Answers
The probability that he will hit at least 6 times in his next 10 attempts is B. 80%.
How to calculate the probability.In this case, the golfer attempts to hit the ball 10 times and has a probability of 0.48 of hitting the ball each time. We want to find the probability of hitting at least 6 times.
We can use the binomial probability formula to calculate this probability:
P(X ≥ 6) = 1 - P(X < 6) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3) - P(X = 4) - P(X = 5)
where X is the random variable representing the number of hits in 10 attempts.
P(X = k) = (10 choose k) * (0.48)^k * (0.52)^(10-k)
Using a calculator or a binomial probability table, we can find each of the probabilities and then add them up to find the probability of hitting less than 6 times.
P(X = 0) = 0.52^10 ≈ 0.000105
P(X = 1) = 10 * 0.48 * 0.52^9 ≈ 0.001027
P(X = 2) = 45 * 0.48^2 * 0.52^8 ≈ 0.005888
P(X = 3) = 120 * 0.48^3 * 0.52^7 ≈ 0.020019
P(X = 4) = 210 * 0.48^4 * 0.52^6 ≈ 0.049026
P(X = 5) = 252 * 0.48^5 * 0.52^5 ≈ 0.088831
Adding these probabilities together, we get:
P(X < 6) ≈ 0.165897
Therefore, the probability of hitting at least 6 times is:
P(X ≥ 6) ≈ 1 - P(X < 6) ≈ 1 - 0.165897 ≈ 0.8341 ≈ 83.41%
So, the closest answer among the options provided is "80%".
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Related Questions
Watch help video Find the length of the third side. If necessary, write in simplest radical form. 7 4√2
Answers
In simplest radicle form, the length of the third side = 9 units.
Given,
Side A = 7 units.
Side B = 4√2 units.
To find Side C, we use the Pythagorean formula,
a² = b² + c²
7² = \(4\sqrt{2}^{2}\) + c²
c² = 49 + 32
c² = 81
√c² = √81
c = -9,9.
c ≠ -9 as negative values are not considered for dimensions.
Hence, the length of the third side is 9 units.
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Your question is incomplete. The complete question is:
With reference to the figure below, find the length of the third side. If necessary, write in the simplest radical form.
Your homework grades are 92, 87, 74, 96, 83, 88, 91, 82, and 85. What score on your next homework will make the median and the mode equal? List the scores in order from least to greatest. You can use the strategy Systematic Guess and Check to help you find the solution.
Answers
Answer:Next homework Score should be 87.
Step-by-step explanation:
STEP 1
Listing the scores in ascending order ie from least to greatest gives
74, 82, 83, 85, 87, 88, 91,92, 96
STEP 2
we find the median--- The median score is the score that is in the middle of the set of results when arranged from lowest to highest as we have done above , which give us 87 as the median.
74, 82, 83, 85, 87, 88, 91,92, 96
Also Mode is the score with the highest frequency , ie the score which appears more than other numbers. For now we have no mode as all the numbers occurred once
Therefore in next exam, I should get a score of 87, making my scores to become
74, 82, 83, 85, 87, 87, 88, 91,92, 96
Now my mode becomes 87 ( highest frequency of occurrence ) and
My median becomes (87+ 87)/2 = 87 ( with the addition of a new score the total score become ten, which is now even, so we divide the addtion of the two middle numbers by 2 )
The Statue of Liberty in New York stands on top of a foundation and a pedestal. The statue, including foundation and pedestal, measures about 305 feet from the ground to the top of the statue’s torch. The statue herself stands 151 feet. What is the height of the foundation and pedestal?
146 feet
154 feet
254 feet
256 feet
Answers
Answer:
B.) 154 feet
Step-by-step explanation:
i got it right on edge
\(hope that helps\)
Which form of payment can Courtney lose and NOT get back?
Answers
Answer: The form of payment that Courtney can lose and not get back would be cash.
