Answers
Answer:
1) [tex]\int\limits^{16}_{2} {\frac{dx}{2\cdot x \cdot \sqrt{\ln x}} } \approx 1.665[/tex]
2) [tex]\frac{dy}{dx} = \pm \frac{1}{\sqrt{4\cdot x^{2}+7\cdot x +3}}[/tex]
3) [tex]\int\limits^{2\sqrt{3}}_{0} {\frac{dx}{\sqrt{4 + x^{2}}} } \approx 1.317[/tex]
Step-by-step explanation:
1) [tex]\int\limits^{16}_{2} {\frac{dx}{2\cdot x \cdot \sqrt{\ln x}} }[/tex]
This integral can be solved easily by using algebraic substitutions:
[tex]u = \ln x[/tex], [tex]du = \frac{dx}{x}[/tex]
Then, the integral can rewritten as follows:
[tex]\int {\frac{dx}{2\cdot x\cdot \sqrt{\ln x}} } = \frac{1}{2}\int {\frac{du}{u^{1/2}} } = \frac{1}{2}\int {u^{-1/2}} \, du[/tex]
[tex]\int {u^{-1/2}} \, du = 2\cdot u^{1/2} + C = 2\cdot \sqrt{\ln x} + C[/tex]
Where [tex]C[/tex] is the integration constant.
[tex]\int\limits^{16}_{2} {\frac{dx}{2\cdot x \cdot \sqrt{\ln x}} } = F(16) - F(2)[/tex]
[tex]F(16) - F(2) = 2\cdot (\sqrt{\ln 16}-\sqrt{\ln 2})[/tex]
[tex]F(16) - F(2) \approx 1.665[/tex]
2) Let be [tex]y = \cosh^{-1} (2\cdot \sqrt{x+1})[/tex], then we obtain the expression by the definition of the derivative for the inverse hyperbolic cosine and the chain rule:
[tex]\frac{dy}{dx} = \pm\frac{1}{\sqrt{4\cdot x + 3}}\cdot \left(\frac{1}{\sqrt{x+1}} \right)[/tex]
[tex]\frac{dy}{dx} = \pm \frac{1}{\sqrt{(4\cdot x + 3)\cdot (x+1)}}[/tex]
[tex]\frac{dy}{dx} = \pm \frac{1}{\sqrt{4\cdot x^{2}+7\cdot x +3}}[/tex]
3) [tex]\int\limits^{2\sqrt{3}}_{0} {\frac{dx}{\sqrt{4 + x^{2}}} }[/tex]
This integral can be solved by the following trigonometric substitutions:
[tex]\frac{2}{\sqrt{4 + x^{2}}} = \cos \theta[/tex]
[tex]\frac{1}{\sqrt{4+x^{2}}} = \frac{\cos \theta}{2}[/tex]
[tex]\frac{x}{2} = \tan \theta[/tex]
[tex]x = 2\cdot \tan \theta[/tex]
[tex]dx = 2\cdot \sec^{2}\theta \,d \theta[/tex]
[tex]\int {\frac{dx}{\sqrt{4+x^{2}}} } = \int {\left(\frac{\cos \theta}{2} \right)\cdot (2\cdot \sec^{2}\theta)} \, d\theta = \int {\sec \theta} \, d\theta[/tex]
[tex]\int {\sec \theta}\,d\theta = \ln |\sec \theta + \tan \theta| + C[/tex]
[tex]\ln \left|\frac{\sqrt{4+x^{2}}}{2} + \frac{x}{2} \right| + C[/tex]
Where [tex]C[/tex] is the integration constant.
[tex]\int\limits^{2\sqrt{3}}_{0} {\frac{dx}{\sqrt{4 + x^{2}}} } = F(2\sqrt{3}) - F(0)[/tex]
[tex]F(2\sqrt{3}) - F(0) = \ln \left|2+\sqrt{3}\right|-\ln \left|1\right|[/tex]
[tex]F(2\sqrt{3}) - F(0) \approx 1.317[/tex]
Related Questions
Use the formula v = IR for current flowing through a resistor, where V is the voltage in volts, I is current in amps, and R is resistance in ohms. Find the current through a resistor with resistance 15 ohms if the voltage across it is 3 volts.
Answers
Answer:
0.2 amps
Step-by-step explanation:
Given data
The formula V=IR is the formula for ohms law
Which state that the voltage is directly proportional to the current and the resistance in an electric circuit
Now
R= 15 ohms
V= 3volts
V= IR
3= I*15
I= 3/15
I= 0.2 amps
Hence he current flowing is 0.2 amps
The endpoints of a diameter are (-3,4) and (5,-2). What is the center of the circle?
