a. The bandwidth (in Hz) of the RF waveform needed to perform the slice selection is 1 kHz.
b. A mathematical expression for the RF waveform B1(t) (in the rotating frame) that is needed to perform the slice selection is:
B1(t) = B1max * sin(2π * γ * Gz * z * t)
where:
B1max is the amplitude of the RF pulse, in tesla (T)
γ is the gyromagnetic ratio, which is a fundamental constant for each type of nucleus (for protons in water at 1.5T, γ = 42.58 MHz/T)
Gz is the strength of the z-gradient, in tesla per meter (T/m)
z is the position along the z-axis, in meters (m)
t is the time, in seconds (s)
a. The bandwidth of the RF waveform is determined by the thickness of the slice that we want to image. In this case, the slice has a thickness of 1 cm, which corresponds to a range of z values of 5 cm ± 0.5 cm. The frequency range required to cover this range of z values is given by the Larmor equation:
Δf = γ * Gz * Δz
where Δf is the frequency range, in Hz, and Δz is the range of z values, in meters. Substituting the values, we get:
Δf = 42.58 MHz/T * 1 T/m * 0.01 m = 1.058 kHz
However, this frequency range covers both the excitation and dephasing of the slice, so the bandwidth of the RF waveform needed to perform the slice selection is half of this value, which is 1 kHz.
b. The RF waveform B1(t) is given by the expression:
B1(t) = B1max * cos(2π * (fo + γ * Gz * z) * t + φ)
where:
fo is the resonant frequency of the spins in the absence of any magnetic field gradient, which is equal to the Larmor frequency, given by fo = γ * Bo
Bo is the strength of the main magnetic field, in tesla (T)
φ is the phase of the RF pulse, which is usually set to 0 for simplicity
To select the slice at z = 5 cm, we need to apply an RF pulse that has a resonant frequency equal to the Larmor frequency at that position, which is given by:
fo' = γ * Gz * z + fo
Substituting the values, we get:
fo' = 42.58 MHz/T * 1 T/m * 0.05 m + 42.58 MHz/T * 1.5 T = 44.947 MHz
The amplitude of the RF pulse, B1max, is usually set to a value that ensures that the flip angle of the spins is close to 90 degrees. In this case, we will assume that B1max is equal to 1 microtesla (μT). Therefore, the final expression for the RF waveform B1(t) is:
B1(t) = 1 μT * cos(2π * 44.947 MHz * t)
To express the RF waveform in the rotating frame, we need to rotate the coordinate system around the y-axis by an angle equal to the Larmor frequency, given by:
B1rot(t) = B1(t) * exp(-i * 2π * fo * t)
Substituting the values, we get:
B1rot(t) = 1 μ
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You work for a city department which is hosting a 5 kilometer run. Your coworker measured the course and doing that it is only 4.75 kilometers long. He ask you to move the finish line forward 0.25 kilometers. Your tape measure is measured in feet and inches. What is the distance he asked you to move in line in the nearest foot?
Answer:
820 feet
Step-by-step explanation:
We can use the rule of three in this scenario since this is a ratio problem with one unknown. To do this we simply multiply the diagonal values and divide by the final value. We know that there are a total of 3280.84 ft in a single kilometer, therefore...
1 km == 3280.84 ft
0.25 == x
(0.25 * 3280.84) / 1 = 820.21
Now we can see that there are 820.21 ft in the 0.25 kilometers. If we round this to the nearest foot we would round down to a total of 820 feet.
Find the value of 0.7x0.08
Answer:
0.056
Step-by-step explanation:
For decimals, you just multiply, and the hundredths would stay, so the answer is 0.056, because 8 x 7 = 56!
Answer:
0.056
Step-by-step explanation:
7*8 is 56 right
looking at 0.7 how many numbers are before that dot
1 right which is seven
then 0.08 has how many digits before the dot thing
2 right which is 0 and 8
in total making three
then in 56 move three times forward from behind
1 5.6
2 0.56
3 0.056
and thats how we got this
dont confuse this technique with numbers like 0.80
the zero at the end of that number is not needed
that is to say that
0.80 = 0.8
when theres a zero at the back of a decimal its not counted
e.g
0.50= 0.5
0.4000000= 0.4
hope this helped
i’m so confused by this does anyone have this figured out
Answer:
you have to find the angels
Step-by-step explanation:
NEEd HELp ASAP AlGEBRA 1
Answer:
Step-by-step explanation:
Joe has 1/2 of a cake he would like to split among 3 people. What part of the cake would each person get?
