The mistake made by Enduro is that he is supposed to divide both sides by -4 instead of adding 4 to each sides
What are inequalities?Inequalities are expressions that have unequal values, when compared
How to determine Enduro's mistake?The inequality is given as
-4x > 120
When 4 is added to both sides, the inequality becomes
4 - 4x > 120 + 4
The above is not the solution to the inequality.
The solution is as follows:
We have:
-4x > 120
Divide both sides inequality by -4
x < -30
Hence, the mistake made by Enduro is that he is supposed to divide both sides by -4 instead of adding 4 to each sides
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There are 8 players on a tennis team. The team is planning to play in a doubles tournament. How many different groups of players of 2 players can the coach make, if the position does not matter?
28
64
20,160
40,320
Using the arrangements formula, it is found that there are 20,160 different groups of players of 2 players that the coach can make.
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
In this problem, all 8 players will play, hence considering the order, the number of ways is:
[tex]A_8 = 8! = 40320[/tex]
However, the position does not matter, as for example, João and Elisa would form the same pair as Elisa and João, hence the removing the order, the number of groups is:
40,320/2 = 20,160.
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Answer:
The answer is 28!!!
Step-by-step explanation:
Use the combinations formula:
[tex]C = \frac{n!}{r!(n-r)!}[/tex]
n = 8
r = 2
[tex]C = \frac{8!}{2!~*~6! } = 28\\[/tex]
I got it right! Look at the pic for proof.
Hope this helps!! :)
In a mathematics class, half of the students scored 79 on an achievement test. With the exception of a few students who scored 49, the remaining students scored 78. Which of the following statements is true about the distribution of scores?
Option C. The mean is less than the median in the distribution of the scores.
How to solve for the medianThe median is given as 79 + 78 / 2
= 78.5
The mode is 79 this is the number that has the highest frequency in the data.
The median is 78.5 this is the middle number in the set of scores of these students.
Hence the mean is less than the mode and the median given that it was it was brought down by the few scores of 49.
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Phil and ava both worked 14 hours this week. phil earned $112.70, and ava earned $113.82. ava wants to know how much more per hour she earns than phil. which strategy is appropriate for ava to use?
Answer:
Find out how much each makes per hour and then compare.
Step-by-step explanation:
Phil: 112.70/14 = 8.05 Phil makes $8.05 per hour
Eva: 113.82/1 =8.13 Eva makes $8.13 per hour
Eva makes $0.08 more an hour.
Sloane kicked a soccer ball off the ground at a speed of 48 feet per second. The height of the ball can be represented by the function H(t) = −16t2 + 48t, where t is the time in seconds. How many seconds did the ball travel before returning the ground?
If the speed of the ball after kicking is 48 feet per second then the ball will return on the ground after 3 seconds.
Given that the speed of the ball after kicking is 48 feet per second and the function that represents the height of the ball is [tex]-16t^{2} +48t[/tex].
We are required to find the time that the ball took to travel before returning the ground.
We know that speed is the distance a thing covers in a particular time period.
The height of the ball after t seconds is as follows:
h(t)=[tex]-16t^{2} +48t[/tex]
It is at ground at the instants of t.
Hence,
[tex]-16t^{2} +48t[/tex]=0
-16t(t-3)=0
We want value of t different of 0, hence :
t-3=0
t=3.
Hence if the speed of the ball after kicking is 48 feet per second then the ball will return on the ground after 3 seconds.
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Answer:
B. t=3
Step-by-step explanation:
i took the test and got it right
Which of the following statements does not describe a characteristic of the line of best fit for a scatter plot?
I'll go for the third option. It seems sensible to having a balance in estimating provided data, even though that may not always be the case.
Hope this helps!
Type the correct answer in each box. use numerals instead of words. the surface area of a cylinder is approximately 640.56 square meters. the radius of the cylinder is 5 meters less than the height of the cylinder. to the nearest whole meter, what are the radius and height of the cylinder? the radius is approximately meters, and the height is approximately meters.
The radius of cylinder = 6 meter
The height of cylinder = 11 meter
According to the question,
Surface area of the cylinder = 640.56 m²
Let the height of the cylinder = x meters
Let the radius of the cylinder = (x-5)meters
Formula for surface area of cylinder = 2πrh ( where 'r' is the radius of the cylinder and 'h' height of the cylinder)
640.56 = 2 (3.14) (x-5) (x)
640.56/(6.28) = x² - 5x
x² - 5x =102
x² - 5x - 102 =0
using quadratic equation, [-b±√(b² - 4ac)]/2a.
b = -5; a=1; c=102
x =[-(-5) ±√(-5)² - 4(1)(102)]/2
= [5 ± √433]/2
x = 11 and -7
since x=-7 neglect negative value, we get x=11.
