Determine the turning points and distinguish between them when necessary y=x³ - 3x - 9x + 4
The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).
To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.
1. Find the derivative of the function:
y' = 3x² - 6x - 9
2. Set the derivative equal to zero and solve for x:
3x² - 6x - 9 = 0
3. Factorize the quadratic equation:
3(x² - 2x - 3) = 0
4. Solve the quadratic equation by factoring or using the quadratic formula:
(x - 3)(x + 1) = 0
This gives us two possible values for x: x = 3 and x = -1.
5. Substitute these critical points back into the original function to find the corresponding y-values:
For x = 3:
y = (3)³ - 3(3)² - 9(3) + 4
= 27 - 27 - 27 + 4
= -23
For x = -1:
y = (-1)³ - 3(-1)² - 9(-1) + 4
= -1 - 3 + 9 + 4
= 9
6. Therefore, the turning points are (3, -23) and (-1, 9).
Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.
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Please help I’ll do anything
Find the coordinates of the point on the unit circle at an angle of 225∘.
Give your answer in the form (x,y) and leave any fractions in fraction form.
The unit circle has the co-ordinates (-√2/2, -√2/2)
What are trigonometric functions?In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.
Given here: The unit circle and the point makes an angle of 225
we know the co-ordinates of any point on the unit circle is given by
x=cost and y=sint where t is the angle that line passing through the origin containing the point makes with x-axis
Thus x=cos225
=-√2/2
and y=sin225
=-√2/2
Hence, The required point is given by co-ordinates (-√2/2, -√2/2)
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!Eric runs everyday.He can run 5 miles in 50 minutes.What is the unit rate that eric runs in one minute.
Answer:
10 is the unit rate that Eric runs in one minute.
A gardener wants to determine which of two brands of fertilizer is best for the plants in a garden. Before using one of the fertilizers on the entire garden, the gardener decides to conduct an experiment using 28 individual plants. Which of the two plans for randomly assigning the treatments should the gardener use? Explain.
Plan A: Choose the 14 unhealthiest-looking plants. Apply Brand X fertilizer to all 14 of those plants. Apply Brand Y fertilizer to the remaining 14 plants.
Plan B: Choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.
Plan A, because the unhealthy plants need the fertilizer the most and should be treated first
Plan B, because the sample of plants is randomly chosen
Plans A and B are equivalent because they both follow experimental design
Plans A and B are both poorly designed because there are not enough plants to test
The plans cannot be evaluated from the information given
Plan B: Choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.
What is a sample and its types?A sample is only a small portion of the population.
Let's imagine you were interested in determining the average income for all Americans in your population.
Instead of knocking on every door in America because of time and money constraints, you decide to ask 1,000 random people. Your sample consists of these a thousand persons.
Given, A gardener wants to determine which of two brands of fertilizer is best for the plants.
And the gardener decides to conduct an experiment using 28 individual plants.
Plan A will be a biased sampling and the experiment would not yield
desired results.
Therefore, The gardener should choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.
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Order cube root of eighty-eight, twenty-eight ninths, square root of nineteen from greatest to least.
cube root of eighty-eight, twenty-eight ninths, square root of nineteen
twenty-eight ninths, square root of nineteen, cube root of eighty-eight
twenty-eight ninths, cube root of eighty-eight, square root of nineteen
cube root of eighty-eight, square root of nineteen, twenty-eight ninths
Answer:
(a) twenty-eight ninths, square root of nineteen, cube root of eighty-eight
Step-by-step explanation:
When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.
OrderThe attachment shows the ordering, least to greatest, to be ...
\(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)
__
Additional comment
We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.
One way to do the comparison is to convert these to values that need to have the same root:
√19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)
∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)
The roots will have the same ordering as 19³ and 88².
Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...
19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859
88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744
Then the ordering is ...
28/9 < 19³ < 88² ⇒ 28/9 < √19 < ∛88
Answer:
the ordering is
28/9 < 19³ < 88² ⇒ 28/9 < √19 < ∛88
Step-by-step explanation:
hi pls help pls pls pls
Answer:
yes but in what help you need
Step-by-step explanation:
first explain me what help
then give brainliest
then give thanks
then rate 5 stars
Which of the following fall(s) at a z-score of 0.0 in a normal distribution? Mean Median Mode Mean, media and mode
Answer: Median Mode Mean
Step-by-step explanation:
A normal distribution a symmetric distribution where most of the values lies around the central peak where Mean, median mode all lies together and the value of z=0 (as z-value given the distance of data values from mean with respect to the standard deviation).
i.e. Z-score of 0 has 50% of the area to the left and 50% area to the right.
Hence, at a z-score of 0.0 in a normal distribution Mean, Median and Mode all fall together.
