Step-by-step explanation:
If the equation is
[tex] \sqrt{x + 2} [/tex]
Then, here is the answer.
The definition of a derivative is
[tex] \frac{f(x + h) - f(x)}{h} [/tex]
Also note that we want h to be a small, negligible value so we let h be a value that is infinitesimal small.
So we get
[tex] \frac{ \sqrt{x + h + 2} - \sqrt{x + 2} }{h} [/tex]
Multiply both equations by the conjugate.
[tex] \frac{ \sqrt{x + h + 2} - \sqrt{x + 2} }{h} \times \frac{ \sqrt{x + h + 2} + \sqrt{x + 2} }{ \sqrt{x + h + 2} + \sqrt{x + 2} } = \frac{x + h + 2 - (x + 2)}{h \sqrt{x + h + 2} + \sqrt{x + 2} } [/tex]
[tex] \frac{h}{h \sqrt{x + h + 2} + \sqrt{x + 2} } [/tex]
[tex] \frac{1}{ \sqrt{x + h + 2} + \sqrt{x + 2} } [/tex]
Since h is very small, get rid of h.
[tex] \frac{1}{ \sqrt{x + 2} + \sqrt{x + 2} } [/tex]
[tex] \frac{1}{2 \sqrt{x + 2} } [/tex]
So the derivative of
[tex] \frac{d}{dx} ( \sqrt{x + 2} ) = \frac{1}{2 \sqrt{x + 2} } [/tex]
Part 2: If your function is
[tex] \sqrt{x} + 2[/tex]
Then we get
[tex] \frac{ \sqrt{x + h} + 2 - ( \sqrt{x} + 2) }{h} [/tex]
[tex] \frac{ \sqrt{x + h} - \sqrt{x} }{h} [/tex]
[tex] \frac{x + h - x}{h( \sqrt{x + h} + \sqrt{x}) } [/tex]
[tex] \frac{h}{h( \sqrt{x + h} + \sqrt{x} ) } [/tex]
[tex] \frac{1}{ \sqrt{x + h} + \sqrt{x} } [/tex]
[tex] \frac{1}{2 \sqrt{x} } [/tex]
So
[tex] \frac{d}{dx} ( \sqrt{x} + 2) = \frac{1}{2 \sqrt{x} } [/tex]
You randomly draw twice from this deck of cards
0 с G|F. D C G
What is the probability of not drawing a C, then not drawing a C,
without replacing the first card? Write your answer as a decimal
rounded to the nearest hundredth.
The probability of not drawing C in neither draw is P = 0.5
How to get the probability?
All the cards have the same probability of being drawn, in this case, our set of cards is {F, D, C, G}
The probability of not drawing C is equal to the probability of drawing F, D or G. So we have 3 options out of 4, then the probability is:
p = 3/4.
Now we draw another, this time there are 3 cards, one of these is C, and the other two cards are not C. Then the probability of not drawing C again is equal to 2 over 3.
q = 2/3.
The joint probability (for both of these events to happen) is equal to the product of the individual probabilities:
P = p*q = (3/4)*(2/3) = 0.5
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1. For each diagram below, find the value of x
Vocabulary
1. Volume: A measure of ________ occupied by a __________-________________ figure.
1. Base: The __________ on which an object _______.
1. Height: The ______ distance from top to bottom, creates a ___-degree angle with the base.
1. Inverse Operation: The ________ of a math operation; the opposite of addition is ________ and the opposite of multiplication is ________.
1. Diameter: A ________ line going from one side of a ______ to the other through the _______.
1. Radius: The distance from the ______ to the ______ of a ______; _____ of the diameter.
Volume of a Cylinder
A ____________ is a _____________________ object with a _________________ base and top.
To find the ____________ of a ______________ we use the following formula:
Answer:
Step-by-step explanation:
. Volume: A measure of _space occupied by a _three dimensional _ figure.
