Answers
The volume of the given shapes are listed below with their options:
11.) 12 in³ = C
12.) 108 in³ = D
13.) 293.33 cm³ = C
14.) 287 mi³ = B
15.) 3801.33 cm³ = D
16.) 452.39 yd³ = C
17.) 3619.11 in³= B
18.) 16 ft³ = C
19.) 64 m³ = A
20.) 769.69 cm³ = C
How to calculate the volume of a pyramid, cylinder and a cone?The formula used to calculate the volume of a cylinder= πr²h
The formula used to calculate the volume of triangular prism = 1/3Bh
For a square based pyramid = 1/3b²h
For a rectangular pyramid = 1/3 lwh
Volume of a cone = 1/3πr²h
For question 11;
Volume of the triangular pyramid =1/3Bh= 1/3×6×6 = 12 in³
For question 12;
Volume of square pyramid =1/3b²h = 1/3 ×6×6×9 = 108 in³
For question 13.)
Volume of a rectangular pyramid = 1/3 lwh= 1/3×11*8*10=293.33 cm³
For question 14.)
Volume of square pyramid =1/3b²h = 1/3*9*9*11= 287 mi³
For question 15.)
Volume of a cylinder = πr²h = 3.14×11*11*10 = 3801.33 cm³
For question 16.)
Volume of a cone= 1/3πr²h= 1/3*3.14*6*6*12= 452.39 yd³
For question 17.)
Volume of a cone= 1/3πr²h= 1/3*3.14*12*12*24= 3619.11 in³.
For question 18.)
Volume of the triangular pyramid =1/3Bh = 1/3*6*8= 16 ft³
For question 19.)
Volume of the triangular pyramid =1/3Bh = 1/3*24*8= 64 m³
For question 20.)
Volume of a cylinder = πr²h = 3.14×7*7*5 = 769.69 cm³
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Related Questions
Hi Please help due today ty!
Answers
what is a exactly 1/4 of a full rotation
Answers
Answer: A quarter or 1/4 rotation is 90°.
Step-by-step explanation:
A full rotation is 360 degrees, usually written as 360°. Half a rotation is then 180° and a quarter rotation is 90°.
The total interest he paid on this loan is \( \$ \) (Round to the nearest cent as needed.)
Vifredo bought a new boat for \( \$ 14,200 \). He paid \( \$ 2,500 \) for the down payment and financed the
Answers
The total interest he paid on this loan is $1,507.69
Vifredo bought a new boat for $14,200. He paid $2,500 for the down payment and financed the remaining amount for 48 months at an APR of 5.6%.
The total interest he paid on this loan is $1,507.69 (Round to the nearest cent as needed.)
To calculate the total amount that Vifredo will pay for his boat after 48 months, we need to add the amount he paid for the down payment to the total amount he will pay in 48 months at an APR of 5.6%.Vifredo's loan amount = $14,200 - $2,500 = $11,700
Calculating total amount for 48 months:Total amount = Monthly payment × Number of months Monthly payment can be calculated using the formula:PMT = (P × r) / (1 - (1 + r)^-n)where,PMT = Monthly paymentP = Principal amountr = Rate of interest per month (APR / 12) = 5.6% / 12n = Number of months= 48In our case,P = $11,700r = 5.6% / 12n = 48PMT = (11700 × (5.6 / 12)) / (1 - (1 + (5.6 / 12))^-48) = $267.34Total amount for 48 months = 267.34 × 48 = $12,840.16The total interest he paid on this loan is $1,507.69 (Round to the nearest cent as needed.)Therefore, the total amount Vifredo will pay for his boat is $2,500 (down payment) + $12,840.16 (total amount for 48 months) = $15,340.16.
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Joe wants $75,000 in 18 years to give his grandkids for college. How much must he deposit now at 3.75% interest, compounded monthly?
Answers
Answer:
$35,734.12
Step-by-step explanation:
To determine the amount Joe must deposit now to have $75,000 in 18 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A is the future value we want to have ($75,000 in this case)
P is the present value we need to deposit now
r is the annual interest rate (3.75%)
n is the number of times interest is compounded per year (12 for monthly compounding)
t is the number of years (18)
Substituting the given values, we get:
$75,000 = P(1 + 0.0375/12)^(12*18)
Simplifying the exponent:
$75,000 = P(1.003125)^216
Dividing both sides by (1.003125)^216:
P = $75,000 / (1.003125)^216
P ≈ $35,734.12
Therefore, Joe must deposit approximately $35,734.12 now to have $75,000 in 18 years at an interest rate of 3.75% compounded monthly.
