A matrix B that has V as its nullspace. (c) Multiply A and B is [tex]I (4 by 4 ).[/tex]
[tex]\mathbb{R}^4[/tex]
What is a Nullspace vector?
The null space of A is all the vectors x for which Ax = 0, and it is denoted by null(A). This means that to check to see if a vector x is in the null space we need only to compute Ax and see if it is the zero vector.
- All vectors whose components are equal.
- All vectors whose components add to zero.
- All vectors that are perpendicular to [tex](1,1,0,0)$ and $(1,0,1,1)$.[/tex]
- The column space and the nullspace of (4 by 4 ).
Solution. These bases are not unique.
[tex]- $(1,1,1,1)$.- $(1,-1,0,0),(1,0,-1,0)$, and $(1,0,0,-1)$.- $(1,-1,-1,0)$ and $(1,-1,0,-1)$.[/tex]
- The columns of are a basis of its column space: [tex]$(1,0,0,0),(0,1,0,0)$, $(0,0,1,0)$, and $(0,0,0,1)$.[/tex]The nullspace contains the zero vector only. By convention, the empty set is the basis of such a space.
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The intensity of an earthquake wave passing through the Earth is measured to be 2.8×106 J/m² .s at a distance of 53 km from the source.
(B) At what rate did energy pass through an area of 1.0 m^2 at 2.0 km?
The rate at which the energy pass through an area of 1.0 m² at 2.0 km is equal to 1.97 × 10⁹ J/s.
How to calculate the intensity of the earthquake from the source?At a constant power, the intensity of a wave is inversely proportional to the distance from the source. Mathematically, the intensity of a wave with respect to the distance from a source can be modeled (represented) by this mathematical expression;
I ∝ 1/r²
Where:
I represents the intensity of a wave.r represents the distance from a source.Next, we would re-write the mathematical expression and then determine the intensity of a wave from source as follows;
I₁/I₂ = r₂²/r₁²
I₁ = I₂(r₂²/r₁²)
Note: We know that its intensity when it passed a point from the source is 2.0 km.
Substituting the given parameters into the formula, we have;
I₁ = 2.8 × 10⁶ × (53²/2²)
I₁ = 1.97 × 10⁹ J/m²s.
Now, we can calculate the rate of the energy by using this formula;
Power = intensity × area
Power = 1.97 × 10⁹ × 1.0
Power = 1.97 × 10⁹ J/s.
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expert that helps you learn core concepts.
See Answer
One item on a questionnaire asks students how many times in a typical week they eat at a fast-food restaurant. The responses for a sample of n = 10 students are summarized in the frequency distribution. What is the mean for this sample?
X f
5 or more 2
4 3
3 2
2 1
1 1
0 1
M = 4
M = 3.5
M = 31/10 = 3.1
The mean cannot be determined for these data.
The arithmetic mean for this value is M=3.1.we can calculate this data from frequency distribution.
what is arithmetic mean?It is sum of collection of number divided by the count of numbers.Its value can be positive or negative both.The collection is often a set of results from an experiments and observational study.
what is the use of arithmetic mean?It is often used as a parameter in statistical distribution or as a result to summarize the observations of an experiment survey.It is simplest way to used to measure the average.Its also measure frequency distribution by considering all of the observations.
Now we are using formula for arithmetic mean
A.M= Sum of (fx)/sum of (f)
by putting values in this formula we have
A.M= 31/10
A.M= 3.1
Hence 3.1 is the arithmetic mean for given frequency data.
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FILL IN THE BLANK. you transfer $100 from your savings account to your checking account. as a result, m1 will and m2 will .
You transfer $100 from your savings account to your checking account as a result, m1 will Remains unchanged and m2 will increase by $100.
Checking and savings accounts are also a part of M2. Thus, moving $100 from a savings account to a checking account won't have an impact on M2. Savings accounts are not included in M1, whereas checking accounts are. Therefore, a $100 transfer from savings to checking accounts will result in a $100 rise in M1.The ability to write checks from and access your bank account in a variety of other ways makes a checking account your default daily transaction bank account. You store money in a savings account that you aren't ready to use quite yet, frequently with the intention of building up more.Hence, You transfer $100 from your savings account to your checking account as a result, m1 will Remains unchanged and m2 will increase by $100.
