The ratiοs are nοt equal fοr all the squares, which means there is nοt a prοpοrtiοnal relatiοnship between diagοnal length and area.
Using the fοrmula fοr finding the area οf a square, we have:
Area οf square A = side length squared
Area οf square A = 4.8 x 4.8
Area οf square A = 23.04 square cm
Similarly, we can find the areas οf squares B, C, and D:
Area οf square B = 5.2 x 5.2 = 27.04 square cm
Area οf square C = 6.4 x 6.4 = 40.96 square cm
Area οf square D = 3.6 x 3.6 = 12.96 square cm
Nοw, let's find the lengths οf the diagοnals οf each square using the Pythagοrean theοrem:
Diagοnal οf square A = √(4.8² + 4.8²) = 6.77 cm
Diagοnal οf square B = √(5.2² + 5.2²) = 7.35 cm
Diagοnal οf square C = √(6.4² + 6.4²) = 9.06 cm
Diagοnal οf square D = √(3.6² + 3.6²) = 5.09 cm
Tο determine if there is a prοpοrtiοnal relatiοnship between the length οf the diagοnals and the areas οf the squares, we need tο cοmpare the ratiοs οf the diagοnals tο the areas fοr each square.
Fοr example, the ratiο οf diagοnal length tο area fοr square A is:
Ratiο οf diagοnal length tο area fοr square A = diagοnal length / area
Ratiο οf diagοnal length tο area fοr square A = 6.77 cm / 23.04 square cm
Ratiο οf diagοnal length tο area fοr square A = 0.294
We can repeat this fοr the οther squares and cοmpare the ratiοs. If the ratiοs are apprοximately equal fοr all the squares, then there is a prοpοrtiοnal relatiοnship between diagοnal length and area.
Ratiο οf diagοnal length tο area fοr square B = 0.272
Ratiο οf diagοnal length tο area fοr square C = 0.221
Ratiο οf diagοnal length tο area fοr square D = 0.393
As we can see, the ratiοs are nοt equal fοr all the squares, which means there is nοt a prοpοrtiοnal relatiοnship between diagοnal length and area.
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if 3 Sin A + 4 cos A= 5 prove that tan A = 3/4
Find the volume generated by rotating the region in the first quadrant bounded by y =e" and the X-axis from = 0 to x = ln(3) about the y-axis. Express your answer in exact form. Volume =
The volume generated by rotating the region in the first quadrant bounded by y = ex and the x-axis from x = 0 to x = ln(3) about the y-axis is (πln(3)3)/3.
To find the volume generated by rotating the region in the first quadrant bounded by y = ex and the x-axis from x = 0 to x = ln(3) about the y-axis, we can use the disk method. The disk method involves slicing the region into thin disks and adding up their volumes.
The volume of each disk is πr2h, where r is the radius of the disk and h is the thickness of the disk. In this case, the radius of each disk is x and the thickness is dx.
So, the volume of the region is:
V = ∫0ln(3)πx2dx
We can use the power rule for integration to solve this integral:
V = π∫0ln(3)x2dx = π[(x3)/3]0ln(3) = π[(ln(3)3)/3 - (03)/3] = (πln(3)3)/3
Therefore, the volume generated by rotating the region in the first quadrant bounded by y = ex and the x-axis from x = 0 to x = ln(3) about the y-axis is (πln(3)3)/3. This is the exact form of the volume.
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Please help me solve this! Please and thank you! :D PLEASE HELP I WILL GIVE BRAINLIEST
The equation that shows a proportional relationship is y = 12x; where the constant of proportionality is 12
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.
A proportion relationship is in the form:
y = kx; where x is the constant of proportionality
Let y represent the number of paper towel rolls and x represent the number of cases. Hence:
y = kx
From the table, using the point (1, 12):
12 = k(1)
k = 12
The equation is y = 12x
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Which describes a financial product offered by insurance companies that, in
return for an investment, provides fixed payments each month for the
remainder of a person's life?
The financial product described is an annuity.
An annuity is a contract offered by insurance companies, where the buyer makes a lump-sum payment or a series of payments in exchange for regular payments made over time, usually until the end of the buyer's life. An annuity can be either fixed or variable, depending on the type of investment chosen by the buyer.
In a fixed annuity, the payments are predetermined and do not change over time, while in a variable annuity, the payments are based on the performance of the underlying investments. An annuity is often used as a retirement income stream.