1. Base: The surface on which an object stands on.
1. Height: The _vertical distance from top to bottom, creates a _90° degree angle with the base.
1. Inverse Operation: The opposite of a math operation; the opposite of addition is subtraction and the opposite of multiplication is division.
1. Diameter: A straight line going from one side of a point on a circle to the other through the _center.
1. Radius: The distance from the center to the point of a circle;or half of the diameter.
Volume of a Cylinder
A cylinder is a three dimensional object with a circular base and top.
To find the volume of a cylinder we use the following formula:πr²h
Determine the values of k for which the function f(x) = 4x^2-3x + 2kx + 1 has two zeros. Check these values in the original equation.
k must be greater than or equal to 22.75 to have two different zeros.
How to determine the value of missing coefficient in second order polynomials
Second order polynomials are algebraic expressions that observe the following form:
[tex]p(x) = a\cdot x^2 + b\cdot x + c[/tex] (1)
Where:
a, b, c - Coefficientsx - Independent variableFor polynomials of the form p(x) = 0, we can infer the nature of their roots by applying the following discriminant:
d = b² - 4 · a · c (2)
According to (2), there are three cases:
If d < 0, then there are two conjugated complex roots.If d = 0, then the two roots are the same real number.If d > 0, then the two roots are two distinct real numbers.Now we have the following discriminant case:
-(3 + 2 · k)² - 4 · (1) · (4) ≠ 0
-(9 + 6 · k + 4 · k²) - 16 ≠ 0
-9 - 6 · k - 4 · k² - 16 ≠ 0
4 · k²+ 6 · k +25 ≠ 0
This characteristic polynomial has two conjugated complex roots, then we conclude that all values of k must positive or negative, but never zero. By graphng tools we find that k must be greater than or equal to 22.75 to have two different zeros.
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Help help math math math math math
Answer:
A
Step-by-step explanation:
You can think about it as an equation without the inequality:
y = 5 - x OR y = -x + 5
Slope = -1
Y-intercept = 5
Graph B is a horizontal line with a slope of zero and y-intercept of 2. Graph A is the only one that fits the above parameters.
Hope this helps!
Answer:
a
Step-by-step explanation:
Need help on number 10
If tan C is 3/4, find the sin C.
Answer:
sin C = 3/5
Step-by-step explanation:
see image.
It helps to draw a picture. Tan C is the ratio of the OPP/ADJ.
Pythagorean theorem or if you know Pythagorean triples are a shortcut to find the hypotenuse.
Once you know the hypotenuse, use the ratio for sine to solve the question. Sine is OPP/HYP.
see image.
Sita saves Rs. 1 today, Rs. 2 the next day, Rs. 4 the succeeding day and so on (each saving being twice of the preceding one). What will be total saving in two weeks time?
a
Answer:
Rs. 32767
Step-by-step explanation:
Because the amount is doubling every day, we can use the expression 1*2^15-1 because there is 1 to start with. Also cool trick! if you need to do 2^1+2^2+2^3+....+2^x, it will be equal to 2^(x+1)-1. So:
2^15-1
32768-1
32767
The loudness (L) of sound in decibels is related to intensity (I)measured in watts per square centimeter by the equation: L = 10log( I 10-16 ). Find the loudness of a whisper at 10-12 W/cm2. A) 35 decibels B) 40 decibels C) 45 decibels D) 50 decibels
The function L= 10 log(I/10^-16) is a logarithmic equation
The loudness of the whisper is 40 decibels
How to determine the loudness?The function of the loudness is given as:
L= 10 log(I/10^-16)
When the intensity is 10^-12, the equation becomes
L= 10 log(10^-12/10^-16)
Evaluate the quotient
L= 10 log(10^4)
Apply the rule of logarithm
L= 10 * 4
Evaluate the product
L = 40
Hence, the loudness of the whisper is 40 decibels
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Can somebody help me pls!
Answer: C
Step-by-step explanation:
Just look at a z-score table and multiply by 100.
-> (0.308538)(100) is about 30.85%
What is the total height of the plants that measured 1
1/8 and
1/4?
