Determine if a triangle with side lengths 8, 14, and 15 is acute, right, or obtuse
Answers
Answer:
Acute
Step-by-step explanation:
The Converse of the Pythagorean Theorem states that:
If [tex]a^2+b^2 > c^2[/tex] then the triangle is acute.If [tex]a^2+b^2 < c^2[/tex] then the triangle is obtuse.If [tex]a^2+b^2 = c^2[/tex] then the triangle is right.The side lengths 8, 14, and 15 are given. We can assume the hypotenuse (or c) is the longest side length, so it is 15.
c = 15It doesn't matter which order of the numbers are plugged in for a and b, so a and b will be 8 and 14.
a = 8b = 14Now we have to add [tex]a^2[/tex] and [tex]b^2[/tex] to see if the sum is greater than, less than, or equal to 15 (c).
[tex]a^2 + b^2[/tex][tex]8^2 + 14^2[/tex]Calculate the rest of the problem.
[tex]8^2=64 \newline 14^2=196[/tex][tex]64+196=260[/tex]We have to find what [tex]15^2[/tex] is before we can make a decision using the Converse of the Pythagorean Theorem.
[tex]15^2=225[/tex]260 ([tex]a^2+b^2[/tex]) is greater than 225 ([tex]c^2[/tex]). This means that the triangle is acute because [tex]a^2+b^2>c^2[/tex].
Related Questions
Compare the functions below: Which function has the smallest minimum?
A. F(x)
B. G(x)
C. H(x)
D. All three functions have the same minimum value
Answers
Answer:
D. All three functions have the same minimum value
Step-by-step explanation:
f(x) = -3 sin (x-pi) +2
Sin has a minimum value of -1, but since it is multiplied by a negative, we want its maximum value
sin has a maximum of 1
f (min) = -3(1) +2 = -1
g(x) has a minimum at x =3
g(minimum) = -1
h(x) = (x+7)^2 -1
The smallest a squared value can be is zero
= 0 -1
h(min) =-1
Answer:
D. All three functions have the same minimum value
Step-by-step explanation:
Just did this :)
Courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams of part thereof. What could be the weight in grams of a package for which the charge is $1.55?
Answers
Answer:
1050 g < weight ≤ 1150 g
Step-by-step explanation:
Let w represent the weight of the package in grams. The the number of 100-gram increments after the first 250 grams is given by ...
⌈(w-250)/100⌉ . . . . . . . where ⌈ ⌉ signifies the ceiling function
and the charges for a package exceeding 250 grams will be ...
0.65 + 0.10⌈(w -250)/100⌉ = 1.55
0.10⌈(w -250)/100⌉ = 0.90 . . . . . . . . subtract 0.65
⌈(w -250)/100⌉ = 9 . . . . . . . . . . . . . . . divide by 0.10
8 < (w-250)/100 ≤ 9 . . . . . . . . . . . . . . meaning of ceiling function
800 < w -250 ≤ 900 . . . . . . . . . . . . . multiply by 100
1050 < w ≤ 1150 . . . . . . . . . . . . . . . . . add 250
The weight in grams could be greater than 1050 and at most 1150 for a charge of $1.55.
Ntoine and Tess have a disagreement over how to compute a 15% gratuity on $46.00. Tess says, "It is easy to find 10% of 46 by moving the decimal point one place to the left to get $4.60. Do that twice. Then add the two amounts to get $4.60 + $4.60 = $9.20 for the 15% gratuity." How should Antoine respond to Tess's method?
Answers
Answer:
Ntoine and Tess have a disagreement over how to compute a 15% gratuity on $46.00.
This in real becomes :
[tex]0.15\times46=6.90[/tex] dollars
But, Tess says, "It is easy to find 10% of 46 by moving the decimal point one place to the left to get $4.60. Do that twice. Then add the two amounts to get $4.60 + $4.60 = $9.20
So, Tess is wrong. Rather she should have done 10% of $46 giving $4.6 and then half of 4.6 that is 2.3 dollars. Getting a total of [tex]4.6+2.3=6.9[/tex] dollars which is the real amount.