Answers
Hope this helps!!
Juan y rosa van a repartirse un pastel por partes iguales sin que sobre nada .Si de la fiesta sobró 3/4pastel .¿cuanto le tocó a cada uno?
Answers
Usando el método de polya:
a. Que se pregunta?
la fracción de cuánto obtendría cada uno de ellos y compartiría por igual.b. ¿Cuáles son los datos dados?
¾ tarta, 2 personas (Juan y Rosa)c. ¿Cuál es la operación que se utilizará?
divisiónd. oración numérica:
¾ ÷ 2e. Solución y respuesta completa:
[tex] \frac{3}{4} \div 2 \\ = \frac{3}{4} \times \frac{1}{2} \\ = \frac{3}{8} [/tex]
explicación paso a paso:
Multiplica por el recíproco: Dividir es equivalente a multiplicar por el recíproco.Multiplicar: multiplica las fraccionesForma decimal: 0.375
☆彡Hanna#CarryOnLearning
FIND THE ∛ OF 188
(USE √
Answers
9514 1404 393
Answer:
∛188 ≈ 5.72865
Step-by-step explanation:
Any scientific or graphing calculator or spreadsheet can tell you the cube root of 188.
∛188 ≈ 5.72865431598...
__
You know that 5³ = 125 and 6³ = 216, so the root will lie between 5 and 6, closer to 6. As a first approximation, you can figure it is about ...
x = ∛188 ≈ 5 + (188-5³)/(6³ -5³) = 5 + 63/89 ≈ 5.71
You can figure this much using a 4-function calculator.
A closer approximation (x') can be had using the iteration formula ...
x' = (2x³ +188)/(3x²)
For x = 5.71, the value of x' is ...
x' ≈ (2×5.71³ +188)/(3×5.71²) ≈ 560.3388/97.8123 ≈ 5.7287
This value is correct when the root is rounded to 4 decimal places. Another execution of the iteration formula using this value will give the root accurate to 9 decimal places.
Consider the following data set with a mean of 12: 9,11,12,16 using the standard deviation formula calculate the standard deviation for this data set
Answers
Answer:The following algorithmic calculation tool makes it easy to quickly discover ... E.g: 11,21,10,42,53 ... Mean = sum of values / N (number of values in set); Variance = ((n1- ... Population Standard Deviation = use N in the Variance denominator if ... for data set 1,8,-4,9,6 compute the SD and the population SD.
Step-by-step explanation:
rule for 15,19,23 please I need it urgently
Answers
Answer:
[tex]a_{n}[/tex] = 4n + 11
Step-by-step explanation:
There is a common difference between consecutive terms, that is
19 - 15 = 23 - 19 = 4
This indicates the sequence is arithmetic with explicit rule
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 15 and d = 4 , then
[tex]a_{n}[/tex] = 15 + 4(n - 1) = 15 + 4n - 4 = 4n + 11
A cargo plane has a maximum take off weight of 910000 pounds which expression can be used to determine the maximum take off weight in tons?
Answers
Answer:
910,000 ÷ 2,000
Step-by-step explanation:
1 ton = 2000 pounds
therefor divide pounds by 2000 to get tons
910,000 ÷ 2,000
A positive real number is 4 less than another. if the sum of the squares of the two numbers is 72, then find the numbers
Answers
Answer:
x+4=72
x=72-4
x=68
Step-by-step explanation:
let x be one number and 4 be anothe number then sum of the two number be x and 4
Triangle ABC is the pre-image and triangle DFE is the image.
What is the scale factor of the dilation?
Please helppp!!!!!
Answers
Answer:
Scale factor = ½
Step-by-step explanation:
The original image is the preimage = ∆ACB
The new image is the image = ∆DFE
The scale of factor of dilation = image/preimage = DF/AC
DF = 6 cm (given)
AC = 12 cm (given)
Plug in the values into the equation to find the scale factor of dilation:
Scale factor = 6/12
Scale factor = ½
A group of 5 students was asked, "How many hours did you watch television last week?" Here are their responses:
14, 6, 18, 15, 13
Find the median and mean number of hours for these students.
If necessary, round your answers to the nearest tenth.
Median: hours
?