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igure 30-44a shows a wire that forms a rectangle (w 20 cm, h 30 cm) and has a resistance of 5.0 m . its
The magnitude of the current induced in the wire is 1.2×10^{-8} and direction of the current induced in the wire is counter clockwise.
In the given question,
A rectangle (W = 20 cm, H = 30 cm) and has a resistance of(R) = 5.0 mΩ.
B(s) = 4.0 μT and B(b) = -2.5
t(s) = 2.0 s
From the question
dB(1)/dt = B(s)/t(s)
dB(1)/dt = 4 μT/2
As μ = 10^{-6}
dB(1)/dt = 2×10^{-6} T/s
dB(2)/dt = 1/2dB(1)/dt
dB(2)/dt = 2×10^{-6} /2
dB(2)/dt = 1×10^{-6} T/s
dB(3)/dt = B(b)dB(1)/dt
dB(3)/dt = -2.5×2×10^{-6} T/s
dB(3)/dt = -5×10^{-6} T/s
Now the change in magnetic field is,
dB/dt = dB(1)/dt + dB(2)/dt + dB(3)/dt
dB/dt = 2×10^{-6} + 1×10^{-6}/2 - 5×10^{-6}
dB/dt = - 2×10^{-6}
Now finding the area
Area = 1/2 wh
Firstly converting the w and h in m
So w = 0.20 m, h = 0.30 m
Area = 1/2 *0.20*0.30
Area = 0.03 square m
The induced EMF is
EMF = -AdB/dt
EMF = -(0.03)*(- 2×10^{-6})
EMF = 0.06×10^{-6}
The magnitude of the current induced in the wire is
I = EMF/R
I = 0.06×10^{-6}/5
I = 0.012×10^{-6}
I = 1.2×10^{-8}
Now, the direction of the current induced in the wire is counter clockwise.
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The right question is:
Figure (a) shows a wire that forms a rectangle (W = 20 cm, H = 30 cm) and has a resistance of 5.0 mΩ. Its interior is split into three equal areas, with magnetic fields B(1), B(2), and B(3). The fields are uniform within each region and directly out of or into the page as indicated. Figure (b) gives the change in the z components B(z) of the three fields with time t; the vertical axis scale is set by B(s) = 4.0 μT and B(b) = -2.5 B(s) and the horizontal axis scale is set by t(s) = 2.0 s. What are the magnitude and direction of the current induced in the wire?
Write an algebraic representation for the reflection
Answer:
A reflection of a point over the line y=−x is shown. The rule for a reflection in the origin is (x,y)→(−y,−x) .
Please help will mark Brainly
Answer:
Below
Step-by-step explanation:
The solution set is the point(s) where the two plotted graphs intersect:
whenever suzan sees a bag of marbles, she grabs a handful at random. she has seen a bag containing four red marbles, five green ones, three white ones, and two purple ones. she grabs eight of them. find the probability of the following event, expressing it as a fraction in lowest terms. she has at least one green one.
For this problem, it is best to consider E to be the case in which she has all of the green ones, and then apply the formula for calculating the probability of a complement.
. To determine the likelihood that she will receive all of the green ones, we must first determine two values: the total number of possible outcomes, n(S), and the total number of favorable outcomes for the given event. Because she selects 8 marbles from a total of 11, n(S) = C(11, 8) = 165. To get all the green ones, she must first select three red marbles from a set of three, and then select the remaining five marbles.
from the 8 non-red ones. There are (3,3)(8, 5) = 56 ways to do this. Thus,
() =56/165
. The probability of not occurring is then (′) = 1 −56/165=109/165
, so this is the probability that she does get all the green one.
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pls do this qwick
What is the product of (−23)(18)(−4)?
−1,656
−322
74
1,656
Answer:
1656
Step-by-step explanation:
Answer: 1656
Step-by-step explanation:
just trust me, that's the answer! I did the same question.
Four different paints are advertised as having the same drying time. To check the manufacturers' claims, five samples were tested for each of the paints. The time in minutes until the paint was dry enough for a second coat to be applied was recorded for each sample. The data obtained follow.Excel File: data 16-21.xls Paint 1 Paint 2 Paint 3 Paint 4 128 137 135 133 144 133 142 146 130 143 137 124 136 141 131a. Use a = .05 to test for any significant differences in mean drying time among the paints. If an amount is zero, enter "0.