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a shopkeeper bought 300 lanterns. he sold 2/3 of them on Saturday and 1/6 of them on Sunday how many lanterns did he have left?
Answer:
150 Lanterns
Step-by-step explanation:
Total lanterns : 300
[tex]\frac{2}{6} * 300 = 100[/tex]
[tex]\frac{1}{6} * 300 = 50[/tex]
so He sold 150 lanterns in total , leaving 300-150 = 150 Lanterns left.
A tissue box is shaped like a rectangular prism the tissue box measures 5. 2cm wide 9. 6cm long and 6 cm tall approximately what is the volume of the tissue box
the approximate volume of the tissue box to the nearest whole number is 300 cubic centimeters.
The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height of the prism, respectively.
Substituting the given values, we get:
V = (5.2 cm)(9.6 cm)(6 cm)
Simplifying, we get:
V = 299.52 cubic centimeters
Therefore, the approximate volume of the tissue box is 299.52 cubic centimeters.
Since the dimensions of the tissue box are given to only two decimal places, we can reasonably assume that the answer accurate to two decimal places is a good approximation. If we want to express the answer to the nearest whole number, we would round it to the nearest integer.
Rounding 299.52 to the nearest integer, we get:
V ≈ 300 cubic centimeters
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Determine the equation of the tangent line to the given path at the specified value of t. (Enter your answer as a comma-separated list of equations in (x, y, z) coordinates.) (sin(3t), cos(3t), 2t^9/2)); t = 1
The equation of the tangent line to the given path at the specified value of t is (x - sin(3), 3cos(3)(y - cos(3)), -3sin(3)(z - 1), 9/2).
To determine the equation of the tangent line to the given path at the specified value of t, we need to find the derivative of the given path with respect to t. The derivative of the given path is (3cos(3t), -3sin(3t), 9t^8/2). Now, we can plug in the specified value of t = 1 to find the slope of the tangent line at that point. The slope of the tangent line at t = 1 is (3cos(3), -3sin(3), 9/2).
Next, we can find the point on the given path at t = 1 by plugging in the specified value of t into the original equation. The point on the given path at t = 1 is (sin(3), cos(3), 1).
Finally, we can use the point-slope form of an equation to find the equation of the tangent line. The equation of the tangent line in (x, y, z) coordinates is (x - sin(3)) = 3cos(3)(y - cos(3)) = -3sin(3)(z - 1) = 9/2.
Therefore, the equation of the tangent line to the given path at the specified value of t is (x - sin(3), 3cos(3)(y - cos(3)), -3sin(3)(z - 1), 9/2).
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can yall help me pls???????
Answer:45%
Step-by-step explanation:
:))))
Answer:
45%
Step-by-step explanation:
99/180 = 55%
100% - 55% = 45% decrease
Answer: 45%
how to algebraically find all the real zeros on a polynomial function
Answer:
To find all the real zeros of a polynomial function algebraically, use the Rational Root Theorem to generate a list of possible rational zeros and use synthetic division to test each possible zero. The zeros that remain after testing all the possible zeros are the real zeros of the polynomial function.
To find all the real zeros of a polynomial function algebraically, you can use the Rational Root Theorem and synthetic division. The Rational Root Theorem states that if a polynomial function has integer coefficients, then any rational zero (i.e., a zero that can be expressed as a fraction) must have a numerator that is a factor of the constant term and a denominator that is a factor of the leading coefficient.
Here are the steps you can follow:
1. Write the polynomial function in descending order of degree, with all like terms combined.
2. Use the Rational Root Theorem to generate a list of possible rational zeros. This list will be a set of all the possible fractions that can be formed by dividing a factor of the constant term by a factor of the leading coefficient.
3. Use synthetic division to test each possible zero. Start with the smallest possible denominator and work your way up. If a possible zero is not a zero of the polynomial function, cross it off the list.
4. Repeat step 3 until all the possible zeros have been tested. The zeros that remain are the real zeros of the polynomial function.
For example, let's say we have the polynomial function f(x) = x^3 - 6x^2 + 11x - 6.
Write the polynomial function in descending order of degree: f(x) = x^3 - 6x^2 + 11x - 6.
Use the Rational Root Theorem to generate a list of possible rational zeros: ±1, ±2, ±3, ±6.
Use synthetic division to test each possible zero. We start with x = 1:
1 │ 1 -6 11 -6
│ 1 -5 6
└─────────────
1 -5 6 0
Since the remainder is zero, we have found a zero of the polynomial function at x = 1. We can write the factorization f(x) = (x - 1)(x^2 - 5x + 6).
