Answer:
a) The amplitud of the plain wave is 25, b) The wave length of the plain wave is [tex]\frac{\pi}{2}[/tex], c) The frequency of the plain wave is [tex]\frac{\pi}{60}[/tex], d) The speed of propagation of the plain wave is 0.082.
Step-by-step explanation:
A plain wave is modelled after the following mathematical model as a function of time and horizontal position. That is:
[tex]y(t, x) = A \cdot \sin (\omega\cdot t - \frac{2\pi}{\lambda}\cdot x)[/tex]
Where:
[tex]y(t, x)[/tex] - Vertical position wave with respect to position of equilibrium, dimensionless.
[tex]A[/tex] - Amplitude, dimensionless.
[tex]\omega[/tex] - Angular frequency, dimensionless.
[tex]\lambda[/tex] - Wave length, dimensionless.
After comparing this expression with the equation described on statement, the following information is obtained:
[tex]A = 25[/tex], [tex]\omega = 120[/tex] and [tex]\frac{2\pi}{\lambda} = 4[/tex]
a) The amplitude of the plain wave is 25.
b) The wave length associated with the plain wave is found after some algebraic handling:
[tex]\frac{2\pi}{\lambda} = 4[/tex]
[tex]\lambda = \frac{\pi}{2}[/tex]
The wave length of the plain wave is [tex]\frac{\pi}{2}[/tex].
c) The frequency can be calculated in term of angular frequency, that is:
[tex]f = \frac{2\pi}{\omega}[/tex]
Where [tex]f[/tex] is the frequency of the plain wave.
If [tex]\omega = 120[/tex], then:
[tex]f = \frac{2\pi}{120}[/tex]
[tex]f = \frac{\pi}{60}[/tex]
The frequency of the plain wave is [tex]\frac{\pi}{60}[/tex].
d) The speed of propagation is equal to the product of wave length and frequency:
[tex]v = \lambda \cdot f[/tex]
Given that [tex]\lambda = \frac{\pi}{2}[/tex] and [tex]f = \frac{\pi}{60}[/tex], the speed of propagation is:
[tex]v = \left(\frac{\pi}{2} \right)\cdot \left(\frac{\pi}{60} \right)[/tex]
[tex]v \approx 0.082[/tex]
The speed of propagation of the plain wave is 0.082.
How many solutions will there be to the following equation?
16X^2= 100
A-more than 2 solutions
B-no solution
C-1 solution
d-2 solutions
Answer:
d. 2 solutions
Step-by-step explanation:
To find the number of solution present in the equation given, we will follow the steps below:
16X²= 100
Take the square root of both-side
√16X²= √100
4x = ± 10
Divide both-side of the equation by 4
4x/4 = ± 10/4
x = ± [tex]\frac{5}{2}[/tex]
x = -[tex]\frac{5}{2}[/tex] or
It has two solutions
The given equation is 16X^2 = 100.
We can solve for X by dividing both sides by 16 and then taking the square root of both sides:
16X^2 = 100
X^2 = 100/16
X^2 = 6.25
Taking the square root of both sides:
X = ±2.5
So, there are 2 solutions to the equation: X = 2.5 and X = -2.5.
Therefore, the answer is (D) 2 solutions.
You work as a health inspector and must visit each of the 15 restaurants in town once each week.
a) In how many different orders can you make these inspections?
b) If you were to work 50 weeks a year and use a different order every week, how long would it take you to try all of the different possible orders
Answer:
Step-by-step explanation:
The no of different ways in which these restaurants can be visited
= ¹⁵P₁₅
= 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 1.30 x 10¹²
b ) Each combination takes 1 week and 50 weeks in a year to work
No of years to take to try all the combination
= 1.30 x 10¹² / 50
= 2.615 x 10¹⁰ years .
An isosceles trapezoid is a quadrilateral with two congruent legs, a pair of parallel bases, and congruent base angles. Prove the diagonals of an isosceles trapezoid are congruent. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.
Answer:
The answer is below
Step-by-step explanation:
We must first define the concepts a little:
We have that when the sides are congruent that is to say that they have the same direction and the same size and also the two opposite sides are parallel, the angles will be the same.
Now, in an isosceles triangle, two angles are congruent, because their two sides are congruent.
Can someone help me with this question please?
Answer:
a) about -12 °C
b) see below (red line)
c) about -24.5°C
Step-by-step explanation:
a) locate the vertical line representing 10°F on the graph. Identify the point where it intersects the graphed line. Read the vertical coordinate of that point of intersection. That is the temperature in °C. (Purple line on the attachment.) It is about -12 °C.
