(1 point) The weight of a lake trout as a function of age satisfies the formula W(t) = 25.6(1 - -0.211)3. where W is in kg and t is in years. a. Differentiate this weight function. W') = Find its second derivative. W"(t) = Give both the t and W values for any points of inflection (t > 0). 1/ = уг. kg. W(t) = The trout is gaining weight most rapidly at this point of inflection. Find this most rapid rate of growth. W' (t) = kg/yr.
Answers
Points of inflection, which occur when the second derivative W"(t) equals zero.
W'(t) = 0
The trout is gaining weight most rapidly at a rate of -4.430 kg/yr when t is close to 0.
W'(0) = -4.430 kg/yr
How to find Points of inflection and second derivative?Let's first find the first and second derivatives of the given weight function W(t) = 25.6(1 - -0.211)³.
a. Differentiate this weight function:
W'(t) = d(W(t))/dt = d(25.6(1 - -0.211)³)/dt = 25.6 * 3(1 - -0.211)² * -0.211
W'(t) = -16.032(1.211)² * 0.211
b. Find its second derivative:
W"(t) = d(W'(t))/dt = d(-16.032(1.211)^2 * 0.211)/dt = -16.032 * 2(1.211) * 0.211²
W"(t) = -6.755 * 0.211²
Now, we want to find the points of inflection, which occur when the second derivative W"(t) equals zero:
-6.755 * 0.211² = 0
However, this equation has no positive solution for t since -6.755 * 0.211² is always negative. Therefore, there are no points of inflection for t > 0.
To find the most rapid rate of growth, we can find the maximum value of the first derivative W'(t). Since there are no points of inflection, we can examine the behavior of W'(t) as t increases:
As t becomes larger, (1.211)² will approach 0, and therefore W'(t) will approach 0 as well. This means that the most rapid rate of growth occurs when t is close to 0.
W'(0) = -16.032(1.211)² * 0.211 = -4.430 kg/yr
So, the trout is gaining weight most rapidly at a rate of -4.430 kg/yr when t is close to 0.
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Related Questions
Part A
The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.
Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has 4 intercepts. Kelsey argues the function can have as many as 3 zeros only. Is there a way for the both of them to be correct? Explain your answer.
Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = x3 − x2 − 4x + 4
g(x) = x3 + 2x2 − 9x − 18
g(x) = x3 − 3x2 − 4x + 12
g(x) = x3 + 2x2 − 25x − 50
g(x) = 2x3 + 14x2 − 2x − 14
Create a graph of the polynomial function you selected from Question 2.
Part B
The second part of the new coaster is a parabola.
Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = ax2 + bx + c. Describe the direction of the parabola and determine the y-intercept and zeros.
The safety inspector notes that Ray also needs to plan for a vertical ladder through the center of the coaster's parabolic shape for access to the coaster to perform safety repairs. Find the vertex and the equation for the axis of symmetry of the parabola, showing your work, so Ray can include it in his coaster plan.
Create a graph of the polynomial function you created in Question 4.
Part C
Now that the curve pieces are determined, use those pieces as sections of a complete coaster. By hand or by using a drawing program, sketch a design of Ray and Kelsey's coaster that includes the shape of the g(x) and f(x) functions that you chose in the Parts A and B. You do not have to include the coordinate plane. You may arrange the functions in any order you choose, but label each section of the graph with the corresponding function for your instructor to view.
Part D
Create an ad campaign to promote Ray and Kelsey's roller coaster. It can be a 15-second advertisement for television or radio, an interview for a magazine or news report, or a song, poem, or slideshow presentation for a company. These are just examples; you are not limited to how you prepare your advertisement, so be creative. Make sure to include a script of what each of you will say if you are preparing an interview or a report. The purpose of this ad is to get everyone excited about the roller coaster.
Answers
Answer:
Tell a Small question i cant read it tho
Step-by-step explanation:
Answer:
i am doing the same thing lol basically the farthest i got was
Step-by-step explanation:
1. They both cannot be correct because a three-degree polynomial can only have 3 maxium terms.
2. i chose g(x) = (x + 2)(x − 1)(x − 2)
3. the graph is the first one shown
I’m just really confused rn
Answers
Answer:
\(\frac{3}{5} *5\) or \(5*\frac{3}{5}\)
Step-by-step explanation:
Each circle has 3/5 shaded, and there are 5 circles.
So our multiplication equation is:
\(\frac{3}{5} *5\) or \(5*\frac{3}{5}\) (they mean the same thing)
\(\frac{3}{5} *5=3\)
Hope this helps!