Now we use synthetic division to test the other possible zeros:
2 │ 1 -6 11 -6
│ 2 12 46
└─────────────
1 -4 23 40
x = 2 is not a zero of the polynomial function.
3 │ 1 -6 11 -6
│ 3 15 78
└─────────────
1 -3 26 72
x = 3 is not a zero of the polynomial function.
-1 │ 1 -6 11 -6
│ -1 7 -4
└────────────
1 -7 18 -10
x = -1 is not a zero of the polynomial function.
-2 │ 1 -6 11 -6
│ -2 16 -50
└────────────
1 -8 27 -56
x = -2 is not a zero of the polynomial function.
-3 │ 1 -6 11 -6
│ -3 27 -102
└────────────
1 -9 38 -108
x = -3 is not a zero of the polynomial function.
6 │ 1 -6 11 -6
Hope this helps, I'm sorry if it doesn't! :]
madison started a bank account with $200. each year, she earns 5% in interest, which means the amount of money in the account is multiplied by 1.05 each year.if madison does not withdraw money from her account, how much will she have in 10 years?
Madison will have $322.65 in her bank account in 10 years. Here is the calculation to find this amount:
Starting balance: $200
Year 1: $200 x 1.05 = $210
Year 2: $210 x 1.05 = $220.50
Year 3: $220.50 x 1.05 = $231.53
...
Year 10: $279.10 x 1.05 = $322.65
Therefore, after 10 years, Madison will have $322.65 in her bank account due to the annual interest earned.
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Find the quotient of 40y^(4)-5y^(3)-30y^(2)-10y divided by 5y
The quotient of [tex]40y^(4)-5y^(3)-30y^(2)-10y[/tex] divided by [tex]8y^(3) - y^(2) - 6y - 2[/tex]
You can use the polynomial long division method to find the product of two polynomials. Following are the steps:
Step 1: Descending in degree, write the dividend polynomial. If any terms are absent from the polynomial, replace them with coefficients of 0.Step 2: Descend the degree of the divisor polynomial as you write it. If any terms are missing from the divisor polynomial, substitute coefficients of 0 for those terms.Step 3: To calculate the first term of the quotient, divide the dividend's first term by the divisor's first term.Step 4: Multiply the divisor by the first term of the quotient to get the first term of the partial product.Step 5: Subtract the partial product from the dividend.Step 6: Bring down the next term of the dividend.Step 7: Repeat steps 3-6 until all the terms of the dividend have been used.Step 8: The final result is the quotient, plus any remainder left over after the last subtraction.To divide [tex]40y^(4)-5y^(3)-30y^(2)-10y[/tex] by 5y, we utilize long division. Divide dividend by divisor to obtain first term of the quotient:
[tex]40y^(4) / (5y) = 8y^(3)[/tex]
Multiply divisor (5y) by first term of quotient (8y^(3)) to obtain first term of partial product:
[tex](8y^(3))(5y) = 40y^(4)[/tex]
Subtract the partial product from the dividend to obtain remainder:
[tex]40y^(4) - 40y^(4) = 0[/tex]
[tex]-5y^(3) / (5y) = -y^(2)(-y^(2))(5y) = -5y^(3)-5y^(3) - (-5y^(3)) = 0[/tex]
[tex]-30y^(2) / (5y) = -6y(-6y)(5y) = -30y^(2)-30y^(2) - (-30y^(2)) = 0[/tex]
Repeat process:
[tex]-10y / (5y) = -2(-2)(5y) = -10y-10y - (-10y) = 0[/tex]
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36 is 15% of what number?
54
240
360
540
Answer:
240
Step-by-step explanation:
15% of 54=8.1
15% of 240=36
15% of 360=54
15% of 540=81
so the answer is 240
36 is 15 percent of 240.
We have,
To find out what number 36 is 15% of, we can set up the equation:
36 = 0.15x
Here, x represents the unknown number we are trying to find.
To solve for x, we divide both sides of the equation by 0.15:
36 / 0.15 = x
Simplifying the right side gives:
240 = x
Therefore,
36 is 15 percent of 240.
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7.03 The Unit Circle
The concept of the unit circle is presented throughout it's answer.
What is the unit circle?The unit circle is a circle with a radius of 1 unit that is centered at the origin (0,0) of a coordinate plane. It is a fundamental concept in trigonometry and geometry, and it is used to define the trigonometric functions (sine, cosine, and tangent) of angles in the Cartesian plane.
