Nitinol is an alloy of nickel and titanium, it has two structures, austenite or martensite, and nickel and titanium are elements, that contain 28 and 22 electrons respectively.
What is nitinol?Nitinol is an alloy containing an equal quantity of elements of nickel and titanium.
It is a superelastic alloy and has shape memory capacity.
It retains its shape after reforming into another shape by an increase in temperature.
Thus, the difference is that Nitinol is an alloy of nickel and titanium, it has two structures, austenite or martensite, and nickel and titanium are elements, that contain 28 and 22 electrons respectively.
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Use a double integral in polar coordinates to find the area of the region. The region inside the circle (x − 4)2 + y2 = 16 and outside the circle x2 + y2 = 16
Answer:
[tex]\mathbf{A = \dfrac{8}{3} \bigg (2 \pi + 3\sqrt{3} \bigg ) }[/tex]
Step-by-step explanation:
From the information given:
Lets first change the given relations into polar coordinates
So, the region of the inner circle into polar coordinates is as follows:
(x - 4)² + y² = 16
x² + y² - 8x = 0
r² - 8r cos θ = 0
r = 8 cos θ
For the outside circle:
x² + y² = 16
r² = 16
Thus, the intersection point are:
64cos²θ = 16
cos²θ = 1/4
θ = -(π/3) , (π/3)
Now: if we are to represent the sketch on a graph, the region of the integration D will be:
[tex]D = \bigg \{ (r,\theta )\bigg |-\dfrac{\pi}{3}\leq \theta \leq \dfrac{\pi}{3}, 4 \leq r \leq 8 cos \theta \bigg \}[/tex]
Therefore, the are of the required region can now be computed as follows:
[tex]A = \int \int _D \ dA[/tex]
[tex]A = \int ^{\pi/3}_{-\pi/3} \int ^{8 \ cos \theta}_{4} \ r dr d \theta[/tex]
[tex]A = \int ^{\pi/3}_{-\pi/3} \bigg (\dfrac{r^2}{2} \bigg ) ^{8 \ cos \theta}_{4} \ d \theta[/tex]
[tex]A = \int ^{\pi/3}_{-\pi/3} \dfrac{1}{2} \bigg (64 \ cos ^2 \theta - 16 \bigg ) \ d \theta[/tex]
[tex]A = \int ^{\pi/3}_{-\pi/3} \dfrac{16}{2} \bigg (4 \ cos ^2 \theta - 1 \bigg ) \ d \theta[/tex]
[tex]A = \dfrac{16}{2} * 2 \int ^{\pi/3}_{0} \bigg (4 \bigg ( \dfrac{ 1+ cos 2 \theta}{2} \bigg) - 1 \bigg ) \ d \theta[/tex]
[tex]A = 16 \int^{\pi/3}_{0} (1 + 2 cos 2 \theta ) d \theta[/tex]
[tex]A =16 ( \theta + sin2 \theta )^{\pi/3}_{0}[/tex]
[tex]A = 16 \begin {bmatrix} \bigg (\dfrac{\pi}{3} + \dfrac{\sqrt{3}}{2} \bigg ) - (0-0) \end {bmatrix}[/tex]
[tex]A = 16 \begin {bmatrix} \bigg (\dfrac{\pi}{3} + \dfrac{\sqrt{3}}{2} \bigg ) \end {bmatrix}[/tex]
[tex]\mathbf{A = \dfrac{8}{3} \bigg (2 \pi + 3\sqrt{3} \bigg ) }[/tex]
The area of the region is equal to [tex]8\sqrt{3} + \frac{16\pi}{3}[/tex] square units.
The double integral formula for the area of a given curve is described below:
[tex]A = \iint\,r(\theta) \,dr\,d\theta[/tex] (1)
Where:
[tex]r[/tex] - Distance with respect to origin.[tex]\theta[/tex] - Angle in standard position.We notice that [tex]r \in [4, 8\cdot \cos \theta][/tex] and [tex]\theta \in \left[-\frac{\pi}{3}, \frac{\pi}{3} \right][/tex], then we have the following integral:
[tex]A = \int\limits_{-\frac{\pi}{3} }^{+\frac{\pi}{3} } \int \limits_{r= 4}^{r = 8\cdot \cos \theta}\,r\,dr\,d\theta[/tex]
Now we proceed to integrate the expression:
[tex]A = \frac{1}{2}\int\limits_{-\frac{\pi}{3} }^{+\frac{\pi}{3} } \,(64\cdot \cos^{2}\theta -16)\,d\theta = 32 \int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } \,\cos^{2}\theta \, d\theta - 8\,\int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } \, d\theta[/tex]
[tex]A = 16\int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } {\cos 2\theta} \, d\theta + 8\int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } \, d\theta[/tex]
[tex]A = 8\sqrt{3}+\frac{16\pi}{3}[/tex]
The area of the region is equal to [tex]8\sqrt{3} + \frac{16\pi}{3}[/tex] square units.