The height of the cylinder is 11 meters
The radius of the cylinder is (11 - 5) = 6 meters.
Hence, The radius of cylinder = 6 meter.
The height of cylinder = 11 meter.
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Answer:
Step-by-step explanation:
The radius of cylinder = 6 meter
The height of cylinder = 11 meter
According to the question,
Surface area of the cylinder = 640.56 m²
Let the height of the cylinder = x meters
Let the radius of the cylinder = (x-5)meters
Formula for surface area of cylinder = 2πrh ( where 'r' is the radius of the cylinder and 'h' height of the cylinder)
640.56 = 2 (3.14) (x-5) (x)
640.56/(6.28) = x² - 5x
x² - 5x =102
x² - 5x - 102 =0
using quadratic equation, [-b±√(b² - 4ac)]/2a.
b = -5; a=1; c=102
x =[-(-5) ±√(-5)² - 4(1)(102)]/2
= [5 ± √433]/2
x = 11 and -7
since x=-7 neglect negative value, we get x=11.
The height of the cylinder is 11 meters
The radius of the cylinder is (11 - 5) = 6 meters.
Hence, The radius of cylinder = 6 meter.
The height of cylinder = 11 meter.
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There 13 yellow cards, 6 blue, 10 red, 8 green cards in a stack of cards turned face down. Once a card is selected, it is not replaced. Find P(2 blue cards). Please be specific with your answer.
Answer:
5/222
Step-by-step explanation:
you need to add all the cards together first
13 + 10 + 8 + 6 = 37
then you take out 1 card to find the first probability of the blue card (there are 6 blue cards out of 37)
so 6/37
that will be your first probability
then for the 2nd probability, you will have 1 less card grom the deck making it only 36 cards (after taking out the first one, there will be only 5 blue cards left)
making it 5/36
that will be the 2nd probability
then you multiply both these probabilities to find the answer
6/37 × 5/36 = 5/222
thu gọn biểu thức : (x-5)(x+5)-(x+1)^2
[tex](x-5)(x+5)-(x+1)^2\\=x^2 -25-(x^2+2x +1)\\=x^2 -25-x^2-2x -1\\=-2x-26[/tex]
ANSWER: -2x -26
Ok done. Thank to me :3
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
[tex] \sqrt{112x {}^{6}y {}^{3} {z}^{5} } \\ \sqrt{(2 {}^{4} \times 7 )x {}^{6}y {}^{2}yz {}^{4} z } \\ 2 {}^{2}x {}^{3} yz {}^{2} \sqrt{7yz} [/tex]
Last optionAndre says that [tex]log_10(55)=1.5[/tex] because 55 is halfway between 10 and 100. Do you agree with Andre? Explain your reasoning.
I know that answer is false, but I don't know how to explain!!
[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lllllllll} \log_{\underline{10}}(10)=1&\implies &\underline{10}^1=10 ~~ \checkmark\\\\ \log_{10}(100)=2&\implies &10^2=100~~ \checkmark\\\\ \log_{10}(55)=1.5&\implies &10^{1.5}=55\implies 10^{\frac{3}{2}}=55\implies \sqrt[2]{10^3}=55\\\\ &&\sqrt{1000}\ne 55 ~~ \bigotimes \end{array}[/tex]
increments over the exponent, are not directly proportional to increments on the resulting values, namely the half-way from 10² and 10⁴ is not 10³, because 10⁴ is 100 times 10², and 10³ is simply 10 times 10².
Quick algebra 1 question for some points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
[tex]let \: the \: number \: be \: denoted \: by \: p \\ five \: times \: a \: number = 5p \\ square\: of \: a \: number = p {}^{2} [/tex]
[tex] \gamma - p {}^{2} = 5p - p {}^{2} [/tex]
A 6-sided die is rolled. what is the probability of rolling a number less than 4?
1/2
Step-by-step explanation:
All outcomes of a single die= 6
Events less than 4 =3
probability=3/6
=1/2
Franco has enough paint to cover an area of approximately 226 square feet. he needs to paint a cylinder that is 5 feet long. what is the maximum possible radius of the cylinder that can be covered by the paint?
The required radius of the cylinder that can be covered by the paint exists at 3.8 feet.
Franco has enough paint to protect an area of about 226 square feet. He must paint a cylinder that exists 5 feet, and the maximum possible radius of the cylinder that can be covered by the paint exists to be determined.
What is a cylinder?The cylinder exists described as a 3D solid that holds two identical bases joined by a curved surface, at a particular distance.
Here, Franco keeps sufficiently paint to cover an area of about 226 square feet.
Area of the cylinder = 226
Area of the cylinder = πr²h = 226
h = 5 feet and π = 3.14
3.14 [tex]*[/tex] 5 [tex]*[/tex] r² = 226
r² = 226/15.70
[tex]$r = \sqrt{14.70}[/tex]
r = 3.80
Therefore, the required radius of the cylinder that can be covered by the paint exists at 3.8 feet.
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Answer: 4
Step-by-step explanation: I got the answer 4 right on the test
A satellite orbits the earth at a height of 343 kilometers. if the satellite makes 8 revolutions around the earth, how many kilometers does it travel? (earth's diameter is 6371 kilometers.) use 3.14 as the approximate value of pi.
The satellite makes 8 revolutions around the earth, it passes 177272 kilometers.
How many kilometers does the satellite make 8 revolutions around the earth?
The orbital velocity of the satellite exists independent of its mass. The radius of the orbit exists as the only variable. If the satellite orbits near the planet at such a low height, its orbital speed must be extremely fast. If the orbital speed exists less than the required value, the satellite will be drawn to the earth's surface by gravity.
The satellite rotates around the earth to form a circle,
diameter of circle = Diameter of earth + 2(Height)
d = 6714 + 2(343)
d = 6714+ 686
d = 7057
Perimeter = πd
Perimeter = 3.14 (7057)
Perimeter = 22158.98
Total Revolution exists 8
Therefore, 8πd = 8(22158.98)
= 177272 kilometers.
Therefore, the satellite makes 8 revolutions around the earth, it passes 177272 kilometers.
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Which graph represents a reflection across the x-axis of g(x) = Three-fourths(3)x?
See attached images for the graph.
Solve this equation. Make sure your answer is
fully reduced.
7/8 + x = 1/4
The solution for the given equation is -5/8. By using simple algebraic operations, the equation is solved.
How a linear equation is solved?A linear equation is represented by ax + b = 0. The solution for this equation is
ax + b = 0
⇒ ax = -b
⇒ x = -b/a
Calculation:The given equation is
7/8 + x = 1/4
On simplifying,
x = 1/4 - 7/8
⇒ x = -5/8
Therefore, the solution of the given equation is -5/8.
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need help!! (check picture)
Answer:
N = 2.1
M = 4.5
Step-by-step explanation:
<p is 25 degrees. I know this because the exterior angle of p corresponds with 155. Since this is a straight angle, angle p must be 25 (180-155). Now I can use the cos and the sin of 25 to find M and N
sin 25 = N/5 multiply both sides by 5 to get
5 sin 25 = N Use your calculator put in 5 sin 25
2.1 rounded to the nearest tenth.
cos 25 = M/5 Multiply both sides by
5 cos 25 = M Use your calculator
4.5
Geometry: complete this proof (ASAP!!! It’s urgent)
Answer:
1. BD bisects <CBE, AE || BD (Given)
2. <EBD ~= <CBD (Definition of < Bisectors)
3. <AEB ~= <EBD (Alternate Interior Angles Theorem)
4. <CAE ~= <CBD (Corresponding Angles Postulate)
5. <CAE ~= <AEB (Transitive Property of Congruence)
6. AB ~= BE (Converse of Isosceles Triangles Theorem)
Consider the complex number z = 27i. what are the characteristics of the cube roots of z? use the drop-down menus to complete each sentence. the cube roots are located on a circle with center at the pole and radius of . the cube roots have arguments which differ by π over 3.
The drop-down menu will be 3 and 2.
What is the complex number?Real and imaginary numbers combine to form complex numbers with two components. Complex numbers serve as the foundation for more complex math, including algebra. They have various practical applications, particularly in electronics and electromagnetism.The complex number z = 27i.
The radius of the cube root is: [tex]r\sqrt[3]{x}[/tex]
[tex]r\sqrt[3]{27}[/tex]
[tex]r=3[/tex]
Cube roots are located in a circle with a center at the origin and a radius of 3 units.