Rationalise the denominator of (6 + √3)(6-√3) √33
Answers
The value of the fraction expression after rationalise the denominator will be √33.
What is the value of the expression?When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ [(6 + √3)(6 - √3)] / √33
Simplify the expression, then we have
⇒ [(6 + √3)(6 - √3)] / √33
⇒ [6² - (√3)²] / √33
⇒ [36 - 3] / √33
⇒ 33 / √33
⇒ √33
The value of the fraction expression after rationalise the denominator will be √33.
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What is the value of the first quartile?
3
6
8
11
Answers
The requried value of the first quartile is 4.5.
What is the Interquartile range?Interquartile range (IQR): The IQR is the range of the middle 50% of values in a data set. To calculate the IQR, we first need to find the quartiles of the data set.
To find the first quartile (Q1), we need to arrange the given values in ascending order and then find the median of the lower half of the values.
The given values arranged in ascending order are:
3, 6, 8, 11
The lower half of the values are:
3, 6
The median of the lower half is:
(Q1) = (3 + 6)/2 = 4.5
Therefore, the value of the first quartile is 4.5.
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In excerpt from baby mammoth mummy: frozen in time What does the narrator think of Sky's view of women? Use two details from the story to
port your response.
Answers
The narrator's thoughts on Sky's view of women is that the view is confusing and hypocritical.
What does the narrator think of sky's view ?The narrator thinks that Sky's perspective on women is unexpected, perplexing, absurd, and at odds with the person Sky appears to be. She is taken aback by Sky's refusal to perform any chores he views as falling under the purview of women.
The narrator is even more shocked that when Sky observes her "struggling with a bucket of water," he advises her not to fill the bucket all the way up rather than offering to assist her.
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Bus #7 left River Street School partially filled with students and then stopped to pick up 15 more students at the Park School. it continued its route as follows:
At the next 4 stops it dropped off two students at each stop.
Three students got off at the following stop.
The next six stops let off one student at each stop.
Ten students then got off at the Centerville after-school-program, where five kindergarten students boarded the bus.
The bus then dropped off seven kids at its last stop, leaving only the driver aboard.
How many students were on the bus when it left the River Street School? Show your work and explain your reasoning.
Answers
14 students were on the bus when it left River Street School.
To find out how many students were on the bus when it left River Street School, we need to work backwards from the end of the route and account for all the students that were picked up and dropped off along the way.
At the last stop, seven students were dropped off, leaving only the driver aboard. This means that there were 7 students on the bus before the last stop.
Before that, five kindergarten students boarded the bus at the Centerville after-school-program, which means that there were 7 - 5 = 2 students on the bus before the kindergarten students boarded.
Before that, ten students got off at the Centerville after-school-program, which means that there were 2 + 10 = 12 students on the bus before they got off.
Before that, the bus made six stops and let off one student at each stop, which means that there were 12 + 6 = 18 students on the bus before those stops.
Before that, three students got off at one stop, which means that there were 18 + 3 = 21 students on the bus before that stop.
Before that, the bus made four stops and dropped off two students at each stop, which means that there were 21 + (4 x 2) = 29 students on the bus before those stops.
Finally, before that, the bus picked up 15 students at the Park School, which means that there were 29 - 15 = 14 students on the bus when it left River Street School.
14 students were on the bus when it left River Street School.
Starting from the end of the route and working backwards, we accounted for all the students that were picked up and dropped off along the way. By subtracting the number of students that were picked up from the number of students that were on the bus at each stop, we were able to find out how many students were on the bus when it left River Street School.
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you finish, write the letters from the remaining boxes Harry can paint a room in 3 hours, and Kerry can paint it in 4 hours. How long will it take if they work together?
Answers
The amount of time it will take them when working together is 12/7 hours, or approximately 1.71 hours.
If Harry can paint a room in 3 hours, and Kerry can paint it in 4 hours, then we can use the formula for combined work (work rate) to find how long it will take if they work together. The formula is:
1/t = 1/t₁ + 1/t₂, where t is the time it takes for them to complete the work together, t₁ is the time it takes for Harry to complete the work alone, and t₂ is the time it takes for Kerry to complete the work alone.