Mean: [hours
Answers
Write x(x+1)^2(x-5)/x(x+2)(x-5)^3 in simplest terms. Show your work
Answers
Answer: (x+1)^2(x-5)^4(x+2)
Step-by-step explanation: 1. Cancel x (x+1)^2(x-5)(x+2)(x-5)^3
Use The product Rule: x^a x^b= x ^a+^b and your answer should be (x+1)^2(x-5)^4(x+2)
Answer (x+1)^2/(x+2)(x-5)^2
Cancel common factor of x
Rewrite expression
Factor
Cancel common factors …. It basically repeats !
What is the radius for the circle given by the equation x^2+(y-1)^2=12?
Round your answer to the nearest thousandth.
Answers
9514 1404 393
Answer:
3.464
Step-by-step explanation:
Comparing the given equation to the standard form equation of a circle:
(x -h)^2 +(y -k)^2 = r^2
we find the center to be (h, k) = (0, 1) and the radius to be √12 = 2√3.
The problem statement tells us to round the radius to the nearest thousandth, so it will be ...
2√3 ≈ 3.4641016 ≈ 3.464 . . . radius of the circle
Kimberly loves science and just subscribed to KiwiCo.
a company that delivers STEAM kits to students to
build and create things at home. KiwiCo charges a
subscription fee of $16.99 for each of its members.
KiwiCo had 300 subscribers in March. In April, 50 new
people subscribed to KiwiCo, and 23 people canceled
their subscriptions. How much more money did KiwiCo
earn from subscriptions in April?
Answers
Answer:
$5555.73
Step-by-step explanation:
$16.99 per 1 person
300+50=350-23=. 327
327×$16.99= 5555.73
Try this and if it doesn't work then let me know
The solution set for -18 < 5x - 3 is _____.
3 > x
3 < x
-3 < x
-3 > x
Answers
Answer:
[tex]-3 < x[/tex]
Step-by-step explanation:
Given
[tex]-18 < 5x-3[/tex]
Required
The solution
[tex]-18 < 5x-3[/tex]
Add 3 to both sides
[tex]3-18 < 5x-3+3[/tex]
[tex]-15 < 5x[/tex]
Divide both sides by 5
[tex]-3 < x[/tex]
Given points (-3;-6), G(3; -2) and H(6; 1); determine:
(a) The equation of line FG
Answers
Answer:
The equation of line FG is [tex]y = \frac{2}{3}x - 4[/tex]
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
[tex]y = mx + b[/tex]
In which m is the slope and b is the y-intercept.
F(-3;-6), G(3; -2)
When we have two points, the slope is given by the change in y divided by the change in x. So
Change in y : -2 - (-6) = -2 + 6 = 4
Change in x: 3 - (-3) = 3 + 3 = 6
Slope: [tex]m = \frac{4}{6} = \frac{2}{3}[/tex]
So
[tex]y = \frac{2}{3}x + b[/tex]
Finding b:
(3; -2) means that when [tex]x = 3, y = -2[/tex]. We use this to find b.
[tex]y = \frac{2}{3}x + b[/tex]
[tex]-2 = \frac{2}{3}(3) + b[/tex]
[tex]2 + b = -2[/tex]
[tex]b = -4[/tex]
The equation of line FG is [tex]y = \frac{2}{3}x - 4[/tex]
A professor wants to estimate the average time it takes his students to finish a computer project. Based on previous evidence, he believes that the standard deviation is approximately 3.6 hours. He would like to be 96% confident that his estimate is within 5 hours of the true population mean. Use RStudio to determine how large of a sample size is required without rounding any interim calculations.
Answers
Answer:
A sample size of 3 is required.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.96}{2} = 0.02[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.02 = 0.98[/tex], so Z = 2.054.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Based on previous evidence, he believes that the standard deviation is approximately 3.6 hours.
This means that [tex]\sigma = 3.6[/tex]
He would like to be 96% confident that his estimate is within 5 hours of the true population mean. Use RStudio to determine how large of a sample size is required without rounding any interim calculations.
The sample size needed is of n, and n is found when M = 5. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]5 = 2.054\frac{3.6}{\sqrt{n}}[/tex]
[tex]5\sqrt{n} = 2.054*3.6[/tex]
[tex]\sqrt{n} = \frac{2.054*3.6}{5}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.054*3.6}{5})^2[/tex]
[tex]n = 2.19[/tex]
Rounding up:
A sample size of 3 is required.
What is a probability ?
A number that measures the likelihood that the event will occur.
An activity involving chance in which results are observed
An observation of an experiment
The result of an experiment
Answers
Answer:
A number that measures the likelihood that the event will occur.