Answer:
Ntoine and Tess have a disagreement over how to compute a 15% gratuity on $46.00.
This in real becomes :
dollars
But, Tess says, "It is easy to find 10% of 46 by moving the decimal point one place to the left to get $4.60. Do that twice. Then add the two amounts to get $4.60 + $4.60 = $9.20
So, Tess is wrong. Rather she should have done 10% of $46 giving $4.6 and then half of 4.6 that is 2.3 dollars. Getting a total of dollars which is the real amount.
Step-by-step explanation:
trust me
What is the determinant of
15
18
154
Answers
Answer:
The determinant is 15.
Step-by-step explanation:
You need to calculate the determinant of the given matrix.
1. Subtract column 3 multiplied by 3 from column 1 (C1=C1−(3)C3):
[tex]\left[\begin{array}{ccc}-25&-23&9\\0&3&1\\-5&5&3\end{array}\right][/tex]
2. Subtract column 3 multiplied by 3 from column 2 (C2=C2−(3)C3):
[tex]\left[\begin{array}{ccc}-25&-23&9\\0&0&1\\-5&-4&3\end{array}\right][/tex]
3. Expand along the row 2: (See attached picture).
We get that the answer is 15. The determinant is 15.
Answer:
The answer is 15
Step-by-step explanation:
What is the discontinuity of the function f(x) = the quantity of x squared minus 4 x minus 12, all over x plus 2?
A. (−6, 0)
B. (6, 0)
C. (−2, −8)
D. (2, −4)
Answers
Answer:
C. (-2, -8)
Step-by-step explanation:
The function reduces to ...
f(x) = (x^2 -4x -12)/(x +2) = (x -6)(x +2)/(x +2) = x -6 . . . . x ≠ -2
At x=-2, the function would evaluate to ...
f(-2) = -2 -6 = -8
but cannot, because there is a hole in the function definition at that point.
There is a hole at (-2, -8).
HELPPPP!!!!
Which model does the graph represent?
Answers
Answer:
C. y = Ae^(-(x-b)²/c)
Step-by-step explanation:
A is a model of exponential growth.
B is a model of exponential decay.
D is a "logistic function" model of growth in an environment of limited resources. It produces an "S" shaped curve.
The given bell-shaped curve can be described by the function of C, which decays either side of an axis of symmetry.
The model that the graph represent is C that is y = Ae^(-(x-b)²/c).
A is an exponential growth model.
B is an exponential decay model.
D is a "logistic function" model of growth in a resource-constrained setting. It results in a "S" shaped curve.
The function of C, which decays either side of an axis of symmetry, can be used to describe the provided bell-shaped curve.
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Brandy watched a beetle and a spider on the sidewalk. The beetle crawled 2/5 of a yard and the spider crawled 3/20 of a yard. How much farther did the beetle crawl than the spider?
Answers
Answer:
¼ yd
Step-by-step explanation:
2/5 - 3/20
1. Find the lowest common denominator of the two fractions.
The LCD of 5 and 20 is 20.
2. Give the fractions the same LCD
2/5 - 3/20 = 8/20 - 3/20
3. Subtract the numerators
Keep the same denominator.
8/20 - 3/20 = 5/20
4. Simplify the fraction
5/20 = ¼
The beetle crawled ¼ yd further than the spider.
A research group wants to find the opinions’ of city residents on the construction of a new downtown parking garage. What is the population of the survey
downtown shoppers
downtown visitors
downtown workers
city residents
Answers
Answer:
downtown workers
Step-by-step explanation:
The research group should do the survey with downtown workers in order to find the opinions for the construction of a new downtown parking garage in downtown. Since the workers need to commute to downtown for work by various modes such as buses, private vehicles, bicycles, taxis, share vehicles, etc., therefore the the research group will get maximum useful information from the downtown workers for the construction of a new parking garage.
