The value of cos A is √(1 + x²)/ (1 - x²) /√1 + x
Trigonometric ratios
It is important to note that
sin A = opposite/ hypotenuse
cos A = adjacent/ hypotenuse
Then,
opposite = [tex]\sqrt{1} - x[/tex]
Hypotenuse = [tex]\sqrt{1} + x[/tex]
Let's find the adjacent side using the Pythagorean theroem
[tex](\sqrt{1} + x)^2 = (\sqrt{1 -x } )^2 + x^2[/tex]
[tex]1 + x^2 = 1 - x^2 + x^2[/tex]
[tex]x = \sqrt{\frac{1 + x^2}{1 -x^2} }[/tex]
cos A = x/hypotenuse
[tex]cos A = \frac{\sqrt{\frac{1+x^2}{1 -x^2} } }{\sqrt{1} +x}[/tex]
cos A = √(1 + x²)/ (1 - x²) /√1 + x
Thus, the value of cos A is √(1 + x²)/ (1 - x²) /√1 + x
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Prove the cofunction identity using the addition and subtraction formulas. sec 2 − u = csc(u) use a reciprocal identity, then apply a subtraction formula to simplify
Proved that the cofunction identity sec([tex]\frac{\pi }{2}[/tex]) - u = csc(u)
We have to prove that the cofunction identity using the addition and subtraction formulas.
sec([tex]\frac{\pi }{2}[/tex]) - u = csc(u)
We can prove this by using the identities given below:
[tex]sec(u)=\frac{1}{cos(u)}[/tex]
[tex]\frac{1}{sin(u)} =csc(u)[/tex]
cos(a-b) = cos a cos b + sin a sin b
Now the explanation,
[tex]sec(\frac{\pi }{2} -u) = csc(u)[/tex]
By using trignometric identities,
[tex]cos(u)=\frac{1}{sec(u)}[/tex] ∴[tex]sec(u)=\frac{1}{cos(u)}[/tex]
So,
[tex]\frac{1}{cos(\frac{\pi }{2}-u) } =csc(u)[/tex]
By substituting the given identities we get,
[tex]\frac{1}{cos(\frac{\pi }{2})cos(u)+sin(\frac{\pi }{2} )sin(u) }[/tex]
= [tex]\frac{1}{0.cos(u)+(1).sin(u)}[/tex]
=[tex]\frac{1}{sin(u)}[/tex]
= csc(u)
csc(u) = csc(u)
Here we proved that the cofunction identity sec([tex]\frac{\pi }{2}[/tex]-u) = csc(u)
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What is the simplest form of this expression? (x − 4)(x^2 + 3x − 5)
Answer:[tex]x^3-x^2-17x+20[/tex]
Step-by-step explanation:
How long can it take for the body to process the alcohol in one standard drink (0. 6 ounces)? 2 hours 1. 5 hours 1 hour 30 minutes
Answer:
1 hour
Step-by-step explanation:
What is the volume of the box pictured below?
fractions 3 and 1 over 10 cubic feet
fraction 3 and 2 over 5 cubic feet
fraction 6 and 5 over 8 cubic feet
fraction 8 and 3 over 4 cubic feet
Sami cuts out a rectangle that has a perimeter of 48 inches and a length of 13 inches.
Answer:
Width is 11 inches
Step-by-step explanation:
I am not sure what the question is. I think you might be looking for the width length. The perimeter is the distance around a rectangle. If the whole distance around is 48. We have 2 lengths and 2 widths. They tell us that the length is 13. We have two lengths so the lengths add up to 26. We can subtract that from 48 and that leaves us with 22 (48-26) This is the total for the 2 widths. Since the 2 widths are the same length we divide that number by 2 to get 11.
11 + 11+ 13 + 13 = 48
(FIRST PERSON TO ANSWER GETS BRAINLIEST!!!) A student earned $2500.75 at his summer job making $12.50 per hour. Let h represent the number of hours the student worked. Which of the following equations could be used to determine how many hours the student worked at his summer job? (answer choices and question is below)
Answer:
[tex]12.50 \space\ h = 2500.75[/tex]
Step-by-step explanation:
We know from the question that the student earned $12.50 per hour.
Using this information, we can say that if the student worked for h hours, they would make a total of 12.50 × h dollars.
We also know that the total money they earned is $2500.75.
