The cone and cylinder above have the same radius and height and the volume of the cone is 171 cubic inches.
Volume of a three-dimensional shape is the space occupied by the shape.
Given that,
Radius and height of the cylinder and the cone are same.
Let r and h be the radius and height of each of the cylinder and the cone.
Volume of the Cone = 1/3 π r² h
Volume of the cone = We have, volume of the cylinder is 57 cubic inches.
1/3 π r² h = 57
Multiplying both sides by 3,
π r² h = 57 × 3
π r² h = 171 cubic inches π r² h
Hence the volume of the cone is 171 cubic inches
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Money Magic
How did you use the 3 meters and the “Show Earnings Report” throughout the game?
THANK YALL I MADE A 60
Answer:
Glad we helped
Step-by-step explanation:
Identify the slope and y-intercept of the following equation:
y = 4x + 1
The slope and y-intercept of the following equation are:
Slope = 4.
y-intercept = 1.
What is the slope-intercept form?In Mathematics, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;
y = mx + c
Where:
m represent the gradient, slope, or rate of change.x and y represent the data points.c represent the vertical intercept, y-intercept or initial number.Based on the information provided above, an equation that models the line is represented by this mathematical equation;
y = mx + c
y = 11x + 41
By comparison, we have the following:
mx = 4x
Slope, m = 4.
Initial number or y-intercept, c = 1.
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A line has a slope of
-5 and includes the points (7,p) and (8,4). What is the value of p?
[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{p})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{p}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{7}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ -5 }\implies \cfrac{4-p}{1}=-5 \\\\\\ 4-p=-5\implies 4=-5+p\implies 9=p[/tex]
Landon measures the angles of two triangles. Four of the angles in the two triangles measure 52°, 70°, 44°, and 36°. Which two angles cannot be the angle measures for the two triangles? OA. 100° and 58° OB. 84° and 74° OC. 88° and 68° O D. 92° and 66°
Option D, which has 92° and 66° curves, is the correct choice. The total of these angles is 158°, which is needed for the final two angles.
Are a triangle's edges proportional to 3 to 4 to 5?The triangle with edges in the ratio $3:4:5 is therefore "yes" a right-angled triangle. Note: We can only apply Pythagoras' Theorem to right-angled triangles; it cannot be applied to any other triangles.
Let's add the given angle measures: 52° + 70° + 44° + 36° = 202°. This means that the sum of the measures of the remaining two angles in the two triangles is:
360° - 202° = 158°
As a result, since both options A and B have one angle that is higher than 90 degrees, we can rule them out.
Option C has angles of 88° and 68°, which add up to 156°.
Since the highest sum of two acute angles is 180°, the other two angles would have to have a sum of 204°, which is not feasible.
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-Solve the equation using the elimination method
-6x+5y=1
6x+4y=-10
To solve this system of equations using the elimination method, we need to eliminate one of the variables. One way to do this is to add the two equations together in a way that will eliminate one of the variables.
First, we can multiply the second equation by -1 to change the sign of all its terms:
-6x + 5y = 1
-6x - 4y = 10
Now we can add the two equations together to eliminate x:
( -6x + 5y ) + ( -6x - 4y ) = 1 + 10
Simplifying the left side and the right side:
-12x + y = 11
Now we have one equation with one variable, y. We can solve for y by isolating it on one side of the equation:
-12x + y = 11
y = 12x + 11
We can substitute this expression for y into either of the original equations to solve for x. Let's use the first equation:
-6x + 5y = 1
-6x + 5(12x + 11) = 1
Simplifying the left side:
54x + 55 = 1
Subtracting 55 from both sides:
54x = -54
Dividing both sides by 54:
x = -1
So the solution to the system of equations is x = -1 and y = 1. We can check this solution by substituting these values into both original equations and verifying that they are true.
18. (5) two conducting plates have charge /- 0.0000470 mc and each has area 0.138 m2. what is the strength of the electric field between the plates? m = milli
The magnitude of the electric field between the plates is 3.86 × [tex]10^7[/tex]N/C. The sign indicates the direction of the electric field, which depends on the sign of the charge on the plates.
