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
victus00 [196]
3 years ago
8

What is the meaning of the term theorem

Mathematics
1 answer:
AURORKA [14]3 years ago
5 0
There are 4 terms in the world of *Mathematical proof*
Lemma, Proposition, Corollary and Theorem.
There is no difference between a lemma,
proposition, theorem, or corollary - they are all claims waiting to be proved. However, we use these terms to suggest different levels of importance and difficulty. A lemma is an easily proved claim which is helpful for proving other propositions and theorems, but is usually not particularly interesting in
its own right. A proposition is a statement which is interesting in its own right, while a theorem is a more important statement than a proposition which says something definitive on the subject, and often takes more effort to prove than a proposition or lemma. A corollary is a quick consequence of a proposition or theorem that was proven recently





You might be interested in
Find each pair of integers, given their sum and product. sum -14, product +24 sum +3, product -18
kvv77 [185]
+3 and -18
The pair of integers are -3 and 6.
-3 + 6 = +3
-3 * 6 = -18

-14 and +24
The pair of integers are -2 and -12
-2 + -12 = -14
-2 * - 12 = +24
3 0
3 years ago
Karen spent all but $8 of her savings in three stores. In each store she spent $2 less than half of what she had when she went i
maksim [4K]

Answer:

36 dollars

Step-by-step explanation:

We need to think backwards to solve this question.

(8 - 2) x 2 = 12

(12 - 2) x 2 = 20

(20 - 2) x 2 = 36

5 0
2 years ago
Hi, I am new to this website :) I'm currently taking an online trig class on De Moivre's theorem and I don't understand it at al
Vladimir [108]
De Moivre's theorem uses this general formula z = r(cos α + i<span> sin α) that is where we can have the form a + bi. If the given is raised to a certain number, then the r is raised to the same number while the angles are being multiplied by that number.

For 1) </span>[3cos(27))+isin(27)]^5 we first apply the concept I mentioned above where it becomes

[3^5cos(27*5))+isin(27*5)] and then after simplifying we get, [243 (cos (135) + isin (135))] 

it is then further simplified to 243 (-1/ √2) + 243i (1/√2) = -243/√2 + 243/<span>√2 i
and that is the answer.

For 2) </span>[2(cos(40))+isin(40)]^6, we apply the same steps in 1)

[2^6(cos(40*6))+isin(40*6)],

[64(cos(240))+isin(240)] = 64 (-1/2) + 64i (-√3 /2)

And the answer is -32 -32 √3 i

Summary:
1) -243/√2 + 243/√2 i
2)-32 -32 √3 i

7 0
3 years ago
Demand for Tablet Computers The quantity demanded per month, x, of a certain make of tablet computer is related to the average u
soldier1979 [14.2K]

x = f ( p ) = \frac { 100 } { 9 } \sqrt { 810,000 - p ^ { 2 } } } \\\\ \qquad { p ( t ) = \dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { t } } + 200 \quad ( 0 \leq t \leq 60 ) }

Answer:

12.0 tablet computers/month

Step-by-step explanation:

The average price of the tablet 25 months from now will be:

p ( 25) = \dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { 25 } } + 200 \\= \dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \times 5 } + 200\\\\=\dfrac { 400 } { 1 + \dfrac { 5 } { 8 } } + 200\\p(25)=\dfrac { 5800 } {13}

Next, we determine the rate at which the quantity demanded changes with respect to time.

Using Chain Rule (and a calculator)

\dfrac{dx}{dt}= \dfrac{dx}{dp}\dfrac{dp}{dt}

\dfrac{dx}{dp}= \dfrac{d}{dp}\left[{ \dfrac { 100 } { 9 } \sqrt { 810,000 - p ^ { 2 } } }\right] =-\dfrac{100}{9}p(810,000-p^2)^{-1/2}

\dfrac{dp}{dt}=\dfrac{d}{dt}\left[\dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { t } } + 200 \right]=-25\left[1 + \dfrac { 1 } { 8 } \sqrt { t } \right]^{-2}t^{-1/2}

Therefore:

\dfrac{dx}{dt}= \left[-\dfrac{100}{9}p(810,000-p^2)^{-1/2}\right]\left[-25\left[1 + \dfrac { 1 } { 8 } \sqrt { t } \right]^{-2}t^{-1/2}\right]

Recall that at t=25, p(25)=\dfrac { 5800 } {13} \approx 446.15

Therefore:

\dfrac{dx}{dt}(25)= \left[-\dfrac{100}{9}\times 446.15(810,000-446.15^2)^{-1/2}\right]\left[-25\left[1 + \dfrac { 1 } { 8 } \sqrt {25} \right]^{-2}25^{-1/2}\right]\\=12.009

The quantity demanded per month of the tablet computers will be changing at a rate of 12 tablet computers/month correct to 1 decimal place.

8 0
3 years ago
8.) Write y = 3/5 x + 4 in standard form using integers.
Tju [1.3M]

Answer:

I believe the answer is c

Step-by-step explanation:

What i got tho was... 3x-5y=-20

7 0
3 years ago
Other questions:
  • A line includes the points (7, -2) and (0, -1). What is its equation in slope-intercept form?<br>​
    13·2 answers
  • Find the equation of the line in slope intercept form that passes through (0,4) and is parallel to the line 4x-3y=12?
    5·2 answers
  • The point (3,4) is translated 6 units left what are the coordinates of the resulting point p
    8·1 answer
  • <img src="https://tex.z-dn.net/?f=%20%5Ccos%28%20%5Calpha%20%20%2B%20%20%5Cfrac%7B%5Cpi%7D%7B2%7D%20%29%20%20%3D%20%20-%20%20%5C
    6·1 answer
  • What is greater 5.7 or5.18 ?what is the answer?
    10·2 answers
  • What is the next number in this sequence 7, 16, 8, 27, 9, ?
    15·1 answer
  • A sample of 50 11th graders were asked to select a favorite pattern out of six choices. The data list below shows what their fav
    6·1 answer
  • The measures of two angles in a triangle are 32o and 78o. Which of the following equations could be used to find the measure of
    6·2 answers
  • HELPPPP PLEASEEEEEE HELP ME
    13·1 answer
  • The circumference of a circular garden is 78.5 feet. What is the radius of the garden? Use 3.14 for it and do not round your ans
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!