∴ Therefore, we can set up the following equation:
[tex]\boxed {12.50 \times h = 2500.75}[/tex]
From here, if we want to, we can find the number of hours worked by simply making h the subject of the equation and evaluating:
h = [tex]\frac{2500.75}{12.50}[/tex]
= 200.6 hours
Answer: 12.50h = 2500.75
Step-by-step explanation:
We know from the question that the student earned $12.50 per hour.
Using this information, we can say that if the student worked for h hours, they would make a total of 12.50 × h dollars.
We also know that the total money they earned is $2500.75.
A serving of fish contains 50 g of protein and 4. 0 g of fat. How many kcal are in the serving report your answer to 2 significant figures
2 x 10² kcal are in the serving report your answer to 2 significant figures.
According to the question
A serving of fish contains 50 g of protein and 4. 0 g of fat.
i.e. content of protein = 50 g
Content of fat = 4 g
kcal are in the serving report your answer to 2 significant figures:
As the serving of fish contains 50g of protein that is 4.0kcal/g
Calories in 50 g protein = (Content of protein) × (caloric value in protein)
50g × (4.0kcal/g) = 200kcal
That means the kcal of the serving is 200kcal
In 2 significant figures: 2 x 10² kcal
Hence,
2 x 10² kcal are in the serving report your answer to 2 significant figures.
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Each of ten tickets is marked with a different number from 1 to 10 and put in a box. if you draw a ticket from the box, what is the probability that you will draw a number greater than 3?
Answer:
7/10
Step-by-step explanation:
take 3, 2, 1 from the equation and your left with 7 numbers. Add those together you get 10. 7/10 is the probability that you will draw a number greater than 3
Omar recorded the number of hours he worked each week for a year. below is a random sample that he took from his data. 13, 17, 9, 21 what is the standard deviation for the data? standard deviation: s = startroot startfraction (x 1 minus x overbar) squared (x 2 minus x overbar) squared ellipsis (x n minus x overbar) squared over n minus 1 endfraction endroot.
The standard deviation exists as the positive square root of the variance.
So, the standard deviation = 4.47.
How to estimate the standard deviation?Given data set: 13 17 9 21
To calculate the mean of the data.
We know that mean exists as the average of the data values and exists estimated as:
Mean [tex]$=\frac{13+17+9+21}{4} \\[/tex]
Mean [tex]$=\frac{60}{4} \\[/tex]
Mean = 15
To find the difference of each data point from the mean as:
Deviation:
13 - 15 = -2
17 - 15 = 2
9 - 15 = -6
21 - 15 = 6
Now we have to square the above deviations we obtain:
4, 4, 36, 36
To estimate the variance of the above sets:
variance [tex]$=\frac{4+4+36+36}{4}$[/tex]
Variance [tex]$=\frac{80}{4}$[/tex]
Variance = 20
The standard deviation exists as the positive square root of the variance. so, the standard deviation [tex]$=\sqrt{20 }=4.47$[/tex].
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Answer:
4.4
Step-by-step explanation:
The answer above is correct.
HELPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
The answer is 314
Step-by-step explanation:
You need to do
3.14(pie) times the radius times the height divided by 3
Answer:
C. 314 [tex]in^{3}[/tex]
Step-by-step explanation:
The volume of a cone is: 1/3[tex]\pi[/tex][tex]r^{2}[/tex]h'
1/3 x 3.14 x [tex]5^{2}[/tex] x 12
1/3 x 3.14 x 25 x 12
1/3 x 3.14 x 300
100 x 3.14
V = 314
A parabola can be represented by the equation y2 = 12x. which equation represents the directrix?
The equation of the directrix is x = -3
What is Parabola?A mirror-symmetrical, roughly U-shaped plane curve known as a parabola. It corresponds to a number of mathematical models that appear to be superficially dissimilar but yet all define the exact same curves. A point and a line are one way to describe a parabola.
According to the given information:Given the general equation of a parabola expressed as
(y-y0)² = 4a(x-x0) ... 1
Equation of the directrix will be expressed as x = x0 - a
From the equation given;
y² = 12x ... 2
Comparing 1 and 2;
x - x0 = x
-x0 = x - x
-x0 = 0
x0 = 0
Similarly;
y-y0 = y
-y0 = y - y
-y0 = 0
y0 = 0
Also;
4a = 12
a = 12/4
a = 3
Substituting x0 =0, y0 = 0 and a = 3 into the equation of the directrix above, we will have;
x = x0 - a
x = 0 - 3
x = -3
Hence,
the equation of the directrix is x = -3
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A convenience store sells two brands of orange juice Brand A contains 11 fluid once and costs
$2.31. Brand B contains 15 fluid ounces and costs $2.70.