The sum of squares of error, treatment, within and between four painters are: 330, 692, 110 and 43.25.
The data provided is for the dying time of four different types of paint.
One-way ANOVA can be used to determine whether all the four paints have the same drying time.
Use Excel to perform the one-way ANOVA.
Go to Data → Data Analysis → Anova: Single Factor
A dialog box will open. Select the data. Select "Grouping" as Columns.
Press OK.
The output is attached below.
The required values are as follows:
(1) Sum of Squares of Treatment (Between Subjects):
SST = 330
(2) Sum of Squares of Error (Within Subjects):
SSE = 692
(3) Mean Squares Treatment (Between Subjects):
MST = 110
(4) Mean Squares Error (Within Subjects):
MSE = 43.25
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A linear relationship is given in the table below. Determine the slope of the relationship.
-1 / -3/ 2/3/4/7/8/15/10/19
The slope of the linear relationship will be 2.
What is Equation of line?The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
A linear relationship is given in the table.
Now,
Let two point on the table are (- 1, - 3) and (2, 3).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (3 - (-3)) / (2 - (-1))
m = 6 / 3
m = 2
Thus, The slope of the linear relationship = 2.
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(100 points plus brainliest) A proportional relationship between the number of pounds of potatoes (x) and the price in dollars (y) is graphed, and the ordered pair (4, 3) is on the graphed line
what is the price of 1 pound of potatoes? SHOW YOUR WORK
Answer: $0.75
Step-by-step explanation:
-We know that the line must also contain the point (0,0), as 0 pounds of potatoes would cost $0. Thus we can find the slope of the line and write an equation:
slope = Δy/Δx = (3-0)/(4-0) = 3/4
y = (3/4)x
(The y-int (aka b) is 0 since the line passes through (0,0))
Plugging in 1 yields $0.75
Answer:
$0.75 per pound-------------------------------------------------------
Proportional relationship equation:
y = kx, where k-constant of proportionalityGiven point (4, 3).
Use its coordinates to find the value of k:
3 = 4kk = 3/4k = 0.75This is representing the price of 1 pound of potatoes.
Nina is driving to her friend’s house. For the first part of the drive, she drove at a constant speed of 55 miles per hour for 36 minutes. For the second part of the drive, she drove at a constant speed of 17.5 miles per hour for 14 miles. What is the total distance, in miles, and total amount of time, in minutes, that Nina drove to her friend’s house?
Answer:
miles: 55(36/60) = 55(0.6) = 33 miles
mins: 60(14/17.5) = 60(0.8) = 48 minutes
Total amount of time, in minutes
36 minutes + 48 minutes84 minutesThe total distance, in miles
33 miles + 14 miles47 milesStep-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-The required distance and time are 47 miles and 84 minutes, respectively.
What is speed?Speed is measured as the ratio between the distance and time, and the SI unit of speed is m/s.
We know that speed = distance / time
Finding for distance =
55(36/60) = 55(0.6) = 33 miles
Therefore, The total distance, in miles =
= 33 miles + 14 miles
= 47 miles
For Time =
60(14/17.5) = 60(0.8) = 48 minutes
Therefore, Total amount of time, in minutes =
36 minutes + 48 minutes
= 84 minutes
Hence, The required distance and time are 47 miles and 84 minutes, respectively.
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noise levels at 3 volcanoes were measured in decibels yielding the following data:142,113,135construct the 90% confidence interval for the mean noise level at such locations. assume the population is approximately normal.step 1 of 4 : calculate the sample mean for the given sample data. round your answer to one decimal place.
The t critical value and confidence interval must be determined.
What is confidence interval?A confidence interval (CI) is a range of estimates for an unknown parameter in frequentist statistics.
The 95% confidence level is the most popular, however other levels, such 90% or 99%, are occasionally used when computing confidence intervals.
The percentage of related CIs over the long run that include the parameter's actual value is represented by the confidence level.
For instance, 95% of all intervals calculated at the 95% confidence level should include the parameter's actual value.
The sample size, sample variability, and confidence level are all variables that have an impact on the width of the CI.
Assuming all other factors remain constant, a larger sample results in a narrower confidence interval, while a sample with more variability results in a wider confidence interval.
According to our question-
At a confidence level of 90%, we have α = 1 - 0.90 = 0.1
α/2 = 0.1/2 = 0.05.