Mary used 10 2/3 yards of fabric to make 4 identical curtain panels.
What equation can be used to model the total number of yards of fabric, y. needed to make x curtain panels? Write the equation in the form
Answers
The equation that can be used to model the total number of yards of fabric, y. needed to make x curtain panels is y = (10 2/4 ÷ 4) × x
How to compute the expression?It should be noted that Mary used 10 2/3 yards of fabric to make 4 identical curtain panels.
Therefore, the equation that can be used to model the total number of yards of fabric, y. needed to make x curtain panels will be:
y = (10 2/4 ÷ 4) × x
where
y = number of yards
x = number of panels
Therefore, the equation is y = (10 2/4 ÷ 4) × x
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x² + 3x +2= 0 solve by factorization
Answers
Answer:
x = -1 or -2\(\: \)
Step-by-step explanation:
\(\: \)
Let us first split the middle term 3x as 2x + 1x [because (2x) × (1x) = 2x² = x² × 2]
\(\: \)
\(\dashrightarrow \sf \: \: \: x^2 + 3x + 2 = 0 \\ \\ \)
\(\dashrightarrow \sf \: \: \: x^2 + 2x + 1x + 2 \\ \\ \)
\(\dashrightarrow \sf \: \: \: x(x + 2) +1 (x + 2) \\ \\ \)
\(\dashrightarrow \sf \: \: \: (x + 1)(x + 2) \\ \\ \)
x² + 3x +2= 0 can be rewritten as (x + 1)(x + 2) = 0\(\: \)
So, the values of x for which x² + 3x +2= 0 are the same for which (x + 1)(x + 2)\(\: \)
i.e., either x + 1 = 0 or x + 2 = 0.
\(\: \)
Now,
\(\dashrightarrow \sf \: \: \: x + 1 = 0 \\ \\ \)
\( \dashrightarrow \sf \: \: \:
x = -1 \\ \\ \)
\(\dashrightarrow \sf \: \: \: x + 2 = 0 \\ \\ \)
\(\dashrightarrow \sf \: \: \: x = -2.
\\ \\ \)
Hence,
\(\dashrightarrow \sf \: \: \: x = -1 \: or \: -2 \\ \\ \)
Helpppppp!!!
(Show work)
Answers
Answer:
( - y - 3 , - x - 1 )
Step-by-step explanation:
( x , y ) ----> ( - y , x ) ----> ( - y - 3 , x + 1 ) ----> ( - y - 3 , - x - 1 )
Write these numbers in standard form.
a) 0.00004
b) 0.000 05
c) 0.000006
d) 0.000 000 000 8
Answers
Answer:
a.4×10 raised to power minus 5
b.5×10 raised to power minus 5
c.6×10 raised to power minus 6
d.8×10 raised to power minus 10
Answer:
do you mean scientific notation, I think they are already in standard form.
Step-by-step explanation:
A. 4 x 10^-5, count how many zeros before the number 4, and do the same with the rest.
B. 5 x 10^-5
C. 6 x 10^-6
D. 8 x 10^-10
The sum of the simple probabilities for a collectively exhaustive set of outcomes must O equal one. O not exceed one. O be equal to or greater than zero, or less than or equal to one. O exceed one. eq
Answers
The sum of the simple probabilities for a collectively exhaustive set of outcomes must be equal to one, serving as a fundamental principle of probability theory. This principle holds true for any situation where events are mutually exclusive and cover all possible outcomes.
The sum of the simple probabilities for a collectively exhaustive set of outcomes must be equal to one.
This fundamental principle is a cornerstone of probability theory and ensures that all possible outcomes are accounted for.
To understand why the sum of probabilities must equal one, let's consider a simple example. Imagine flipping a fair coin.
The two possible outcomes are "heads" and "tails." Since these two outcomes cover all possibilities, they form a collectively exhaustive set. The probability of getting heads is 0.5, and the probability of getting tails is also 0.5.
When we add these probabilities together (0.5 + 0.5), we get 1, indicating that the sum of probabilities for the complete set of outcomes is indeed one.
This principle extends beyond coin flips to any situation involving mutually exclusive and collectively exhaustive events.
For instance, if we roll a standard six-sided die, the probabilities of getting each face (1, 2, 3, 4, 5, or 6) are all 1/6.
When we add these probabilities together (1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6), we again obtain 1.
The requirement for the sum of probabilities to equal one ensures that the total probability space is accounted for, leaving no room for events outside of it.