The strength of the electric field between the plates can be calculated using the formula:
E = σ/ε0
where σ is the surface charge density, ε0 is the permittivity of free space, and E is the electric field strength.
The surface charge density is given by:
σ = Q/A
where Q is the charge on each plate and A is the area of each plate.
Substituting the given values, we get:
σ = ±0.0000470 C / 0.138 [tex]m^2[/tex] = ±0.000341 C/[tex]m^2[/tex]
The permittivity of free space is:
ε0 = 8.85 × [tex]10^{-12[/tex] F/m
Substituting the values, we get:
E = σ/ε0 = ±0.000341 C/[tex]m^2[/tex] / 8.85 × [tex]10^{-12[/tex] F/m = ±3.86 × [tex]10^7[/tex] N/C
The magnitude of the electric field between the plates is 3.86 × [tex]10^7[/tex]N/C. The sign indicates the direction of the electric field, which depends on the sign of the charge on the plates.
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Shaggy,Velma, and Fred are camping in the woods.They each have their own tent and the tents are set up in a triangle.Shaggy and Velma are 20 meters apaart.The angle formed at Shaggy is 30 degrees and the angle formed at fred is 105 degrees.How far apart are Velma and Fred?
By using the cosines law we can say that, Velma and Fred are approximately 17.39 meters apart.
What is law of cosine?
The Law of Cosines is a formula used in trigonometry to relate the sides and angles of a triangle. It states that for any triangle with sides a, b, and c and angles A, B, and C opposite those sides, the following equation holds:
[tex]$c^2 = a^2 + b^2 - 2ab \cos(C)$[/tex]
where c is the side opposite angle C.
We can solve this problem using the law of cosines. Let's call the distance between Velma and Fred "[tex]$d$[/tex]". Then, we have:
[tex]$c^2 = a^2 + b^2 - 2ab \cos(C)$[/tex]
where [tex]$c$[/tex] is the distance between Velma and Fred (which we want to find), [tex]$a$[/tex] is the distance between Shaggy and Velma (which is 20 meters), [tex]$b$[/tex] is the distance between Shaggy and Fred, and [tex]$C$[/tex] is the angle formed at Shaggy (which is 30 degrees).
We can rearrange this equation to solve for [tex]$d$[/tex]:
[tex]$d^2 = a^2 + b^2 - 2ab \cos(C)$[/tex]
[tex]$d^2 = 20^2 + b^2 - 2(20)(b) \cos(30)$[/tex]
[tex]$d^2 = 400 + b^2 - 20b \sqrt{3}$[/tex]
We also know that the angle formed at Fred is 105 degrees, which means that the angle formed at Velma is 45 degrees (since the angles in a triangle sum to 180 degrees). This means that we can use the law of sines to find the value of [tex]$b$[/tex]:
[tex]$\dfrac{b}{\sin(B)} = \dfrac{a}{\sin(A)}$[/tex]
[tex]$\dfrac{b}{\sin(105)} = \dfrac{20}{\sin(45)}$[/tex]
[tex]$b = 20 \dfrac{\sin(105)}{\sin(45)}$[/tex]
[tex]$b \approx 27.68$[/tex]
Now we can substitute this value of [tex]$b$[/tex] into the equation we derived earlier to find [tex]$d$[/tex]:
[tex]$d^2 = 400 + (27.68)^2 - 20(27.68)\sqrt{3}$[/tex]
[tex]$d \approx 17.39$[/tex]
Therefore, Velma and Fred are approximately 17.39 meters apart.
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b. Use ratio language to write two different sentences that compare the amount
of ribbon and the number of bouquets.
The ratio of ribbon to bouquets is 2:5, meaning for every 2 meters of ribbon, 5 bouquets can be made. For every 7 bouquets, 3 meters of ribbon are needed, meaning the ratio is 3:7.
What is ratio?A ratio is a comparison of two numbers or quantities that are related to each other in some way. It is the relationship between the sizes of two or more things, expressed as the quotient of one divided by the other.