Find the missing information for the triangle.
*not drawn to scale
• Make sure to find the missing angle measure and the 2 missing side
lengths.
missing angle:
180° - 90° - 30°
180° - 120°
60°
missing sides:
(a)
[tex]\rightarrow \sf tan(x)= \dfrac{opposite}{adjacent}[/tex]
[tex]\rightarrow \sf tan(30)= \dfrac{4}{adjacent}[/tex]
[tex]\rightarrow \sf adjacent= \dfrac{4}{tan(30)}[/tex]
[tex]\rightarrow \sf adjacent= 4\sqrt{3}[/tex]
[tex]\rightarrow \sf adjacent= 6.93 \ cm[/tex]
(b)
[tex]\sf \rightarrow sin(x)= \dfrac{opposite}{hypotensue}[/tex]
[tex]\sf \rightarrow sin(30)= \dfrac{4}{hypotensue}[/tex]
[tex]\sf \rightarrow hypotensue= \dfrac{4}{ sin(30)}[/tex]
[tex]\sf \rightarrow hypotensue= 8 \ cm[/tex]
Answer:
m∠X = 60°
BX = 8 cm
BM = 4√3 cm
Step-by-step explanation:
The sum of the interior angles of a triangle is 180°
Given:
m∠B = 30°m∠M = 90°⇒ m∠B + m∠M + m∠X = 180°
⇒ 30° + 90° + m∠X = 180°
⇒ 120° + m∠X = 180°
⇒ m∠X = 180° - 120°
⇒ m∠X = 60°
Using the sine rule to find the side lengths:
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
(where A, B and C are the angles, and a, b and c are the sides opposites the angles)
Given:
m∠X = 60°m∠B = 30°m∠M = 90°MX = 4 cm[tex]\implies \dfrac{4}{\sin 30\textdegree}=\dfrac{BX}{\sin 90\textdegree}=\dfrac{BM}{\sin 60\textdegree}[/tex]
[tex]\implies BX=\sin 90\textdegree \cdot\dfrac{4}{\sin 30\textdegree}[/tex]
[tex]=1 \cdot \dfrac{4}{\frac12}[/tex]
[tex]=1 \cdot 4 \cdot 2[/tex]
[tex]=8 \textsf{ cm}[/tex]
[tex]\implies BM=\sin 60\textdegree \cdot\dfrac{4}{\sin 30\textdegree}[/tex]
[tex]=\dfrac{\sqrt{3}}{2}\cdot \dfrac{4}{\frac12}[/tex]
[tex]=\dfrac{\sqrt{3}}{2}\cdot 4 \cdot 2[/tex]
[tex]=4\sqrt{3} \textsf{ cm}[/tex]
How can i prove this property to be true for all values of n, using mathematical induction.
ps: spam/wrong answers will be reported and blocked.
Proof -
So, in the first part we'll verify by taking n = 1.
[tex] \implies \: 1 = {1}^{2} = \frac{1(1 + 1)(2 + 1)}{6} [/tex]
[tex] \implies{ \frac{1(2)(3)}{6} }[/tex]
[tex]\implies{ 1}[/tex]
Therefore, it is true for the first part.
In the second part we will assume that,
[tex] \: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} = \frac{k(k + 1)(2k + 1)}{6} }[/tex]
and we will prove that,
[tex]\sf{ \: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 1 + 1) \{2(k + 1) + 1\}}{6}}}[/tex]
[tex] \: {{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 2) (2k + 3)}{6}}[/tex]
[tex]{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k (k + 1) (2k + 1) }{6} + \frac{(k + 1) ^{2} }{6} [/tex]
[tex]{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k(k+1)(2k+1)+6(k+1)^ 2 }{6} [/tex]
[tex]{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)\{k(2k+1)+6(k+1)\} }{6}[/tex]
[tex]{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2 +k+6k+6) }{6} [/tex]
[tex]{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2+7k+6) }{6} [/tex]
[tex]{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(k+2)(2k+3) }{6} [/tex]
Henceforth, by using the principle of mathematical induction 1²+2² +3²+....+n² = n(n+1)(2n+1)/ 6 for all positive integers n.