Step-by-step explanation:
The reason why cash couldn't be returned back because it doesn't have a piece of U.S money wouldn't have a specific certified owner that they can be returned to.
Other forms of payment like credit cards, debit cards, and checks have specific bank information with the card holder's name on it so if Courtney actually lost one of those, she would be most likely to receive it back without any complicated verification process.
Therefore, Courtney would not be able to receive her cash back if she accidentally loses it. Hope this helps you with your Imagine Math homework or assignment!
-From Certified 5th Grade Honors Student
PLEASE ANSWER USE PEMDAS
What is the correct mathematical description of the expression (14.8 ÷ 2) + 6 x 3 − 12?
14 and 8 tenths divided by 2 plus 6 times 3 minus 12
14 and 8 tenths divided by 2 plus 6 times the difference of 3 minus 12
The quotient of 14 and 8 tenths divided by 2 plus six times 3 minus 12
The quotient of 14 and 8 tenths divided by 2 plus the product of 6 and 3 minus 12
Answers
Answer: D or the Fourth Choice-The quotient of 14 and 8 tenths divided by 2 plus the product of 6 and 3 minus 12
PEDMAS means Parentheses, Exponents, Divide, Multiply,Add,Subtract. The first thing we must solve is what is in the parentheses, that is 14.8 divided by 2. We don't have any exponents, so we move to divide. We have already solved the division sentence that was in the parentheses, so we have to multiply 6x3 next. 6x3 will then be added to the answer that was divided by 14.2 and 2, and lastly we will subtract 12. The only answer choice that follows that pattern is D or The quotient of 14 and 8 tenths divided by 2 plus the product of 6 and 3 minus 12.
I hope this helped & Good Luck <3!!!!
pennsylvania sales tax is charged at the rate of 6%. Find the tax and the total price you would pay for an $860 TV
Answers
The sales tax will be $51.6, bringing the total cost of $860 TV to $911.6.
What do we mean by sales tax?A sales tax is a tax levied on the sale of certain goods and services and paid to a governing body. Generally, laws allow the seller to collect tax funds from the consumer at the point of purchase.A use tax is a tax on goods or services that is paid directly to a governing body by a consumer. Food, education, and medicines, for example, are frequently exempt from sales and use tax under state law. A value-added tax (VAT) on goods and services is similar to a sales tax. Key differences can be found in the comparison with sales tax.So, to find the sales tax we need to find out the 6% of $860.
= 860/100 × 6= 8.60 × 6= 51.6So, the total price will be 860 + 51.6 = $911.6Therefore, the sales tax will be $51.6 and the total price we would pay for an $860 TV will be $911.6.
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can someone please help me with this:)
Answers
Answer: c
Step-by-step explanation:
please help me prove this
Answers
Answer:
Step-by-step explanation:
n,m.
Cassandra noticed heavy rain outside. She decided to investigate how much rain would fall in a 1/2 hour by placing an empty cup outside. After a 1/2 hour (30 minutes), she measured the height of the water in the cup. There was 9/8 inches of rain. If the rain continues to fall, what is the rate of the rain in 1 hour? [INCLUDE UNITS] *
URGENT PLEASE HELP!!
Answers
Answer:
18/8 or 9/4 or 2 1/4 inches of rain per hour
Step-by-step explanation:
Since the rain is falling at 9/8 inches per half hour, we can double that to get the inches of rain per hour.
9/8 x 2/1 = 18/8
Simplify
9/4 or 2 1/4
The vector
u
u has magnitude
2
2 and direction
5
5
∘
.
55
∘
. If vector
v
=
−
2
u
,
v=−2u, then what is the magnitude and direction of vector
v
?
v? Write your direction in degrees in the interval
0
∘
≤
θ
<
36
0
∘
.
0
∘
≤θ<
Answers
The magnitude and direction of vector v can be found by multiplying the magnitude of vector u by 2 and subtracting 180 degrees from the direction of vector u. Therefore, the magnitude of vector v is 44 (22*2), and the direction of vector v is 235 degrees (55-180).
