With ϕ ≈ 1.61803 the golden ratio, we have 1/ϕ = ϕ - 1, so that
[tex]I = \displaystyle \int_0^\infty \frac{\sqrt[\phi]{x} \tan^{-1}(x)}{(1+x^\phi)^2} \, dx = \int_0^\infty \frac{x^{\phi-1} \tan^{-1}(x)}{x (1+x^\phi)^2} \, dx[/tex]
Replace [tex]x \to x^{\frac1\phi} = x^{\phi-1}[/tex] :
[tex]I = \displaystyle \frac1\phi \int_0^\infty \frac{\tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx[/tex]
Split the integral at x = 1. For the integral over [1, ∞), substitute [tex]x \to \frac1x[/tex] :
[tex]\displaystyle \int_1^\infty \frac{\tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx = \int_0^1 \frac{\tan^{-1}(x^{1-\phi})}{\left(1+\frac1x\right)^2} \frac{dx}{x^2} = \int_0^1 \frac{\pi2 - \tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx[/tex]
The integrals involving tan⁻¹ disappear, and we're left with
[tex]I = \displaystyle \frac\pi{2\phi} \int_0^1 \frac{dx}{(1+x)^2} = \boxed{\frac\pi{4\phi}}[/tex]
Which list of angle measures could be the angle measures of a triange?
Answer:
angles of triangle adds up to 180 degrees
6. Higher Order Thinking The manager of a restaurant wants to add two new side dishes to the menu. She surveys customers about side dish preferences and records the results in the table shown at the right. a. Find the experimental probability that a customer prefers either baked potato or asparagus. b. Find the experimental probability that a customer prefers either steamed broccoli or sweet potato.
Using it's concept, considering the number of desired and total outcomes, it is found that the probabilities are given by:
a. 0.6 = 60%.
b. 0.4 = 40%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In an experimental probability, these numbers of outcomes are taken from previous trials.
Researching the problem on the internet, it is found that there is a total of 127 + 44 + 95 + 104 = 370 customers.
Item a:
127 + 95 = 222 customers prefer either baked potato or asparagus, hence the probability is given by:
p = 222/370 = 0.6 = 60%.
Item b:
44 + 104 = 148 customers prefer either steamed broccoli or sweet potato, hence the probability is given by:
p = 148/370 = 0.4 = 40%.
More can be learned about probabilities at https://brainly.com/question/14398287
please help me solving this question please i want all solve please help
What is the volume of this right prism?
1200 in³
1800 in³
2040 in³
3600 in³
Right triangular prism. The height of the prism is labeled as 15 in. The base of the prism is a triangle with the base labeled as 30 in., the height labeled as 8 in., and the other 2 sides of the triangle labeled as 17 in.
brainleiest whoever answers
Answer:
1800 in^3
Step-by-step explanation:
Rewrite the expression 2 square root X•4x^-5/2 in the form k•x^n
Answer:
(4x)
2
=16×x
2
Step-by-step explanation:
hope it's help
Help!!!
Rationalize the denominator of;
[tex]1) \frac{1}{ \sqrt{7} } [/tex]
[tex]2) \frac{2}{ \sqrt{3} - \sqrt{2} } [/tex]
[tex]3) \frac{ \sqrt{6} + \sqrt{3} }{9 + 2 \sqrt{18} } [/tex]
Answer:
see below for explanation:-
Step-by-step explanation:
#1
[tex] \displaystyle{ \frac{1}{ \sqrt{7} } }[/tex]
[tex]\displaystyle{ \frac{1}{ \sqrt{7} } \times \frac{ \sqrt{7} }{ \sqrt{7} } }[/tex]
[tex]\displaystyle{ \frac{ \sqrt{7} }{7} }[/tex]
#2
[tex]\displaystyle{ \frac{2}{ \sqrt{3} - \sqrt{2} } }[/tex]
[tex]\displaystyle{ \frac{2}{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} } }[/tex]
[tex]\displaystyle{ \frac{2( \sqrt{3} + \sqrt{2} }{( \sqrt{3} {)}^{2} - ( \sqrt{ 2 } {)}^{2} } }[/tex]
[tex]\displaystyle{ \frac{2( \sqrt{3} + \sqrt{2} ) }{3 - 2} }[/tex]
[tex]\displaystyle{2( \sqrt{3} + \sqrt{2} )}[/tex]
#3
[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{9 + 2 \sqrt{18} } }[/tex]
[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{ 9 + 2 \sqrt{9 \times 2} } }[/tex]
[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{9 + 6 \sqrt{2} } }[/tex]
[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{3(3 + 2 \sqrt{2}) } }[/tex]
[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{3(3 + 2 \sqrt{2}) } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} } }[/tex]
[tex]\displaystyle{ \frac{3 \sqrt{6} - 2 \sqrt{12} + 3 \sqrt{3} - 2 \sqrt{6} }{3( {3}^{2} - (2 \sqrt{2} {)}^{2} ) } }[/tex]
[tex]\displaystyle{ \frac{ \sqrt{6} - 4 \sqrt{3} + 3 \sqrt{3} }{3(9 - 8)} }[/tex]
[tex]\displaystyle{ \frac{ \sqrt{6} - \sqrt{3} }{3} }[/tex]
ΔQRS is a right triangle.
Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle.
Select the correct similarity statement.
Answer:
∆QRS is a right triangle
Step-by-step explanation:
correct similarity statement is RST
Answer:
I think its B
Step-by-step explanation:
Edge 2022
The sum of three numbers is 11 . The sum of twice the first number, 5 times the second number, and 6 times the third number is 44. The difference between 4 times the first number and the second number is 10. Find the three numbers.
Answer:
4, 6, 1
Step-by-step explanation:
We can solve this problem using a system of equations:
1) a + b + c = 11
2) 2a + 5b + 6c = 44
3) 4a - b = 10
First, we can substitute the value of b from equation #3 into equation #1:
b = 4a - 10
a + (4a - 10) + c = 11
5a - 10 + c = 11
5a + c = 21
c = 21 - 5a
Now, we can plug the values of b and c into equation #2, as b and c are represented in terms of a:
2a + 5(4a - 10) + 6(21 - 5a) = 44
2a + 20a - 50 + 126 - 30a = 44
-8a + 76 = 44
-8a = -32
a = 4
b = 4a - 10 = 4(4) - 10 = 6
c = 21 - 5a = 21 - 5(4) = 1
PLEASE HELP ME WITH THIS QUESTION
Answer:
The second option, 1,008 cm²
Step-by-step explanation:
This shape has 5 sides to solve for with reguards to surface area.
Let us solve for them all.
[1 & 2 - the triangles]
12 * 9 = 108 cm²
-> I am not going to divide since we have 2 congruent triangles
[3 - the bottom side]
25 * 12 = 300 cm²
[4 - the side facing away]
25 * 9 = 225 cm²
[5 - the side facing up]
25 * 15 = 375 cm²
Now we will add them together for the total.
108 + 300 + 225 + 375 = 1,008 cm²
The surface area for the triangular prism shown is 1,008 cm².
Answer:
Your answer would be:
C.) 1,350 cm2
Volume = 0.5 x b x h x length
0.5 x (25 x 12) x 9 =
0.5 x 300 x 9 =
= 1,350 cm2
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
Jameson wants to construct a ladder that has 8 rungs. Each rung is
3.2 feet wide. The two sides measure 10.6 feet each. The wood is
sold for $2.25 per linear foot. Find how much the wood to construct
this ladder will cost Jameson. 5.NBT.7
Answer:
$23.85
Step-by-step explanation:
Linear foot- sold by the lenght.
Therefore you dont worry about the 3.2 feet wide
So now we multiply 10.6 * 2.25
which is...
$23.85
Which is the better choice: $1000 deposited for a year at a rate of 4.8% compounded semiannually 19) or at a rate of 4.7% compounded quarterly?
[tex]~~~~~~ \stackrel{\textit{\Large 4.8\% semiannually}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1000\\ r=rate\to 4.8\%\to \frac{4.8}{100}\dotfill &0.048\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &1 \end{cases}[/tex]
[tex]A=1000\left(1+\frac{0.048}{2}\right)^{2\cdot 1}\implies \boxed{A\approx 1048.58}~~\textit{\Large \checkmark} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \stackrel{\textit{\Large 4.7\% quarterly}}{\textit{Compound Interest Earned Amount}}[/tex]
[tex]A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1000\\ r=rate\to 4.7\%\to \frac{4.7}{100}\dotfill &0.047\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &1 \end{cases} \\\\\\ A=1000\left(1+\frac{0.047}{4}\right)^{4\cdot 1}\implies \boxed{A\approx 1047.83}[/tex]
Find the slope of the line that passes through (56, 49) and (-18, 35).