Thus, option "downtown workers" is correct.
The population of the survey would be the city residents.
Explanation:The population of the survey would be the city residents. The research group wants to find the opinions of the city residents on the construction of a new downtown parking garage. While downtown shoppers, visitors, and workers could provide valuable insights, the opinions of the city residents would be the most relevant and encompassing for understanding the overall impact of the new downtown parking garage.
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Hello, this was one of the questions in a test and above the answer choices, I couldn't find what I found to be the result. I would appreciate it if you help me.
Answers
[tex](5ab)^{\tfrac{3}{2}}=\sqrt{(5ab)^3}=\sqrt{125a^2b^3}[/tex]
f(x)=8−4x−x^3
g(x)=x^2+7x−9
Find f(x)+g(x).
Select one:
a. x^3+x^2+3x−1
b. −x^3+x+3x−1
c. −x^3+x^2+11x−9
d. 8x^2+3x−9x^3
Answers
Answer:
its answer is -x^3+x^2+3x-1
Step-by-step explanation:
f(x) +g(x)
= 8-4x-x^3+x^2+7x-9
= -x^3+x^2+3x-1
Answer:
The value of f(x)+g(x) is [tex]-x^3+x^2+3x-1[/tex].
Step-by-step explanation:
The given functions are
[tex]f(x)=8-4x-x^3[/tex]
[tex]g(x)=x^2+7x-9[/tex]
We have to find the value of f(x)+g(x).
[tex]f(x)+g(x)=(8-4x-x^3)+(x^2+7x-9)[/tex]
[tex]f(x)+g(x)=8-4x-x^3+x^2+7x-9[/tex]
On combining like terms we get
[tex]f(x)+g(x)=-x^3+x^2+(-4x+7x)+(8-9)[/tex]
On simplification we get
[tex]f(x)+g(x)=-x^3+x^2+3x-1[/tex]
Therefore the value of f(x)+g(x) is [tex]-x^3+x^2+3x-1[/tex].
Consider the quadratic function f(x)=8x2−7x+6. What is the constant of the function?
−7
6
7
8
Answers
Answer:
6
Step-by-step explanation:
The 8 is the leading coefficient, the -7 is the linear term, and the 6 is the constant.
Answer:
the constant term is 6.
Second option is correct.
Step-by-step explanation:
The quadratic function is [tex]f(x)=8x^2-7x+6[/tex]
The general form of a quadratic function is [tex]y=ax^2+bx+c[/tex]
Here c is the constant term and a can't be zero.
On comparing the given equation with the general form, we get
a = 8
b = -7
c = 6
Therefore, the constant term is 6.
Second option is correct.
A simple random sample of size nequals=200200 drivers were asked if they drive a car manufactured in a certain country. of the 200200 drivers surveyed, 105105 responded that they did. determine if more than half of all drivers drive a car made in this country at the alpha equals 0.05α=0.05 level of significance. complete parts (a) through (d).
Answers
Answer:
Is there supposed to be a photo
Step-by-step explanation:
Bina kept a list of her expenses and income for one month. If she started the month with no money, how much money did she have left at the end of the month?
Answers
Answer:
Step-by-step explanation:
Income less expenses
Answer:
15
Step-by-step explanation:
i got it right pls mark brainliest
Spins a fair spinner numbered 1 - 5 and flips a fair coin. What is the probability of obtaining a factor of 15 and a tail?
Answers
Answer: [tex]\dfrac{3}{10}[/tex]
Step-by-step explanation:
Let A be the event of getting a factor of 15 when a fair spinner numbered 1 - 5 spins and B be the event that a fair coin is tossed.