To understand why we subtract 180 degrees from the direction of vector u, we must consider the fact that vector v is in the opposite direction of vector u, as indicated by the negative sign.
Thus, when we multiply the magnitude of vector u by -2, we are essentially reversing the direction of vector u.
To find the new direction of vector v, we subtract 180 degrees from the original direction of vector u, which effectively reflects the direction across the y-axis (i.e., flips the vector horizontally).
This results in a direction of 235 degrees, which falls within the interval 0 degrees to less than 360 degrees as specified in the question.
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How can you apply it triangle congruence to real life situation?
Answers
Congruent triangles are also frequently employed in architectural designs, carpet patterns, stepping stone patterns, and geometric art.
The following are the two most typical instances of this: Equilateral triangles are used to make truss bridges, which are built on both sides.
Congruence :
If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. A term used to describe an object and its mirror counterpart is congruence. If two things or shapes superimpose on one another, they are said to be congruent. They are identical in terms of size and shape. Line segments having the same length and angles with the same measure are congruent in the context of geometric figures.
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HELP !!! Evaluate f(-2) for the function f(x) = 3x2 + 2x - 5
Answers
Answer:
3
Step-by-step explanation:
So we have the function:
\(f(x)=3x^2+2x-5\)
To evaluate the value of f(-2), substitute -2 for x. Thus:
\(f(-2)=3(-2)^2+2(-2)-5\)
Square first:
\(f(-2)=3(4)+2(-2)-5\)
Multiply:
\(f(-2)=12-4-5\)
Now, subtract:
\(f(-2)=8-5=3\)
So:
\(f(-2)=3\)
And we're done!
Determine the intercepts of the line. Do not round your answers. 3x+2y=5
Answers
Answer:
\(\textsf{$x$-intercept}: \quad \left(\dfrac{5}{3},0 \right)\)
\(\textsf{$y$-intercept}: \quad \left(0,\dfrac{5}{2} \right)\)
Step-by-step explanation:
Given equation:
\(3x+2y=5\)
The x-intercept is when y = 0:
\(\implies 3x+2(0)=5\)
\(\implies 3x=5\)
\(\implies x=\dfrac{5}{3}\)
Therefore, the x-intercept is:
\(\left(\dfrac{5}{3},0 \right)\)
The y-intercept is when x = 0:
\(\implies 3(0)+2y=5\)
\(\implies 2y=5\)
\(\impiles y=\dfrac{5}{2}\)
Therefore, the y-intercept is:
\(\left(0,\dfrac{5}{2} \right)\)
Find the circumference of the circle shown
Answers
The circumference of the circle is 54. 64 mm. Option B
How to determine the circumference of the circleIt is important to note that the formula for calculating the circumference of a circle is expressed as;
C = 2πr
Given that the parameters are;
C is the circumference of the circle2 is the constant valueπ takes the constant value 3.14 or 22/7r is the radius of the circleFrom the information given, we have that;
Circumference = 2 × 3.14 × 8.7
Now, multiply the values, we get;
Circumference = 54. 636
Approximate to two decimal place, we get;
Circumference = 54. 64 mm
Hence, the value is 54. 64 mm
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For the school play, the advance tickets cost 3, while tickets at the door cost 5. Thirty more tickets were sold at door than in advance, and was collected. How many of each kind of ticket were sold? Write your answer in a sentence.
Answers
Answer:
Number of tickets sold in advance = 310
Number of tickets sold at the door = 340
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
For the school play, the advance tickets cost $3, while tickets at the door cost $5. Thirty more tickets were sold at the door than in advance, and $2630 was collected. How many of each kind of ticket were sold?