Ratios can be used to compare different aspects of a set of data, such as the ratio of boys to girls in a classroom, or the ratio of red cars to blue cars on a street. They are also used in many real-world applications, such as finance, engineering, and science.
Ribbon to bouquets ratio is 2:5, which means that for every 2 units of ribbon, there are 5 bouquets.
With a ribbon to bouquet ratio of 1:3, the number of bouquets is three times the amount of ribbon.
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9. The Star Point Ranger Station and the Twin Pines Ranger Station are 30 miles apart along a straight, mountain road. Each station gets word of a cabin fire in a remote area known as Ben's Hideout. A straight path from Star Point to the fire makes an angle of 34° with the road, while a straight path from Twin Pines makes an angle of 14° with the road. Find the distance, d, of the fire from the road. 34° Star Point Ben's Hideout D d 30 mi 14° Twin Pines 10. In problem 9 we had two expressions that were both equal to d. Use both of your expressions and the value you found for d in problem 7 to check your answers. Explain why they were not exactly equal. Does it matter if this application were real life? Why or why not?
The distance of the fire from the road is d ≈ 6.15 miles + 2.94 miles ≈ 9.09 miles.
The two expressions for d give slightly different values. This is due to the fact that we rounded the values of x and y in our calculations.
How to Solve the Problem using Trigonometry?In problem 9, we can use trigonometry to find the distance, d, of the fire from the road. Let x be the distance from Star Point Ranger Station to the fire, and let y be the distance from Twin Pines Ranger Station to the fire. Then, we have:
tan(34°) = d/x
tan(14°) = d/y
Multiplying both sides of each equation by the respective denominator and simplifying, we get:
d = x tan(34°)
d = y tan(14°)
Since the two expressions for d are both equal, we can set them equal to each other and solve for x and y:
x tan(34°) = y tan(14°)
x = (y tan(14°))/tan(34°)
Substituting the value we found for y in problem 7, which was y = 6.15 miles, we get:
x = (6.15 miles) * tan(14°) / tan(34°) ≈ 2.94 miles
Therefore, the distance of the fire from the road is d ≈ 6.15 miles + 2.94 miles ≈ 9.09 miles.
Now, let's check our answers using both expressions for d:
d = x tan(34°) ≈ 2.94 miles * tan(34°) ≈ 2.94 miles * 0.704 = 2.07 miles
d = y tan(14°) ≈ 6.15 miles * tan(14°) ≈ 6.15 miles * 0.249 = 1.53 miles
As we can see, the two expressions for d give slightly different values. This is due to the fact that we rounded the values of x and y in our calculations. If we use the exact values, we would get slightly different values for d, but they would still be very close.
In real life, it is important to be as accurate as possible when dealing with emergencies such as fires. However, in this case, the difference between the two values of d is relatively small, so it may not have a significant impact on the response to the fire. Nevertheless, it is important to use the most accurate values possible to ensure the safety of those involved.
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Hannah has a cone made of steel and a cone made of granite.
• Each cone has a height of 10 centimeters and a radius of 4 centimeteres.
• The density of steel is approximately 7.75 grams per cubic centimeter.
• The density of granite is approximately 2.75 grams per cubic centimeter.
What is the difference, to the nearest gram of the masses of the cones?
As a result, the difference is 837 grammes between the cones' respective masses.
Describe density.
Mass per unit volume is measured using density. It is described as a substance's mass per unit volume. The following is the density formula:
Mass / Volume equals density.
So, The formula m = V, where m is the mass, is the density, and V is the volume, can be used to determine each cone's mass.
The formula below can be used to determine each cone's mass:
- The mass of a steel cone weighs 1298.21 grams or 7.75 grams per cubic centimeter.
- The granite cone weighs 460.76 grams, or 2.75 grams per cubic centimeter.
- Mass of steel cone = 7.75 g/cm³ × 167.55 cm³ = 1298.21 grams
- Mass of granite cone = 2.75 g/cm³ × 167.55 cm³ = 460.76 grams
for difference of masses = 1298.2 grams - 460.76 grams = 837 grams
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Figure A is a scale image of Figure B, as shown.
The scale that maps Figure A onto Figure B is
Enter the value of x.