The factors of 15 = [tex]1,\ 3,\ 5[/tex]
Then ,the probability of obtaining a factor of 15 is given by :-
[tex]P(A)=\dfrac{3}{5}[/tex]
The probability of getting a tail :-
[tex]P(B)=\dfrac{1}{2}[/tex]
Since both the events are independent , thus
The probability of obtaining a factor of 15 and a tail is given by :-
[tex]P(A)\times P(B)\\\\=\dfrac{3}{5}\times\dfrac{1}{2}=\dfrac{3}{10}[/tex]
Hence, the required probability : [tex]\dfrac{3}{10}[/tex]
wingspans of adult herons have approximate normal distribution with mean 125cm and a standard deviation 12cm. what proportion of herons have wingspan of excatly 140cm?
Answers
Answer:
[tex]P (X = 140) = 0[/tex]
Step-by-step explanation:
We know that the heron wingspan follow a normal distribution with an mean of 125 cm.
In this case we seek to find
[tex]P (X = 140)[/tex]
If X is a random variable that represents the length of the heron wingspan, then X follows a normal distribution and therefore is a continuous random variable.
Then by definition of continuous random variable we have to:
[tex]P (X = a) = 0[/tex] where a is a constant.
That is to say that only the ranges of values can have a different probability of zero. The probability that a continuous random variable is equal to some exact value is always zero.
Finally we can conclude that
[tex]P (X = 140) = 0[/tex]
To find the proportion of herons with a wingspan of exactly 140cm, calculate the z-score using the given mean and standard deviation. Use the z-score to find the area under the normal curve and determine the proportion. The resulting area is approximately 0.8944 or 89.44%.
Explanation:To find the proportion of herons with a wingspan of exactly 140cm, we need to calculate the z-score for 140cm using the formula:
z = (x - μ) / σ
where x is the value being analyzed, μ is the mean, and σ is the standard deviation. Plugging in the values:
z = (140 - 125) / 12 = 1.25
To find the proportion, we can use the z-table or calculator to find the area under the normal curve to the left of z = 1.25. The resulting area is approximately 0.8944 or 89.44%.
Can someone help me with this math question WILL GIVE 20 POINTS. By the way it’s not 51.496
Answers
Below is the formula for the circumference of a circle
C = 2πr
This question gives us the diameter. To find the radius (r) you would divide the diameter by two like so...
16.4/ 2 = 8.2
Plug what you know into the formula and solve...
π = 3.14
r = 8.2
C = 2(3.14)(8.2)
C = 6.28(8.2)
C = 51.496
In the question it asks to round to the nearest tenth like so...
51.5
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
Step-by-step explanation:
51.496 rounded to the nearest tenth is 51.5
Kelly is willing to pay $5.20 for a gallon of gasoline. The price of gasoline at her local gas station is $3.80. If she purchases ten gallons of gasoline, then Kelly's consumer surplus is A. $3.80. B. $52. C. $14. D. $1.40.
Answers
As a part of a project for his statistics class, Marcus wanted to find out the percentage of American households that still have a landline phone.
*There wasn’t a question for this so I thought I would post it. The answer is C. 463 households!*
Answers
How many households is 463 households
Answer:
C
Step-by-step explanation:
Just got it right.
The binomial distribution that has a probability of success equal to .20 would be left skewed for sample size 20.
True or false
Answers
Answer:
True
Step-by-step explanation:
The binomial distribution that has a probability of success equal to .20, would be left skewed for sample size of 20.
The given statement "The binomial distribution that has a probability of success equal to .20 would be left skewed for sample size 20" is false.
The statement is incorrect. The binomial distribution with a probability of success equal to 0.20 and a sample size of 20 would not necessarily be left-skewed. The shape of the binomial distribution depends on the values of the probability of success and the sample size.
In general, for a binomial distribution with a small probability of success (such as 0.20) and a large sample size (such as 20), the distribution tends to approximate a normal distribution. As the sample size increases, the binomial distribution becomes more symmetric and bell-shaped.