The explation of the answer is now given as follows:
Let a represents number of tickets sold in advance. Therefore, we have:
a = number of tickets sold in advance at $3 each
a + 30 = number of tickets sold at the door at $5 each
The total amount collected can be represented by this equation:
3a + 5(a + 30) = 2630
Solving for a, wee have:
3a + 5a + 150 = 2630
8a = 2630 - 150
8a = 2,480
a = 2,480 / 8
a = 310
Therefore, this implies:
Number of tickets sold in advance = 310
Number of tickets sold at the door = a + 30 = 310 + 30 = 340
1. Graph the equation y=-3/2x+1 2. Write the equation of the line in slope intercept form
Answers
Answer:
The equation is already in slope intercept form, -3/2 is the slope and 12 is the y intercept.
Is this a trick question?
Step-by-step explanation:
May I have brainliest please? :)
The variance of a sample or a population cannot be _____. a. zero b. calculated c. negative d. less than1
Answers
The variance of a sample or a population cannot be negative. This means that option c, negative, is the correct answer.
Variance is a statistical measure that quantifies the dispersion or spread of data points around the mean. It tells us how much the individual data points deviate from the average. The variance is always a non-negative value because it is calculated by summing the squared differences between each data point and the mean, divided by the total number of data points.
If the variance were negative, it would imply that the sum of the squared differences between each data point and the mean is less than zero. However, this is not possible because squared differences are always positive or zero.
On the other hand, options a, zero, and d, less than 1, are incorrect. The variance can be zero if all the data points in the sample or population are the same, indicating no dispersion. Additionally, the variance can be any positive value, including values less than 1.
To summarize, the variance of a sample or a population cannot be negative, making option c, negative, the correct answer.
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If you water water it grows
Answers
Answer:
........i dont understand but i think
Step-by-step explanation:
if your body is water and you grow that means that water grows too!!
Answer:
if you water water it grows
Step-by-step explanation:
Your teacher wants to use a point system to select the winning pet. She wants each pet to get a certain number of points for each 1st choice vote and a certain number of points for each 2nd choice vote.
Your teacher decides to use these rules for her point system:
Points need to be positive whole numbers
Points for a 1st choice vote have to be greater than or equal to the points for a 2nd choice vote.
Determine point values for the 1st and 2nd choice that would result in the turtle winning. Use words and numbers to explain how this point system results in the turtle winning
Answers
In the above case, the possible point system will be:
1st choice vote: 4 points
2nd choice vote: 2 points
What is the point system?In arranging for the turtle to win in this point framework, the point values relegated for 1st choice and 2nd choice votes have to be meet the taking after criteria:
The point got to be positive entire numbersThe point for a 1st choice vote need to be more noteworthy than or rise to to the focuses for a 2nd choice voteLets say:
1st choice vote: 4 points
2nd choice vote: 2 points
Thus by the use of these point values, the turtle would have the next chance of winning since 1st choice votes would be worth more point (4 point ) compared to 2nd choice votes (3 point ). This would push individuals to select the turtle as their 1st choice, because it would allow the turtle a better add up to point gains and increase its chances of winning.
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A statistical study involves a data set of the different types of shoe designs by the designer Calvin Klein over the years from 1987 to 2014.
What type of observational study is this?
A) cross-sectional study
B) Retrospective study
C) Prospective study
D) Experiment
Answers
The study described is a retrospective study.
A retrospective study, also known as a historical study, involves the collection and analysis of data from past events or behaviors. In this case, the study involves collecting and analyzing data on the different types of shoe designs by the designer Calvin Klein over the years from 1987 to 2014. The data has already been collected in the past, and the researcher is analyzing it to draw conclusions or make inferences about the shoe designs.
In contrast, a cross-sectional study involves the collection of data from a population at a specific point in time, while a prospective study (also known as a longitudinal study) involves the collection of data over a period of time to observe changes or trends in a population. An experiment involves the manipulation of one or more variables to observe their effect on a dependent variable, with the aim of establishing cause-and-effect relationships.