Degree of freedom = 4-1 = 3
When we look this up in the t critical value table,
t critical = 2.353
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A group of friends is playing a board game. As part of the game, each player is given the same number of cards. There are 6 players and 58 cards. How many cards will each player get if each player gets the same number of cards?
Answer:Each player would get 9 cards each with a reaminder of 4 cards left
Step-by-step explanation:6 times 9 is 54 + 4 is 58
Answer: 9
Step-by-step explanation:
To figure out the given problem below:
P = 6
C = 58
You have to divide the problem.
So [tex]58[/tex] ÷ [tex]6 = 9[/tex].
4. The diagram shows a right triangle and the lengths of two of its sides in inches.
11.9
d
¡0m
7.9 in.
Which measurement is closest to the value of din inches?
Answer:
Step-by-step explanation:
Compare the key features of f(x)=2x-3 and the
linear function g shown below.
23. What do the slopes and the y intercepts
indicate about the linear functions f and g?
Answer:
f slopes was [tex]\frac{3}{2}[/tex] ,the y intercepts was -3
g slopes was [tex]-\frac{1}{3}[/tex],the y intercepts was -2
Step-by-step explanation:
g slopes :
functions g has point (0,-2) and (3,-3)
the slopes =[tex]\frac{-2-(-3) }{0-3} =-\frac{1}{3}[/tex]
Calculate the area, in square units, bounded by f(x) = 3x³ -3x²-x+8 and
g(x) = 2x³ - 10x² + 29x + 8 over the interval [1, 5].
Answer:
164
Step-by-step explanation:
Assuming that you are allowed to use graphing tools:
f(x) is below g(x) for interval [1,3]
g(x) is below f(x) for interval [3,5]
Rules of finding area between two graphs:
[tex]\int\limits^a_b {|upper - lower|} \, dx[/tex]
For interval [1,3]:
[tex]\int\limits^3_1 {g(x) - f(x)} \, dx[/tex]
[tex]\int\limits^3_1 {|(2x^{3} - 10x^{2} +29x+8)-(3x^{3}-3x^{2} -x+8) } \, dx[/tex]
[tex]\int\limits^3_1 {-x^{3} -7x^{2} +30x} \, dx[/tex]
[tex]= [-\frac{1}{4}x^{4} - \frac{7}{3}x^{3} + 15x^{2}]^3_1[/tex]
[tex]= [-\frac{1}{4}3^{4} - \frac{7}{3}3^{3} + 15*3^{2}] - [-\frac{1}{4}1^{4} - \frac{7}{3}1^{3} + 15*1^{2}][/tex]
[tex]= -\frac{81}{4} - \frac{189}{3} + 135+\frac{1}{4} + \frac{7}{3}- 15\\[/tex]
[tex]= \frac{118}{3}[/tex]
For interval [3,5]
[tex]\int\limits^5_3 {f(x)-g(x)} \, dx[/tex]
[tex]\int\limits^5_3 {|(3x^{3}-3x^{2} -x+8)-(2x^{3} - 10x^{2} +29x+8)|} \, dx[/tex]
[tex]\int\limits^5_3 {|x^{3}+7x^{2} -30x|} \, dx[/tex]
[tex]= [\frac{1}{4}x^{4} +\frac{7}{3}x^{3} - 15x^{2}]^5_3[/tex]
[tex]= [\frac{1}{4}5^{4} +\frac{7}{3}5^{3} - 15*5^{2}] -[\frac{1}{4}3^{4} +\frac{7}{3}3^{3} - 15*3^{2}][/tex]
[tex]= \frac{625}{4} +\frac{875}{3} - 375 -\frac{81}{4}} -\frac{189}{3} + 135[/tex]
[tex]=\frac{374}{3}[/tex]
Total area
[tex]= \frac{118}{3} + \frac{374}{3}\\[/tex]
[tex]= 164[/tex]
Alex tracked the number of cups of coffee he drank each day for the following month and
created a new probability distribution.
Number of Cups of Coffee, X 0
1 2 3 4
Relative Frequency, P(X) 0.035 0.579 0.286 0.080 0.020
According this new data, Alex is expected to drink 1.471 cups per day.
4. Calculate s(X) of Alex's new probability distribution. (1 point)
0.599
0.775
1.471
4.223
The standard deviation of Alex's new probability distribution is given as follows:
0.775.