Therefore, it is not accurate to claim that the binomial distribution with a probability of success equal to 0.20 and a sample size of 20 would be left-skewed.
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Identify the area of the figure rounded to the nearest tenth. HELP PLEASE!!
Answers
This is equivalent to an 11x15 rectangle with 2 circles each of radius 2cm cut out of it (4 semi-circles = 2 circles in area).
11x11 rectangle = 165cm^2 area.
2 circles of 2cm radius = 2*4pi = 8pi = 25.13
165 - 25.13 = 139.87 [tex]\approx[/tex] 139.9 [tex]cm^2[/tex] (A)
Answer:
139.9
Step-by-step explanation:
First find the area of the circles.
A = pi*r^2
So pi*2^2
2^2 = 4
4*pi = 12.57
Then divide 12.57 by 2 because its only half a circle.
12.57/2 = 6.285
Then multiply 6.285 by 4 since there are 4 half circles.
6.285*4 = 25.14
Now find the area of the square.
A = lw
A= 15*11
A = 165
Now subtract 165 and 25.14.
165 - 25.14 = 139.86
Now round 139.86 to the nearest tenth
So 139.9
At a school dance, the ratio of boys to girls is 7 to 5. What fraction of students at the dance consists of girls? (You must use the fraction form of a ratio
Answers
Answer:
5/12
Step-by-step explanation:
The fraction that is girls is the ratio of girls to the total of boys and girls:
girls/(boys+girls) = 5/(7+5) = 5/12
I really need help with this question!
Answers
Answer:
(s-6)/r
option D
Step-by-step explanation:
The slope-intercept form a line is y=mx+b where m is the slope and b is the y-intercept.
Compare y=mx+b and y=cx+6, we see that m=c and c is the slope.
Now we are also given that (r,s) is on our line which means s=c(r)+6.
We need to solve this for c to put c in terms of r and s as desired.
s=cr+6
Subtract 6 on both sides:
s-6=cr
Divide both sides by r:
(s-6)/r=c
The slope in terms of r and s is:
(s-6)/r.
QUESTION IS GIVEN IN PICTURE NEED HELP!!!
Answers
Answer:
The slopes of f(x) and g(x) are the same.Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
========================================
We have:
[tex]f(x)=3x+6\to m_f=3[/tex]
From the table:
[tex](1,\ 3),\ (2,\ 6)\\\\m_g=\dfrac{6-3}{2-1}=\dfrac{3}{1}=3[/tex]
[tex]m_f=m_g=3[/tex]
Answer:
1st one
Step-by-step explanation:
A rancher has 800 feet of fencing to put around a rectangular field and then subdivide the field into 2 identical smaller rectangular plots by placing a fence parallel to one of the field's shorter sides. Find the dimensions that maximize the enclosed area. Write your answers as fractions reduced to lowest terms.
Answers
Answer:
The dimensions of enclosed area are 200 and 400/3 feet
Step-by-step explanation:
* Lets explain how to solve the problem
- There are 800 feet of fencing
- We will but it around a rectangular field
- We will divided the field into 2 identical smaller rectangular plots
by placing a fence parallel to one of the field's shorter sides
- Assume that the long side of the rectangular field is a and the
shorter side is b
∵ The length of the fence is the perimeter of the field
∵ We will fence 2 longer sides and 3 shorter sides
∴ 2a + 3b = 800
- Lets find b in terms of a
∵ 2a + 3b = 800 ⇒ subtract 2a from both sides
∴ 3b = 800 - 2a ⇒ divide both sides by 3
∴ [tex]b=\frac{800}{3}-\frac{2a}{3}[/tex] ⇒ (1)
- Lets find the area of the field
∵ The area of the rectangle = length × width
∴ A = a × b
∴ [tex]A=(a).(\frac{800}{3}-\frac{2a}{3})=\frac{800a}{3}-\frac{2a^{2}}{3}[/tex]
- To find the dimensions of maximum area differentiate the area with
respect to a and equate it by 0
∴ [tex]\frac{dA}{da}=\frac{800}{3}-\frac{4a}{3}[/tex]
∵ [tex]\frac{dA}{da}=0[/tex]
∴ [tex]\frac{800}{3}-\frac{4}{3}a=0[/tex] ⇒ Add 4/3 a to both sides
∴ [tex]\frac{800}{3}=\frac{4}{3}a[/tex] ⇒ multiply both sides by 3
∴ 800 = 4a ⇒ divide both sides by 4
∴ 200 = a
- Substitute the value of a in equation (1)
∴ [tex]b=\frac{800}{3}-\frac{2}{3}(200)=\frac{800}{3}-\frac{400}{3}=\frac{400}{3}[/tex]
* The dimensions of enclosed area are 200 and 400/3 feet
Because of Theorem 5.47 any function that is continuous on (0, 1) but unbounded cannot be uniformly continuous there. Give an example of a continuous function on (0, 1) that is bounded, but not uniformly continuous.