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I need help please quickly
Answers
A. k= 49°
B. RSQ= 157°
explanations:
A. the angle shown is a right angle, right angles are 90°. so to get the measure of angle k you must subtract the already known angle from 90°. thus giving the answer 49°
B. a straight line has a measure of 180°. to get the measure of RSQ, you have to subtract the already known angle from 180°. thus giving the answer 157°.
Cleveland, OH, where the maximum and minimum temperatures were 70
∘
F and 58
∘
F respectively, experienced a mean temperature of
∘
F (round up if necessary). a. 58 b. 60 c. 64 d. 66 11. The mean temperature derived from the maximum and minimum temperatures at Cleveland indicates degree days were accumulated. a. heating (HDD) b. cooling (CDD) 12. Therefore, Cleveland accumulated degree day(s) on 6-7 September 2022. a. 0 b. 1 c. 3 d. 7 13. Based on the plotted temperatures across the rest of Ohio, remaining stations HDD on 6-7 September 2022. a. accumulated b. did not accumulate You can observe and calculate HDD or CDD as we progress into the fall and through the winter. Wind Chill HDD and CDD values and their effect on homeowners' utility bills may stress tight budgets through the seasons. Since energy bills are dependent on the human who uses the energy, another factor for homeowners to consider when budgeting energy consumption is wind chill. The wind chill is an air temperature index that takes into account heat loss from exposed skin caused by the combined effect of wind and low air temperature. Outdoors, the cooling effect of wind along with the ambient temperature is reflected by using the wind chill equivalent temperature. Go to NWS Daily Weather Map for the most recent map. The pane to the left allows you to select any date back to 1 January 2003. Each day's map series includes the surface map, colorcoded maps of maximum and minimum temperatures, mid-tropospheric flow at the 500−mb level, and total precipitation. The surface and 500−mb maps are for 12Z(8a.m. EDT or 7a.m. EST, etc.) while the temperatures and precipitation maps are for the entire day. Clicking on the maps opens a more detailed map. Bring up the daily weather map set for 23 January 2022 . Scroll down and click on either the Maximum or Minimum Temperature map. 14. For 23 January 2022, on the North Dakota-Minnesota border, Fargo had a minimum temperature of −25
∘
F. With the minimum temperature there, assume Fargo was experiencing a wind speed of 10mph. With the NWS Wind Chill Chart in Figure 4A-5 from Investigation 4A, the wind chill for this combination of temperature and wind speed would have been
∘
F. a. −16 b. −20 c. −35 d. −41 e. −47
Answers
The mean temperature in Cleveland, OH, was 64°F. The accumulated degree days for Cleveland on 6-7 September 2022 were 1. The rest of Ohio accumulated degree days during the same period.
Based on the given information, the maximum temperature in Cleveland was 70°F and the minimum temperature was 58°F. To find the mean temperature, we add the maximum and minimum temperatures and divide by 2: (70°F + 58°F) / 2 = 128°F / 2 = 64°F.
Degree days are a measure of heating or cooling requirements. In this case, since the mean temperature in Cleveland was lower than a certain base temperature, degree days were accumulated. The base temperature is typically set at 65°F for cooling and 55°F for heating. Since the mean temperature in Cleveland was below the base temperature, the accumulated degree days are heating degree days (HDD).
For the specific date of 6-7 September 2022, Cleveland accumulated 1 heating degree day (HDD). This means that the average temperature for that period was 1 degree below the base temperature of 55°F.
The remaining stations in Ohio also accumulated heating degree days (HDD) on 6-7 September 2022. This indicates that the temperatures across the rest of Ohio were below the base temperature during that period.
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Helppp!!!!!!!!!!!!!!!!!!!!!
Answers
The value of x is equal to 15°
How to determine the value of x?In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.
Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.
By substituting the given parameters, we have the following:
3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.
3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.
23x + 15 = 360°.
23x = 360 - 15
23x = 345
x = 345/23
x = 15°.