On a particular production line, the likelihood that a light bulb is defective is 10%. seven light bulbs are randomly selected. What is the probability that at most 4 of the light bulbs will be defective
Answer:
0.9995
Step-by-step explanation:
10% = 0.10
1 - 0.10 = 0.9
n = number of light bulbs = 7
we calculate this using binomial distribution.
p(x) = nCx × p^x(1-p)^n-x
our question says at most 4 is defective
= (7C0 × 0.1⁰ × 0.9⁷) + (7C1 × 0.1¹ × 0.9⁶) + (7C2 × 0.1² × 0.9⁵) + (7C3 × 0.1³ × 0.9⁴) + (7C4 × 0.1⁴ × 0.9³)
= 0.478 + 0.372 + 0.1239 + 0.023 + 0.0026
= 0.9995
we have 0.9995 probability that at most 4 light bulbs are defective.
1. BOWLING Brooke went bowling with her friends. She bowled 3 games, and
her average score for those games was 121. She had 117 her first game and
108 her second game. Write and solve an equation to find g, the score of
her third game.
pls show your work
Answer: x = 138
Step-by-step explanation:
\(108+117+x=3 * 121\\3 * 121 = 363\\Rearrange unknown terms to the left side of the equation\\x=(363-108)-117\\\\255-117=138\\x=138\)
Bayat wants to order DVD's over the internet. Each DVD costs $20 and shipping the entire order costs $5. If he can spend no more than $100, how many DVD's could he buy?
Please help. My exam is close and I need the answer.
Simplify 10square root 3x+4square root 3x+5square root 3x
Answer:
Step-by-step explanation:
given equuation 10\(\sqrt{3x\)+4\(\sqrt{3x\)+5\(\sqrt{3x}\)
=19\(\sqrt{3x}\)
the answer is 19\(\sqrt{3x}\)
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Felipe mixes 8 oz a raven 8 oz of sunflower seeds 12 oz of almonds and 12 oz of dried fruit for a recipe how many pounds of mix does Felipe make with his recipe
HELPPPPPPPPPPPPPPPPPPPPPPPPPP
Which intervals is this function graph decreasing? Select 2 answers. *
[ -5.5, -5]
[ -5, -4]
[ -3, 1]
[1,2]
Choice B. [-5, -4]
Choice D. [1, 2]
===================================================
Explanation:
We're looking for portions when the graph goes downhill when we move from left to right.
The first portion is from x = -5 to x = -4. So we write [-5, -4] which represents \(-5 \le x \le -4\)
The second portion is [1, 2] which goes downhill since the interval starts at x = 1 and stops at x = 2.
The portions are highlighted in the diagram below.
As you can see, we only care about the x values for any given interval. The y values don't matter as long as they decrease along the interval.
Someone please help
Answer:
Angle 1 and angle 8
angle 2 and angle 7
angle 3 and angle 6
angle 4 and angle 5
I think its tat.
Step-by-step explanation:
A contractor explains that they have a minimum charge of $500 and they charge $100/hr to fix damage to a fence caused by a fallen tree. However, they say that if the work takes 5 hours or more, they will not charge more than $1000 for the repair. Which of the following piecewise functions best describes this pricing strategy?
The best piecewise function that describes this pricing strategy is a total charge, t = 500 + 100x ≤ 1,000.
What is a piecewise function?A piecewise function is a function built from pieces of different functions over different intervals.
Since the different piecewise functions are not provided in this question, we have worked out a function that answers the question.
Data and Calculations:Minimum charge = $500
Charger per hour = $100
Maximum charge for repair = $1,000
Total charge, t = 500 + 100x
t = 500 + 100x ≤ 1,000
Where x = x ≤ 5
t = total charge.
Thus, the best piecewise function that describes this pricing strategy is a total charge, t = 500 + 100x ≤ 1,000.
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a summer soccer cam ordered a total of 84 soccer balls and t-shirts for the season. Soccer balls cost $25 each and t-shirts cost $9.50 each. if they paid $1,046 total for the purchase, how many of each item was ordered?
The Number of Soccer Balls is 16 and the Number of T-Shirts is 68
What is Linear Equation in Two Variables?
A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.
Solution:
Let,
Number of Soccer Balls = x
Number of T-Shirts = y
Equation 1:
x + y = 84 -----------(i)
Equation 2:
25x + 9.5y = 1046 ----------(ii)
Multiplying Equation 1 by 25
25x + 25y = 2100 ---------(iii)
Substracting Equation2 from Equation 1
15.5y = 1054
y = 68
So, x = 16
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can someone solve this please 5(5t + 1) = 25t – 7
The water level in a pool drops 8 iches in a day so what is the average level drop in each hour
Maria bought a bag of mixed fruit that is 40% oranges, 33% green apples, and 27% red apples, If she
randomly selects 5 pieces of fruit from the
bag, how many would you expect to be oranges?
A 1
B 2
C 3
D 4
Answer:
b
Step-by-step explanation:
Need the help thanks guys
Answer:
1/4
Step-by-step explanation:
x^2 - x
Take the coefficient of x
-1
Divide by 2
-1/2
Square it
(-1/2)^2 = 1/4
Add it
x^2 -x +1/4
How tall is the tree?