What is the difference in cost, in dollars, per fluid ounce between the two brands of juice
Answer:
$0.03
Step-by-step explanation:
2.31/11 =.21
2.70/15 =.18
.21-.18 = .03
Find the values of the unknown angles marked with letters.
a=
b=
c=
Answer:
a = 97° , b = c = 146°
Step-by-step explanation:
a and 83° are same- side interior angles and sum to 180°
a + 83° = 180° ( subtract 83° from both sides )
a = 97°
34° and b are same- side interior angles and sum to 180°
b + 34° = 180° ( subtract 34° from both sides )
b = 146°
b and c are corresponding angles and are congruent , so
c = b = 146°
Answer:
< a = 97 degrees.
< b = 146 degrees.
< c = 146 degrees.
Step-by-step explanation:
We have 2 lines crossing 2 parallel lines.
Internal angles between the 2 parallel lines add up to 180 degrees, so
34 + <b = 180
<b = 180 - 34 = 146 degrees
Also
<a + 83 = 180 degrees (also internal angles)
---> <a = 97 degrees
< c and < b are corresponding angles so are congruent, therefore
<c = < b = 146 degrees.
Instructions: Find the missing side. Round your answer to the
nearest tenth.
x=
30
38⁰
X
The value of the missing side x is 38.40 units given the triangle is a right angled triangle with angle 38° and side opposite to the angle is 30 units. This can be obtained by using trigonometric ratios.
Find the value of the missing side:Trigonometric identities,
If in a right triangle ΔABC where A is the right angle
sin A = [tex]\frac{opposite\ side}{hypotenuse}[/tex]cos A =[tex]\frac{adjacent\ side}{hypotenuse}[/tex]tan A = [tex]\frac{opposite\ side}{adjacent\ side}[/tex]
In the question,
x is the adjacent side of the angle 38° and 30 units is the opposite side.
The ratio with opposite side and adjacent side is tan A
Therefore,
⇒ tan 38° = [tex]\frac{opposite\ side}{adjacent\ side}[/tex]
⇒ tan 38° = 30/x
⇒ x = 30/tan 38°
∵ tan 38° = 0.781285627
⇒ x = 30/0.781285627
⇒ x = 38.398249
⇒ x = 38.40
Hence the value of the missing side x is 38.40 units given the triangle is a right angled triangle with angle 38° and side opposite to the angle is 30 units.
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An experiment consists of drawing 1 card from a standard 52 card deck. let e be the event that the card drawn is a red card. find p(e)
The probability of drawing a red card from a standard deck of cards is 1/2.
Given that there is a standard deck of cards.
We are required to find the probability of drawing a rd card from a standard deck of cards.
Probability is the calculation of chance of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative.
Probability=Number of items/Total items.
Total number of cards=52
Number of red cards =26
Number of black cards=26
Probability of drawing a red card =Number of red cards/ Total cards.
=26/52
=1/2
Hence the probability of drawing a red card from a standard deck of cards is 1/2.
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i dont know how to do this could someone help
Answer:
17, 5
Step-by-step explanation:
Let the width be x
width = x
length = x + 12
length x width = x(x + 12)
length x width = x² + 12x
x² + 12x = 85
x² + 12x - 85 = 0
Now it is just a quadratic:
The 2 numbers we need are 17 and -5
(x + 17)(x - 5) = 0
x = -17 or x = 5.
Since width and length cannot be negative, x must equal 5.
Width = 5
length = 17
The answer is 17, 5.
We are given two things :
Length exceeds width by 12 inchesArea = 85 square inchesWe can represent the length and width as x + 12 and x respectively.
Now, the formula for the area of a rectangle is :
Area = Length x width
Now, let's substitute the values for length and width in the formula along with the area.