Plugging in the values we have, we get:
1/t = 1/3 + 1/4.
Multiplying both sides of the equation by 12t, we get:
12 = 4t + 3t.
Simplifying, we get:
12 = 7t.
Dividing both sides of the equation by 7, we get:
t = 12/7.
Therefore, it will take Harry and Kerry 12/7 hours, or approximately 1.71 hours, to paint the room together.
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How does the concept of conservation of mass apply to chemical reactions?
1.The reactants and products have exactly the same atoms.
2.The reactants and products have exactly the same molecules.
3.The change in the amount of matter is equal to the change in energy.
4.The change in the amount of matter is only a small percentage of the total mass.
Answers
Since the elements in the reactants and products are identical, the principle of conservation of mass is applicable to chemical processes. Choice (b) is accurate.
What is the short meaning of a chemical reaction?chemical reaction, the transformation of one or even more substances (the reactants) into one or more distinct substances (the products). Chemical components or chemical combinations make up substances.
How does a chemical reaction start?When atoms create or break molecular bonds, chemical processes take place. Reactants are the substances that begin a chemical reaction, and products are the substances that are created as a result of the reaction.
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5-6 MathXL for School: Practice and Application Cop Solve the equation by factoring. v^(2)-2v+1=0
Answers
The equation v^(2)-2v+1=0 can be solved by factoring. Factoring is a process of breaking down a number or expression into its component parts. In this case, we can factor the equation into (v-1)(v-1), which is equal to zero. Therefore, the solution to the equation is v = 1.
Factoring is a useful tool for solving equations. By factoring, we can break a complex equation into simpler parts, which makes it easier to solve. It can also be used to identify solutions that are not obvious by looking at the equation. It is a valuable skill to have in mathematics, as it can be used to solve many equations quickly and efficiently. It is also an important skill to have when working with polynomials, as it allows us to identify the zeros of a polynomial.
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You can fill a 15 gallon tank of gas for $26. 99 or buy gas for $2. 10 gallon
Answers
Answer: finish the question if you need help
Step-by-step explanation:
Answer: 15 gallon for 26.99
Step-by-step explanation:
15 (gallons) x 2.10 ($ per gallon) = 31.5
therefore cheaper to buy 15 gallons
4. Let X be uniformly distributed on [10, 100). Calculate Tx (a) by using Risk Adjusted Premium Principle with risk index p = 2 (b) by using Risk Adjusted Premium Principle with risk index p = 10
Answers
Let X be uniformly distributed on [10, 100). By using Risk Adjusted Premium Principle
(a) Tx = 106.9615242
(b) Tx = 314.8076211
We can calculate Tx using the formula:
Tx = E[X] + p * σ[X]Where E[X] is the expected value of X, p is the risk index, and σ[X] is the standard deviation of X.For a uniformly distributed random variable X on the interval [a, b), the expected value is:
E[X] = (a + b) / 2And the standard deviation is:
σ[X] = √((b - a)² / 12)For X uniformly distributed on [10, 100), we have:
a = 10b = 100
So:
E[X] = (10 + 100) / 2 = 55σ[X] = √((100 - 10)² / 12) = 25.98076211
Now we can calculate Tx for each risk index:
(a) For p = 2:Tx = 55 + 2 * 25.98076211 = 106.9615242
(b) For p = 10:Tx = 55 + 10 * 25.98076211 = 314.8076211
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PLEASE HELP
Find the value of each trigonometric value.
Answers
The values of the trigonometric functions for angle C in the given right-angled triangle are
[tex]sin(C) = 0.6 \\ cos(C) = 0.8 \\ tan(C) = 0.75 \\ csc(C) = 1.7\\ sec(C) = 1.25 \\ cot(C) = 1.3[/tex]
What is Pythagoras theorem?
According to Pythagorean theorem to find the length of the other leg of the triangle,
[tex]a^2 + b^2 = c^2[/tex] where a and b are the legs of the triangle and c is the hypotenuse.
So, in this case,
[tex]a^2 + 30^2 = 50^2 \\ a^2 + 900 = 2500 \\ a^2 = 1600 \\ a = 40
[/tex]
Here given all three sides of the triangle.