5ft
35°
-20ft-
[?]ft
Round to the nearest foot.
Answer:
19
Step-by-step explanation:
tan35=x/20
20tan35=x
x=14.0041507641942
x+5=19.0041507641942
The nearest foot is 19
Solve for x
4^x/9^x=½
Answer:
x = 0.85476
Step-by-step explanation:
4ˣ/9ˣ=½
9ˣ / 4ˣ = 2
(9/4)ˣ = 2
2.25ˣ = 2 .... aⁿ = x logₐx = n
log₂.₂₅2 = x
x = 0.85476
Explain why the function is differentiable at the given point.
f(x, y) = 5 + x ln(xy − 9), (5, 2)
Step-by-step explanation:
Given the function
f(x, y) = 5 + x ln(xy − 9) at the point (5, 2)
For the function to be differentiable at the given point, the differential of the function with respect to x and y must be continuous at the point.
Fx is the differential of the function with respect to x.
Using product rule to get f(x):
fx = 0 + x(1/(xy-9)y) + ln(xy-9)
fx = xy(1/(xy-9)) + ln(xy-9)
Substitute point (5, 2) into fx
fx = 5(2)(1/5(2)-9) + ln(5(2)-9)
fx = 10(1/(10-9)) + ln(10-9)
fx = 10(1/1) + ln1
fx = 10 + 0
fx = 10
For fy:
fy = 0 + x²(1/(xy-9))+ 0
fy = x²(1/(xy-9))
Substitute point (5, 2) into fy
fy = 5²(1/(5(2)-9))
fy = 25(1/10-9)
fy = 25(1/1)
fy = 25
Next is to calculate f(5,2)
f(5,2) = 5 + 5 ln(2(5) − 9)
f(5,2) = 5 + 5 ln(10− 9)
f(5,2) = 5 + 5 ln1
f(5,2) = 5 + 5(0)
f(5,2) = 5
Since fx ≠ fy, hence the function is not differentiable at the given point
Given 1 || m ||
|| n, find the value of x.
(x-6)⁰
60⁰
1
m
n
The value of x in the lines is 126 degree
We are given that;
Three parallel line and one intersecting line
Angles= (x-6) and 60
Now,
By supplementary angles property
Angle 1 + Angle 2 = 180 degree
Substituting the values of angles
x-6 + 60 = 180
x + 54 = 180
x = 180-54
x = 126
Therefore by supplementary angles answer will be 126 degree.
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What is the name for an upward trend for an exponential function?
Exponential Growth
Scientific Notation
Growth-Decay Notation
Exponential Decay
Answer:
Step-by-step explanation:
Exponential growth
Integral of 1/(x+cosx)
The integral is ln|x + cos(x)| + C, where C represents the constant of integration.
To find the integral of the function 1/(x + cos(x)), we can employ a combination of algebraic manipulation and the use of standard integration techniques. Here's the solution:
First, let's rewrite the integral in a slightly different form to simplify the process:
∫(1/(x + cos(x))) dx
We notice that the denominator, x + cos(x), is not amenable to direct integration. To overcome this, we employ a substitution. Let's set u = x + cos(x). Now, differentiate u with respect to x: du/dx = 1 - sin(x).
Rearranging this equation, we get dx = du/(1 - sin(x)).
Substituting these values, the integral becomes:
∫(1/(u(1 - sin(x)))) du
Next, we simplify further by factoring out 1/(1 - sin(x)) from the integral:
∫(1/(u(1 - sin(x)))) du = ∫(1/u) du = ln|u| + C
Replacing u with its original expression, we have:
ln|x + cos(x)| + C
Therefore, the answer to the integral is ln|x + cos(x)| + C, where C represents the constant of integration.
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Use the histogram to answer the following questions.
Frequency
The frequency of the class 90-93 is
The frequency of the class 94-97 is
This means that a total of
5.5
5
4.5
Your answers should be exact numerical values.
The frequency of the class 86-89 is
86
94
90
Duration of Dormancy (minutes)
dormancy periods were recorded.
The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.
The total number of periods is given as follows:
5 + 6 + 4 = 15.
The frequency of each class is given as follows:
86 - 89: 5/15 = 1/3.90 - 93: 6/15 = 2/5.94 - 97: 4/15.Learn more about the concept of probability at https://brainly.com/question/24756209
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An object falls from an airplane
that is flying at an altitude of
6400 ft. How many seconds later
will the object hit the ground? Use
the equation 16t2 = d, where d is
the distance in feet and f is the
time in seconds.
Answer:
t = 20 seconds
Step-by-step explanation:
The force of gravity upon an object results in that object accelerating at 16ft/s². By substituting 6400ft in the equation 16t² = d you get:
16t² = 6400
Next, isolate t by dividing both sides by 16
t² = 400
Now, solve for t by taking the square root of both sides
\(\sqrt{t^2} = \sqrt{400}\)
t = 20
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