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4. Solve the equation x2 = 10
Answers
Answer:
x=5
Step-by-step explanation:
u should know this not that hard to do
A sailor is up a mast so that her eyes are 10 meters above water. A lighthouse is 40 meters tall. From how far away will the sailor first see the lighthouse?
Answers
The sailor is 10 meters above the water and the lighthouse is 40 meters tall, so the total height between the two is 50 meters. Therefore, the sailor will first see the lighthouse from 50 meters away.
Assuming the lighthouse is directly in front of the sailor, the light from the lighthouse will reach the sailor first when the total distance between them is 50 meters. This means the sailor will first see the lighthouse from 50 meters away. In addition, the angle between the sailor and the lighthouse will be equal to the angle of the light when it reaches the sailor's eyes. The angle of the light will depend on the curvature of the earth, the height of the lighthouse, and the height of the sailor.
Assuming the lighthouse is at sea level, the angle of the light when it reaches the sailor's eyes can be calculated using the following equation:
Angle
= arcsin (50 / (2 * 6371))
Where 6371 is the radius of the earth in km.
This calculation gives an angle of 0.0058°. This means the light from the lighthouse will reach the sailor from a distance of 50 meters with an angle of 0.0058°.
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3х – 6 = 4 (2 - 3х) — 8x
what is x?
Answers
Answer:
x = 2/5 or 0.4
Step-by-step explanation:
3x - 6 = 4(2 - 3x) - 8x
distribute
3x - 6 = 4*2 - 4*3x - 8
3x - 6 = 8 - 12x - 8
combine like terms
3x - 6 = -12x
add 12x to both sides of the equation
3x - 6 + 12x = -12x + 12x
3x - 6 + 12x = 0
15x - 6 = 0
add 6 to both sides of the equation
15x - 6 + 6 = 0 + 6
15x = 6
divide both sides of the equation by 15
15x/15 = 6/15
x = 6/15
x = 2/5
x = 0.4
The length of the hypotenuse of a right triangle is 137 units. The length of one leg of the triangle is 105. Gina wrote the following step to find the length of the unknown leg: Length of the unknown leg = 1372 − 1052 = 18,769 − 11,025 = 7,744 units Which statement best explains whether Gina's step is correct or incorrect?
A. It is incorrect because the length of the unknown side is the square root of 29,794.
B. It is incorrect because the length of the unknown side is the square root of 7,744.
C. It is correct because the length of the unknown side is the difference of the lengths of the sides.
D. It is correct because the length of the unknown side is the difference of the squares of the sides
Answers
Answer:
B. It is incorrect because the length of the unknown side is the square root of 7,744
Step-by-step explanation:
Givena = 137b = 105c = ?SolutionAs per Pythagorean theorem:
c² = a² - b²c² = 137² - 105² = 18769 - 11025 = 7744c = √7744 = 88 unitsGina's incorrect step is:
B. It is incorrect because the length of the unknown side is the square root of 7,744Answer:
it is incorrect because the length of the unknown side is the square root of 7,744.
Step-by-step explanation:
a^2 + b^2 = c^2
105^2+ b^2 = 137^2
11025+ b^2= 18769
11025-11025+ b^2 = 18769-11025
b^2= 7704
sqr b^2= sqr 7704
b=87.77243303
b=87.8 simplified
therefore,this gina is wrong because the lenght of the unknown leg is the square root of 7,744.
hope it helps.
Find the center of mass of the wire that lies along the curve r and has density =4(1 sin4tcos4t)
Answers
The mass of the wire is found to be 40π√2 units.
How to find the mass?To calculate the mass of the wire which runs along the curve r ( t ) with the density function δ=5.
The general formula is,
Mass = \(\int_a^b \delta\left|r^{\prime}(t)\right| d t\)
To find, we must differentiate this same given curve r ( t ) with respect to t to estimate |r'(t)|.
The given integration limits in this case are a = 0, b = 2π.