Step-by-step explanation:
Probability is a measure of the frequency of occurrence of a phenomenon, the value of which can be expressed qualitatively or quantitatively. Probability is quantified as a real number between 0 and 1, although sometimes probability is also expressed as a percentage. The probability is 0 when the event cannot or will never happen, and the probability is 1 when it happens for sure or it always happens. If the probability is between these values, the event is not common and its occurrence is uncertain. The higher the probability value, the more common the event is or the more certain it will occur.
GIVING OUR BRAINLIEST HELP ME PLEASE !! 10 PTS!
Answers
Answer:
The solution is D. x² + y² + 4x - 2y = -1
Step-by-step explanation:
The standard form of a circle with a center at (h,k) and a radius r is:
(x-h)² + (y-k)² = r²
Since the center is (-2,1) and the radius is
2, we know that:
h = -2k = 1r = 2Thus, the equation of the circle is:
(x-(-2))² + (y-1)² = 2²
This simplifies to be
(x+2)² + (y-1)² = 4
The equation of the circle is:
(x+2)² + (y-1)² = 4
x²+4x+4+y²-2y+1 = 4
x²+y²+4x-2y+5 = 4
x²+y²+4x-2y = 4-5
x²+y²+4x-2y = -1
Lowest 15 percent is showing incorrect
Answers
Answer:
Ok, cool
Step-by-step explanation:
holaaaaaaaaaaaa plz help me i need it quick △SEA is rotated 270 degrees about the origin. Draw the image of this rotation.
Answers
Answer:
A will have this new coordinate (2, 1).
S will have this new coordinate (-2, 7).
E will have this new coordinate (2, 7).
Step-by-step explanation:
A is the coordinate (-1, 2).
S is the coordinate (-7, -2).
E is the coordinate (-7, 2).
To rotate that figure 270 grades (is the same to rotate 90 grades) we need to convert those coordinates to this (y, -x).
So,
A will have this new coordinate (2, 1).
S will have this new coordinate (-2, 7).
E will have this new coordinate (2, 7).
I know the answer I just need a step by step explain. The answer is $1000
Answers
sorry, I can help with this question but the question is cut off on the right, reply to me with the full question and id be happy to help :)
3. Betty rode her bike down a block that was 50 meters long. How many millimeters did she ride?
Answers
Answer:
50,000 millimeters
Step-by-step explanation:
Hope this helps : ) I have no explanation but it's correct
An engineering consulting firm wanted to evaluate the diameter of rivet heads. The following data represent the diameters (in hundredths of an inch) for a random sample of 25 rivet heads:
(20 pts) 6.81 6.79 6.69 6.59 6.65 6.60 6.74 6.70 6.76 6.84 6.81 6.71 6.66 6.76 6.76 6.77 6.72 6.68 6.71 6.79 6.72 6.72 6.72 6.79 6.83
a. Set up a 95% confidence interval estimate of the average diameter of rivet heads (in hundredths of an inch)
b. Set up a 95% CI estimate of the standard deviation of the diameter rivet heads (in hundredths of an inch)
Answers
Answer:
a)CI 95 % = ( 6.7063 ; 6.7593) ( in hundredths of an inch)
b) CI 95 % = ( 0.05 < σ < 0.089 ) ( in hundredths of an inch)
Step-by-step explanation:
From the problem statement, we have a manufacturing process and we we assume a normal distribution, from sample data:
x = 6.7328 and s = 0.0644
a) CI 95 % = ( x ± t(c) * s/√n )
t(c) df = n -1 df = 25 - 1 df = 24
CI = 95 % α = 5 % α = 0.05 α /2 = 0.025
Then from t-student table t(c) = 2.060
s/√n = 0.0644/ √ 25 s/√n = 0.01288
CI 95 % = ( x ± t(c) * s/√n ) = ( 6.7328 ± 2.060*0.01288)
CI 95 % = ( 6.7328 ± 0.02653 )
CI 95 % = ( 6.7063 ; 6.7593) ( in hundredths of an inch)
b) CI 95 % of the variance is:
CI 95 % = ( ( n - 1 ) * s² / χ²₁ - α/₂ ≤ σ² ≤ ( n - 1 )*s² / χ²α/₂ )
( n - 1 ) * s² = ( 25 - 1 ) * (0.0644)² = 24* 0.00414
( n - 1 ) * s² = 0.09936
And from χ² table we look for values of
χ² α/₂ ,df df = 24 and α/2 = 0.025
χ² (0.025,24) = 12.40 and χ²₁ - α/₂ = χ² (0.975, 24)
χ² (0.975, 24) = 39.36
Then
CI 95 % = ( 0.09936 / 39.36 ≤ σ² ≤ 0.09936 / 12.40)
CI 95 % = ( 0.0025 ≤ σ² ≤ 0.0080)
Then for the standard deviation, we take the square root of that interval
CI 95 % = ( 0.05 < σ < 0.089 )
Write the following equation in the general form Ax + By + C = 0.