The value of x is equal to 21 units when scale is 1:7 and a given side on figure A is 3 units.
We know that Figure A is a scaled image of Figure B, with a scale of 1:7. This means that every length in Figure A is one-seventh the length of the corresponding length in Figure B. For example, if a side in Figure B is 14 units long, the corresponding side in Figure A would be 2 units long (14 divided by 7).
In question a side on figure A is 3 units:
Side on Figure B = 7 * Side on Figure A
x = 7 * 3
x = 21 units
Therefore, x is equal to 21 units when scale is 1:7 and a given side on figure A is 3 units.
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The complete question is :
Figure A is a scale image of Figure B, as shown.
The scale that maps Figure A onto Figure B is 1:7
Enter the value of x.
A cone with a diameter of 8 centimeters has volume 143.6 cubic centimeters. Find the height of the cone
By answering the presented question, we may conclude that height of the cone is approximately 2.9 centimeters.
what is a cone?A cone is a three-dimensional geometric shape having a flat base and a smooth tapering apex, also known as a vertex. A cone is formed on a plane with no vertices by joining a sequence of line segments, half-lines, or lines that are common to all points on the base. A cone is a three-dimensional structure with a smooth transition from a flat, usually circular, base to the vertex or apex, which acts as the axis to the centre of the base. A cone is a three-dimensional geometric form having an upwardly flattened curving surface.
volume of a cone:
[tex]V = 1/3 * \pi * r^2 * h\\r = 4 cm\\V = 143.6 cm^3\\143.6 = 1/3 * \pi * 4^2 * h\\143.6 = 16/3 * \pi * h\\h = 143.6 / (16/3 * \pi)\\h = 2.9 cm\\[/tex]
height of the cone is approximately 2.9 centimeters.
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y = - 10/9 + x/7 linear or nonlinear?
Answer:
linear
Step-by-step explanation:
yw
The initial amount of money borrowed or deposited?
Answer:
yes
Step-by-step explanation:
What is the area of the rhombus shown?
Answer:
Step-by-step explanation:
[tex]168yd^{2}[/tex]
Answer:
168 yd²
Step-by-step explanation:
4 × 7 yd × 12 yd / 2 = 168 yd²
[Questions in the image]
Answer:
a) 675
b) 12
c) y = 12x + 675
d) y = 12 (500) + 675 = $6,675
Factor
F(x)= x^2 + 2x - 35
Answer:
Step-by-step explanation:
The population of Vatican City is approximately 800 people. The population of China is about 1.75 × 106 times greater. What is the approximate population of China?
A.
1.4 × 106
B.
1.4 × 107
C.
1.4 × 108
D.
1.4 × 109
To find the approximate population of China, we need to multiply the population of Vatican City by 1.75 × 106:
Population of China = Population of Vatican City × 1.75 × 106
Population of China = 800 × 1.75 × 106
Population of China = 1.4 × 109
Therefore, the approximate population of China is 1.4 × 109, which is option D.
Pls help
write an exponetial fuction given an intial value of 50 and a growlth of 1. 2
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &50\\ r=rate\to 20\%\to \frac{20}{100}\dotfill &0.2\\ t=\textit{elapsed time} \end{cases} \\\\\\ A = 50(1 + 0.2)^{t} \implies \boxed{A =50(1.2)^t}[/tex]
How do you do this step by step please thank uu
Answer: 2sw or 2ab
Step-by-step explanation:
Express the function f(x) = -2(x-4)² + 1 graphically, with a table of values, with a
mapping diagram, and using set notation with integers over the interval 1 ≤x≤7.