_______________________________
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Find the area of sector RST Enter your answer in terms of a fraction of it and rounded to the nearest
hundredth.
Fort nite battle pass is 8 dollars
Which function has a maximum with the same maximum value as
f(x) = – |x + 3| – 2? f(x) = (x + 3)2 – 2 f(x) = –(x – 6)2 – 3
Answer:
The answer is c on edge or f(x) = 1 sqt x + 6 -2
Step-by-step explanation:
From the given two options, none of them has a function that has the same maximum value as f(x) = -|x+3|-2.
What is a function?A function is a correspondence between input numbers (x-values) and output numbers (y-values). It is used to describe an equation.
Given that:
f(x) = -|x + 3| - 2Suppose that x = c is a critical point of (x) then,
If f'(x) > 0 to the left of x = c and f'(x) < 0 to the right of x = c;
then x = c is a local maximum.If f'(x) < 0 to the left of x = c and f'(x) > 0 to the right of x = c;
then x = c is a local minimum.If f'(x) is the same sign on both sides of x = c;
then x = c and is neither a local maximum nor a local minimum.From the given equation, the critical points: x = -3
The intervals is: Increasing at -∞ < x < -3 and decreasing at -3<x<∞If we put the point x = -3 into - |x+3|-2
Then, y = -2 and it is Maximum at (-3, -2) Only f(x) = (x+3)^2 - 2 has a minimum at (-3,-2)We can therefore conclude that none of them has a function that has the same maximum value as f(x) = -|x+3|-2.
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The square root of 7^16 is equal to 7^n for some positive integer n. Find n.
[tex]\sqrt{7^{16}} = 7^n\\\\\implies \left(7^{16}\right)^{\tfrac 12} = 7^n\\\\\implies 7^{\left(\tfrac 12 \times 16\right)}=7^n\\\\\implies 7^8 = 7^n\\\\\implies \ln 7^8 = \ln 7^n\\\\\implies 8\ln 7 = n \ln 7\\\\\implies n =8[/tex]
find the value of x
Answer:
See below, please
Step-by-step explanation:
[tex](2x + 9) + (4x - 3) = 90[/tex]
[tex]6x + 6 = 90[/tex]
[tex]6x = 90 - 6 = 84[/tex]
Hence
[tex]x = 14[/tex]
i need help
Simplify the expression 63 + 5(4 − 2).
28
36
226
234
Answer:
226
Step-by-step explanation:
Given:
Simplify 6^3+5(4-2)
Note:
I think you meant 6^3 because if you solve 63+5(4-2):
63+5(4-2)
63+5 * 2
63 + 10
73
Solve:
6^3 + 5(4 - 2 )
6^3 + 5 x 2
6 x 6 x 6 = 216
226 + 5 x 2
5 x 2 = 10
216 + 10 = 226
~Lenvy~
How can you tell that (496 + 77 + 189) x 10 is twice as large as (496 + 77 +189) x 5 without doing complicated calculations?
Answer:
Because 10 is twice as large as 5.