How to obtain the standard deviation of a discrete distribution?The standard deviation of a discrete distribution is calculated as the square root of the sum of the differences squared between each observation and the mean, multiplied by their respective probabilities.
Hence the standard deviation of Alex's new probability distribution is calculated as follows:
S(X) = square root(0.035 x (0 - 1.471)² + 0.579 x (1 - 1.471)² + 0.286 x (2 - 1.471)² + 0.08 x (3 - 1.471)² + 0.02 x (4 - 1.471)²)
S(X) = 0.775.
Meaning that the second option is correct.
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find each angle measure to nearest degree Cos C= 0.9613
The angle C can be obtained rom the computation below as 16 degrees.
What is the angle?We know that the cosine is one of the angular measures that we have. The trigonometric ratios that we have are the sine the cosine and the tangent. We can be able to obtain the angle of the when we take the inverse of the cosine of the angle.
Now we know that the cosine of the angle can be defined as the ratio of the adjacent and the hypotenuse. The value of the cosine of the angle can be gotten from the table of the standard measure of the angles or by the use of a calculator.
We then have that;
Cos C= 0.9613
C = Cos-1( 0.9613)
By the time we make use of a good calculator we obtain the angle as;
C = 16 degrees
This is the value of the angle.
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Math geometry,
GIVEN
The SSS congruence theorem is used to prove that triangles MAH and THA are congruent to each other. See proof below.
How to Apply the SSS Congruence Theorem?"SSS" stands for side-side-side congruence theorem, which says that given the criteria that two triangles both have three corresponding sides that are equal or congruent to each other, both triangles are congruent.
The proof below shows how we can apply the SSS to prove that triangles MAH and THA are congruent to each other.
Statement Reason
1. MA ≅ TH 1. Given
2. MH ≅ AT 2. Given
3. AH ≅ HA 3. Reflexive property of congruence
4. ΔMAH ≅ ΔTHA 4. SSS congruence theorem
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32. A company's profit varies directly as the number of products it sells. The company makes a
profit of $13,000 on 325 products. What is the company's profit when 999 products are sold?
This is a proportion.
Answer:
39960
Step-by-step explanation:
first you have to divide how much money they made by the products to find the base price of each product so 13,000 / 325 which has a quotient of $40 per product then you multiply 40 by 999, so 40 x 999 has a product of 39960
Alex boards a Ferris wheel at the 3-o'clock position and rides the Ferris wheel for multiple revolutions. The Ferris wheel rotates at a constant angular speed. Let h represent Ricky's height above the center of the Ferris wheel (in feet) and let t represent the number of mintues since the ride started д. Suppose the radius ofthe Ferris wheel is 20 feet and the Ferris wheel rotates at 1 radian per minute. Plot the relationship between h and t for this scenario 20+ -30 es helis 0 the radius diaser mise Ferris wheel r Plot the relationship between h and t for this scenario. 20+ 10- 2322 -104 -20 -30 Clear All Draw c Now suppose the radius of the Ferris wheel is 30 feet and the Ferris wheel rotates at 2 radians per nute Plot the relationshup between h and t for thes scenario
The relationship between 'h' and 't' when r=20 and rate = 1 rad/min is [tex]h=20sin(t)[/tex] and when r=30 and rate = 2 rad/min is [tex]h=30sin(2t)[/tex]
Given,
The Ferris wheel is rotating at constant angular speed.
"h" represents Alex's height above the center of the Ferris wheel (in feet)
"t" represents the number of minutes since the ride started.
a)
Here, the conditions are
the radius if ferris wheel is, r = 20 feet
and the ferris wheel is rotating at the ratei.e. angular speed, [tex]\omega = 1 rad/min[/tex]
Here, 'h' represents the height of Alex's measured in the y-direction.
As per the given conditions the relationship between 'h' and 't' can be determined by the equation,
[tex]y= rsin\theta[/tex]
Where, [tex]\theta =\omega t[/tex]
here y=h,
then,[tex]h=rsin(\omega t)\\\\h=20sin(t)...i[/tex]
b)
Now, the given conditions are
radius of ferris wheel is ,r = 30 feet
ferris wheel is rotating at ratei.e angular speed , [tex]\omega = 2 rad/min[/tex]
Now, the relationship between h and t becomes ,
[tex]h=30sin(2t)....ii[/tex]
Thus, the graph plots for eq. i and eq.ii are shown in the figure.