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Which operation would you use to solve for x in the equation 3x = 15?
Answer:
Division
Step-by-step explanation:
3x = 3 times x so, you must do the opposite of multiplication to get rid of the 3, which is division.
The solution of the equation with a single variable 3x = 15 will be 5.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The equation is given below.
3x = 15
Divide the equation by 3 into both sides, then we have
3x / 3 = 15 / 3
x = 5
The solution of the equation with a single variable 3x = 15 will be 5.
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Which of the following expressions is equivalent to the one below? 3x + 6y
A.
6(2x + y)
B.
6x + 3y
C.
3(x + 2y)
D.
9(x + y)
Jason left for school and forgot his math homework on the kitchen table. His mother found the homework 10 minutes after Jason left, and started driving 36 mph to catch him. Jason bikes 12 mph.
a.How long will it take Jason's mother to catch him?
b. How many miles has Jason biked when his mother catches him?
c. If Jason's school is 2.5 miles from his apartment, how fast must his mother drive to catch him at the school door?
Answer: 5 minutes
Step-by-step explanation:
a. Jason's mother to catch him after time of 5minutes.
b. Jason biked for distance of 3miles when his mother catches him.
c. Mother has to drive with speed of 60mph to catch him at the school door, if Jason's school is 2.5 miles from his apartment.
What is speed?
" Speed is defined as the total distance travelled per unit time."
Formula used
[tex]Speed = \frac{total distance travelled}{total time taken}[/tex]
According to the question,
Speed of Jason bike = 12mph
1hour = 12miles
60minutes = 12miles
1minutes = [tex]\frac{12}{60}[/tex] miles
Speed of Jason's mother bike = 36mph
Time after mother found the homework = 10 minutes
After 10 minutes
Jason is at distance = [tex]\frac{12}{60} (10)[/tex]
=2miles
After 15 minutes = [tex]\frac{12}{60} (15)[/tex]
= 3miles
To cover three miles mother has to drive for
1hour = 36miles
60minutes = 36miles
1miles = [tex]\frac{60}{36}[/tex] minutes
3miles = [tex]\frac{60}{36} (3)[/tex]
= 5minutes
If Jason's school is 2.5 miles from his apartment,
Time taken by Jason to reach school door = [tex]\frac{2.5}{12.5} (60)[/tex] minutes
= 12.5 minutes
Time in which mother has to cover distance of 2.5miles
= [tex](12.5-10)[/tex]minutes
= 2.5minutes
Substitute the value in the formula we get,
Speed of mother's bike = [tex]\frac{2.5}{2.5} (60)[/tex] mph
= 60mph
Hence,
a. Jason's mother to catch him after time of 5minutes.
b. Jason biked for distance of 3miles when his mother catches him.
c. Mother has to drive with speed of 60mph to catch him at the school door, if Jason's school is 2.5 miles from his apartment.
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please helppp! and thank you
Answer:53
Step-by-step explanation:
What is the annual interest for a principal of $3,500 at a simple annual interest
rate of 2.3%?
Answer:
Step-by-step explanation:
Given principal p =$3500
Time t =1 year
Rate of interest r =2.3%
So annual interest=p×r×t/100
=3500×2×2.3/100
=7000×2.3/100
=16100/100
=161.
So annual interest is $161
Find PM pls help fast
Answer:
I think it is 4 but, im not sure
There are a total of 120 bicycles and tricycles in a shop. There are 302 wheels in allmany bicycles and how many tricycles are in the shop?
Answer: There are 62 tricycles in the shop.
Step-by-step explanation:
Given: Number of wheels in a bicycle = 2
Number of wheels in a tricycle = 3
Let x = Number of bicycles , y = Number of tricycles.
As per given , we have
x+y =120 (i)
2x+3y=302 (ii)
Multiplying 2 on both sides of (i)
2x+2y=240 (iii)
Subtract (iii) from (ii) , we get
y= 62
Put value of y in (i) , we get
[tex]x+62=120\\\\\Rightarrow\ x=120-62\\\\\Rightarrow\ x= 58[/tex]
Hence, there are 58 bicycles and 62 tricycles in the shop.
Como es la fórmula del perímetro de un hexágono?
Espero respuesta
Gracias
Answer:
El Perímetro de un hexágono es igual a la suma de todos sus lados.
Step-by-step explanation:
el perimetro siempre es la suma de los lados de cualquier figura
Houses can be either domed or octagonal.
True
False
Answer:
true
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
Houses can be either domed or octagonal: True
Solving systems of linear equations algbraically.