Step-by-step explanation:
Question 2:
If the following frequency distribution shows the average number of students per teacher in the 50 major cities of Pakistan
Class Limits Frequency
9-11 3
12 – 14 5
15 – 17 12
18 – 20 18
21 – 23 8
24 – 26 4
Table 1
Determine
• Range
• Mean
• Median
• Mode
• Standard Deviation
• Relative Dispersion
• Variance
• Kurtosis
With the frequecy distribution shown in the 50 cities of pakistan,
range = 18mean = 18.1median = 19.8333mode = 19.125kurtosis = 2.7508Standard deviation = 3.75How to find the Range= highest value - lowest value
= 26.5 - 8.5
= 18
How to find the mean= ∑ f x / ∑ f
= ∑ f x / N
= 905 / 50
= 18.1
median
= lower limit + ( N/2 - C ) * h / ( frequency of the class interval )
C = cumulative frequency preceeding to the median class frequency
h = class interval
= 18.5 + ( 50 / 2 - ( 5 + 12 ) ) * 3 / 18
= 18.5 + 1.3333
= 19.8333
How to find the modeThe mode is the value with the highest frequency occurence. This is under class 18 - 20
mode = lower limit + ( ( f1 - f0 ) / (2*f1 - f0 - f2 ) ) * h
f1 = fequency of the modal class
f0 = freqency of the preceeding modal class
f2 = frequency of the next modal class
h = class interval
= 18.5 + ( ( 18 - 12 ) / (2 * 18 - 12 - 8 ) ) * 3
= 18 + ( 0.375 ) * 3
= 19.125
How to find the standard deviation= sqrt ( 1 / N ∑ f ( x - x' )^2 )
= sqrt (1 / 50 * 706.5
= 3.7589
How to solve for relative dispersion= standard deviation / mean
= 3.7589 / 3
= 1.2530
What is the variance?= ( standard deviation )^2
= ( 3.7589 )^2
= 14.1293
How to solve for kurtosis= ∑ f ( x - x' )^4 / ( N * ( standard deviation )^4 )
= 27459.405 / ( 50 * 3.7589^4 )
= 2.7509
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A perfect score on a test with 25 questions is 100. Each question is worth the same number of points. How many points is each question on the test worth
Answer:
4
Step-by-step explanation:
100 divided by 25 equals 4.
Please the answer ... Integral
Answer:
[tex]\frac{dx^{2} (x+1)S^{2} }{2(x^{2} +6x+3)^{2} }+ C[/tex]
Step-by-step explanation:
Can somebody please help with this, I have been stuck on it for a while
Answer:
$2821.50
Step-by-step explanation:
value = 2700 (deposit) x 0.003 (rate) x 15 (time) + 2700
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$2700\\ r=rate\to 0.3\%\to \frac{0.3}{100}\dotfill &0.003\\ t=years\dotfill &15 \end{cases} \\\\\\ A=2700[1+(0.003)(15)]\implies A=2700(1.045)\implies A=2821.5[/tex]
What is the approximate volume of a cone with a height of 9 ft and radius of 3 ft? Use 3.14 to approximate pi, and express your final answer to the nearest hundredth Enter your answer as a decimal in the box. ft3
the equation is :
answer x:
Answer:
A) x would be 21 if i interpreted it right
Step-by-step explanation:
4x - 11 = 73
i think anyways
4x = 73 + 11
4x = 84
x = 21
i d k what B means?
Find the area if the pentagon. I’ll mark the brainiest :)
Answer:
688.19 inches
Step-by-step explanation:
A card is picked from a standard deck of 52 cards. Determine the odds against and the odds in favor of selecting a red face card (king, queen, or jack).
6 red face cards
->in favour:
6/52
= 3/26
-> against:
52-6= 46
46/52
=23/26
According to the line plot how many apples weigh 5/8 of a pound
Answer:
Answer:4 apples weigh 5/8 pound.
Step-by-step explanation:
Answer:
2(−5) − 10 = 2(0)
Step-by-step explanation:
If you substitute the values x = 0 and y = −5 into the second equation, you get a false statement
WILL GIVE EXTRA POINTS FOR ANSWER ⭐️⭐️!! PLEASE EXPLAIN IF POSSIBLE
Answer:
B. (-3, 10)
Step-by-step explanation:
I am going to graph the given equation. I then will see which of the points given are within the required area.
-> See attached.
-> I have explained in the image more in-depth as well.