Answer:
[tex]\displaystyle \frac{7}{37}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-49 + 35}{-56 - 18} = m \hookrightarrow \frac{-14}{-74} = m \\ \\ \boxed{\frac{7}{37} = m}[/tex]
I am joyous to assist you at any time.
Michelle is fishing from a small boat. A fish swimming at the same depth as the hook at the end of her fishing line is 16 meters away from the hook. If Michelle is 20 meters away from the fish, how far below Michelle is the hook?
Answer:
12 meters
Step-by-step explanation:
You have to use the inverse of the pythagorean theorem to do this so you do square root of (20x20-16x16) which is 12
Classify each of the following statements as true or false.
a 4 × n can be written as 4n. say if it is true or false thanks smarties
b n × 3 can be written as 3n.
c 4 × b can be written as b + 4.
d a × b can be written as ab.
e a × 5 can be written as 50a.
Step-by-step explanation:
a- true
b- true
c- false, it can be written 4b
d- true
e- false, 5a
Answer:
A.true B.true C.False D.true E.False
A candy maker produces 465 pounds of chocolate bites. It is placed in equal amounts into 145 empty bags. Each bag can hold up to 3 pounds. How many pounds of chocolate bites are left over after the bags are filled?
Answer:
30 pounds are left over after the bag filled
Step-by-step explanation:
145×3
= 435
now,
465-435
= 30
The length is :____ meters and the width is ____meters.
Answer:
Length= 8, Width= 4
Step-by-step explanation:
Say the length is l, and the width is w.
We can set l, the length as 2w, as it is double the length.
The perimeter= 2l + 2w= 24
Input l as 2w, get
4w+2w=24
6w=24, w=4.
Length is w*2, so length is 8.
which fraction is larger: 3/10 or 2/7
Plot on a number line
Answer:
3/10 is bigger
Step-by-step explanation:
covert into a decimal so 0.3 is bigger than 0.2857
The Oriental Pearl Tower in Shanghai, China, is a 468-meter high tower with 11 spheres along the tower. Two spheres are larger than the rest and house meeting areas, an observation deck, and a revolving restaurant. The lower of the two larger spheres has a radius of 25 meters, and the higher sphere has a radius of 22.5 meters. What is the approximate total volume of the two largest spheres on the Oriental Pearl Tower?
The approximate total volume of the two largest spheres on the Oriental Pearl Tower 113105.45 m³.
How to find the volume of a sphereThe volume of the sphere is calculated as follows:
volume = 4 / 3 πr³
where
r = radiusThe lower two larger spheres in the tower has a radius of 25 meters and 22.5 meters. Therefore, the total volume of the two largest sphere is as follows:
volume of lower sphere = 4 / 3 × 3.14 × 25³
volume of lower sphere = 196250 / 3
volume of lower sphere = 65416.6666667
volume of lower sphere = 65416.7 m³
volume of higher sphere = 4 / 3 × 3.14 × 22.5³
volume of higher sphere = 143066.25 / 3
volume of higher sphere = 47688.75
volume of higher sphere = 47688.8 m³
The approximate total volume = 65416.7 + 47688.8 = 113105.45 m³
learn more on sphere here: https://brainly.com/question/13833611
please answer and use statement reason
Answer:
x = 15
Step-by-step explanation:
FD and AC are parallel because both are perpendicular to EB. Angle EDF and Angle DCA are congruent because they are corresponding angles. The measure of Angle DCA is also 3x because congruent angles have the same measure.
Now consider Triangle ACD. Because the sum of all three measures of the angles in a triangle add up to 180°.
x + 8x + 3x = 180°
12x = 180°
12x/12 = 180/12
x = 15
a large University with over 40,000 took a recent survey in which 31% of the students claimed to exercise at least 3 times a week. A simple random sample of 250 students was selected. b = the proportion of students in the sample who claimed to work out 3 at least 3 times a week. What is the standard deviation of the sampling??
Answer:
A large university with over 40,000 students recently took a survey in which 31% of the students claimed to exercise at least 3 times a week. A simple random sample …
✓ approximately Normal, because we would expect at least 10 success and 10 failures
Step-by-step explanation:
For 1-6, classify each triangle by its sides and then by its angle
Answer:
1) right angled triangle
2) isosceles triangle
3) equilateral triangle
4) scalen triangle
5) isosceles triangle
6) right angled triangle
An angle that measures exactly 180° is known as a/an _____ angle
Answer:
An angle that measures exactly 180° is known as a straight angle
Step-by-step explanation:
A straight angle is basically just a line. It is equal to two right angles (which are 90 degrees) and it is also half of a circle.