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URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Question 7
The first blank as required to be filled in the task content should be filled with; two.
The second blank as required to be filled in the task content should be filled with; 134.1 in³.
What is the volume of the cone?According to the information given; the diameter of the beachball is; 8 inches. Therefore, it's radius is half that; 4 inches.
On this note, the volume of the beachball which is spherical in shape given by the formula;
Volume of a sphere = (4/3)πr³ where;
Radius, r = 4;
Therefore, volume of beachball is;
4/3 π (4)³ = 256π / 3.
Also, the volume of the cone which is given by the formula;
Volume of a cone = (1/3) π r² h
where; Radius, r = 4 and Height, h = 8.
Therefore, volume of the cone is;
(1/3) π (4²) × 8 = 128π / 3.
On this note, by dividing the volume of beachball by that of cone; we have that;
( 256π / 3 ) / ( 128π / 3 ) = 2.
On this note, the cone will fit into the beachball about 2 times.
Also, the volume of the cone given that; π = 22 / 7 can be evaluated as;
( 128 × 22 ) / ( 7 × 3 )
= 134.1 in³.
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You want to be able to withdraw $30,000 each year for 25 years. Your account earns 8% interest.
a. How much do you need in your account at the beginning
Answer: you need to have at least $312,500 in your account at the beginning.
Step-by-step explanation:
The total amount of money you will need to withdraw over the 25-year period is $30,000 * 25 years = $750,000. To find the total amount of interest you will earn, we need to use a compound interest formula. The formula for compound interest is:
A = P(1 + r/n)^nt
where A is the total amount of money you will have in your account after 25 years, P is the initial amount of money in your account, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In our case, we have A = $750,000, P = ?, r = 8%, n = 1 (since the interest is compounded annually), and t = 25. Plugging these values into the formula, we get:
$750,000 = P * (1 + 0.08/1)^1 * 25
We can simplify this equation to:
$750,000 = P * 1.08^25
To find the value of P, we can divide both sides of the equation by 1.08^25:
$750,000 / 1.08^25 = P
We can use a calculator to compute the value of 1.08^25, which is approximately 2.4. This means that the initial amount of money you need in your account is $750,000 / 2.4 = $312,500.
Therefore, to be able to withdraw $30,000 each year for 25 years and earn 8% interest on your account, you need to have at least $312,500 in your account at the beginning.
Use the maximum magnitude of the remainder term to find the maximum error in the following approximation on the given interval.In (1-x)=-x x^2/2:I-02.021Find the maximum error. Select the correct choice below and fill in the answer box to complete your choice (Use scientific notation. Use the multiplication symbol in the math palette as needed. Do not round until the final answer. Then round to two decimal places as needed.)O Error < for M = 0 O Error < for M = 1O Error < for M = 2O Error < 5.33x10^-3 for M=4
2.833 10 6 is the largest error as a result.
What is differentiation?Finding a function's derivative, or rate of change, is the process of differentiation in mathematics.
The practical approach of differentiation can be performed utilizing only algebraic operations, three fundamental derivatives, four principles of operation, and an understanding of how to manipulate functions, in contrast to the theory's abstract character.
The three fundamental derivatives (D) are: (1) D(xn) = nxn 1 for algebraic functions, where n is any real number; (2) D(sin x) = cos x and D(cos x) = sin x for trigonometric functions; and (3) D(ex) = ex for exponential functions.
Hence, 2.833 10 6 is the largest error as a result.
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The equation the quantity x plus 28 end quantity over 5 equals 3 times x models the workload of a class project, where x is the number of hours each student must contribute. How many hours does each student work on the project?
2 hours
5 hours
7 hours
12 hours
The number of hours that each student work on the project is 2 hours.
How many hours will be illustrated?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this situation, the equation the quantity x plus 28 end quantity over 5 equals 3 times x models the workload of a class project, where x is the number of hours each student must contribute.
This will be:
(x + 28) /5 = 3x
Cross multiply
x + 28 = 15x
Collect like terms
15x - x = 28
14x = 28
Divide
x = 28 / 14
x = 2
The number of hours is 2 hours.