The format of each coordinate on the unit circle is given as follows:
[tex](\cos{\theta}, \sin{\theta})[/tex].
Hence we can calculate the trigonometric measures for any angle, as the tangent, the secant, the cossecant and the cotangent of an angle are all functions of the sine and the cosine obtained by the unit circle.
Missing InformationThe problem is incomplete, hence the unit circle concept is presented in this answer.
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A coin is flipped and a card is randomly selected from a deck of 52. What is the probability the coin will land on heads and the card will be a club? There are 13 clubs in a deck of cards.
A. 1/8
B. 1/24
C. 4/9
D. 1/2
My answer:
There are 4 cards of number eight in a deck of 52 cards, namely: 8 Spades, 8 Diamond, 8 Clubs, and 8 Hearts. So the probable outcomes are 4 and the total cards are 52. So, x 100 = 1/13. So there is a 1/13 chance for getting an eight, i.e, for every 13 cards, one card will be an eight.
hope it helps :)
also please mark brainliest it means alot
Calculate 15% of 12000 for two (2) years
Answer:
look below
13,800
need help asap pleasee
Answer:
a
Step-by-step explanation:
Can someone pls answer this
How do these numbers compare?
Drag the correct comparison symbol to the box.
10.09 10.9
< = >
Addressing issue at hand, we can state that the correct linear equation comparison symbol to the box. 10.09 10.9 f < = > is => 10.09 < 10.9
What is a linear equation?The algebraic equation y=mx+b is known as a linear equation. M serves as the y-intercept, and B serves as the slope. The previous clause has two variables, y and x, and is sometimes referred to as a "linear equation with two variables". Bivariate linear equations are those with two independent variables. The following are a few examples of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation takes the form y=mx+b, with m denoting the slope and b denoting the y-intercept, it is referred to as being linear. The term "linear" refers to an equation having the form y=mx+b, where m stands for the slope and b for the y-intercept.
the correct comparison symbol to the box.
10.09 10.9
< = >
10.09 < 10.9
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Please ASAP Help
Will mark brainlest due at 12:00
Answer:
the vertex of∠5 is point M
Step-by-step explanation:
Answer: M
Step-by-step explanation: M represents the vertex. Think of the vertex almost like the starting point of an angle.
Solve for x. Please show all steps needed.
x+8/(x+3)(x+4) = 3/x+3
Answer:
[tex]x = -2[/tex]
Step-by-step explanation:
[tex] \frac{(x + 8)}{[(x + 3) (x + 4)]} = \frac{3}{(x + 3)}[/tex]
Multiplying both sides by (x + 3) (x + 4), we get:
[tex](x + 8) = 3 (x + 4)[/tex]
Expanding the right-hand side, we get:
[tex]x + 8 = 3x + 12[/tex]
Subtracting x and 8 from both sides, we get:
[tex]2x = -4[/tex]
Dividing both sides by 2, we get:
[tex]x = -2[/tex]
Therefore, the solution to the given equation is x = -2. We can check this solution by substituting x = -2 into the original equation and verifying that both sides are equal.
Sam invests $500 for two years at an interest rate of 12%, compounded twice a year. How much will his total investment be worth after 2 years?
Answer:
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time the money is invested (in years)
In this case, P = $500, r = 0.12, n = 2 (compounded twice a year), and t = 2.
So, A = 500(1 + 0.12/2)^(2*2) = $673.01
Therefore, Sam's total investment will be worth $673.01 after 2 years.
Step-by-step explanation:
Find the area of the shaded parts.
[tex]\textit{area of a circular ring}\\\\ A=\pi (R^2 - r^2) ~~ \begin{cases} R=\stackrel{outer}{radius}\\ r=\stackrel{inner}{radius}\\[-0.5em] \hrulefill\\ R=4\\ r=2 \end{cases}\implies A=\pi (4^2 - 2^2) \\\\\\ A=12\pi \implies A\approx 37.70~in^2[/tex]
Answer:
12πin² = 37.7in² (3sf)
Step-by-step explanation:
area of whole circle = π(4)² = 16π
area of small circle = π(2)² = 4π
area of shaded = 16π - 4π = 12π
12π = 37.6991... ≈ 37.7in² (3sf)
Select the correct answer. Which equation represents a circle with center T(5,-1) and a radius of 16 units? A. (x − 5)2 + (y + 1)2 = 16 B. (x − 5)2 + (y + 1)2 = 256 C. (x + 5)2 + (y − 1)2 = 16 D. (x + 5)2 + (y − 1)2 = 256
The equation of the given circle is: (x - 5)² + (y+ 1)² = 256
How to find the equation of the circle?The center-radius form (most formally called the standard form) of a circle is usually expressed as;
(x - h)² + (y - k)² = r²
where (h, k) is the center and r is the radius.