__
b) When F = -20, C = 2F = 2(-20) = -40. So, (-20, -40) is one point on the line.
When F = 10, C = 2F = 2(10) = 20. So, (10, 20) is another point on the line.
In the attached graph, we have drawn a (red) straight line between these points.
__
c) The Celsius temperature where it is double the Fahrenheit temperature is about -24.5 °C. (Blue line on the attachment.) It is exactly -24 8/13 °C. The graph cannot be read with that precision.
Ratio and Proportion problem
Please help meh
Answer:
hope its helpful to uh.......
The area of a rectangle is 3 2/3square meters. If the rectangle is 2 3/4meters long, find the width of the rectangle?
A print shop purchases a new printer for $25,000. The equipment depreciates at a rate of 5% each year. The relationship between the value of the printer, y, and the year number, x, can be represented by the equation, y = 25 , 000 ⋅ 0.95 x . Complete the table below with the value of the printer, to the nearest cent, in years 1, 2, and 3. Include proper decimals and commas in your answer and show your answer to the nearest cent.
Answer:
The value of the printer on the first year was $ 23,750.00. On the second year it was $ 22,562.5. On the third year it was $ 21,434.38.
Step-by-step explanation:
Since the printer depreciates at a rate of 5% per year, I believe the stated equation is miss typed. Therefore I'll answer this with the correct equation that would represent that setting:
[tex]y(x) = 25,000*0.95^x[/tex]
In the first year the value of the printer is:
[tex]y(1) = 25,000*0.95^1 = 23,750[/tex]
On the second year the value of the printer is:
[tex]y(2) = 25,000*0.95^2 = 22,562.5\\[/tex]
On the third year the value of the printer is:
[tex]y(3) = 25,000*0.95^3 = 21,434.38\\[/tex]
The value of the printer on the first year was $ 23,750.00. On the second year it was $ 22,562.5. On the third year it was $ 21,434.38.
Shouldn't it be the last answer?
Answer:
x=4
Step-by-step explanation:
The solution is where the two lines intersect
f(x) = g(x) is where x=4 and y = 2
The x =4 is value where f(x) = g(x)
The triangles below are similar. What is the length of ? A. 17 cm C. 19 cm B. 18 cm D. 20 cm
Answer:
B. 18 cm.
Step-by-step explanation:
Because they are similar, we can say that segment AC corresponds to segment DF, and segment AB corresponds to segment ED. So, we can set up a proportion.
[tex]\frac{16}{24} =\frac{12}{x}[/tex]
[tex]\frac{2}{3} =\frac{12}{x}[/tex]
2 * x = 12 * 3
2x = 36
x = 18
So, the length of ED is B. 18 cm.
Hope this helps!
Expand (5a/3 -2b/5)^3
Answer:
Hello!
~~~~~~~~~~~~~~~~~~~~
Expanded form of (5a/3 -2b/5)^3 =
[tex]\frac{125a^3}{27} - \frac{10a^2b}{3} + \frac{4ab^2}{5} - \frac{8b^3}{125}[/tex]
Step-by-step explanation: You have to Simplify the expression.
Hope this helped you. Brainliest would be nice!
Find C and a so that f(x)equalsCa Superscript x models the situation described. State what the variable x represents in your formula. There are initially 3000 bacteria, and this sample doubles in size every hour.
Answer: x represents the time period.
C= 3000 and a = 2
Step-by-step explanation:
The given equation is [tex]f(x)=Ca^x[/tex] which is an exponential equation. (i)
The general form of the exponential equation is :
[tex]f(x)=Ab^x[/tex] (ii)
, where A = initial value and b= multiplicative factor, and x is the time.
As compare both of the equation in (i) and (ii) , we get
A= C , and b= a
Since there are initially 3000 bacteria, and this sample doubles in size every hour.
i.e. C= 3000 (Initial) and a= 2 (multiplicative factor).
What is the perimeter of the larger of the two similar parallelograms? A 12cm B 16cm C 24cm D 18cm
Answer:
D
Step-by-step explanation:
The scale factor from small to large is
scale factor = [tex]\frac{6}{4}[/tex] = 1.5 , thus
side of larger parallelogram is 1.5 × 2 = 3 cm
Thus
perimeter = 6 + 6 + 3 + 3 = 18 cm → D
Solve the following expression: (2÷3- 4÷9) × 3 ×2∕5
Answer:
[tex]\frac{4}{15}[/tex] (0.26)
Step-by-step explanation:
(2 ÷ 3 - 4 ÷ 9) × 3 × 2 ÷ 5
[tex](\frac{2}{3} - 4/9) * 3 * 2/5\\\\(\frac{2}{3} - \frac{4}{9}) * 3 * 2/5\\\\\frac{2}{9} * 3 * 2/5[/tex]
[tex]\frac{2}{9} * \frac{3*2}{5}[/tex]
[tex]\frac{2}{3} * \frac{2}{5} = \frac{4}{15}[/tex] (Or 0.26)
Hope this helps! :)
Find the complementary angle for 93
Answer:
Complementary means they add up to 90, so you want 2 angles that add up to 90...so what do you mean for 93? Are you talking supplementary,(add to 180), because that would be 87.