It provides a mathematical framework for reasoning about uncertain events and allows us to quantify the likelihood of various outcomes.
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These two triangles are similar. Find the value of ab
Answers
Simplify the expression: 5^2 - 3 * 6 A)7 B)24 C)132 D)144
Answers
Answer:
7
Step-by-step explanation:
5^2 = 5 x 5 = 25
3 x 6 is 18
25 - 18 is 7
also, use PEMDAS
Answer:
The answer is 7.
5^2-3×6.
25-18=7.
A widget making machine is supposed to make widgets that are 0.05 inches thick. Ten widgets are tested each day to ensure the machine is properly calibrated. Today's test averaged 0.053 inches thick with a standard deviation of 0.003. At the 5% level of significance, is the machine properly calibrated?
Answers
At the 5% level of significance, the machine is not properly calibrated.
To determine if the machine is properly calibrated, we need to conduct a hypothesis test using the given data. Let's define our null and alternative hypotheses as follows:
Null hypothesis (H0): The machine is properly calibrated and the true mean thickness of the widgets is 0.05 inches.
Alternative hypothesis (Ha): The machine is not properly calibrated and the true mean thickness of the widgets is not equal to 0.05 inches.
We will use a two-tailed t-test to test the hypothesis since we have a sample size of 10, and the population standard deviation is unknown. The test statistic for this hypothesis test is calculated as:
t = (x - μ) / (s / sqrt(n))
where x is the sample mean thickness, μ is the hypothesized population mean thickness (0.05 inches), s is the sample standard deviation, and n is the sample size (10).
Plugging in the given values, we get:
t = (0.053 - 0.05) / (0.003 / sqrt(10)) = 3.055
The degrees of freedom for this test is 9 (n - 1). Using a t-table or calculator, we can find the critical t-value for a two-tailed test with 9 degrees of freedom and a significance level of 0.05 to be approximately 2.262.
Since our calculated t-value (3.055) is greater than the critical t-value (2.262), we can reject the null hypothesis at the 5% level of significance. This means that there is sufficient evidence to suggest that the machine is not properly calibrated and that the true mean thickness of the widgets is likely not equal to 0.05 inches.
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Hurry help meh pls real fast no links they are viruses or files help pls help
Answers
Answer:
For the triangle, its area is 32.1 inches.
For the trapezoid, its area is 170 feet.
Step-by-step explanation:
The formula for finding the area of a triangle is A = h * b/2, where h is for height and b is for base. There seems to be two measurements at the base of the triangle so what I did is I added together 3.5 and 7.2 and got 10.7. The slant measurement of the triangle isn't important in this formula so just pretend 5.5 in isn't there. Multiply 10.7 (base) to 6 (height) and you'll get 64.2. Now divide the product by 2 and you'll get 32.1 inches as the area of the triangle.
The formula for finding the area of a trapezoid is A = ((a + b)/2)h, where a is base A, b is base B, and h is the height. This formula looks a bit complicated but if you know a bit of PEMDAS, then you'll understand the formula. Again, there are two measurements at the base of the trapezoid but simply, I added them to get 24 and the slants don't make any use for this formula either. Add 10 (base A) and 24 (base B) to get 34. Now divide 34 by 2 and you'll get 17. Finally, multiply the product to 10 (height) and you'll get 170 feet as the area of the trapezoid.
If you don't know PEMDAS, just comment something related to "Can you explain what PEMDAS is?" or "What is PEMDAS?" and I will answer your question as quick as I possibly can. I hope this helps!
Answer two question about equations a and b: 2x-1=5x b. -1=3x1
Answers
Answer:
For 2x-1=5x (x = -0.33)
Step-by-step explanation:
3x＝－1
x＝－1/3
－1＝3x×1
－1＝3x
x＝－1/3
Hope my answer helped u :)
Find the price of a $75.00 mea with a 18% tip.
Answers
Answer:
$88.50
Step-by-step explanation:
you start by turning the decimal to a fraction by moving the decimal dot 2 places to the left so now you have 0.18
then multiply 0.18 * 75 to get 13.5
then add 15.5 + 75 to get the total meal price which is 88.5
Which describes Myra's distance as time increases?
The table shows the total distance that Myra runs over
different time periods.
Time and Distance Ran by Myra
increasing
decreasing
zero
constant
Time
(minutes)
0
2
4
6
8
Distance
(miles)
0.0
0.4
0.8
1.2
1.6
Answers
Answer:
(A)increasing
Step-by-step explanation:
Given the time and total distance ran by Myra in the table below.