We are given a circle with center T(5,-1) and a radius of 16 units
The equation then becomes:
(x - 5)² + (y - (-1))² = 16²
(x - 5)² + (y+ 1)² = 256
Thus, we can conclude that is the equation of the circle.
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The length of human pregnancies is approximately normal with mean μ=266days and standard deviation σ=16days.
(a) What is the probability that a randomly selected pregnancy lasts less than 262 days?
(b) Suppose a random sample of 51 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.
(c) What is the probability that a random sample of 51 pregnancies has a mean gestation period of 262 days or less?
(d) What is the probability that a random sample of 106 pregnancies has a mean gestation period of 262 days or less?
The probability that a random sample of 106 pregnancies has a mean gestation period of 262 days or less is 0.00003.
What is probability?
Probability is a measure of the likelihood that an event will occur. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probabilities are usually expressed as fractions, decimals, or percentages.
(a) To find the probability that a randomly selected pregnancy lasts less than 262 days, we need to standardize the value using the formula z = (x - μ) / σ, where x is the value we're interested in, μ is the mean, and σ is the standard deviation.
z = (262 - 266) / 16 = -0.25
Using a standard normal distribution table or calculator, we find that the probability of getting a z-score of -0.25 or less is 0.4013. Therefore, the probability that a randomly selected pregnancy lasts less than 262 days is 0.4013.
(b) The sampling distribution of the sample mean length of pregnancies is approximately normal with mean μ = 266 and standard deviation σ = 16 / sqrt(51) = 2.2449. This is known as the central limit theorem.
Using a standard normal distribution table or calculator, we find that the probability of getting a z-score of -2.8304 or less is 0.0023. Therefore, the probability that a random sample of 51 pregnancies has a mean gestation period of 262 days or less is 0.0023.
(d) Using the same formula as in part (c), we have:
z = (262 - 266) / (16 / sqrt(106)) = -4.0077
Using a standard normal distribution table or calculator, we find that the probability of getting a z-score of -4.0077 or less is 0.00003.
Therefore, the probability that a random sample of 106 pregnancies has a mean gestation period of 262 days or less is 0.00003.
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What percent of data population falls between a z-score of -1. 5 and 0. 5
Around 62.47% of the data population is situated between a z-score of -1.5 and 0.5.
Assuming a standard normal distribution, the percentage of the data population that falls between a z-score of -1.5 and 0.5 can be calculated using a standard normal table or a calculator.
Using a standard normal table, we can find the area under the curve between z = -1.5 and z = 0.5.
The area to the left of z = 0.5 is 0.6915, and the area to the left of z = -1.5 is 0.0668. Therefore, the area between z = -1.5 and z = 0.5 is:
0.6915 - 0.0668 = 0.6247
So, approximately 62.47% of the data population falls between a z-score of -1.5 and 0.5.
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Which of the following tables represents a linear function? x −4 −2 0 2 4 y 5 1 −3 −7 −11 x −3 −2 0 2 3 y 5 2 0 2 4 x 3 3 0 3 3 y −3 −2 0 2 −3 x 0 2 3 4 5 y −3 2 0 2 −3
A table that represents a linear function include the following: A.
x −4 −2 0 2 4
y 5 1 −3 −7 −11
What is a linear function?In Mathematics, a linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.
This ultimately implies that, a linear function has the same (constant) slope and it is typically used for uniquely mapping an input variable to an output variable, which both increases simultaneously.
Next, we would determine the slope by using the points contained in the table as follows;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (1 - 5)/(-2 + 4) = (-3 - 1)/(0 + 2) = (-7 + 3)/(2 - 0)
Slope (m) = -2.
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What is 0.06 written as a percent?
Answer:
6%
Step-by-step explanation:
0.06 is 6% as a decimal
A cone radius 10 cm and height 18cm fits exactly over a cylinder so that the cylinder is just touching hte inside surface of the cone. The radius of the cylinder is 4cm,
Score: 1/6 1/6 answered
Question 1
Given the triangle
H=
* <>
15
/33°
answer to 4 decimal places.