We need to find the values of the trigonometric functions:
[tex]sin(C) = \frac{opposite \: leg}{hypotenuse }= \frac{30}{50} = 0.6 \\ cos(C) = \frac{adjacent}{hypotenuse} = \frac{40}{50} = 0.8 \\ tan(C) = \frac{opposite}{adjacent} =\frac{ 30}{40} = 0.75 \\ csc(C) =\frac{ hypotenuse}{opposite} = \frac{50}{30} = 1.666... \\ sec(C) = \frac{hypotenuse}{adjacent} = \frac{50}{40} = 1.25 \\ cot(C) = \frac{adjacent}{opposite} = \frac{40}{30} = 1.333...
[/tex]
Therefore, the values of the trigonometric functions for angle C in the given right-angled triangle are
[tex]sin(C) = 0.6 \\ cos(C) = 0.8 \\ tan(C) = 0.75 \\ csc(C) = 1.666... = 1.7\\ sec(C) = 1.25 \\ cot(C) = 1.333... = 1.3[/tex]
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If Tina is x years old then what is her age two years befor
Answers
Answer:
x-2
Step-by-step explanation:
If you start of with X, you don't know what the value of X is, so you take away two from what we label as X
Graph the system of equations below on the coordinate grid provided.
y= 4x - 2
y= 1/2x + 5
SHOW ALL OF YOUR WORK and write the answer as an ordered pair.
Answers
A solution to the given system of linear equations is (2, 6).
How to graph the solution to this system of equations?In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
y = 4x - 2 ......equation 1.
y = 1/2(x) + 5 ......equation 2.
Next, we would use an online graphing calculator to plot the given system of equations as shown in the graph attached below.
Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I and it is given by the ordered pair (2, 6).
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if tan 45 is equal to 1 what is the value of sin 45 + cos 45
Answers
Answer: [tex]\sqrt2[/tex] or 1.41
And we know that tan=sin/cos
We need to change sin(45) +cos(45) to be sin(45)/cos(45) = 1
Or you could find the value if sin(45) which is = 0,7071067812 and cos(45)=0,7071067812 and when you divide the values of sin and cos your answer is 1
read the ss
PLS HELP
Answers
Answer:
x intercept
Step-by-step explanation:
please give brainliest
Brendan is 5 years older than Valerie. In 6 years the sum of their ages will be 81 . How old is Brendan now? years old
Answers
Brendan is currently 37 years old.
To solve this problem, we can use algebra. Let's let V represent Valerie's age and B represent Brendan's age. We can set up the following equations based on the information given in the question:
B = V + 5 (Brendan is 5 years older than Valerie)
B + 6 + V + 6 = 81 (In 6 years, the sum of their ages will be 81)
Simplifying the second equation, we get:
B + V + 12 = 81
B + V = 69
Substituting the first equation into the second equation, we get:
V + 5 + V = 69
2V = 64
V = 32
Now that we know Valerie's age, we can use the first equation to find Brendan's age:
B = 32 + 5
B = 37
So Brendan's current age is calculated to be 37 years
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Every pyramid is a prism, is it True? and why?
Answers
No, it is not true that every pyramid is a prism, because they have different properties.
A pyramid is a solid shape that has a base and triangular faces that meet at a point called the apex. The base of a pyramid can be any polygon, such as a square, triangle, or rectangle. A pyramid is named according to the shape of its base. For example, a pyramid with a square base is called a square pyramid.
A prism, on the other hand, is a solid shape that has two identical bases that are parallel to each other and rectangular faces that connect the bases. The bases of a prism can also be any polygon, and a prism is named according to the shape of its bases. For example, a prism with a rectangular base is called a rectangular prism.
So, while both pyramids and prisms are three-dimensional shapes with bases and faces, they have different properties and are not the same. Therefore, it is not true that every pyramid is a prism.
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what is 3/8 divided by 1/4
Answers
Answer:[tex]1\frac{1}{2}[/tex]
If \( f(x)=5 x, g(x)=-2 x+1 \), and \( h(x)=x^{2}+6 x+8 \), find f(h \( (-3)] \).
Answers
The f(h \((-3)]\) = -5.
To find f(h \((-3)]\), we need to first find the value of h \((-3)]\) and then plug that value into the function f(x).