(x + 12)(x) = 85x² + 12x = 85x² + 12x - 85 = 0We now have a quadratic equation, which can either be solved by splitting the middle term, or by using the quadratic formula. For convenience purposes, we'll go with the first one.
x² + 17x - 5x - 85 = 0x (x + 17) - 5 (x + 17) = 0(x + 17)(x - 5) = 0x = 17, 5Three friends decide to go out to eat, and then go shopping. if there are 5 local restaurants and 4 good stores for shopping, how many possibilities are there for their big night out
Using the Fundamental Counting Theorem, there are 20 possibilities for their big night out.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For this problem, we have that:
There are 5 restaurants, hence [tex]n_1 = 5[/tex].There are 4 stores, hence [tex]n_2 = 4[/tex].The number of possibilities is given by:
N = 5 x 4 = 20.
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An airplane travels 1350 miles in 5 hours, going against the wind. The return trip is with the wind, and takes only 3.75 hours. Find the rate of the airplane with no wind. Find the rate of the wind.
Solving a system of equations we can see that:
The airplane rate is 315 mi/hThe wind rate is 45 mi/h.How to find the rate of the airplane?Let's define:
A = rate of the airplane.W = rate of the wind.When the airplane travels against the wind, the total speed is:
(A - W)
In this way, we know that the airplane travels 1350 miles in 5 hours, then:
(A - W) = 1350mi/5h
When the airplane travels with the wind, it takes 3.75 hours to travel the same distance, then:
(A + W) = 1350mi/3.75h
We have now a system of equations:
(A - W) = 1350mi/5h
(A + W) = 1350mi/3.75h
If we isolate A on the first equation, we get:
A = 270mi/h + W
Replacing that in the other equation we get:
270mi/h + W + W = 360 mi/h
Solving for W we get:
2*W = 360mi/h - 270mi/h = 90mi/h
W = 90mi/h = 45mi/h
And the airplane rate is:
A = 270mi/h + W = 270mi/h + 45mi/h = 315 mi/h
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Which statement is most likely to be true for this distribution?
Answer:
A
Step-by-step explanation:
the means is less than the median
Pls answer both the question its urgent
Answer:
not sure but I think it is this
When graphing the inequality y ≤ 2x − 4, the boundary line needs to be graphed first. Which graph correctly shows the boundary line? A. A linear inequalities graph of dotted boundary line intersects X-axis at the unit (2, 0) and Y-axis at the unit (0, minus 4) B. A linear graph of solid line intercepts X-axis at the unit (2, 0) and Y-axis at the unit (0, minus 4) C. A linear inequalities graph of dotted boundary line intercepts at the X-axis (0.5, 0) and Y-axis (0, 2) D. A linear graph of a solid boundary line intersects X-axis at the unit (0.5, 0) and Y-axis at the unit (0, 2)
The correct graph is in the attached image.
Answer:
B. A linear graph of solid line intercepts X-axis at the point (2, 0) and Y-axis at the point (0, -4)
Step-by-step explanation:
The boundary line of an inequality is graphed as though the expression were an equality. The nature of the line used will depend on the nature of the inequality.
Form of the lineWhen the inequality includes the "or equal to" case (≤ or ≥), the boundary line is part of the solution set. It is drawn as a solid line.
When the inequality excludes the "or equal to" case (< or >), the boundary line is not part of the solution set. It is drawn as a dotted or dashed line.
The given inequality
y ≤ 2x -4
includes the "or equal to" case, so the boundary line is solid.
Y-interceptThe equation of the boundary line is written in slope-intercept form:
y = mx +b . . . . . . . line with slope m and y-intercept b
y = 2x -4 . . . . . . . boundary line with slope 2 and y-intercept -4.
This tells you that the boundary line intercepts the y-axis at the point (0, -4).
The population of a town in 2007 is 113, 505
and is increasing at a rate of 1.2% per year.
What will the population be in 2012?
What number will you fill in for a to solve the
equation?
(Hint: For this one, how many years
after 2007 is 2012?
from 2007 to 2012 is only 5 years, so we can see this as a compound interest with a rate of 1.2% per annum for 5 years, so
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$113505\\ r=rate\to 1.2\%\to \frac{1.2}{100}\dotfill &0.012\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A=113505\left(1+\frac{0.012}{1}\right)^{1\cdot 5}\implies A=113505(1.012)^5\implies A\approx 120481[/tex]
Sloane kicked a soccer ball off the ground at a speed of 48 feet per second. The height of the ball can be represented by the function H(t) = −16t2 + 48t, where t is the time in seconds. How many seconds did the ball travel before returning the ground?
If the speed of the ball after kicking is 48 feet per second then the ball will return on the ground after 3 seconds.