I hope this was helpful! If you need any more information on straight angles or any other angles, let me know! Have a lovely day! :)
PLEASE HELP!!! TOTAL 50 POINTS IF GIVEN BRAINLIEST ANSWER!!!
Find the average value of the function f over the given region.
f(x, y) =10x +3y over the triangle with vertices (0, 0), (9, 0), and (0, 2).
The average value of f(x, y) over the given region (I'll call it T) is
[tex]\dfrac{\displaystyle \iint_T f(x,y) \, dA}{\displaystyle \iint_T dA}[/tex]
In other words, it's the ratio of the integral of f(x, y) over the region to the area of the region.
The set T can be expressed as
[tex]T = \left\{(x,y) \,:\, 0\le x\le9 \text{ and } 0\le y\le -\dfrac29x+x\right\}[/tex]
Since it's a triangle, the denominator is easily computed to be
[tex]\displaystyle \iint_T dA = \frac12 \times 9 \times 2 = 9[/tex]
In the numerator, we have
[tex]\displaystyle \iint_T (10x+3y) \, dA = \int_0^9 \int_0^{-2x/9+2} (10x+3y) \, dy \, dx \\\\ = \int_0^9 \left(\frac32\left(-\frac{2x}9+2\right)^2+10x\left(-\frac{2x}9+2\right)\right) \, dx = 288[/tex]
and hence the average value is 288/9 = 32.
The number 3 is a factor of _________.
A) 4
B) 8
C) 12
=================================================
3 is a factor of 12 because 12 is evenly divisible by 3
4 and 8 are not evenly divisible by 3.
the key word here is evenly (without a remainder)
===================================================
note:-Hope everything is clear; if you need any more explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
Solve for p.
3(p + 4) = 48
A. 13
B. 12
C. 14
D. 19
Step-by-step explanation:
3 ( p + 4 ) = 48
3p + 12 = 48
3p = 48 - 12
3p = 36
p = 36 ÷ 3
p = 12...
A T.V. se was bought for Rs. 13950, when 10% discount is given. , calculate the marked price of the T.V.
Answer:
15500
Step-by-step explanation:
Solution
here
price of tv after discount: 13950
discount : 10%
now,
price of tv without discount= 13950÷90×100price of tv without discount= Rs15500Carrie ate some of the oranges that her mother brought home from the grocery store. Of the oranges her mother brought 1/4 were left over. Shyla,Carrie's sister ate 2/5 of the oranges that were left over. What fraction of the oranges did shyla eat?
Answer:
3/5
Step-by-step explanation:
Answer:
1/10
Step-by-step explanation:
We can put an actual number to this just for easier purposes
So let's say there was 100 oranges at the grocery store
Mom brought home 1/4 which is 25 oranges
100 * [tex]\frac{1}{4}[/tex] = 25
So now we have 25 oranges
Then, Shyla ate 2/5 of the oranges
So we want 2/5 of the 25 left oranges
25 * [tex]\frac{2}{5}[/tex] = 10
And 10 out of 100 is:
1/10
The easier way to do it is to just multiply the fractions together:
[tex]\frac{1}{4} * \frac{2}{5} = \frac{2}{20} = \frac{1}{10}[/tex]
If you have any questions feel free to comment and if this helped a brainliest would be appreciated :)
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?
Help picture below problem 9
Answer:
42 degrees
Step-by-step explanation:
Complimentary angles are two angles whose total is equal to 90 degrees. Since we already know that Angle N measures at 48 degrees, all we have to do is subtract that from 90 degrees to find the measure of Angle I.
90 - 48 = 42
So, the measure of Angle I is 42 degrees! It's pretty easy finding complementary angles once you know how to. I hope this helps! Have a lovely day!! :)
(p.s. I do teaching textbooks too)
Answer:
Step-by-step explanation:
Complementary angles add up to 90°
∠I + ∠N = 90
∠I + 48 = 90
∠I = 90 - 48
∠I = 42°
What are the x-intercepts of this conic section?
no x-intercepts
(−1, 0) and (1, 0)
(0, −2) and (0, 2)
(0, −1) and (0, 1)
Using it's concept, it is found that the conic section has no x-intercepts.
What is a x-intercept of a function?
A x-intercept of a function is given by the value of x when y = 0. On a graph, it is the value of x when the function crosses the x-axis.
In this problem, the conic section given in the graph does not cross the x-axis, hence it has no x-intercepts.
More can be learned about x-intercepts at https://brainly.com/question/24737967