Question Help: Video
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X find the length of side 2 using the Law of Cosines. Round your final
3
27 a
The length of side 2 of the given triangle is 16.22.
What is Law of Cosines?The Law of Cosines is a mathematical formula that is used to calculate the length of sides and angles in a triangle. It is based on the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides
The Law of Cosines helps to solve for the side length in triangles when we are given two sides and the angle between them. In this triangle we are given side 1 (15) and the angle between the two sides (33°). To find side 2, we will use the formula:
c² = a² + b²- 2ab*cosC
Where c is the length of the unknown side, a is the length of the given side, b is the length of the other given side, and C is the angle between the two given sides.
In this case, c is side 2, a is 15, b is unknown, and C is 33°. We will plug in the known values and solve for b:
b² = 15² + c² - 2*15*c*cos(33°)
b² = 225 + c² - 30c*cos(33°)
We can solve this equation for c:
c = (225 + b² - 30b*cos(33°))/2
Now, we can solve for b using the values for c and a given in the problem:
b²= 225 + 27² - 30*27*cos(33°)
b² = 225 + 729 - 690.8
b²= 264.2
b = 16.22
Therefore, the length of side 2 is 16.22.
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Geometry: Find the unknown lengths of these 30-60 right triangles (ASAP!!!)
The lengths of the sides of the special 30°–60° right triangles are;
14. a = 8
b = 8·√3
c = 16
15. a = 4
b = 4·√3
c = 8
16. a = 7
b = 7·√3
c = 14
17. a = 12
b = 12·√3
c = 24
18. a = 5
b = 5·√3
c = 10
19. a = 9
b = 9·√3
c = 18
20. a = 10
b = 10·√3
c = 20
21. a = (√6)/2
b = 3·(√(2))/s
c = √6
What are special right triangles?Special right triangles are triangles that have 30°, 60°, and 45° interior angles.
The unknown lengths of the 30-60 special right triangle can be found as follows;
14. The length of the side a = 8
The length of the hypotenuse side, c can be found as follows;
sin(30°) = 1/2
sin(θ) = a/c
sin(30°) = 1/2 = 8/c
c = 2 × 8 = 16
c = 16
cos(θ) = b/c
cos(30°) = √3/2
Therefore; √3/2 = b/16
b = 16 × (√3/2) = 8·√3
b = 8·√3
15. a = 4, therefore;
c = 2 × 4 = 8
c = 8
b = (√3/2) × 8 = 4·√3
b = 4·√3
16. a = 7
b = 7·√3
c = 2 × 7 = 14
c = 14
17. a = b/√3, therefore;
a = 12·√3/√3 = 12
a = 12
b = 12·√3
c = 2 × a, therefore;
c = 2 × 12 = 24
c = 24
18. a = 5
b = a × √3, therefore;
b = 5 × √3 = 5·√3
b = 5·√3
c = 2 × a, therefore;
c = 2 × 5 = 10
c = 10
19. c = 18
a = c/2, therefore;
a = 18/2 = 9
a = 9
b = a × √3, therefore;
b = 9 × √3 = 9·√3
b = 9·√3
20. a = 10
b = a × √3, therefore;
b = 10 × √3 = 10·√3
b = 10·√3
c = 2 × a, therefore;
c = 2 × 10 = 20
c = 20
21. c = √6
a = c/2, therefore;
a = (√6 )/2
b = a × √3, therefore;
b = ((√6)/2) × √3 = (√(18))/2 = 3·√2/2
b = 3·√2/2
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The angle between the lines of sight from a lighthouse to a tugboat and to a cargo ship is 27°. The angle between the lines of sight at the cargo ship is twice the angle between the lines of sight at the tugboat. What are the angles at the tugboat and at the cargo ship?
The angle between the line of sight from the lighthouse to the tugboat is 27° and the angle between the line of sight from the lighthouse to the cargo ship is 54°.
Let's call the angle between the line of sight from the lighthouse to the tugboat "x". Then, we know that the angle between the line of sight from the lighthouse to the cargo ship is x+27, since the given angle between the lines of sight is 27°.
We also know that the angle between the lines of sight at the cargo ship is twice the angle between the lines of sight at the tugboat. Using this information, we can set up the equation:
2x = x+27
Solving for x, we get:
x = 27
So the angle between the line of sight from the lighthouse to the tugboat is 27°. Then, we can use this to find the angle between the line of sight from the lighthouse to the cargo ship:
x+27 = 27+27 = 54
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