Answer: no complement
Explanation: To find the complement of a 93 degree angle, we take 90 minus the measure of the angle which in this case is 90° - 93°.
Notice that this gives us a negative angle measure
and since we can't have a negative angle,
we say that the given angle has no complement.
Watch out for negative answers to geometry problems.
Since we're usually talking about angle measures
or segment lengths, negatives will not work.
Make a copy of this document for yourself. Solve each problem. Remember to combine like terms and use inverse operations when necessary. Get the variable by itself.
Answer:
the answer is 5.
given, 2c-7c+8=-17
or, -5c=-17-5
or, c=-25/-5
therefore the value of c is 5...
Step-by-step explanation:
[tex]2c -7c +8 =-17\\Collect- like- terms\\2c-7c=-17-8\\Simplify\\-5c = -25\\Divide-both-sides-of-the-equation-by -5\\\frac{-5c}{-5} = \frac{-25}{-5} \\\\c = 5[/tex]
The price of a watch was increased by 7% to £1350. What was the price before the increase? Give your answer to the nearest penny.
Answer:
1261.68
Step-by-step explanation:
1350 = the increased watch price= 107% of the original
1350= 1.07x
1261.68224299
Check:
7% of 1261.68224299 is 88.317757
1261.68224299 + 88.317757 = 1349.9 = 1350
Round:
1261.68224299
To the penny= to the hundreth= 1261.68
x = [? ]°
117
124°
107
102
145
Answer:
x = 125°
Step-by-step explanation:
The sum of angles in an n-sided polygon is (180°)(n -2). For a hexagon, the sum of angles is ...
(180°)(6 -2) = 720°
We can use this to find x.
x +117° +124° +102° +145° +107° = 720°
x = 720° -595°
x = 125°
Find the area of a regular octagon with
a side length of 12 cm. Round to the
nearest tenth.
12 cm
[ ? ] cm2
Answer:
A= 695.3cm²
Step-by-step explanation:
We khow that the area of anctagon is : A= 2(1+[tex]\sqrt{2}[/tex])*a² with a the side so A= 2(1+√2)*a² = 695.29= 695.3 cm²how to do this question plz?
Answer:
y+y-8=<41,I think that's the answer
Each ferry in the Sydney Harbour has a capacity of 230 people. If there are 9 ferries in operation today, how many people could travel using this service today?
Answer:
2070
Step-by-step explanation:
Multiply 230 people by 9 ferries, if each ferry is used once.
FUNCTIONS HELP ME ASAP
Hey there! :)
Answer:
f(-2) = 2.
Step-by-step explanation:
To find f(-2), we simply need to look at the y value at x = -2.
At x = -2, the y value is equal to 2.
Therefore:
f(-2) = 2.
Answer: b)2
Step-by-step explanation:
Visually, when x = -2, y = 2
What is -1 2/5 times 1 1/7
Answer: -8/5
Step-by-step explanation:
I know this because -1 2/5 is -7/5 and 1 1/7 is 8/7. Multiply the numerator and denominator together and you get the answer
Hi! :)
Answer:
-1.6 or -1 3/5
Step-by-step explanation:
This is how I got -1 3/5
First we have to convert the mixed number into fractions.
Than you have to use the formula
(Top) -7 x 8
(Bottom) 5x7
And you will get -56/35
Now you have to convert-56/25 into mixed number
Which will be -1 3/5
So the answer is -1 3/5 or -1.6
Hope this helps!
By, BrainlyMember ^-^
I hope I am correct, brainliest would be great!
✨Good luck!✨
a vertical flag pole TAD is supported by two wires AB and AC, given that angle ABD=67°,AB =2 m and AC =2.5m . find the length of AD
Answer:
a) 1.84m
b) 42.53°
Step-by-step explanation:
First, look though the diagram provided by the question.