y - x - 1 = 0
2x - 3y + 6 = 0
2x - 3y - 6 = 0
-2x + 3y - 6 = 0
Answers
2*-3y-6
Step-by-step explanation:
Which function is continuous across its domain?
Answers
Answer:
B.
Step-by-step explanation:
a function is continuous, if the functional values are the same at the "connection" points of the various segments (and the segments themselves are continuous).
"continuous" simply means that the graph of the function is a continuous line without any "rips". it can have corners and such, but no "interruptions".
specifically it means : for every possible y value in the defined range of the function there is an x value that causes this y.
all defined segments are continuous functions.
so, let's look at
A. the first connection point is x=-2.
-2 + 6 = 0.5×(-2)²
4 = 0.5×4 = 2
4 = 2 is wrong. => here, at this point, the function "rips" apart and is not continuous.
B. x=-2
-2 + 4 = 0.5×(-2)²
2 = 2 is correct. continuous at this point.
second connection point x=4
0.5×4² = 20 - 3×4
0.5×16 = 20 - 12
8 = 8 is correct. continuous at this point
C. x=-2
-2 - 2 = 0.5×(-2)²
-4 = 2 is wrong. not continuous
D. x=-2
-2 + 4 = 0.5×(-2)²
2 = 2 is correct. continuous here.
now for x=4
4 + 4 = 25 - 3×4
8 = 25 - 12 = 13
8 = 13 is wrong. not continuous.
Which problem can be solved using the equation shown?
2 dollars and 50 cents x minus 2 dollars = 10 dollars and 50 cents
A. Will bought several books that cost $2.50 each and received a $2.00 discount on his total bill. If he paid $10.50, how many books did he buy?
B. Will bought several books that cost $2.00 each and received a $2.00 discount on his total bill. If he paid $10.50, how many books did he buy?
C. Will bought several books that cost $10.50 each and received a $2.00 discount on his total bill. If he paid $2.50, how many books did he buy?
D. Will bought several books that cost $10.50 each and received a $2.50 discount on his total bill. If he paid $2.50, how many books did he buy?
Answers
Answer:
A
Step-by-step explanation:
i hope it help!!!!!!!!!
f(x)=|x-6| written as piecewise function
Answers
The function g is a transformation of f. If g has a y-intercept at 4, which of the following functions could represent g?
g(x) = f(x) - 2
g(x) = f(x + 2)
g(x) = f(x) + 4
O g(x) = f(x-4)
Answers
Answer:
g(x) = f(x) - 2
g(x) = f(x + 2)
Step-by-step explanation:
y-intercept of a function:
The y-intercept of a function is the value of y when x = 0.
Function f:
Graph given in this question
When [tex]x = 0, y = 6[/tex], so the y-intercept is 6.
Additionally, when [tex]x = -2, y = 4[/tex]
If g has a y-intercept at 4, which of the following functions could represent g?
Either we subtract 2 from f, that is:
[tex]g(x) = f(x) - 2[/tex]
Or we can also add 2 on the domain, that is, moving 2 units to the right, so:
[tex]g(x) = f(x+2)[/tex]
So the first two options are correct.
Answer:
the answer would be g(x)=f(x)-2
Step-by-step explanation:
i got it right
Question 10 (1 point) Find the volume of the figure. 2.5 ft 3 ft 2 ft 6 ft. What is the volume of the figure?
Answers
Answer:
I don’t know what type of figure you are talking about. But if there is supposed to be a picture attached, we see nothing
Step-by-step explanation:
You could repost this question though, I’ll be glad to help on that other question!
If a1 = 6 and an
-5an-1 + 4 then find the value of a4.
Answers
9514 1404 393
Answer:
a4 = -666
Step-by-step explanation:
Use the recursive definition repeatedly.
a1 = 6
a2 = -5(6) +4 = -26
a3 = -5(-26) +4 = 134
a4 = -5(134) +4 = -666