Answers
Answer:
[tex]f: (0,1) \to \mathbb{R}[/tex]
[tex]f(x) = \sin(1/x)[/tex]
Step-by-step explanation:
f is continuous because is the composition of two continuous functions:
[tex]g(x) = \sin(x)[/tex] (it is continuous in the real numbers)
[tex]h(x) = 1/x[/tex] (it is continuous in the domain (0,1))
It is bounded because [tex]-1 \leq \sin(\theta) \leq 1[/tex]
And it is not uniformly continuous because we can take [tex]\varepsilon = 1[/tex] in the definition. Let [tex] \delta > 0[/tex] we will prove that there exist a pair [tex]x,y\in \mathbb{R}[/tex] such that [tex]|x-y|< \delta[/tex] and [tex]|f(x) -f(y)|> \varepsilon = 1[/tex].
Now, by the archimedean property we know that there exists a natural number N such that
[tex] \frac{1}{N} < 2\pi \delta[/tex]
[tex]\Rightarrow \frac{1}{2\pi N} < \delta[/tex].
Let's take [tex]x = \frac{1}{2\pi N + \pi/2}[/tex] and [tex]y = \frac{1}{2\pi N + 3\pi/2}[/tex]. We can see that
[tex]|x-y| = \frac{1}{2\pi N + \pi/2}-\frac{1}{2\pi N + 3\pi/2}<\frac{1}{2\pi N} <\delta[/tex]
And also:
[tex]|f(x)- f(y)| = |f(2\pi N + \pi/2) - f(2\pi N + 3\pi/2)| = |1 - (-1)| = 2 > \varepsilon[/tex]
And we conclude the proof.
The mean weight of trucks traveling on a particular section of I-475 is not known. A state highway inspector needs an estimate of the population mean. He selects and weighs a random sample of 49 trucks and finds the mean weight is 15.8 tons. The population standard deviation is 3.8 tons. What is the 95% confidence interval for the population mean?
Answers
Answer:
(14.7 , 16.9)
Step-by-step explanation:
it is given that [tex]\bar{x}=15.8[/tex] tons
σ=3.8 tons
n=49
at 95% confidence level α=1-.95=0.05
[tex]z_\frac{\alpha }{2}=z_\frac{0.05}{2}=z_{0.025}\\[/tex]
=1.96 ( from the standard table)
at 95% confidence level the coefficient interval for μ is
[tex]\bar{x}\pm z_\frac{\alpha }{2}\times \frac{\sigma }{\sqrt{n}}[/tex]
[tex]15.8\pm 1.96\times \frac{3.8}{ \sqrt{49}}[/tex]
[tex]15.8\pm 1.1[/tex]
(14.7, 16.9)
The A-1 Car Rental Agency charges $23 per day plus $.10 per mile. The EZ Rental Agency charges $30 per day and $.05 per mile. If x is miles and y is total cost, write the ordered pair (x,y) that shows at what point the two companies charge the same amount.