Now, as per the question;
The equation of the curve is given as;
r(t) = (4cost)i + (4sint)j + 4tk
Now, differentiate this same given curve r ( t ) with respect to t.
\(\begin{aligned}\left|r^{\prime}(t)\right| &=\sqrt{(-4 \sin t)^2+(4 \cos t)^2+4^2} \\&=\sqrt{16 \sin ^2 t+16 \cos ^2 t+16} \\&=\sqrt{16\left(\sin t^2+\cos ^2 t\right)+16}\end{aligned}\)
Further simplifying;
\(\begin{aligned}&=\sqrt{16(1)+16} \\&=\sqrt{16+16} \\&=\sqrt{32} \\\left|r^{\prime}(t)\right| &=4 \sqrt{2}\end{aligned}\)
Now, use integration to find the mass of the wire;
\(\begin{aligned}&=\int_a^b \delta\left|r^{\prime}(t)\right| d t \\&=\int_0^{2 \pi} 54 \sqrt{2} d t \\&=20 \sqrt{2} \int_0^{2 \pi} d t \\&=20 \sqrt{2}[t]_0^{2 \pi} \\&=20 \sqrt{2}[2 \pi-0] \\&=40 \pi \sqrt{2}\end{aligned}\)
Therefore, the mass of the wire is estimated as 40π√2 units.
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The complete question is-
Find the mass of the wire that lies along the curve r and has density δ.
r(t) = (4cost)i + (4sint)j + 4tk, 0≤t≤2π; δ=5
Determine all values of h and f for which the system x + 3y = h and -4x + ky = -9 has no solution.
Answers
For any price of h and k = -12, the system x + 3y = h and -4x + ky = -9 will haven't any answer.
To determine the values of h and okay for which the device of equations has no answer, we want to locate the situations underneath which the equations are inconsistent or parallel.
The given system of equations is:
Equation 1: x + 3y = h
Equation 2: -4x + ky = -9
For the gadget to haven't any answer, the lines represented with the aid of these equations should be parallel and in no way intersect. In different phrases, the slopes of the traces need to be equal, but the y-intercepts should be specific.
Let's first discover the slopes of the traces. The slope-intercept form of Equation 1 is y = (-1/3)x + (h/3), wherein the slope is -1/3. The slope-intercept shape of Equation 2 is y = (4/k)x - (9/k), wherein the slope is 4/k.
For the strains to be parallel, the slopes should be equal. Therefore, we have the condition: -1/3 = 4/k.
To locate the values of h and okay for which the gadget has no answer, we need to locate the values of h that satisfy the situation -1/3 = 4/k.
Solving this equation for ok, we've got:
-1/3 = 4/k
-1 = 12/k
k = -12
Substituting k = -12 returned into the equation -1/3 = 4/k, we've:
-1/3 = 4/(-12)
-1/3 = -1/3
Since the equation holds real for any value of h, there aren't any restrictions at the price of h.
Therefore, for any price of h and k = -12, the system x + 3y = h and -4x + ky = -9 will haven't any answer.
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The system of equations has no solution when k is equal to 12. The value of h can be any real number.
To determine the values of h and f for which the system has no solution, we need to analyze the coefficients of the variables and the constants in the equations.
The given system of equations is:
x + 3y = h
-4x + ky = -9
We can rewrite the second equation as:
-4x + ky = -9
Dividing both sides of the equation by -4, we get:
x - (k/4)y = 9/4
Comparing the coefficients of x and y in the two equations, we can see that the slopes of the lines represented by the equations are different when k is not equal to 12.
Therefore, for the system to have no solution, k must be equal to 12.
As for the value of h, it can be any real number since it does not affect the slopes of the lines.
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find the volume of the triangular prism 2.4 cm 3.6 cm 6 cm
Answers
Answer:
25.92cm²
Step-by-step explanation:
First, do 2.4x3.6=8.64
then multiply by length so 8.64x6=25.92
Hope this helps