Given that the speed of the ball after kicking is 48 feet per second and the function that represents the height of the ball is [tex]-16t^{2} +48t[/tex].
We are required to find the time that the ball took to travel before returning the ground.
We know that speed is the distance a thing covers in a particular time period.
The height of the ball after t seconds is as follows:
h(t)=[tex]-16t^{2} +48t[/tex]
It is at ground at the instants of t.
Hence,
[tex]-16t^{2} +48t[/tex]=0
-16t(t-3)=0
We want value of t different of 0, hence :
t-3=0
t=3.
Hence if the speed of the ball after kicking is 48 feet per second then the ball will return on the ground after 3 seconds.
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Answer:
B. t=3
Step-by-step explanation:
i took the test and got it right
My street hockey team plays three games each week. My team lost all 12 games in the first four weeks. Then, my team won two games and lost one game in the fifth week, bringing our record to 2 wins and 13 losses. Each week after that, my team won two games and lost one game. My team first wins at least 50% of all its games by the end of the first n weeks. What is n?
Using proportions, it is found that the value of n is of [tex]n \geq 11[/tex].
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
On the first 15 games, the team wins 2 games and losses 13. Then, in each week, the team plays 3 games, winning 2. Then:
After n weeks, the team will have won 2 + 2n games.After n weeks, the team will have played 15 + 3n games.The proportion of wins is given as follows:
[tex]\frac{2 + 2n}{15 + 3n}[/tex]
The proportion is of at least 50%, hence:
[tex]\frac{2 + 2n}{15 + 3n} \geq 0.5[/tex]
We solve the inequality for n, similarly to how we would solve an equality, applying cross multiplication. Then:
[tex]2 + 2n \geq 7.5 + 1.5n[/tex]
[tex]0.5n \geq 5.5[/tex]
[tex]n \geq \frac{5.5}{0.5}[/tex]
[tex]n \geq 11[/tex]
The value of n is of [tex]n \geq 11[/tex].
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Choose the expression that represents a cubic expression. 2x 11 −3x2 − 2x 11 4x3 − 3x2 − 2x 11 5x4 4x3 − 3x2 − 2x 11
(C) [tex]8x^{3} -7x^{2} -6x+5[/tex] represents a cubic expression.
What is a cubic expression?A cubic polynomial has the generic form [tex]p(x): ax^{3} +bx^{2} +cx+d[/tex], a 0, where a, b, and c are coefficients and d is the constant, all of which are real integers. A cubic equation is one that involves a cubic polynomial.To determine which expression represents a cubic expression:
[tex]8x^{3} -7x^{2} -6x+5[/tex] is a cubic expression.The variable is x. [tex]8x^{3} -7x^{2} -6x+5[/tex] : The variable x has the highest power as 3. [tex]8x^{3} -7x^{2} -6x+5[/tex] is a polynomial.[tex]-7x+4[/tex] is a linear expression because the highest power of the variable x is 1.[tex]7x^{2} -5x+6[/tex] is a quadratic expression because the highest power of the variable x is 2.[tex]9x^{4} +8x^{3} -6x^{2} -2x+11[/tex] is a polynomial with the highest power of the variable being 4.Therefore, (C) [tex]8x^{3} -7x^{2} -6x+5[/tex] represents a cubic expression.
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The complete question is given below:
Choose the expression that represents a cubic expression.
(A) −7x + 14
(B) 7x2 − 5x + 6
(C) 8x3 − 7x2 − 6x + 5
(D) 9x4 + 8x3 − 6x2 − 2x + 11
he cashier service time at the local branch of the Rivertown bank has an exponential distribution with a mean of 2.5 minutes. What is the probability that the service time: Exceeds 3 minutes
The probability that the service time will be more than three minutes is 0.3012.
Given that the average wait time at the Rivertown bank's neighborhood branch is 2.5 minutes and has an exponential distribution,
The time it takes to succeed in a continuous sequence of independent trials is described by the exponential distribution, which is a continuous probability distribution.