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Answer: that answer is right ^
Step-by-step explanation:
If the point (K,-5) lies on the line whose equation is 3x + y = 7, then the value of K is
Answer:
K = 4
Step-by-step explanation:
The x-y point ( K, -5 ) means that ...
x = K and y = -5
Let's plug in K and -5 for y in the equation to find the value of K (which is the same as x).
3(K) + (-5) = 7
3K - 5 = 7
3K = 7 + 5
3K = 12
K = 4
Consider a propeller driven aircraft in forward flight at a speed of 150 mph. The propeller is set up with an advance ratio such that the propeller disc average flow speed is 170 mph. The propeller diameter is 6 ft. The aircraft flies at sea level. a. Calculate the thrust of the propeller. b. Calculate the induced velocity c. Calculate the velocity in the downstream far field away from the propeller disc. d. Calculate the power absorbed by the fluid (energy added per unit mass x mass flow rate) e. Calculate the propeller power (thrust * flight speed) f. If propeller efficiency is defined by the ratio of e to d, calculate the propeller efficiency.
a) The thrust of the propeller is 23,834 lbf and b) The induced velocity is 8.44 mph c) The velocity in the downstream far field away from the propeller disc is 161.56 mph
a)The thrust of the propeller can be calculated using the equation,
Thrust = 2πρR^2V^2, where ρ is the air density, R is the propeller radius, and V is the average velocity of the propeller disc. For sea level at a speed of 150 mph, the air density is about 0.002377 slugs/ft^3.
the thrust of the propeller can be calculated as: Thrust = 2π x 0.002377 x (6 ft)^2 x (170 mph)^2 = 23,834 lbf
b)The induced velocity can be calculated using the equation v_ind = (1/2) V ∞ [1–(V_∞/V_tip)^2]^(1/2), where V_∞ is the free stream velocity and V_tip is the tip velocity of the propeller. For the given problem, the induced velocity can be calculated as: v_ind = (1/2) x 150 mph x [1–(150 mph/170 mph)^2]^(1/2) = 8.44 mph
c) The velocity in the downstream far field can be calculated using the equation V_∞ = V_tip – v_ind, where V_tip is the tip velocity of the propeller and v_ind is the induced velocity. For the given problem, the velocity in the downstream far field can be calculated as: V_∞ = 170 mph – 8.44 mph = 161.56 mph
d)The power absorbed by the fluid can be calculated using the equation P_fluid = (1/2) ρ V_ind^3 A_disc, where ρ is the air density, V_ind is the induced velocity, and A_disc is the area of the propeller disc. For the given problem, the power absorbed by the fluid can be calculated as P_fluid = (1/2) x 0.002377 x (8.44 mph)^3 x (π x (6 ft)^2) = 42.7 hp
e)The power absorbed by the propeller can be calculated using the equation P_prop = T x V, where T is the thrust of the propeller and V is the flight speed of the aircraft. For the given problem, the power absorbed by the propeller can be calculated as: P_prop = 23,834 lbf x 150 mph = 3,575,500 ft-lbf/s = 4,844.08 hp
f)The efficiency of the propeller can be calculated using the equation η = P_prop/P_fluid, where P_prop is the power absorbed by the propeller and P_fluid is the power absorbed by the fluid. For the given problem, the efficiency of the propeller can be calculated as: η = 4,844.08 hp/42.7 hp = 113.6%
Hence, d) The power absorbed by the fluid is 42.7 hp e) the propeller power (thrust flight speed) is 4,844.08 hp f) The propeller efficiency is 113.6%
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gift box find the perimeter and the area of this net. be sure to include appropriate units. cut out this net along the solid curves and fold along the dotted curves to form a gift box.
You can then add up the lengths of the sides to find the perimeter, and add up the areas of the faces to find the total surface area of the gift box.
What is a perimeter?
The perimeter of a shape is the total length of the outer boundary of the shape. It is the sum of all the sides of the shape.
To find the perimeter and the area of a gift box, you can use the given dimensions of the net to calculate the lengths of the sides and the areas of the faces. You can then add up the lengths of the sides to find the perimeter, and add up the areas of the faces to find the total surface area of the gift box.
Hence, you can then add up the lengths of the sides to find the perimeter, and add up the areas of the faces to find the total surface area of the gift box.
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Solve
2 2/7 +(-4 5/7)
Answer:
2 2/7 - 4 5/7
= -2 3/7
Step-by-step explanation:
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