Answers
Answer:
(140, 37)
Step-by-step explanation:
If we are looking for the point where the 2 companies charge the same amount, we need to set the 2 cost function equal to each other and solve for the number of miles that makes the cost the same. The number of miles will also be the same at this cost. That means we need cost functions for each. x is the number of miles that is driven, our independent variable. If A-1 charges .10 per mile, the expression is .1x. If the flat fee is 23, regardless of how many miles you drive, you can expect to pay
y = .1x + 23
If EZ charges .05 per mile, the expression is .05x. If the flat fee is 30, regardless of how many miles you drive, you can expect to pay
y = .05x + 30
If we want to see where the cost functions are equal, we set the right sides of those equations equal to one another and solve for the number of miles that makes the cost the same.
.1x + 23 = .05x + 30 and
.05x = 7 so
x = 140 miles.
In order to find the cost we will pick one of the equations and sub in 140 for x and solve for y.
y = .1(140) + 23
y = 14 + 23
y = 37
The coordinate pair is (140 miles, $37)
This means that at 140 miles driven, the cost is $37 no matter which rental agency you choose.
If RT = 6 and RS = 9, then RX =
A - sqrt(54)
B - 13.5
C - 7.2
D - 4
Answers
Answer:
Option D RX=4 units
Step-by-step explanation:
we know that
In the right triangle RTS
The cosine of angle TRS is equal to
cos(TRS)=RT/RS
substitute
cos(TRS)=6/9 -----> equation A
In the right triangle RTX
The cosine of angle TRX is equal to
cos(TRX)=RX/RT
substitute
cos(TRX)=RX/6 -----> equation B
∠TRS=∠TRX -----> is the same angle
Match equation A and equation B
6/9=RX/6
RX=6*6/9=4 units
How do you solve for n^3 + 3n^2 + n - 33 = 0?
Answers
Answer:
one real root: n ≈ 2.38450287889
Step-by-step explanation:
My favorite solution method for higher-degree polynomials is to use a graphing calculator.
Descartes' rule of signs tells you the one sign change among coefficients means there will be one positive real root. A graph shows you it is about 2.4, hence irrational (not a divisor of 33, so not rational).
You can use a cubic formula to find an explicit expression for the root, or you can find its value using any of several iteration methods. The attachment shows Newton's method iteration being used to refine the graph value of 2.385 to the more accurate 2.38450287889.
__
Factoring that root from the cubic results in a quadratic with irrational coefficients. Its vertex form is approximately ...
y = (n +2.692)² + 6.591
Hence, the complex roots will be near -2.692±i√6.591.
_____
There are formulas for the roots of a cubic. The formula tells you the real root for this cubic is ...
n = 2√(2/3)cosh(1/3·arccosh(24√(3/2))) -1 ≈ 2.38450287889
A cylindrical pail that has the base area of 9 pi inches squared and a height of 10 inches. One friend bought a pyramid mold with a square base with edge length of 4 inches and height of 7 inches. The other friend bought a cone with a radius of 2.5 inches and the height of six inches. What is the volume of these three objects?
Answers
Answer:
cylinder — 90π in³pyramid — 37 1/3 in³cone — 12.5π in³Step-by-step explanation:
The volume of a cylinder is given by ...
V = Bh . . . . . where B is the base area and h is the height
The volume of a pyramid or cone is given by ...
V = (1/3)Bh . . . . . where B is the base area and h is the height
The area of a square of side length s is ...
A = s²
The area of a circle of radius r is ...
A = πr²
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Using these formulas, the volumes of these objects are ...
cylinder: (9π in²)(10 in) = 90π in³
square pyramid: (1/3)(4 in)²(7 in) = 37 1/3 in³
cone: (1/3)(π(2.5 in)²)(6 in) = 12.5π in³ . . . . slightly larger than the pyramid
Answer:
12.5
Step-by-step explanation: