The lamina's moment of inertia about the origin is given by, [tex]I_0=640 \pi[/tex].
What is a moment of inertia?The tendency of a body to withstand an object's angular acceleration is known as its moment of inertia. Inertia can be calculated by multiplying the mass by the orthogonal distance.Given:
Density - [tex]\delta=d(x, y)=5[/tex]Circle - [tex]x^2+y^2=16[/tex]Find the moment of inertia [tex]I_y[/tex] and [tex]I_0[/tex].
The lamina's moment of inertia about the x-axis is:
[tex]I_x=\iint_D y^2 d(x, y) d A[/tex]In the above equation, substitute the given value:
[tex]I_x=\iint_D 5 y^2 d A[/tex]Make use of polar coordinates:
[tex]\begin{aligned}x &=r \cos \theta \\y &=r \sin \theta \\d A &=d x d y=r d r d \theta \\D &=\{(r, \theta) \mid 0 \leq r \leq 4,0 \leq \theta \leq 2 \pi\}\end{aligned}[/tex]
As we all know, the general equation of a circle is:
[tex]x^2+y^2=r^2[/tex]The given circle equation is:
[tex]x^2+y^2=4^2[/tex]As a result, r ranges from 0 to 4.
And ranges from 0 to 2[tex]\pi[/tex].
As a result, the integral is shown below; simply enter all of the values and then integrate.
[tex]\begin{aligned}&I_x=\iint_D 5 y^2 d A \\&I_x=\int_0^{2 \pi} \int_0^4 5(r \sin \theta)^2 r d r d \theta \\&I_x=\int_0^{2 \pi} \int_0^4 5 r^3 \sin ^2 \theta d r d \theta \\&I_x=5 \int_0^{2 \pi}\left(\frac{r^4}{4}\right)_0^4 \sin ^2 \theta d \theta \\&I_x=320 \int_0^{2 \pi} \sin ^2 \theta d \theta \\&I_x=320 \int_0^{2 \pi}\left(\frac{1-\cos 2 \theta}{2}\right) d \theta \\&I_x=320\left(\theta-\frac{\sin 2 \theta}{2}\right)_0^{2 \pi} \\&I_x=320\left(\frac{2 \pi}{2}\right) \\&I_x=320 \pi\end{aligned}[/tex]
Now, calculate [tex]I_y[/tex] and [tex]I_0[/tex].
Make use of polar coordinates.
[tex]\begin{aligned}&x=r \cos \theta \\&y=r \sin \theta \\&d A=d x d y=r d r d \theta \\&D=\{(r, \theta) \mid 0 \leq r \leq 4,0 \leq \theta \leq 2 \pi\}\end{aligned}[/tex]
As we all know, the general equation of a circle is:
[tex]x^2+y^2=r^2[/tex]The given circle equation is:
[tex]x^2+y^2=4^2[/tex]As a result, r ranges from 0 to 4.
And ranges from 0 to 2[tex]\pi[/tex].
As a result, the integral is shown below; simply enter all of the values and then integrate.
[tex]\begin{aligned}&I_y=\iint_D 5 x^2 d A \\&I_y=\int_0^{2 \pi} \int_0^4 5(r \cos \theta)^2 r d r d \theta \\&I_y=\int_0^{2 \pi} \int_0^4 5 r^3 \cos ^2 \theta d r d \theta \\&I_y=5 \int_0^{2 \pi}\left(\frac{r^4}{4}\right)_0^4 \cos ^2 \theta d \theta \\&I_y=320 \int_0^{2 \pi} \cos ^2 \theta d \theta \\&I_y=320 \int_0^{2 \pi}\left(\frac{1-\cos 2 \theta}{2}\right) d \theta \\&I_y=320\left(\theta-\frac{\sin 2 \theta}{2}\right)_0^{2 \pi} \\&I_y=320\left(\frac{2 \pi}{2}\right) \\&I_y=320 \pi\end{aligned}[/tex]
The lamina's moment of inertia about the origin is given by:
[tex]\begin{aligned}&I_0=\iint_D\left(x^2+y^2\right) d(x, y) d A \\&I_0=\iint_D 5 r^2 r d r d \theta \\&I_0=5 \int_0^{2 \pi} \int_0^4\left(\frac{r^4}{4}\right)_0^4 d \theta \\&I_0=320 \int_0^{2 \pi} d \theta \\&I_0=320(\theta)_0^{2 \pi} \\&I_0=640 \pi\end{aligned}[/tex]
So, the moment of inertia is [tex]I_x=320 \pi[/tex].
The worth of, [tex]I_y=320 \pi[/tex].
Therefore, the lamina's moment of inertia about the origin is given by, [tex]I_0=640 \pi[/tex].
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The correct question is given below:
Find the moment of inertia about the x-axis of a thin plate with density δ=5 bounded by the circle x2+y2=16. Then use your result to find Iy and Io.
Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.
If you have three points A, B , and C , then A, B, C are noncollinear.
The given conjecture "If you have three points A, B , and C , then A, B, C are noncollinear" is false.
How to Interpret Conditional Statements?Notice that the given conjecture does not necessarily be always true.
To be precise, there are no reasons as to why A, B and C must be noncollinear.
They could lie on the same line.
Therefore, the given conjecture "If you have three points A, B , and C , then A, B, C are noncollinear" is false.
A Counterexample of the given statement is; A, B, C are three points that lie on the same line and so they are collinear.
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What is the mapping for the reflection where ABC maps to A’B’C’ ?
A - (x,y) —> (x,-y)
B - (x,y) —> (x,y)
C - (x,y) —> (-x,y)
D - (x,y) —> (x, 1/2y)
Answer:
(x, y) --> (x, - y)
Step-by-step explanation:
.......
Each year a certain amount of money is deposited in an account that pays an annual
the interest rate so that at the end of each year the balance in the account is multiplied by a
the growth factor of z = 1+r. $500 is deposited at the start of the first year, and an additional $200
is deposited at the start of the next year, and $600 at the start of the following year.
b. What is the amount (to the nearest cent) in the account at the end of three years if the
interest rate is 2%?
Answer:
What is the amount (to the nearest cent) in the account at the end of three years if the interest rate is 2%? $1,350.68
Step-by-step explanation:
DATA:
Deposits (at beginning of year):
Year 1 = $500
Year 2 = $200
Year 3 = $600
growth factor: z = 1 + r
interest rate is 2% so replace r with 2%. Growth factor equation is now:
z = 1 + 2%
z = 1.02
Year 1 account balance end of year = account balance + growth factor
= $500 + 1.02
= $ 510 account balance at end year 1
Year 2 account balance end of year = (previous year ending balance + current year deposit) * growth factor
= ($510 + $200) * 1.02
= $724.20
Year 3 account balance end of year = (previous year ending balance + current year deposit) * growth factor
= ($724.20 + $600) * 1.02
=$1,350.684
rounded: = $1,350.68 (This answer assumes no money has been withdrawn at any time.)
3. Two quantities, p and q, are in direct proportion. The sum of the values of q when p = 6 and when p = 11 is 51.
(a) Find an equation connecting p and q. (b) Find the value of p when q = 72.
Step-by-step explanation:
this just means
q = k×p
and we need to find k.
the sum of both q values when p = 6 and p = 11 is then
k×6 + k×11 = 51
17k = 51
k = 51/17 = 3
so, our equation is
q = 3p
and when q = 72
72 = 3p
p = 72/3 = 24
Lesson 8 Practice Problems
1. A number line can represent positions that are north and south of a truck stop on a
highway. Decide whether you want positive positions to be north or south of the
truck stop. Then plot the following positions on a number line.
a. The truck stop
b. 5 miles north of the truck stop
c. 3.5 miles south of the truck stop
The graph can be viewed at the conclusion of the response. We want to graph a number line and certain points on it.
Let A denote the truck stop and then it is 0 miles away from the truck stop.
Let us take the north side of the truck stop as the negative side.
Then the south side of the truck stop is the positive side.
We are asked to represent the following positions on the number line:
a. The truck stop
b. 5 miles to the north of the truck stop
c. 3.5 miles to the south of the truck stop
Point A refers to the truck stop.
Let B denote the point 5 miles away from A towards the north side of the truck stop.
And let C denote the point 3.5 miles away from A towards the south side of the truck stop.
Refer to the attached image for the required number line.
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john is playing a game with a standard deck of playing cards. he wants to draw a jack on the first try. which of the following statements is true?
John is playing a game with a standard deck of playing cards - this statement is true.
What is the purpose of playing cards?playing a card game, set of cards that are numbered or outlined (or both) and are utilized for messing around, for schooling, for divination, and for conjuring. Generally, Western playing a card game are made of rectangular layers of paper or slight cardboard stuck together to frame a level, semirigid material. Some have proposed that the playing a card game previously worked as "play cash" and addressed the stakes utilized for other betting games, and later turned out to be essential for the actual games. Others have proposed associations between playing a card game and chess or dice games, yet this is again theoretical. Different games, for example, a 25-card variation of Euchre which involves the Joker as the most elevated trump, make it one of the main in the game. Frequently, the Joker is a special case, and subsequently permitted to address other existing cards.
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Which of the expressions below is equal to 6 (2 + 2)? Select all that apply. A) (6 x 2) + (6 x 2) B) 6 x 2 + 2 C) 12 x 2 D) 6 x 4
If B is between A and C, and AB = 4x + 1, BC = 2x – 7, and AC = 24. What is the value of length of BC?
*
a. 3 units
b. 17 units
c. 7 units
d. 21 units
Answer:
a. 3 units
Step-by-step explanation:
The length of BC can be found in 3 main steps, namely the formation of equations, solving for x and substitution.
Let's rewrite the given lengths:
AB= 4x +1 -----(1)
BC= 2x -7 -----(2)
AC= 24 -----(3)
Form an equation which relates the 3 lengths:
Given that B is between A and C,
AC= AB +BC -----(4)
Substituting equations (1) to (3) to equation (4):
24= 4x +1 +2x -7
Simplify:
24= 6x -6
Add 6 to both sides:
6x= 24 +6
6x= 30
Divide both sides by 6:
x= 5
Substitute x= 5 into (2):
BC
= 2x -7
= 2(5) -7
= 10 -7
= 3 units
Thus, option a is correct.
Additional:
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solve the equation. (find only the real solutions. enter your answers as a comma-separated list.) 2x x 7
Answer:
14x
Step-by-step explanation:
2x*7=
2*7=14x
Name a point that is coplanar
The missing points are listed below:
RPXWSQXPWhat points in a parallelepiped are coplanar?
The picture attached aside shows us a right-angled parallelepiped and the Euclidean geometry indicates that a plane is generated by three non-colinear points, that is, three points that cannot be contained by a line.
Therefore, coplanar points are points that can be contained by one and same plane. Parallelepipeds are solids with eight vertices and twelve sides, each of them corresponding to a plane.
In this problem we must determine what fourth point is contained by the same plane that comprises the other three. Now we show the corresponding answers:
Q, P, S → RW, Z, S → PW, Z, Y → XQ, X, P → WY, Z, R → SR, Y, X → QQ, R, Y → XW, X, Q → PTo learn more on coplanar points: https://brainly.com/question/1593959
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Which inequality is represented by the graph?
Answer:
Step-by-step explanation:
x < 0
Answer : x is less than or equal to 0
First, the direction of the number line in the graph is the negative number side, so it has to be 0 or less.
If it is less than 0, the dot that starts at the point 0 must have a hollowed out part in the middle. If it is 0 or less, the dot that starts at the point 0 is completely filled with no hollowed middle part.
Since the dot is completely blacked out, the answer is the second option.
2. Which expression is equivalent to 2(2x + 11)-(-5+ 3x)?:
a.
7x + 27
b. 7x + 17
C.
x + 27
d. 3(- 8 + 2x) - 5(- 8 + x) + 11
e. 2x - (- 7x + 3) + 44
Question Progress
Homework Progress
10/41
Expand and simplify (x+3)(x + 5)
Answer:
x2 + 8x + 15
Step-by-step explanation:
First - take the first terms of the brackets (so, x and x) and multiply them together: for this example that gives x2.
Outside - take the two outermost terms of the brackets (x and 5) and multiply them together: for this example that gives 5x.
Inside - take the two innermost terms of the brackets (3 and x) and multiply them together: for this example that gives 3x.
Some people may draw lines between terms when doing this (as seen in the diagram above) leaving you with a “crab claw” around the brackets.
Write down everything you have worked out as one long expression:
x2 + 5x + 3x + 15
Then, we will simplify this expression by grouping any “like” terms (this just means adding together any bits with x where they have the same power).
This leaves us with our final answer, which is:
x2 + 8x + 15
Which expression is equivalent to the given expression after using the distributive property?
