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
jenyasd209 [6]
3 years ago
15

Which is precisely defined using the undefined terms point and plane?

Mathematics
1 answer:
yan [13]3 years ago
8 0
Defined ray and line
You might be interested in
Help evaluating the indefinite integral
Dafna11 [192]

Answer:

\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }

General Formulas and Concepts:
<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Derivative Property [Multiplied Constant]:
\displaystyle (cu)' = cu'

Derivative Property [Addition/Subtraction]:
\displaystyle (u + v)' = u' + v'
Derivative Rule [Basic Power Rule]:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Integration

  • Integrals

Integration Rule [Reverse Power Rule]:
\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C

Integration Property [Multiplied Constant]:
\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx

Integration Methods: U-Substitution and U-Solve

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify given.</em>

<em />\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx

<u>Step 2: Integrate Pt. 1</u>

<em>Identify variables for u-substitution/u-solve</em>.

  1. Set <em>u</em>:
    \displaystyle u = 4 - x^2
  2. [<em>u</em>] Differentiate [Derivative Rules and Properties]:
    \displaystyle du = -2x \ dx
  3. [<em>du</em>] Rewrite [U-Solve]:
    \displaystyle dx = \frac{-1}{2x} \ du

<u>Step 3: Integrate Pt. 2</u>

  1. [Integral] Apply U-Solve:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-x}{2x\sqrt{u}}} \, du
  2. [Integrand] Simplify:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-1}{2\sqrt{u}}} \, du
  3. [Integral] Rewrite [Integration Property - Multiplied Constant]:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \frac{-1}{2} \int {\frac{1}{\sqrt{u}}} \, du
  4. [Integral] Apply Integration Rule [Reverse Power Rule]:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = -\sqrt{u} + C
  5. [<em>u</em>] Back-substitute:
    \displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }

∴ we have used u-solve (u-substitution) to <em>find</em> the indefinite integral.

---

Learn more about integration: brainly.com/question/27746495

Learn more about Calculus: brainly.com/question/27746485

---

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

5 0
2 years ago
Explain why ∠4 is equal to the sum of the measures of the two nonadjacent interior angles (Angle 1 and Angle 2).
Akimi4 [234]
Angle 4 is 77 degrees. Since angles 1, 2, and 3 must add up to 180 degrees, and angles 3 and 4 must also add up to 180 degrees, angles 1 + 2 must be equal to angle 4
3 0
3 years ago
What kind of exponent does this graph have? Help pls ?
otez555 [7]
It’s 42 but Carrier the 2
4 0
3 years ago
Please rewrite 5x − 15y = − 60 in the slope intercept form
Margarita [4]
Basically solve for y
minus 5x fromboth sides
-15y=-5x-60
divide both sides by -15
y=1/3x+4
4 0
3 years ago
A parabola has a focus of F(2, -0.5) and a directrix of y=-1.5 P(x,y) represents any point on the parabola, while D(x, -1.5) rep
prohojiy [21]
The sketch of the parabola is attached below

We have the focus (a,b) = (2, -0.5)
The point P(x,y)
The directrix, c at y=-1.5

The steps to find the equation of the parabola are as follows

Step 1
Find the distance between the focus and the point P using Pythagoras. We have two coordinates; (2, -0.5) and (x,y).
We need the vertical and horizontal distances to find the hypotenuse (the diagram is shown in the second diagram).
The distance between the focus and point P is given by
\sqrt{ (x-a)^{2}+ (y-b)^{2} }

Step 2
Find the distance between the point P to the directrix c. It is a vertical distance between y and c, expressed as y-c

Step 3
The equation of parabola is then given as 
\sqrt{ (x-a)^{2}+ (y-b)^{2} }=y-c
(x-a)^{2}+ (y-b)^{2}= (y-c)^{2} ⇒ substituting a, b and c
(x-2)^{2}+ (y--0.5)^{2}  = (y--1.5)^{2}
(x-2)^{2}+ (y+0.5)^{2}= (y+1.5)^{2}⇒Rearranging and making y the subject gives

y= \frac{ x^{2} }{2} -2x+1

7 0
3 years ago
Other questions:
  • An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 5 cm long. A second side of the
    6·1 answer
  • Which expression is equivalent to the given expression?
    14·1 answer
  • Can you plz help me??
    8·1 answer
  • What is 8 divided by 2/3
    14·2 answers
  • Which equation represents a line that passes through the two points in the
    11·1 answer
  • Please help me with this
    11·1 answer
  • Plz plz answer this i'll give 11 points
    9·1 answer
  • ONLY ANSWER IF YOU KNOW HOW TO DO THIS.
    11·1 answer
  • What is the approximate solution of this system of equaltion y=x^2+3x+3 , y=x^2+x+2
    6·1 answer
  • Prove that:
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!