[tex]\large \rm \sum \limits_{n = 0}^ \infty \frac{( { - 1)}^{1 + 2 + 3 + \dots + n} }{(2n + 1 {)}^{2} }[/tex]
The sum we want is
[tex]\displaystyle \sum_{n=0}^\infty \frac{(-1)^{T_n}}{(2n+1)^2} = 1 - \frac1{3^2} - \frac1{5^2} + \frac1{7^2} + \cdots[/tex]
where [tex]T_n=\frac{n(n+1)}2[/tex] is the n-th triangular number, with a repeating sign pattern (+, -, -, +). We can rewrite this sum as
[tex]\displaystyle \sum_{k=0}^\infty \left(\frac1{(8k+1)^2} - \frac1{(8k+3)^2} - \frac1{(8k+7)^2} + \frac1{(8k+7)^2}\right)[/tex]
For convenience, I'll use the abbreviations
[tex]S_m = \displaystyle \sum_{k=0}^\infty \frac1{(8k+m)^2}[/tex]
[tex]{S_m}' = \displaystyle \sum_{k=0}^\infty \frac{(-1)^k}{(8k+m)^2}[/tex]
for m ∈ {1, 2, 3, …, 7}, as well as the well-known series
[tex]\displaystyle \sum_{k=1}^\infty \frac{(-1)^k}{k^2} = -\frac{\pi^2}{12}[/tex]
We want to find [tex]S_1-S_3-S_5+S_7[/tex].
Consider the periodic function [tex]f(x) = \left(x-\frac12\right)^2[/tex] on the interval [0, 1], which has the Fourier expansion
[tex]f(x) = \frac1{12} + \frac1{\pi^2} \sum_{n=1}^\infty \frac{\cos(2\pi nx)}{n^2}[/tex]
That is, since f(x) is even,
[tex]f(x) = a_0 + \displaystyle \sum_{n=1}^\infty a_n \cos(2\pi nx)[/tex]
where
[tex]a_0 = \displaystyle \int_0^1 f(x) \, dx = \frac1{12}[/tex]
[tex]a_n = \displaystyle 2 \int_0^1 f(x) \cos(2\pi nx) \, dx = \frac1{n^2\pi^2}[/tex]
(See attached for a plot of f(x) along with its Fourier expansion up to order n = 10.)
Expand the Fourier series to get sums resembling the [tex]S'[/tex]-s :
[tex]\displaystyle f(x) = \frac1{12} + \frac1{\pi^2} \left(\sum_{k=0}^\infty \frac{\cos(2\pi(8k+1) x)}{(8k+1)^2} + \sum_{k=0}^\infty \frac{\cos(2\pi(8k+2) x)}{(8k+2)^2} + \cdots \right. \\ \,\,\,\, \left. + \sum_{k=0}^\infty \frac{\cos(2\pi(8k+7) x)}{(8k+7)^2} + \sum_{k=1}^\infty \frac{\cos(2\pi(8k) x)}{(8k)^2}\right)[/tex]
which reduces to the identity
[tex]\pi^2\left(\left(x-\dfrac12\right)^2-\dfrac{21}{256}\right) = \\\\ \cos(2\pi x) {S_1}' + \cos(4\pi x) {S_2}' + \cos(6\pi x) {S_3}' + \cos(8\pi x) {S_4}' \\\\ \,\,\,\, + \cos(10\pi x) {S_5}' + \cos(12\pi x) {S_6}' + \cos(14\pi x) {S_7}'[/tex]
Evaluating both sides at x for x ∈ {1/8, 3/8, 5/8, 7/8} and solving the system of equations yields the dependent solution
[tex]\begin{cases}{S_4}' = \dfrac{\pi^2}{256} \\\\ {S_1}' - {S_3}' - {S_5}' + {S_7}' = \dfrac{\pi^2}{8\sqrt 2}\end{cases}[/tex]
It turns out that
[tex]{S_1}' - {S_3}' - {S_5}' + {S_7}' = S_1 - S_3 - S_5 + S_7[/tex]
so we're done, and the sum's value is [tex]\boxed{\dfrac{\pi^2}{8\sqrt2}}[/tex].
y=5/2x-9 find the y intercept
Answer:
(0,-9) You have to substitute 0 for x and solve for y