The complex number,z=a+ib is; Θ = tan⁻¹(b/a)
The complex number z=0+27i is:
Θ = tan⁻¹(27/0)
Θ = π/2
Cube roots have more than 3 arguments that differ by 2 π.
Therefore, The drop-down menu will be 3 and 2.
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The cube roots exist found on a circle with a center at the origin and a radius of 3. The cube roots contain arguments that vary by 2π over 3.
What is the complex number?A complex number is one that has both a real and an imaginary component, both of which are preceded by the letter I which stands for the square root of -1.
The given complex number as;
z = 27i
The radius of the cube root is found as;
r = ∛x
substituting the values in the above equation, we get
r = ∛27
r = 3
The cube roots are located on a circle with a center at the origin and a radius of 3 units.
The argument of a complex number, z = a+ib will be
[tex]\theta[/tex] = tan⁻¹(b/a)
The argument of a complex number z = 0+27i
[tex]\theta[/tex] = tan⁻¹(27/0)
[tex]\theta[/tex] = π/2
The cube roots have arguments that differ by 2π over 3.
Therefore, the correct answer for the drop-down menu exists in 3 and 2.
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If $20.00 was spent on Shoes, what was the total amount spent on the shopping trip?
Answer: Total = $200
Step-by-step explanation:
Given information
Money spent on shoes = $20.00
Percent of Money spent on shoes = 10%
Given formula
The total amount of money spent × Percent = Money spent on shoes
⇵
The total amount of money spent = Money spent on shoes / Percent
Substitute values into the given formula
The total amount of money spent = Money spent on shoes / Percent
Total = (20.00) / (10%)
Convert percentage into decimal
Total = 20.00 / 0.1
Simplify the fraction
[tex]\Large\boxed{Total~=~200~Dollars}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
A yoga studio sells monthly memberships. the function f(x) = −x2 50x − 264 models the profit in dollars, where x is the number of memberships sold. determine the zeros, and explain what these values mean in the context of the problem.
The zeros represent the number of monthly memberships where no profit is made; x = 6, x = 44.
To determine the zeroes, calculate:The function we have is: [tex]f(x) = -x^{2} +50x-264[/tex]
That models the profit in dollars, where [tex]x[/tex] is the number of memberships sold.
In order to get the zeros we'll use the quadratic formula:
[tex]x_{1,2} =\frac{-b+-(b^{2}-4ac) }{2a} \\[/tex]
For,
[tex]a=-1,b=50,c=-264: x^{1,2} =\frac{-50+-\sqrt[]{50^{2} -4(-1)(-264)} }{2(-1)} \\x_{1} =\frac{-50+\sqrt[]{50^{2} -4(-1)(-264)} }{2(-1)} =\frac{-50+\sqrt[]{50^{2} -4*1*264} }{2(-1)}=\frac{-50+\sqrt[]{1444} }{-2} =6\\x_{2} =\frac{-50+\sqrt[]{50^{2} -4(-1)(-264)} }{2(-1)} =\frac{-50-\sqrt[]{50^{2} -4*1*264} }{2(-1)}=\frac{-50-\sqrt[]{1444} }{-2} =44\\[/tex]
So, the zeroes are [tex]x=6, x=44[/tex].
Therefore, the zeros represent the number of monthly memberships where no profit is made; x = 6, x = 44.
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The complete question is given below:
A yoga studio sells monthly memberships. The function f(x) = −x2 + 50x − 264 models the profit in dollars, where x is the number of memberships sold.
Determine the zeros, and explain what these values mean in the context of the problem.
x = 6, x = 44; The zeros represent the number of monthly memberships that produce a maximum profit.
x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made.
x = 25, x = 361; The zeros represent the number of monthly memberships where no profit is made.
x = 25, x = 361; The zeros represent the number of monthly memberships that produce a maximum profit.
Answer:
The answer is: x = 6, x = 44; The zeros represent the number of monthly memberships when no profit is made.
Find the rule.
pattern:
[|(-1)|; |(0)|; |(1)| ; |(m)|; |(3)|]
[|(-3)|; |(-1)|; |(1)| ; |(3)|; |(n)|]
write down the rule in the form y= ...
The first series uses a linear function with - 1 as first element and 1 as common difference, then the rule corresponding to the series is y = |- 1 + x|.
The second series uses a linear function with - 3 as second element as 2 as common difference, then the rule corresponding to the series is y = |- 3 + 2 · x|.
What is the pattern and the function behind a given series?