\(\left|\begin{array}{c|c}Time(minutes)&Distance(miles)\\--&--\\0&0.0\\2&0.4\\4&0.8\\6&1.2\\8&1.6\end{array}\right|\)
We observe that as time increases, Myra's distance also increases. It is the speed(0.2 miles per minute) which is constant.
Therefore Option A is the correct option.
Answer:
its a
Step-by-step explanation:
I keep getting HPG I do not understand how it’s wrong can someone please explain.
Answers
Answer:
GPH
Step-by-step explanation:
Technically that's correct, but I think the problem wants you to orient the angle so that M corresponds with G and O corresponds with H.
Help me I’m very stupidddd
Answers
Answer:
\(2 \sqrt{7} - \sqrt{28} \\ = 2 \sqrt{7} - \sqrt{2 {}^{2} \times 7 } \\ = 2 \sqrt{7} - 2 \sqrt{7} \\ = 0\)
So , the answer is 0... second optionis the correct answer...It is rational and equal to 0....Hopes to get BRAINLIEST....Thank you ☺️
Danny is thinking of buying a gym membership. He has two gums available to choose from. Gym A has a $35 initial fee and costs $42 per month.Gym B has $65 initial fee and costs $36 per month. After how many months will the overall cost if both gym memberships be the same? How much will that be?
Answers
65+36x=35+42x
Solving this equation results in x=5, which means that he has to have the memberships for 5 months for them to be equal. Now just plug that in to one side of the equation to get the amount he has to spend:
65+36(5) = $245
The following rectangle has an area of 3x^2-5x-12. What are the possible side lengths, in terms of x? Explain your answer and justify how you know that the sides you found are possible lengths
Answers
Answer:
the possible side lengths:
3x+4 and x-3
Step-by-step explanation:
factorize the the expression and you will get two expressions in terms of x. those expressions are the lengths of the rectangle
\(3 {x}^{2} - 5x - 12\)
1) write -5x as a difference
\(3 {x}^{2} + 4x - 9x - 12\)
2) factor out x from the expression 3x²+4x
\(x(3x + 4) - 9x - 12\)
3) factor out -3 from the expression -9x-12
\(x(3x + 4) - 3(3x + 4)\)
4) factor out 3x+4 from the expression
\((3x + 4)( x - 3)\)
the possible lengths are 3x+4 and x-3
to check whether the answer is correct, you can just multiply the both lengths using the area of rectangle formulae
area of rectangle formulae
\(length \times height\)
(3x+4)(x-3)
= 3x²-9x+4x-12
= 3x²-5x-12 ( proven )
3 gallons to quarts? pls answer now im being timed
Answers
By Unitary method, 3 gallons = 12 quarts
We know that the the unit conversion,
one liquid gallons is equals to the four liquid quarts
i.e., 1 gallon = 4 quarts
We need to find the 3 gallons to quarts.
Let us assume that x represents the required amount of liquid quarts.
By Unitary method,
⇒ x = 3 × 4
⇒ x = 12 quarts of liquid
Therefore, the unit conversion 3 gallons equals to 12 quarts.
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The polynomial (x – 2)(x^2 + 1) – x(x – 3) can be written in the form: ax^3 + bx^2 + cx + d where a, b, c, and d are constants. What are the values of a, b, c, and d? Show your work.
Answers
Therefore the polynomial (x – 2)(x^2 + 1) – x(x – 3) can be written in the form: ax^3 + bx^2 + cx + d = x^3 - 2x^2 + 4x - 6 where a = 1, b = -2, c = 4, and d = -2
What is the polynomial after simplificationThe polynomial (x – 2)(x^2 + 1) – x(x – 3) can be written as:
ax^3 + bx^2 + cx + d = (x - 2)(x^2 + 1) - x(x - 3)
To find the values of a, b, c, and d, we need to multiply out the binomials and combine like terms. Using the distributive property, we get:
ax^3 + bx^2 + cx + d = x^3 - 2x^2 + x^2 + x - x^2 + 3x - 2
Now we can combine like terms:
ax^3 + bx^2 + cx + d = x^3 - 2x^2 + 4x - 2
So we can see that:
a = 1, b = -2, c = 4, and d = -2
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A compound inequality is shown below.
x ≤ 3 and x ≥ 0
Which graph represents the solution of the inequality?
Answers
Answer:
It is the first graph
Step-by-step explanation:
The line under the > and < sign means that it must include the 3 and the 0. The closed circle is showing that the 3 and 0 or included.