Step 1: Find h \((-3)]\)
h(x) = x^2 + 6x + 8
h(-3) = (-3)^2 + 6(-3) + 8
h(-3) = 9 - 18 + 8
h(-3) = -1
Step 2: Plug the value of h(-3) into the function f(x)
f(x) = 5x
f(h(-3)) = 5(-1)
f(h(-3)) = -5
Therefore, f(h \((-3)]\) = -5.
I hope this helps! Let me know if you have any further questions.
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Find all the zeros. Write the answer in exact form. p(x)=4x^(4)-15x^(3)+9x^(2)+16x-12
Answers
The zeros of the polynomial p(x)=4x^(4)-15x^(3)+9x^(2)+16x-12 are approximately -0.764, 0.621, 2.572, and 3.071.
To find the zeros of the given polynomial p(x)=4x^(4)-15x^(3)+9x^(2)+16x-12, we need to solve the equation p(x)=0.
First, let's try to factor the polynomial. We can use the Rational Root Theorem to find the possible rational zeros of the polynomial. The possible rational zeros are ±1, ±2, ±3, ±4, ±6, and ±12.
Let's try each of these possible zeros until we find one that makes the polynomial equal to zero.
When we plug in x=1, we get p(1)=4(1)^(4)-15(1)^(3)+9(1)^(2)+16(1)-12=2, which is not equal to zero.
When we plug in x=2, we get p(2)=4(2)^(4)-15(2)^(3)+9(2)^(2)+16(2)-12=20, which is not equal to zero.
When we plug in x=3, we get p(3)=4(3)^(4)-15(3)^(3)+9(3)^(2)+16(3)-12=90, which is not equal to zero.
When we plug in x=-1, we get p(-1)=4(-1)^(4)-15(-1)^(3)+9(-1)^(2)+16(-1)-12=-30, which is not equal to zero.
When we plug in x=-2, we get p(-2)=4(-2)^(4)-15(-2)^(3)+9(-2)^(2)+16(-2)-12=4, which is not equal to zero.
When we plug in x=-3, we get p(-3)=4(-3)^(4)-15(-3)^(3)+9(-3)^(2)+16(-3)-12=-162, which is not equal to zero.
So, none of the possible rational zeros are actually zeros of the polynomial.
Therefore, the polynomial does not have any rational zeros. The zeros of the polynomial are irrational or complex numbers.
To find these zeros, we need to use a different method, such as the Quadratic Formula or synthetic division.
Unfortunately, these methods are beyond the scope of this answer. However, you can use a graphing calculator or an online polynomial solver to find the approximate values of the zeros.
The approximate zeros of the polynomial are -0.764, 0.621, 2.572, and 3.071.
So, the zeros of the polynomial p(x)=4x^(4)-15x^(3)+9x^(2)+16x-12 are approximately -0.764, 0.621, 2.572, and 3.071.
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Question 4 \( 1 \mathrm{pts} \) The norm of vector \( v=\left[\begin{array}{c}4 \\ \sqrt{3} \\ \sqrt{6}\end{array}\right] \) is \( \|v\|=? ? ? \) ? \[ \begin{array}{l} 50 \\ \sqrt{13} \\ 4+\sqrt{3}+\s
Answers
\(\|v\|=\sqrt{50}\)
The norm of vector \(v\) is \( \|v\|=\sqrt{4^2 + \sqrt{3}^2 + \sqrt{6}^2}=\sqrt{50} \). Therefore, the answer is \(\|v\|=\sqrt{50}\).
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A spring oscillates with a frequency of 1 cycle per second. The distance between the maximum and minimum points of the oscillation is 3 centimeters. Which function can be used to model the oscillation if y
represents the distance in centimeters from the equilibrium position and t
is given in seconds?
A) y = 1. 5sin(2πt)
B) y = 1. 5sin(πt)
C) y = 3sin(2πt)
D) y = 3sin(πt)
Answers
y = 3sin(πt). This function models the oscillation by representing the distance in centimeters from the equilibrium position as the sine of π multiplied by the time in seconds.
y = 3sin(πt). This function can be used to model the oscillation because it represents the distance in centimeters from the equilibrium position as the sine of π multiplied by the time in seconds. This means that for any given value of t, the value of y will be the sine of π multiplied by t, which will correspond to a certain distance from the equilibrium position. As the oscillation has a frequency of 1 cycle per second, the value of t will increase linearly, and the value of y will oscillate between a maximum and a minimum value. As the distance between the maximum and minimum points of the oscillation is 3 centimeters, the maximum and minimum values of y will be 3 when t is an integer multiple of π. Therefore, the function y = 3sin(πt) can be used to accurately model the oscillation.