6 · 13 + 6 · 7
6 · 7(13 + 6 )
6 · 7(13 + 6 )
6 · (13 + 6) · 7
6 · (13 + 6) · 7
6 (13 + 7)
6 (13 + 7)
6(13 + 6) + 7
6(13 + 6) + 7
The equivalent expression to the given expressions after using distributive property is [tex]6(13+7)[/tex]
As per the question statement, we are supposed to find the expression equivalent to the given expression [tex]6*13 + 6*7[/tex] after using the distributive property. Before solving this problem, we should know about the distributive property, which states that [tex]a(b+c) = a*b + a*c[/tex].
Therefore, [tex]6*13 + 6*7[/tex]
[tex]=6(13+7)[/tex], as per the definition of the distributive property.
Distributive property: The distributive Property says that it is essential to multiply each of the two numbers by the factor prior to performing the addition operation when a factor is multiplied by the sum or addition of two terms.To learn more about distributive property, click on the link given below:
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The midpoint of KL is M(8, 3). One endpoint is L(8, 0). Find the coordinates of the other
endpoint K.
Answer: K(8,6)
Step-by-step explanation:
M(8,3) - the midpoint of KL L(8,0) K(x,y)=?
[tex]\displaystyle\\Mx=\frac{Kx+Lx}{2}[/tex]
Multiply both parts of the equation by 2:
[tex]2Mx=Kx+Lx\\2Mx-Lx=Kx+Lx-Lx\\2Mx-Lx=Kx\\Mx=8\ \ \ \ Lx=8\\Hence,\\2(8)-8=Kx\\16-8=Kx\\8=Kx\\\\2My-Ly=Ky\\My=3\ \ \ \ Ly=0\\Hence,\\2*(3)-0=Ky\\6-0=Ky\\6=Ky\\Thus,\\K(8,6)[/tex]
A store buys 9 blue hats for every 6 red hats a. What’s is the ratio of blue hats to red hats b. What is the ratio of the blue hats all hats c. If the store purchased 45 hats, how many hats were blue
The ratio of blue hats to red hats IS 3:2 , the ratio of the blue hats all hats is 3:5 and If the store purchased 45 hats, 27 hats were blue
The ratio of blue hats to red hats is 9:6, which can be simplified to 3:2
Therefore the ratio of blue hats to red hats is 3: 2
The total number of hats is the summation of blue hats and red hats = 9+6= 15
So, The ratio of blue hats to all hats is 9:15, which can be simplified to 3:5
Therefore the ratio of blue hats to red hats is 3: 5
If the store purchased 45 hats, and we need to find out the number of blue hats
We have to assume the number of blue hats be x
Then the ratio becomes x: 45::3:5
We can also write this as
X= 3a and 45= 5a
The value of a comes out to be 9
So the number of blue hats purchased in the lot is 3a= 3 9 = 27
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Ex) what is the ratio? Of 5:35
Answer:
1:
Step-by-step explanation:
5 divided by 5 is 1, and 35 divided by 5 is
Here are the city gas mileages for 13
different midsized cars in 2008.
16, 15, 22, 21, 24, 19, 20, 20, 21, 27,
18, 21, 48
What is the maximum?
Answer: 48
Step-by-step explanation: 48 is the highest mileages
Apen cost 20php each, if you buy more than 10pens you will be given 50percent discount on the next pens you're about to buy. make a procedure that defines the cost of the pen
Cost of pen = 20x when x< 10
and
=10x when x>10
Let the number of pens bought be x.
So the total pen cost is 20x when the number of the pen is less than 10.
Now let's take that the number of pens bought is more than 10
So the pen will cost a 50% discount
50% of 20x
= 20/100 × 20x
= 10x
So the cost of the pen will be 10x when the number of the pen is greater than 10.
From this, we get to know that
Cost of pen = 20x when x<10
and
= 10x when x>10
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solve the linear equation 4x-(2x-1)=x+5+x-6
The linear equation doesn't have a solution.
How to compute the value?The linear equation given is illustrated as: 4x-(2x-1) = x+5+x-6
This will be solved thus:
4x - 2x + 1 = x+5+x-6
4x - 2x + 1 = 2x - 1.
2x + 1 = 2x - 1
Collect like terms
2x - 2x = -1 - 1
0 = -2
This illustrates that the equation doesn't have a solution.
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Nabhitha buys cookies and onions at the store.
She pays a total of $60.39.
She pays a total of $4.79 for the cookies.
• She buys 8 bags of onions that each cost the same amount.
.
.
Write and solve an equation which can be used to determine x, how much each bag
of onions costs.