The expression of the function using the specified formats are presented as follows;
Please find attached the required graph of the function f(x) = -2·(x - 4)² + 1 created with MS Excel
The table of values for the function can be presented as follows;
[tex]\begin{tabular}{|c|c|c|} \cline{1-2}x& f(x) \\ \cline{1-2}1 & -17\\ \cline{1-2} 2 & -7 \\ \cline{1-2} 3 & -1 \\ \cline{1-2} 4 & 1 \\ \cline{1-2} 5 & -1\\\cline{1-2} 6 & -7 \\ \cline{1-2} 7 & -17 \\ \cline{1-2}\end{tabular}[/tex]
The mapping diagram can be presented as follows;
x [tex]{}[/tex] f(x)
1 → -17
2 → -7
3 → -1
4 → 1
5 → -1
6 → -7
7 → -17
The function expressed using set notation can be presented as follows;
f(x) = {-17, -7, -1, 1, -1, -7, -17} where x ∈ {1, 2, 3, 4, 5, 6, 7}
What is a function?A function is a rule that assigns a unique value for the output for each input value.
The specified function is; f(x) = -2·(x - 4)² + 1
Please find attached the graph of the parabola, created with MS Excel, which is a parabola that opens downwards, with a vertex of (4, 1)
The table of values can be presented as follows;
x | f(x)
-----|------
1 | -17
2 | -7
3 | -1
4 | 1
5 | -1
6 | -7
7 | -17
Mapping diagram:
A mapping diagram is a diagram that illustrates how an element of a set is paired with elements in another set.
The mapping diagram for the function can be made to show how the x-values are mapped to the f(x) values as follows;
1 → -17
2 → -7
3 → -1
4 → 1
5 → -1
6 → -7
7 → -17
Set notation;
The function, f(x) = -2·(x - 4)² + 1 can be expressed using set notation for the interval 1 ≤ x ≤ 7, which is the set of integers between 1 and 7, inclusive, which is presented as follows;
Set of x-values; {1, 2, 3, 4, 5, 6, 7}
Set of f(x) values is therefore; {-17, -7, -1, 1, -1, -7, -17}
Therefore, we get f(x) = -2·(x - 4)² + 1 expressed using set notation can be presented as follows;
f(x) = {-17, -7, -1, 1, -1, -7, -17}, where, x ∈ {1, 2, 3, 4, 5, 6, 7}
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Solve for x. Type your answer as a number
From the figure, the value of x is given as 17 units
How to find the value of x?In mathematics, a ratio shows how many times one number contains another.
The ratio of the sides of the figure is as follows
3x-7/x+5 = 2/1
cross and multiply to have 3x - 7 = 2(x+5)
opening the brackets to have
3x -7 = 2x +10
collecting like terms to have
3x-2x = 10+7
x = 17 units
In conclusion, the value of x is 17 units
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calculate the probability that at most 13% of the residents in the sample received a jury summons in the previous 12 months.
The probability that at most 13 of the residers in the sample entered a jury process in the once 12 months is 0.000158.
What's Normal Distribution?A normal distribution, also known as a Gaussian distribution or bell wind, is a probability distribution that's symmetric and bell- shaped. It's characterized by its mean( μ) and standard divagation( σ).
Given
Sample size( n) = 500
Probability of an individual entering a jury process( p) = 15 = 0.15
We want to calculate the probability that at most 13 of the residers in the sample entered a jury process.
Let X be the arbitrary variable representing the number of residers who entered a jury process in the sample.
Using the binomial accretive distribution function( CDF), we can calculate the probability as follows
P( X ≤ 13 of n) = Σ( k = 0 to k = 0.13 n)( n C k)
Here, n = 500
p = 0.15
k = int(0.13 n)
So, binom.cdf( int(0.13 500), 500,0.15) ≈0.000158
Thus, The likelihood that 13% of the sample's residents received a jury summons in the previous year is 0.000158.
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The question attached here is seems to be incomplete, the complete question is
What proportion of US Residents receive a jury summons each year? A polling organization plans to survey a random sample of 500 US Residents to find out. Let be the proportion of residents in the sample who received a jury summons in the previous 12 months. According to the National Center for State Courts, 15 \% of US residents receive a jury summons each year. Suppose that this claim is true.
5. Calculate the probability that at most 13% of the residents in the sample received a jury summons in the past 12 months.
If all three dimensiona of
a pyramid increase by a factor of two, by what factor does the volume of pyramid increase
Answer:
8.
Step-by-step explanation:
That would be by a factor of 2^3 = 8.
estimate the area of the circle to the nearest unit.