Answer:
(3,-6)
Step-by-step explanation:
[1] x - 2y = 15
[2] 2x + 4y = -18
Graphic Representation of the Equations :
-2y + x = 15 4y + 2x = -18
Solve by Substitution :
// Solve equation [1] for the variable x
[1] x = 2y + 15
// Plug this in for variable x in equation [2]
[2] 2•(2y+15) + 4y = -18
[2] 8y = -48
// Solve equation [2] for the variable y
[2] 8y = - 48
[2] y = - 6
// By now we know this much :
x = 2y+15
y = -6
// Use the y value to solve for x
x = 2(-6)+15 = 3
Solution :
{x,y} = {3,-6}
What is the slope of the line?
I'll brainlist!!
Plant A is 18 inches tall after one week, 36 inches tall after two weeks, 56 inches tall after three weeks. Plant B is 18 inches tall after one week, 36 inches tall after two weeks, 54 inches tall after three weeks. Which situation represents a proportional relationship between the plants?
Height and number of weeks?
Answer:
There are 2 given situations:
Plant A and Plant B growing in 3 weeks. Find which plant grows proportional
Plant A
=> 1st week = 18 inches
=> 2nd week = 36 inches
=> 3rd week = 56 inches
=> 18 + 18 = 36 + 20 = 56
Thus, this is not proportional
Plant B
=> 1st week = 18 inches
=> 2nd week = 36 inches
=> 3rd week = 54 inches
=> 18 + 18 = 36 + 18 = 54 inches
thus, the growth of this plant is proportional
17) A dog kennel charges $40 per night for boarding
and $5 for walking your dog.
a) Write an equation in standard form that models the
possible combinations if you plan to spend $200.
b) Graph the equation using x and y intercepts.
I
11
10
5
1 3 4 5 6 7 8 9 10 11 12 13
c) List all combinations that can be used.
Answer:
c
Step-by-step explanation:
A rocket is launched from a tower. The height of the rocket , y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot.
Y=-16x^2+147x+118
========================================================
Explanation:
The general equation
y = ax^2 + bx + c
has the vertex (h,k) such that
h = -b/(2a)
In this case, a = -16 and b = 147. This means,
h = -b/(2a)
h = -147/(2*(-16))
h = 4.59375
The x coordinate of the vertex is x = 4.59375
Plug this into the original equation to find the y coordinate of the vertex.
y = -16x^2+147x+118
y = -16(4.59375)^2+147(4.59375)+118
y = 455.640625
The vertex is located at (h,k) = (4.59375, 455.640625)
The max height of the rocket occurs at the vertex point. Therefore, the max height is y = 455.640625 feet which rounds to y = 455.6 feet
A fair six-sided die is rolled. Find the probability of getting a 4.
Answer:
A fair six-sized die is rolled. Find the probability of getting at least a 4.
There are 6 outcomes and three of them are 4, 5 or 6, so the probability of greater than or equal to 4 is 3/6=½.
Hadley paddled a canoe 2 miles in 1/9 of
an hour How far could Hadley paddle in
1 hour?
Answer: 18 miles
explanation: set up a proportion. (2 over 1/9 = x over 1). cross multiply, 2x1=2, then divide 2/(1/9)=18.
The table below represents a linear function. Determine the missing values in the table using the function rule.
Answer: In order: 25, 15, 67.
Step-by-step explanation:
In picture
By selling a book for Rs.400 a student got two successive profits of 12% and 40% respectively. Then his total profit is
a.62%
b.50%
c.55%
d.56.8%
The total profit made by the student is 56.8%
The correct answer is D
Given parameters:
final price in which he book was sold = Rs.400
the first profit made by the student = 12% = 0.12
the final profit made by the student = 40% = 0.4
To find:
the total profit of the studentTo find the total profit made by the student, we have to find the initial cost price of the book.
The cost price of the book before the student made the profit of 40%.
Let this cost price = y
100%y + 40%y = 400
140%y = 400
1.4y = 400
[tex]y = \frac{400}{1.4} \\\\y = 285.71[/tex]
This cost price become the new selling price before the student made the profit of 12%.
The cost price of the book before the student made the profit of 12%.
Let this cost price = x
100%x + 12%x = 285.71
112%x = 285.71
1.12x = 285.71
[tex]x = \frac{285.71}{1.12} \\\\x = 255.1[/tex]
This is the initial cost price of the book
The total profit made by the student is calculated as;
[tex]Profit \ \%= \frac{selling \ price - cost \ price }{cost \ price} \times 100\%\\\\Profit \ \%=(\frac{400 - 255.1}{255.1} )\times 100\%\\\\Profit \ \%= 56.8\%[/tex]
Thus, the total profit made by the student is 56.8%
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Jessica is shopping for a new car. She found a blue car that has a 12-gallon gas tank and can go 384 miles on one tank. She found a silver car that has a 14-gallon gas tank and can go 504 miles on one tank. Which car gets better gas mileage?