Answer:
1/6
Step-by-step explanation:
Given data
Joe has 1/2 of a cake
he would like to split among 3 people
n= 3
Hence each person will take
=1/2/3
=1/2*1/3
= 1/6 part of the cake
there are 16 appetizers available at a restaurant. From these, janet is to chose 13 for her party. How many groups of 13 appetizers are possible
Answer:
560
Step-by-step explanation:
The best way to do this is to write it out, but with large ones like this you should use the equation:
C(n,r) = n!/(r!(n-r)!),
where:
C(n,r) is the number of combinations;
n is the total number of elements in the set; and
r is the number of elements you choose from this set.
You purchase five municipal bonds on the first of the year. The current market value price is [tex]101\frac{1}{4}[/tex]. The commission charge is $8 per bond. What is the cost of purchasing these bonds?
a.$5546.25
b.$5102.50
c.$5062.50
d.$546.25
Answer:
B $5102.50
Step-by-step explanation:
answer on edge :)
Answer:
its b.
Step-by-step explanation:
write the equation of a line in point-slope form for a line that passes through the point (-2,1) and has a slope of -3
Answer:
y-1=-3(x+2)
Step-by-step explanation:
A rectangular paddock has perimeter 100 m. Find the width of the paddock if its length is 30 m.
Answer:
Step-by-step explanation:
W= L x 2/P
= 30 x 2/ 100
= 60 /100 = 0.6
4 = y - 4
3 = 9 - y
1 = 8 - y
2 = 9 - y
4 = y - 3
Answer: a a a a. Aa
E s. Ss s
Step-by-step explanation:
s. S s s s. S s s s s
The ratio of one side of ACDE to the corresponding side of a similar AFGH IS 2:5. The perimeter of A CDEIS 9.2 inches.
Find the perimeter of AFGH.
Answer:
25:16 is the ans hope that helps!
9514 1404 393
Answer:
23 inches
Step-by-step explanation:
The perimeters have the same ratio. Multiplying the ratio figures by 4.6 gives ...
2 : 5 = (4.6)2 : (4.6)5 = 9.2 : 23
The perimeter of ΔFGH is 23 inches.
Miles and Lucy decide to sell lemonade to earn some money. They buy pitchers, ice, and mix for a cost of $13.50. The mix makes 8 quarts of lemonade. They decide to sell one cup of lemonade for $0.75. If they sell all 8 quarts, how much revenue will they make and will they make enough to earn $12 each? (4c=1q)
Answer:
Altogether they made $24 which is enough to earn $12 each
Step-by-step explanation:
Important information:
1 cup: $0.75
4 cups = 1 quart
8 quarts of lemonade altogether
If we are looking to solve for the revenue earned based on quarts, we must first solve for how much money they make on 1 quart
Since 1 cup sells for $0.75 and 4 cups makes up a quart, we must multiply
0.75 × 4 = 3
They make $3 per 1 quart
We are looking for the amount for 8 quarts though, not just 1. Again we must multiply
3 × 8 = 24
They will make $24 if they sell all 8 quarts
The questions ask if they will each earn $12
Since there are two of them, Miles and Lucy, we must divide revenue earned by 2, the number of people
24 ÷ 2 = 12
$12
On a coordinate plane, if you take a point from (2, -5) and move it up 3 units to point "A" what is the distance of point a to coordinates (5, 0)?
A. 3
B. Square root of 11
C. Square root of 13
D. 5
Answer:
C
Step-by-step explanation:
(2,-5) move up three steps is (2, -2). if you draw it on a paper(and draw lines to connect them), you can see that they form a right triangle. apply a²+b²=c² and you should get 3²+2²=(√13)²
First we need to find the point after the translation of 3 units up.
(2,-5)->(2,-2)
Now we have the point (2,-2) we just need to use the difference formula to find the distance between this point and (5,0)
Distance=[tex]\sqrt{(5-2)^2+(0-(-2))^2}[/tex]
Now we need to simplify/solve this expression
=[tex]\sqrt{3^2+2^2}[/tex]
=[tex]\sqrt13[/tex]
Therefore the answer is C!
What is the equation of the line that passes through the point (8,1) and has a slope
Answer:
Answer:
x=1y
Step-by-step explanation:
How tall are 2 chairs stacked together? The height of the chairs
5 chairs are 51 inches high
3 chairs are 45 inches high
8 chairs are 60 inches high
Answer: 20.4 damm this easy
What is the length of a base of a right triangle with an area of 15 meters and a height of 3 meters?
Question 1 options:
5 meters
12 meters
10 meters
Answer:
10
Step-by-step explanation:
15 = 1/2 * b * 3
15 * 2 = 3 * b
b = 30/3
b = 10 m
Please help with this, it’s Khan Academy A.K.A annoying
B makes sense.
On the first play, they gained 6 yards.
On the 2nd play, they lost 8 yards, which can be shown as + (-8)
On the 3rd play, they lost two yards, which can be shown as + (-2)
If you input it in a calculator, you'd find that the answer is a negative, which makes sense considering that they lost more yards than they gained.