Answer:
Step-by-step explanation: We know that ,
Area of circle =πr² and
r = radius of circle.
Now,
Diameter of circle =56 cm [given]
So, radius of circle=D/2=56/2
Radius of circle=28
Now,
Area of circle=πr²
Area of circle=22/7 ×(28)² [π=22/7]
Area of circle=22×4×28
Area of circle=2464cm²
Hence, Area of circle is 2464cm²
I hope it's help you.
Answer:
48 cm²
Step-by-step explanation:
Area of circle formula: A = πr²
= π (d/2)²
= 3.14 * (4)²
= 50.24
The area of the circle is closest to Option D, 48 cm²
if 30% of r is 33, what is 70% of R
Answer:
77
Step-by-step explanation:
We Know
30% of r = 33
Find 1% by taking
33 / 30 = 1.1
What is 70% of R?
We take
1.1 x 70 = 77
So, 70% of R is 77
The question requires to first find the value of R by solving the equation (0.30*R = 33). Then, calculate 70% of R by multiplying the found R value with 0.70.
Explanation:The question tells us that 30% of R equals 33. To find the value of R, we can set up an equation where 0.30 (which is 30% in decimal form) times R equals 33. Dividing both sides of the equation by 0.30 will give us the value for R. Once we have found R, we can then find 70% of R by multiplying R by 0.70 (70% in decimal form).
Step-by-step:Set up an equation: 0.30*R = 33Solve for R: R = 33 ÷ 0.30 Calculate 70% of R: 0.70 * R Learn more about Percentage Calculations here:https://brainly.com/question/329987
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Rodrigo practiced playing the guitar 15
1
3
hours over the past 3 weeks. He practiced for 5
1
4
hours during the first week and 4
2
3
hours during the second week.
How much time did Rodrigo spend practicing during the third week? Use the numbers and symbols to select the equation that represents the problem. Then solve the equation. Symbols may be used more than once or not at all.
15
1
3
5
1
4
4
2
3
x = +
a) The time that Rodrigo spent practicing during the third week is 5.42 hours.
b) The equation that represents the problem is 15¹/₃ = 5¹/₄ + 4²/₃ + x.
What is an equation?An equation is a mathematical statement showing that two or more mathematical or algebraic expressions are equal or equivalent.
Equations are represented using the equal symbol (=), unlike algebraic expressions that contain variables, constants, numbers, and values.
The time spent during the first week = 5¹/₄ hours
The time spent during the second week = 4²/₃ hours
The total time spent during the three weeks period = 15¹/₃ hours
Let the time spent during the third week = x
15¹/₃ = 5¹/₄ + 4²/₃ + x
x = 15¹/₃ - (5¹/₄ + 4²/₃)
x = 5.41663
Thus, solving the equation, Rodrigo spent 5.42 hours practicing the guitar during the third week.
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What is the equation of the line that passes through the point (4,1) and has a slope of 1/2 ?
Answer: 37
Step-by-step explanation: so first you have to realize that i what I’m doing and you not listen to me
Need to find the value of c but confused which trig function to use etc. thanks a bunch!
Therefore, the value of x in each triangle is approximately 5.4 and 11.1, respectively.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It involves the study of trigonometric functions such as sine, cosine, and tangent, which are used to relate the angles of a triangle to the lengths of its sides. Trigonometry has a wide range of applications in fields such as physics, engineering, navigation, surveying, and astronomy. For example, trigonometry is used in navigation to calculate the angles between a ship and a lighthouse, or between two ships, in order to determine their relative positions. In engineering, trigonometry is used to calculate the forces acting on structures such as bridges and buildings, and to design and build machines that rely on the principles of motion and energy.
Here,
For the first triangle, we have:
Using the sine ratio,
sin(36) = x / 9
Solving for x, we get:
x = 9 sin(36)
≈ 5.4
Rounding to the nearest tenth, we get:
x ≈ 5.4
For the second triangle, we have:
Using the tangent ratio,
tan(27) = x / 21
Solving for x, we get:
x = 21 tan(27)
≈ 11.1
Rounding to the nearest tenth, we get:
x ≈ 11.1
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