At the River Town Bank's neighborhood branch, the random variable X service time has an exponential distribution with a mean value of 2.5 minutes. Therefore,
[tex]f(x)=\left\{\begin{array}{ll}\theta e^{-\theta x},& \theta \geq 0,0\leq x\leq \infty\\0&\text{otherwise}\end{array}[/tex]
E(x)=1/θ
θ=1/2.5
θ=0.4
The probability that the service time will be longer than three minutes:
[tex]\begin{aligned}P(X > 3)&=1-P(X\leq 3)\\ &=1-(1-e^{-0.4\times 3}\\ &=e^{-1.2}\\ &=0.3012\end[/tex]
Since the service duration has an exponential distribution and a mean of 2.5 minutes, the needed chance that it will exceed 3 minutes is 0.3012.
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How many of the first 1000 positive integers contain only 0s and 1s when
written in base 3?
There are 105 numbers in the the first 1000 positive integers contain only 0s and 1s when written in base 3
How to determine the count of the numbers?The number base is given as:
Base 3
To determine the count of numbers, we make use of the following Python program
count = 0
for n in range(1,1001):
digits = []
while n:
digits.append(int(n % 3))
n //= 3
myStr = ''.join(map(str,digits[::-1]))
if(myStr.count('0')+myStr.count('1') == len(myStr)):
count+=1
print(count)
The above program counts the numbers in the the first 1000 positive integers contain only 0s and 1s when written in base 3
The output of the program is 105
Hence, there are 105 numbers in the the first 1000 positive integers contain only 0s and 1s when written in base 3
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If B = { p : p is a factor of 12 } list the elements of this set and find n ( B )
Answer:
B={1,2,3,4,6and12}
n (B) =6
Step-by-step explanation:
Greetings !Factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.
Hope it helps!
i need help please? thank you :)
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {z}^{2} - 14z + 48 }{ {z}^{2} + 6x - 27} ÷ \cfrac{z -8}{z-3} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {z}^{2} - 8z - 6z+ 48 }{ {z}^{2} + 9z- 3z- 27} ÷ \cfrac{z -8}{z-3} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {z(}^{} z- 8) - 6(z - 8) }{ {z}^{} (z+ 9)- 3(z + 9)} ÷ \cfrac{z -8}{z-3} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {(}^{} z- 8) (z - 6) }{ {}^{} (z+ 9)(z - 3)} ÷ \cfrac{z -8}{z-3} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ (z - 6) }{ {}^{} (z+ 9)}[/tex]
Break into two parts and simplify
[tex]\\ \rm\dashrightarrow \dfrac{z^2-14z+48}{z^2+6z-27}[/tex]
[tex]\\ \rm\dashrightarrow \dfrac{z^2-8z-6z+48}{z^2+9z-3z-27}[/tex]
[tex]\\ \rm\dashrightarrow \dfrac{(z-8)(z-6)}{(z+9)(z-3)}[/tex]
Now divide by the denominator
[tex]\\ \rm\dashrightarrow \dfrac{(z-8)(z-6)(z-3)}{(z+9)(z-3)(z-8)}[/tex]
[tex]\\ \rm\dashrightarrow \dfrac{z-6}{z+9}[/tex]
The height of the pyramid in the diagram is three times the radius of the cone. The base area of the pyramid is the same as the base area of the
cone. What is the expression for the volume of the pyramid in terms of the radius of the cone?
OA V=²²
OB. V-2²
V=
OC V=2²2²
OD. V-²³
OE V-3²³
base area = B
base area B
The expression for the volume of the pyramid in terms of the radius of the cone is [tex]V=\pi r^{3}[/tex].
What is the pyramid?A pyramid is a structure that substantially resembles a pyramid in the geometric sense when its exterior surfaces are triangular and converge to a single step at the summit. A pyramid foundation might be triangular, quadrilateral, or any other type of polygon. A pyramid therefore has a minimum of three exterior triangular surfaces.The numerous forms of pyramids are categorized based on the base's shape. Let's now go over each sort of pyramid shape individually.It is thought that one of many ramp possibilities was made to drag the stones to the top as they were built higher after being transported across the desert.The expression for the volume of the pyramid in terms of the radius of the cone:
B= base area of the cone.
[tex]V=\pi r^{2}[/tex]
The volume of the Pyramid,
[tex]V=\frac{1}{3} *B*height[/tex]
[tex]$\Rightarrow V=\frac{1}{3} \times \pi r^{2} \times 3 \gamma$[/tex]
[tex]V=\pi r^{3}[/tex]
The expression for the volume of the pyramid in terms of the radius of the cone is [tex]V=\pi r^{3}[/tex]
To learn more about Pyramid, refer to:
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