Best answer = More points!
Answer: Silver
Step-by-step explanation:
Answer:silver
Step-by-step explanation: I did it
The graph shows the printing rate of Printer A. Printer B can print at a rate of 25 pages per minute. Complete this sentence: The rate for Printer B is (a) ____________ the rate for Printer A because the rate of 25 pages per minute is (b) _____________ the rate of (c) __________ pages per minute for Printer A.
Answer:
a equal to c 25 b greater than
Step-by-step explanation:
Answer:
As per graph the rate of Printer A is 15 pages per minute.
Missing words are:
(a) greater than(b) greater than(c) 15The rate for Printer B is greater than the rate for Printer A because the rate of 25 pages per minute is greater than the rate of 15 pages per minute for Printer A.
Can some one help me find x?
Answer:
x = 20
Step-by-step explanation:
Exterior angles are equal.
7x - 3 = 6x + 17
Add 3 and subtract 6x to both sides.
x = 20 is the answer.
Michael threw a baseball 17.6 meters. His older brother, Kyle, threw a baseball 3.5 times farther than Michael. How far did Kyle throw the baseball?
Answer: 61.6
Step-by-step explanation:
17.6 X 3.5 = 61.6
Answer:
Kyle threw the baseball 61.6 meters
Step-by-step explanation:
You multiply 17.6 by 3.5 which results in 61.6
Find the area of a triangle with base of 4 and height of 3x-5
Answer:
Area of a triangle is 1/2B x H
In this case, BH = 0.5(3x-5)·4x
A = 4/2 · (3x²-5x)
plisss helppppppppppñp
Answer:
The value of x is 37.36
Step-by-step explanation:
The given triangle is a right-angled triangle where
Base = 25
Angle = 48°
Hypotenuse = x
As the triangle is a right angled triangle, trigonometric ratios can be used to find the missing value. We can use a ratio which uses base and hypotenuse.
[tex]cos\ 48 = \frac{base}{hypotenuse}\\cos\ 48 = \frac{25}{x}\\0.6691 = \frac{25}{x}\\x = \frac{25}{0.6691}\\x = 37.36[/tex]
Hence ,
The value of x is 37.36
In science class, Polly learned that trees help make the oxygen that people breathe. One tree makes about 250 pounds of oxygen each year. Polly wonders how much oxygen the trees on her street make. When she gets home, she counts 32 trees on her street. How many tons of oxygen do they make in a year?
Answer:
They make 4 approximately tons of oxygen each year.
Step-by-step explanation:
( 250lbs × 32 ) ÷ 2000 = 4t
250 pounds because each tree makes about 250 pounds of oxygen a year.
× 32 because there are 32 trees, so they'll make 32 times more oxygen than one tree.
÷ 2000 because before that everything was in pounds, and the question asks about tons. There are 2000 pounds in a ton, so you divide by 2000 to get the answer, which is 4 tons.
pleaseeeeeeeeeeeeeeeeee helpppppppppppppppppp
Answer:
Option c is the answer
Step-by-step explanation:
3/5 = 0.6
2 divided by 0.6 = 3.3333333
3.33333 = 10/3
10/3 = 3 1/3
Hope this helps :)
Answer:
3 1/3 or 3, depending on if he can play a fraction of a match
Step-by-step explanation:
The question is asking us how many times 3/5 can go into the whole number 2. to find this we can multiply the denominator of the fraction (5) by the whole number we are trying to get with the fraction (2), and this results in 10. if we put this over the denominator, we get 10/5, which results in 2. to find how many times 3/5 can go into 10/5, we will divide 10/5 by 3/5. this results in 3 and 1/3. so he can play 3 1/3 matches.
Which of the following is parallel to the line
Answer:
1
Step-by-step explanation:
h
Answer:
I know it is 1
Step-by-step explanation:
A line passes through the point (10, -1) and has a slope of 3/2 .
Write an equation in slope-intercept form for this line.
Answer:
y=3/2x-16
Step-by-step explanation:
The equation of the line passing from points (10, -1) is y = 3x/2 - 16.
What is equation of a line?A straight line's equation is a mathematical formula that describes the relationship between the coordinate locations along the line. It conveys the slope, x-intercept, and y-intercept of the line and can be expressed in a variety of ways. Y = mx + c and axe + by = c are the two versions of the equation of a straight line that are most frequently employed.
Given slope = 3/2 and points (10, -1)
equation of line is given by y = mx + c
m = 3/2
y = 3/2x + c
substitute points,
-1 = 10*3/2 + c
c = -16
equation of line is y = 3x/2 - 16
Hence the equation is y = 3x/2 - 16.
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What is the angle of elevation?
Answer:
Step-by-step explanation:
tan x° = [tex]\frac{3}{4}[/tex] ⇒ x° ≈ 36.87° ≈ 36.9°