And use the formula: [tex]\frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}[/tex]
Based on Additional Mathematics Form 4 (Dual Language Programme) KSSM from Malaysia
To find the length of AD
[tex]\frac{AD}{sin 67}=\frac{2}{sin 90}[/tex]
[tex]AD=\frac{2}{sin 90} * sin 67[/tex]
AD= 1.84 m
Find the angle C
[tex]\frac{sin 90}{2.5}=\frac{sin C}{1.84}[/tex]
sin C=[tex]\frac{sin 90}{2.5} * 1.84[/tex]
= 0.736
[tex]sin^{-1} (0.736)=47.39[/tex] degree
So, we have the value of AD and the value of angle C. Now , we can solve the the angle of CAD.
Same as the first question use the formula of sine rule and you will get the answer.
[tex]\frac{sin 90}{2.5}=\frac{sin ACD}{1.69}[/tex]
[tex]sinA = \frac{sin90}{2.5} * 1.69[/tex]
=0.676
=42.53°
So, the answer of the angle of CAD is 42.53°
Check the answer:
90°+47.39°+42.53°
=179.92°
=180°(rounded off)(Proved)
That is all from me. I hope you will understand my solution.
Determine whether the lines passing through the pairs of points are parallel, perpendicular or neither. Line a: (−4,4) and (8,−10) Line b: (4,8) and (18,20)
Answer:
Perpendicular.
Step-by-step explanation:
Find the slopes of each line through [tex]m = \frac{(y_2-y_1)}{(x_2-x_1 )}[/tex]
Line a:
m = (-10-4) / (8--4)
= -14/12
= -7/6
Line b:
m = (20-8) / (18 -4)
= 12/14
= 6/7
When lines are parallel, they have the same slope. Since -7/2≠6/7, they are not parallel.
When lines are perpendicular, the product of the slopes equals -1.
-7/6 x 6/7 = -1
The product is -1, hence they are perpendicular lines.
The lines passing through the pairs of points are perpendicular.
What is an equation of a line?The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.
The slope for Line a:
m = (-10-4) / (8--4)
m= -14/12
m= -7/6
The slope for Line b:
m = (20-8) / (18 -4)
m= 12/14
m= 6/7
When lines are parallel, they have the same slope. Since -7/2≠6/7, they are not parallel.
When lines are perpendicular, the product of the slopes equals -1.
-7/6 x 6/7 = -1
The product is -1, hence they are perpendicular lines.
To know more about equations follow
https://brainly.com/question/2972832
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What is "5t + 76" if t = 6?
Answer:
106
Step-by-step explanation:
given: 5t + 76
If t = 6, we substitute t=6 into the equation and solve:
5t + 76
= 5(6) + 76
= 30 + 76
= 106
Hi there! Hopefully this helps!
---------------------------------------------------------------------------------------------------
Answer: 106.
First, we need to evaluate.
(Note: when a letter and a number are close to together [5t] it means to multiply)
So if "t" = 6 we rewrite the problem like this:
5(6) + 76.
5 x 6 = 30.
Now we rewrite the problem again.
30 + 76 = 106.
Frank is going to plant c vegetable seeds in one garden and 2c +8 vegetable seeds in another.
How many seeds is Frank going to plant?
Answer:
3c+8
Step-by-step explanation:
Add the numbers of seeds together
c + 2c+8
Combine like terms
3c+8
Help!!!!! please!!!!!
Answer:
A
Step-by-step explanation:
Diameter = 32 in
r = 32/2 = 16 in
Surface area of sphere = 4πr²
= 4 * 3.142 * 16 * 16
= 3217.408
= 3217 in²
Answer:
[tex]3217 \: {in}^{2} [/tex]Solution,
Diameter (d)= 32 in
Radius (r)= 32/2= 16 in
Surface area of sphere:
[tex]4\pi {r}^{2} \\ = 4 \times \pi \times {(16)}^{2} \\ = 4 \times \pi \times 256 \\ = 1024\pi \\ = 1024 \times 3.142 \\ = 3217.108 \: {in}^{2} [/tex]
Hope this helps...
Good luck on your assignment...
What’s 10 to the power of 10 A.100,000 B.10,000,000 or C.1,000,000,000
Answer:
10,000,000,000
hopefully this helped :3
Answer:
C.10,000,000,000
Step-by-step explanation:
Find the lateral surface area in square kilometers, of the 3-dimensional figure shown below
Answer:
108
Step-by-step explanation:
Add the sides of the triangle
5+3+4 = 12 then look for the height
which is 9
12*9 is 108
What is the slope for the equation
-1/2 x - y = 3/4
a. 1/2
b. 3/4
c. -1/2
d. -3/4