y = 2x + 3
--------------------------------------------------------------

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Hello, Can I get some help with #30 a and b, please? Don't forget to show your work.
Murljashka [212]

Answer:

a. dy/dx = -2/3

b. dy/dx = -28

Step-by-step explanation:

One way to do this is to assume that x and y are functions of something else, say "t", then differentiate with respect to that. If we write dx/dt = x' and dy/dt = y', then the required derivative is y'/x' = dy/dx.

a. x'·y^3 +x·(3y^2·y') = 0

y'/x' = -y^3/(3xy^2) = -y/(3x)

For the given point, this is ...

dy/dx = -2/3

___

b. 2x·x' +x^2·y' -2x'·y^3 -2x·(3y^2·y') + 0 = 2x' + 2y'

y'(x^2 -6xy^2 -2) = x'(2 -2x +2y^3)

y'/x' = 2(1 -x +y^3)/(x^2 +6xy^2 -2)

For the given point, this is ...

dy/dx = 2(1 -0 +27)/(0 +0 -2)

dy/dx = -28

_____

The attached graphs show these to be plausible values for the derivatives at the given points.

6 0
3 years ago
Read 2 more answers
Y = 2x + 3<br> y = -3x + 3
AnnyKZ [126]

Answer:

y = -1

Step-by-step explanation:

hopefully it helped

5 0
3 years ago
A cone-shaped paper drinking cup is to be made to hold 27 cm of water. Find the height h and radius r of the cup that will use t
andreyandreev [35.5K]

Answer:

  • r = 2.632 cm
  • h = 3.722 cm

Step-by-step explanation:

The formula for the volume of a cone of radius r and height h is ...

  V = (1/3)πr²h

Then r² can be found in terms of h and V as ...

  r² = 3V/(πh)

The lateral surface area of the cone is ...

  A = (1/2)(2πr)√(r² +h²) = πr√(r² +h²)

The square of the area is ...

  T = A² = π²r²(r² +h²)

Substituting for r² using the expression above, we have ...

  T = π²(3V/(πh))((3V/(πh) +h²) = 9V²/h² +3πVh

We want to find the minimum, which we can do by setting the derivative to zero.

  dT/dh = -18V²/h³ +3πV

This will be zero when ...

  3πV = 18V²/h³

  h³ = 6V/π . . . . . multiply by h³/(3πV)

For V = 27 cm³, the value of h that minimizes paper area is ...

  h = 3∛(6/π) ≈ 3.7221029

The corresponding value of r is ...

  r = √(3V/(πh)) = 9/√(π·h) ≈ 2.6319242

The optimal radius is 2.632 cm; the optimal height is 3.722 cm.

_____

The second derivative test applied to T finds that T is always concave upward, so the value we found is a minimum.

__

Interestingly, the ratio of h to r is √2.

8 0
3 years ago
Please answer correctly !!!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!
cestrela7 [59]

Answer:

x = √47

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

<u>Trigonometry</u>

  • [Right Triangles Only] Pythagorean Theorem: a² + b² = c²

Step-by-step explanation:

<u>Step 1: Define</u>

We have a right triangle. We can use PT to solve for the missing side length.

<u>Step 2: Identify Variables</u>

Leg <em>a</em> = 5

Leg <em>b </em>= <em>x</em>

Hypotenuse <em>c</em> = √72

<u>Step 3: Solve for </u><em><u>x</u></em>

  1. Substitute [PT]:                    5² + x² = (√72)²
  2. Exponents:                           25 + x² = 72
  3. Isolate <em>x</em> term:                      x² = 47
  4. Isolate <em>x</em>:                               x = √47
8 0
3 years ago
I have no idea what the answer is
Digiron [165]
Sin is opposite over hypotenuse so the answer would be sqrt3\2
7 0
3 years ago
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