Is the expression x to the power of 3 times x to the power of 3 times x to the power of 3 equivalent to x to the power of 3 times 3 times 3 ? why or why not ? explain your reasoning
Answers
The expression x to the power of 3 times x to the power of 3 times x to the power of 3 is not equivalent to an expression x to the power of 3 times 3 times 3.
For given question,
We have been given a statement 'x to the power of 3 times x to the power of 3 times x to the power of 3 '
We can write above statement in expression form as,
x³ × x³ × x³
Now, we simplify above expression.
We know that the product rule of exponents states that, 'To multiply expressions with the same base, add the exponents while keeping the base the same.'
So, x³ × x³ × x³ = \(x^{3+3+3}\)
⇒ x³ × x³ × x³ = \(x^{9}\) ....................................(1)
Also, we have been given a statement that 'x to the power of 3 times 3 times 3'
We can write above statement in expression form as,
\(x^{3\times 3\times 3}\)
Now we simplify above expression.
By power of a product rule of exponents,
\(x^{3\times 3\times 3}=x^{27}\) .....................................(2)
From (1) and (2),
x³ × x³ × x³ ≠ \(x^{3\times 3\times 3}\)
Therefore, the expression x to the power of 3 times x to the power of 3 times x to the power of 3 is not equivalent to an expression x to the power of 3 times 3 times 3.
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WHATS THE MEASURE OF THE ANGLE INDICATED?
GEOMETRY/PLS HELP/GOD BLESS
Answers
Answer:
∠SQR = 1/2 m ∠SR = 1/2 x 86 = 43°
What is the value of x?
45°
m
(2x-5)
n
Answers
Answer:
x = 70
Step-by-step explanation:
The two angles are same side interior angles and same side interior angles add to 180
45+ (2x-5) = 180
Combine like terms
2x +40 = 180
Subtract 40 from each side
2x+40-40 =180-40
2x =140
Divide by 2
2x/2 = 140/2
x = 70
Answer:
x=70
Step-by-step explanation:
hope it helped! :)
have a nice day
A salesperson at a jewelry store earns 6% commission each week. Last week, jarrod sold $680 worth of jewelry. How much did make in commission? How much did the jewelry store make from sales?
Answers
Answer:
1/ $ 4.08
2/ $675.92
Step-by-step explanation:
Take 68 times 0.06% = $4.08
680 - 4.08= 675.92
Answer:
Step-by-step explanation:
40.80 it told me the answer
Rosa invests $2300 in the bank at a 7% interest for 9 years. What is the simple interest?
Answers
WARNING - I wasn't told whether if it was annual or monthly contributions so this might not be correct.
Answer:
$1449.00
Step-by-step explanation:I = 2300 × 0.07 × 9 = 1449
I = $ 1,449.00
Susan has a collection of 98 nickels and dimes. If the number of nickels is six times the number of dimes, how many nickels and how many dimes does she have?
Answers
Answer:
14 (nickels)84 (dimes)
Step-by-step explanation:
Susan has a collection of 98 nickels and dimes. If the number of nickels is six times the number of dimes, how many nickels and how many dimes does she have?
nickels = x
dimes = 6x
6x + x = 7x
98 : 7 = 14 (nickels)
14 x 6 = 84 (dimes)
-----------------------
14 + 84 = 98 (the answer is good)
a cylinder whose height is 5 meters has a volume of 320pi cubic meters. find the radius of the cylinder.
Answers
Answer:
8m
Hope this answers the question. Have a nice day.
Deside weather each equation is true for all one or no values of x? 9(x-2)= 7x+5
Answers
Equation is true for one x and that x = 23/2
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
Find x.
9(x - 2) = 7x + 5
Distribute x
9x - 18 = 7x + 5
9x - 7x = 5 + 18
2x = 23
x = 23/2
Equation is true for one x and that x = 23/2
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4. In a class of students, the following data table
summarizes how many students have a cat or a dog. What
is the probability that a student chosen randomly from the
class has a dog?
Has a dog
Does not have a dog
Has a cat Does not have a cat
16
4
6
3
Answers
The probability that a student who had a dog also had a cat would be = 7/25.
How to calculate the possible outcome of the given event?To calculate the possible outcome of the given event, the formula for probability should be used and it's given below as follows. That is;
Probability = possible outcome/sample space
possible outcome = 7
sample space = 7+2+3+13 = 25
Probability = 7/25
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