The equation is 8x + 4.79= 60.39 and the value is x is $6.95
How to solve the equation ?Nabhitha pays a total of $60.39 for the cookies and onions
She pays a total of $4.79 for the cookies
She buys 8 bags of onions that each costs the same amount of money
The equation used to find the value of x is written as
8x + 4.79= 60.39
Collect the like terms
8x= 60.39 - 4.79
8x= 55.6
Divide both sides by the coefficient of x which is 8
8x/8 = 55.6/8
x= 6.95
Hence the price of each bag of onions is $6.95
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Assist me with this graph.
Answer:
3.1.1. A(-4, 0) B(0, -2) E(4, 0)
3.1.2. k = -16
3.1.3. (-∞, ∞)
3.1.4. [-16, ∞)
3.1.5. [-6, 4]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=x^2+k\\g(x)=-2x+8\\h(x)=\dfrac{6}{x-2}+1\end{cases}[/tex]
Question 3.1.1.Points A and B are the x-intercept and y-intercept of function h(x).
Point E is the x-intercept of function g(x).
The x-intercept of function h(x) is when h(x) = 0:
[tex]\begin{aligned}h(x) & = 0\\\implies \dfrac{6}{x-2}+1 & = 0\\\dfrac{6}{x-2} & = -1\\6 & = -1(x-2)\\6 & = -x+2\\4 & = -x\\x & = -4\end{aligned}[/tex]
Therefore, the coordinates of point A are (-4, 0).
The y-intercept of function h(x) is when x = 0:
[tex]\begin{aligned}h(x) & = \dfrac{6}{x-2}+1\\\implies h(0) & = \dfrac{6}{0-2}+1\\ & = -3+1\\& = -2\end{aligned}[/tex]
Therefore, the coordinates of point B are (0, -2).
The x-intercept of function g(x) is when g(x) = 0:
[tex]\begin{aligned}g(x) & = 0\\\implies -2x+8 & = 0\\-2x & = -8\\x & = 4\end{aligned}[/tex]
Therefore, the coordinates of point E are (4, 0).
Question 3.1.2.As function f(x) passes through point C (-6, 20), substitute the point into the equation of the function to find the value of k:
[tex]\begin{aligned}f(-6) & = 20\\\implies (-6)^2 + k & = 20\\36 + k & = 20\\k & = 20 - 36\\k & = -16\end{aligned}[/tex]
Hence, proving that the value of k is -16.
Question 3.1.3.The domain is the set of all possible input values (x-values).
The domain of function f(x) is unrestricted, therefore its domain is:
Solution: -∞ < x < ∞Interval notation: (-∞, ∞)Question 3.1.4.The range is the set of all possible output values (y-values).
The range of function f(x) is restricted, since the minimum point of the parabola is at (0, -16). Therefore its range is:
Solution: f(x) ≥ -16Interval notation: [-16, ∞)Question 3.1.5.[tex]\begin{aligned}g(x) - f(x) & \geq 0\\\implies g(x) &\geq 0+f(x)\\ \implies g(x) & \geq f(x)\end{aligned}[/tex]
Therefore, find the interval for which g(x) is greater than or equal to f(x).
From inspection of the given graph this is between points C and E:
Solution: -6 ≤ x ≤ 4Interval notation: [-6, 4]simplify the expression
Answer:
8x - 4y
Step-by-step explanation:
First: solve the parentheses
8x - 7y - (3-6y)
Second: combine like terms (terms that both have y or x, or other variable)
8x - 7y - (-3y)
Third: there are no more like terms, so you are left with this as your answer
8x - 4y
find parametric equations and symmetric equations for the line (use the parameter t.) the line through the point (−3,3,−1) and perpendicular to both ⟨1,1,0⟩ and ⟨
The second vector that's perpendicular to the line we want (call it L) is missing; I'll denote it by ⟨a, b, c⟩.
The cross product of ⟨1, 1, 0⟩ and ⟨a, b, c⟩ is perpendicular to both of these vectors. The direction vector of L will be parallel to this cross product.
Compute the cross product.
⟨1, 1, 0⟩ × ⟨a, b, c⟩ = ⟨1•c - 0•b, 0•a - 1•c, 1•b - 1•a⟩ = ⟨c, -c, b - a⟩
Then the vector equation of L is
L(t) = ⟨c, -c, b - a⟩ t + ⟨-3, 3, -1⟩
As parametric equations, we write
x(t) = ct - 3
y(t) = -ct + 3
z(t) = (b - a) t - 1
Eliminating the parameter above, we get
x + y = (ct - 3) + (-ct + 3) = 0 ⇒ x = -y
and substituting
x = ct - 3 ⇒ t = (x + 3)/c
into z(t), we get
z = (b - a) (x + 3)/c - 1 ⇒ x = c (z + 1)/(b - a) - 3
As symmetric equations, then, we write
x = -y = c (z + 1)/(b - a) - 3
eric is randomly drawing cards from a deck of 52. he first draws a red card, places it back in the deck, shuffles the deck, and then draws another card. what is the probability of drawing a red card, placing it back in the deck, and drawing another red card? answer choices are in the form of a percentage, rounded to the nearest whole number.
The probability of drawing a red card, placing it back in the deck, and drawing another red card is 1/4.
According to the given question.
Total number of cards in a deck is 52.
As we know that total number of red cards in a well shuffled deck is 26.
Since, Eric first draws a red card, places it back in the deck, shuffles the deck, and then draws another card. Which means there is a replacement of cards.
So, the probability of drawing the first card is red = 26/52 = 1/2
And the probability of drawing the another card is red = 26/52 = 1/2
Therefore,
The probability of drawing a red card, placing it back in the deck, and drawing another red card
= 1/2 × 1/2
= 1/4
Hence, the probability of drawing a red card, placing it back in the deck, and drawing another red card is 1/4.
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Jessie surveyed some dentists and found that 42 out of 60 favored toothpaste with
fluoride. Can 42 out of 60 can be represented as a terminating or non-terminating
decimal?
Answer:non terminating
Step-by-step explanation:
Hexagonal chess is played on a regular hexagonal board comprised of 92 small hexagons in three colors. The chess pieces are arranged so that a player can move any piece at the start of a game.
a. What is the sum of the measures of the interior angles of the chess board?
The sum of the measures of the interior angles of the chess board is equal to 720°.
What is a polygon?A polygon can be defined as a two-dimensional geometric shape that comprises straight line segments and a finite number of sides. Also, some examples of a polygon include the following:
TriangleQuadrilateralPentagonHexagonHeptagonOctagonNonagonNote: The number of sides (n) of a hexagon is 6.
In Geometry, the sum of the interior angles of both a regular and irregular polygon is given by this formula:
Sum of interior angles = 180 × (n - 2)
Sum of interior angles = 180 × (6 - 2)
Sum of interior angles = 180 × 4
Sum of interior angles = 720°.
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These are fractions 4/5 x 3/8=?
Answer:
3/10
Step-by-step explanation:
4/5 * 3/8
We can rewrite the fractions as
4/8 * 3/5
4/8 simplifies to 1/2
1/2 * 3/5
Multiply the numerators
1*3 = 3
Multiply the denominators
2*5 = 10
Numerator over denominator
3/10
a washer and a dryer cost combined. the cost of the washer is three times the cost of the dryer. what is the cost of the dryer?
$250 is the cost of the dryer.
What do we mean by cost?
The amount of money spent by a company on the creation or production of goods or services is referred to as the cost.It does not include the profit margin. From the standpoint of a seller, the cost is the amount of money spent to produce a good or product.To find the cost of the dryer:
The dryer is priced at x dollars.The washer costs 3 times as much.Then,
3x + x = 10004x = 1000x = 250Therefore, $250 is the cost of the dryer.
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The correct question is given below;
A washer and a dryer cost $1000 combined. The cost of the washer is three times the cost of the dryer. What is the cost of the dryer?
If m ∠ F L G = 14 x + 5 ° and m ∠ H L G = 17 x − 1 ° , find m ∠ F L H .
The value of ∠ F L H is 3x-6°
∠FLG and ∠FLH are adjacent angles with L being the common vertex and both the angles form the ∠HLG
As ∠FLG is given as 14x + 5° and ∠ H L G is given as 17 x − 1 °
We need to find the value of ∠ F L H
We can write that ∠FLG +∠FLH = ∠ H L G
by putting the values given
14 x + 5 ° + ∠ F L H = 17 x − 1 °
∠ F L H = 17x-1 - (14x + 50
Here we got a linear equation in one variable and by solving the equation we will get the value of ∠ F L H
∠ F L H = 17x - 1 - 14x -5
∠ F L H = 3x-6
Hence, the value of ∠ F L H is 3x-6°
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