In this problem we have two cases of arithmetic series, which are sets of elements generated by a condition in the form of linear function and inside absolute power. Linear functions used in these series are of the form:
y = a + r · x (1)
Where:
a - Value of the first element of the series.r - Common difference between two consecutive numbers of the series.x - Index of the element of the series.The first series uses a linear function with - 1 as first element and 1 as common difference, then the rule corresponding to the series is y = |- 1 + x|.
The second series uses a linear function with - 3 as second element as 2 as common difference, then the rule corresponding to the series is y = |- 3 + 2 · x|.
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Question 3
What's the height of a cone if the volume is 562 cubic inches and the radius is 5 inches.
O 72.05 units
O 120.62 units
O21.47 units
O38.90 units
Previous
[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=562\\ r=5 \end{cases}\implies 562=\cfrac{\pi (5)^2 h}{3}\implies 1686=25\pi h \\\\\\ \cfrac{1686}{25\pi }=h\implies 21.47\approx h[/tex]
Home Run Derby
Data are shown below for three baseball players at a recent minor league home run hitting contest.
Juan:
The ball followed a path modelled by the equation h = −0.001! + 0.5 + 2.5 where h is the height of the ball in feet and is the horizontal distance in feet.
1) Represent the distance-height relationship for each player’s ball as an equation, in a table and on a graph. Record each representation and clearly label which player the information belongs to.
2) Supposed there were no obstacles.
a. Whose ball would travel the greatest distance before hitting the ground?
b. Whose ball would travel the shortest distance before hitting the ground?
3) Suppose the fence was 350 ft from home plate. At what height was each ball when it passed over the fence?
Juan's ball would travel the greatest distance while Barry's ball would travel the shortest.
Represent the distance-height relationship for each player’s ball as an equation, in a table and on a graph.Juan
Juan's equation is given as:
h = -0.001d^2 + 0.5d + 2.5
h =
Set d to multiples of 50 from 0 to 400.
So, the table of values of Juan's function is:
d (ft) h(ft)
0 2.5
50 25
100 42.5
150 55
200 62.5
250 65
300 62.5
350 65
400 42.5
See attachment for the graph of Juan's function
Mark
A quadratic function is represented as:
h = ad^2 + bd + c
Using the values on the table of values, we have:
c = 3 -- the constant value
So, the equation becomes
h = ad^2 + bd + 3
Using the two other values on the table of values, we have:
23 = a(50)^2 + b(50) + 3
38 = a(100)^2 + b(100) + 3
Using a graphing tool, we have:
a = -0.001
b = 0.45
So, Mark's equation is h(d) = -0.001d^2 + 0.45d + 3
See attachment for Mark's graph.
Barry
From the graph, we have the table of values of Barry's function to be:
d (ft) h(ft)
0 2.5
50 21
100 35
150 44
200 48
250 46
300 41
350 30
400 14
450 0
Using a graphing tool, we have the quadratic function to be:
y = -0.001x^2 +0.4x +2.5
The shortest and the greatest distance before hitting the groundFrom the graphs, equations and tables, the distance travelled by the balls are:
Juan = 505 feet
Mark = 457 feet
Barry = 450 feet
This means that Juan's ball would travel the greatest distance while Barry's ball would travel the shortest.
The height the balls hit a fence at 350 ft distanceTo do this, we set d = 350
From the graphs, equations and tables, the height at 350 ft by the balls are:
Juan = 65 feet
Mark = 38 feet
Barry = 30 feet
The above represents the height the balls hit the fence
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A grandfather's age in years is the same as his granddaughter's age is months. Together, they are 91 years old. How old is the grandfather?
Answer:
Step-by-step explanation:
"if i purchase this product for $79.99 and two accessories for $9.99 and $7.00, how much would i owe after the 8.75% tax is applied?" employee: "your total would be __________."
Answer:$96.98
Step-by-step explanation: all you just do is to add it all up to the total amount.
Answer: $105.47
I hope you get the job!!!!!
help pleaseee and explain how , I’m confused thanks
Answer:
The rope is worth 13.
The shoe is worth 5.
The clock is worth 3.
Step-by-step explanation:
We know that the weights are 8 so we will use 8 for the weights.
Let s = show
Let r = rope
Let c = clock
We have three unknowns so we need three equations.
8 + s = r c + s = 8 s= c +2
There are a number of ways that we can approach this. Let's substitute
c + 2 for s in the first 2 equations.
8 + s = r
8 + c + 2 = r
10 + c = r
c + s = 8
c + c + 2 = 8
2c + 2 = 8
2c = 6
c = 3 we found the value of the clock.
Now, let's substitute 3 in for 3 in the bold equation above.
10 + c = r
10 + 3 = r
13 = r we found the value of the rope.
We can use any of the equations to find the shoe.
s= c + 2
s = 3 + 2
s = 5
This is tricky. It takes a lot of practice. Don't give up!
Shoe= 5
Rope= 13
Clock= 3
We can start by giving each item a variable. Shoe= s, rope= r, clock= c. The weight is 8, so we don't need to give it a variable. Our equations are now:
8+s= r
c+s= 8
s= c+2
Now, we can isolate a variable to solve for it using the substitution method. Let's start with s.
c+s=8
-c -c
s= 8-c
Now, we'll take another equation and plug s in.
8-c=c+2
+c +c
8= 2c+2
-2 -2
6=2c
c=3
Now we know that the clock is 3. Put 3 into the last equation, and add 3+2 to get 5 for the shoe. 5 in the first equation for the shoe plus 8 as the weight means the rope is 13.
hope this helped!
A cube shaped box has a side length of 15 inches and contains 27 identical cube shaped blocks. what is the surface area of all 27 blocks compared to the surface area of the box?
The surface area of all 27 blocks compared to the surface area of the box is 3 times the surface area of the box.
What is a cube?A cube is a three-dimensional solid object with six square faces, facets, or sides, three of which meet at each vertex.To find the total surface area of the 27 blocks:
A cube's surface area
SA = 6s² (where s is the side length)Given that the box's side length is 15 inches:
SA of box = 6152 = 1350 in2Surface Area of 3-inch side length blocks:
⇒ SA = 6 · 3² = 54 in²27 blocks SA = 27 54 = 1458 in2Surface Area of 4-inch side length blocks:
⇒ SA = 6 · 4² = 96 in²27 96 = 2592 in2 SA of 27 blocksSurface Area of 5-inch side length blocks:
⇒ SA = 6 · 5² = 150 in²27 blocks SA = 27 150 = 4050 in2Therefore, from the given answer options for the total surface area of the 27 blocks, the side length of the blocks must be 5 inches.
To calculate how many times the total surface area of the 27 blocks is to the surface area of the box:
So,
The side length of the blocks is 5 inches.
The total surface area of the 27 blocks is 4050 square inches.
This is 3 times the surface area of the box.
Therefore, the surface area of all 27 blocks compared to the surface area of the box is 3 times the surface area of the box.
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The linear density in a rod 5 m long is 10 x + 4 kg/m, where x is measured in meters from one end of the rod. Find the average density ave (in kg/m) of the rod.
The average density of the rod is 0.704 kg/m.
For given question,
We have been given the linear density in a rod 5 m long is 10 / x + 4 kg/m, where x is measured in meters from one end of the rod.
We need to find the
The length of rod is, L = 5 m.
The linear density of rod is, ρ = 10/( x + 4) kg/m
To find the average density we need to integrate the linear density from x₁ = 0 to x₂ = 5,
The expression for the average density is given as,
⇒ ρ'
[tex]=\int\limits^5_0 {\rho} \, dx\\\\=\int\limits^5_0 {\frac{m}{L} } \, dx\\\\=\int\limits^5_0 {\frac{10}{5(x+4)} }\, dx\\\\=\int\limits^5_0 {\frac{2}{x+4} }\, dx[/tex] ......................(1)
Using u = x + 4
du = dx
u₁ = x₁ + 4
u₁ = 0 + 4
u₁ = 4
and
u₂ = x₂ + 4
u₂ = 5 + 4
u₂ = 9
By entering the values above into (1), we have:
⇒ ρ'
[tex]=2\int\limits^9_4 {\frac{1}{u} } \, du\\\\ = 2[(log~u)]_4^{9}\\\\=2[(log~9-log~4)]\\\\=2\times[0.352][/tex]
= 0.704
Thus, we can conclude that the average density of the rod is 0.704 kg/m.
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Area=
Help me please thanks :)
Answer:
16 square units
Step-by-step explanation:
You find the area by multiplying the base times the height. The base or horizonal length is 4. You get this from the ordered point x (4,0). The x coordinate 4, tells us that the point x is 4 spaces to the right of zero, so the length or base is 4.
The height is also 4. You get this from the point S (2,4) The y coordinate of 4 tells you how high up the point is.
4 x 4 = 16