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Verify the identity. 2 sec? y - 2 cot? = cot(" - y) = 2 - 2 cot'( % - y) = 2 (sec?y- 2 sec? y - 2 2 ) X = 2 Need Help? Read it Watch It
Answers
2(cot2 y + tan2 y) = 2(1) Verified
Verify the identity:
2 sec2 y - 2 cot2 y = cot(2y) - 2 cot(2y) = 2 - 2 sec(2y)
To prove the identity, start by applying the identity:
cot2 y = 1 - tan2 y
Substitute this in the left side of the equation:
2 sec2 y - 2(1 - tan2 y) = 2 sec2 y - 2 + 2 tan2 y
Simplify the equation by factoring out a 2 from the right side:
2 sec2 y - 2 + 2 tan2 y = 2(sec2 y - 1 + tan2 y)
Next, apply the identity:
sec2 y - 1 = cot2 y
Substitute this in the equation and simplify:
2(sec2 y - 1 + tan2 y) = 2(cot2 y + tan2 y)
Finally, apply the identity:
cot2 y + tan2 y = 1
Substitute this in the equation and simplify:
2(cot2 y + tan2 y) = 2(1)
The identity is thus verified.
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Given a circle centered at point O and any three points A, B, and C on the circle, show that the angle BAC is half the corresponding central angle BOC. What does this say about the angle BAC if we keep points B and C fixed, but allow the point A to move around the circle? What if B and C are endpoints of the diameter of the circle?
Answers
The angle BAC will always be a right angle (90 degrees).
Given a circle centered at point O and any three points A, B, and C on the circle, the angle BAC will always be half of the corresponding central angle BOC.
If we keep points B and C fixed and allow point A to move around the circle,
then the angle BAC will stay the same.
If points B and C are endpoints of the diameter of the circle, then the angle BAC will always be a right angle (90 degrees).
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Someone help me solve this!
I’ll mark brainiest!
Answers
Answer: 10,210$
Step-by-step explanation:
Its simple really. The formula is 800 x 2.65 x 1. 10,210.
Use this next time, good luck :)
Answer: $879.50
Step-by-step explanation:
The simple interest formula is I = prt
Plug values in:
(Percent move decimal over 2 and time has to be in years, so 3 years and 9 months is 3.75 years)
I = (800)(0.0265)(3.75)
I = (21.2)(3.75)
I = 79.5
Add the interest to the principle:
800 + 79.5 = $879.50
Hope this helps!
18. Determine the exact value of the product: 3 sin(37.5°) cos( 7.5°) 19. Determine the exact value of the sum: cos (phi/12) - cos (5phi/12)
Answers
18. The exact value of the product 3 sin(37.5°) cos( 7.5°) can be determined using the double angle formula for sine:
sin(2x) = 2 sin(x) cos(x)
Substituting x = 22.5° into the formula gives:
sin(45°) = 2 sin(22.5°) cos(22.5°)
Dividing both sides by 2 gives:
sin(45°)/2 = sin(22.5°) cos(22.5°)
Substituting the given values into the equation gives:
3 sin(37.5°) cos( 7.5°) = 3 (sin(45°)/2) (cos(45°)/2)
Simplifying gives:
3 sin(37.5°) cos( 7.5°) = 3/4
Therefore, the exact value of the product is 3/4.
19. The exact value of the sum cos (phi/12) - cos (5phi/12) can be determined using the sum-to-product formula for cosine:
cos(x) - cos(y) = -2 sin((x+y)/2) sin((y-x)/2)
Substituting x = phi/12 and y = 5phi/12 into the formula gives:
cos (phi/12) - cos (5phi/12) = -2 sin((phi/12 + 5phi/12)/2) sin((5phi/12 - phi/12)/2)
Simplifying gives:
cos (phi/12) - cos (5phi/12) = -2 sin(3phi/12) sin(2phi/12)
Therefore, the exact value of the sum is -2 sin(3phi/12) sin(2phi/12).
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Answer:
Step-by-step explanation:
first you find the numbers that go with the numbers like base times height
times length then you add it all up read this two times to understand