What is the first error Holden made in his proof?
Answer:
Step-by-step explanation:
He didn’t show his work.
Answer:
Holden wanted to build “Australia's Own Car” and in 1948 the first Holden car was produced.
Hope this helps, pls mark me as brainliest
10) -15xy + 25x ????????????????????
Factor (−15x)(y)+25x
−15xy+25x
=5x(−3y+5)
Answer:
5x(−3y+5)
PPPPPPPPPPPPPPPPPPPPPPPPPPPPplwlwlwlwlwlwlwlEEEEEEEEEEEEEEEEASE
just the 11b. due in 12 hrs. Need this very soon. :) thx
Answer:
28 litres of mango juice will be required
Step-by-step explanation:
11). b. Internal dimensions of the rectangular prism are,
Length = 40 cm
Width = 20 cm
Height = 35 cm
Volume of the rectangular prism = Length × Width × Height
= 40 × 20 × 35
= 28000 cm³
Since, 1 cm³ = 1 mL
Therefore, 28000 cm³ = 28000 mL
Since, 1000 mL = 1 L
28000 mL = 28 L
Therefore, to fill this jar 28 L of orange juice will be required.
Use the zero product property to find the solutions to the equation (x + 2) (x + 3) = 12
OX= -6 or x = 1
OX=-3 or x = -2
x= -1 or x = 6
Ox=2 or x=3
Answer:
x = -6 and x = 1
Step-by-step explanation:
Given the equation (x + 2) (x + 3) = 12
Equate to zero;
(x + 2) (x + 3) - 12 = 0
Expand
x^2+3x+2x+6-12 = 0
x^2+5x - 6 = 0
Factorize
x^2 + 6x - x - 6 = 0
x(x+6)-1(x+6) = 0
(x+6)(x-1) = 0
x+6 = 0 and x -1 = 0
x = -6 and x = 1
Hence the zeros are x = -6 and x = 1
Answer:
It's A: -6 or 1
Step-by-step explanation:
Edg 2022
are these questions correct ?
Answer:
not all of em
Step-by-step explanation:
some are
Combine like terms to write an equivalent expression. Then complete the statements.
2f + 5 + f – 3
The constants, _________, are like terms.
_________ are also like terms.
Combine the constant terms by __________
Combine the variable terms by adding the _________
The equivalent expression is ________
Answer:
The constants, 5 and -3, are like terms
2f and f are also like terms. Combine the constant terms by adding them together.
Combine the variable terms by adding the
Equivalent expression is 3f+2
Step-by-step explanation:
Like terms are terms that are the same so in this case the variables are like terms. And the constants or just the numbers are the same.
(3f and f)
(5 and -3)
Uma colônia de bactérias duplica de tamanho a cada dois dias. Começando com apenas um representante, quantos membros terá a colônia depois de um mês?
Answer:
Espero que isto ajude!
Step-by-step explanation:
q duplica logo a razão q =2
1 hora = 60 minutos
4 hs * 60 min = 240 minutos ou 240 : 6 = 40 vezes 6 minutos
Nota > 240 minutos tem 40 * 6 minutos
n = 40
a1 = 6 min = 3
a2 = 12 min = 3 * 2 = 6
q3 = 18 min = 6 *2 =12
an = a1 * q^n-1
a40 = 3 * 2^40-1
a40 = 3 * 2^39
a40 = 3 * 5497559 =16492677 >>>>>
this is a yes or no question... if a box has equal and opposite forces acting on it, will the box be accelerate??
Answer:
no
............................
At a carnival, the cost to play a bowling game is $2, plus $0.40 for each attempt to knock over the pins. Which inequality would you use to find the number of attempts you can make if you have less than $4.30
Answer:
a
Step-by-step explanation:
What is the slope and y intercept?
Answer:
slope: 1/2 Y Intercept: 25 (I'm just guessing by the coordinates (60,25)Step-by-step explanation:
Lets all remember rise over run to figure out slop and at coordinates (60, 25) we see that we go up 1 (rise) and go on the positive side 2 (run)
For the Y intercept (I'm really not sure about this answer) I figured it out by looking at the first point I saw (60, 25)
so I inferred that the y intercept is 25
A bakery sold a total of 500 cupcakes in a day, and 390 of them were vanilla flavored. What percentage of cupcakes sold that day were vanilla flavored?
Answer:
Your answer
78% are vanilla
Mark it as Brainlist. Follow me for more answer.
Step-by-step explanation:
The hospital is putting in a wheelchair ramp at one of its entrances. Only 6 feet of sidewalk can be covered by the ramp, and the ramp needs to reach 0.5 feet up the wall to reach the entrance. How long does the ramp need to be?
Answer:
3
Step-by-step explanation: