Let k(t) be a measure of the knowledge you gain by studying for a test for t hours. which do you think is larger, k(8) − k(7) or k(3) − k(2)
Answers
To determine which is larger between k(8) - k(7) and k(3) - k(2) , compare the specific values. If the graph of k(t) is concave upward, studying more hours yields a larger knowledge increase.
To determine which is larger between k(8) - k(7) and k(3) - k(2) , and to understand the concavity of the graph of k(t) , consider the following:
1. Larger Increase in Knowledge:
- Evaluate k(8) - k(7) and k(3) - k(2) .
- If k(8) - k(7) is greater, it implies that studying for an additional hour (from 7 to 8 hours) provides a larger increase in knowledge than studying for an hour from 2 to 3 hours.
2. Concavity of the Graph:
- If k''(t) > 0 (second derivative is positive), the graph is concave upward.
- If k''(t) < 0 (second derivative is negative), the graph is concave downward.
3. Reasoning for Concavity:
- If the graph is concave upward, it suggests that the rate of knowledge gain is increasing. Studying more hours leads to a larger increase in knowledge.
4. Final Answer:
- The comparison between k(8) - k(7) and k(3) - k(2) depends on the specific function k(t) . As for concavity, if the graph is concave upward, studying more hours yields a larger increase in knowledge.
In summary, compare the specific values k(8) - k(7) and k(3) - k(2) and analyze the concavity of the graph to determine the relationship between studying hours and knowledge gain.
Question. Let k(t) be a measure of the knowledge you gain by studying for a test for t hours, . Which do u think is larger, k(8)-k(7) or k(3) - k(2) ? is the graph of k concave upward or concave downward? why?
Related Questions
almonds cost 3.49$ per pound. a bag of almonds cost 6.95$. to the nearest whole pound, about how many pounds of almonds are in the bag?
Answers
Derrick's garden is 18 1/2 feet long. He plants 3/8 of a foot apart. How many bulbs can Derrick plant in one row?
Answers
20/2 divided by 3/8=20/2*8/3=26.6(reoccurring) or 26 bulbs in one row...
Select "Rational" or "Irrational" to classify each number. Rational Irrational 0.25 √ 0.25 √0.33
Answers
√0.25: Rational (=0.5)
√0.33: Irrational
A rainstorm in Portland Oregon wiped out the electricity in 5% of the households in the city. Suppose that a random sample of 60 Portland households is taken after the rainstorm. a. Estimate the number of households in the sample that lost electricity by giving the mean of the relevant distribution (that is the expectation of the relevant random variable do not round your response.) b. Quantify the uncertainty of your estimate by giving the standard deviation of the distribution run your response to at least three decimal places.
Answers
ps Portland is the most fun city in Oregon.
John has painted 4/5 of his house the next day he painted 2/3 of what he had left what fraction of the house is left to paint
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so... he painted 4/5 of the house first..... now the whole house is 5/5, from 4/5 to 5/5 is just 1/5, so 1/5 was left for the next day.
the next day, he painted only 2/3 of what was left, what is 2/3 of 1/5? well is just their product.
[tex]\bf \cfrac{2}{3}\cdot \cfrac{1}{5}\implies \cfrac{2}{15}\impliedby \textit{only painted the next day the slacker} \\\\\\ \textit{so he has painted in total }\cfrac{4}{5}+\cfrac{2}{15}\impliedby \textit{LCD of 15}\implies \cfrac{12+2}{15} \\\\\\ \stackrel{painted}{\cfrac{14}{15}}\qquad \qquad \stackrel{whole}{\cfrac{15}{15}}-\stackrel{painted}{\cfrac{14}{15}}\implies \stackrel{unpainted}{\cfrac{1}{15}}[/tex]
write 784 miles per 40 gallons as a rate in simplest form?
Answers
I believe it would be
784 miles/40 gallons = 19.6 miles per gallon
Suppose r contains a reference to a new rectangle(5, 10, 20, 30). which of the following assignments is legal? (look inside the api documentation to check which interfaces the rectangle class implements.)
a. rectangle a = r;
e. measurable e = r;
b. shape b = r; f. serializable f = r;
c. string c = r; g. object g = r;
d. actionlistener d = r;
Answers
The Java Rectangle class implements both the Shape and Serializable interfaces. Therefore, Rectangle r can be legally assigned to Rectangle, Shape, Serializable, and Object data types. It can't be assigned to a String, Measurable, and ActionListener as Rectangle doesn't implement these.
Explanation:In Java, the Rectangle class implements the Shape and Serializable interfaces. Therefore, the legal assignments would be:
Rectangle a = r; because r is a Rectangle, you can assign r to another Rectangle object.Shape b = r; because Rectangle implements the Shape interface, you can assign r to a Shape object.Serializable f = r; because Rectangle implements the Serializable interface, you can assign r to a Serializable object.Object g = r; because all classes in Java extend the Object class implicitly, you can assign r to an Object.The rest assignments are not legal because the Rectangle class doesn't implement Measurable, ActionListener interfaces and it cannot be assigned to a String.
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A rocket is launched with an initial velocity of 360 ft/s. The height of the rocket in meters is modeled by the function shown below, where t is time in seconds. h(t)=‒10t2 + 360t Which statement is true?
A. The rockets maximum height is 324 feet.
B. The rockets maximum height is 3240 feet.
C. In the interval from 9 seconds to 18 seconds, the rocket is descending.
D. The rocket hits the ground in 18 seconds.
Answers
hope it helps
Right triangle ABC is shown below.
Answers
Thanks
How many terms are in the arithmetic sequence 7, 0, −7, . . . , −175?
Hint: an = a1 + d(n − 1), where a1 is the first term and d is the common difference
Answers
What is the value of the range of the function f(x)=x^2+2 for the domain value 1/4?
Answers
This is the range when the domain is 1/4. Usually a domain contains more than one number.
Use the distributive property in two different ways to find the product of 127 and 32.
Answers
2.) 32(100+20+7)= 3200+640+224=4064
Answer and explanation:
Use the distributive property in two different ways to find the product of 127 and 32.
Distributive property says that,
[tex]a(b+c)=ab+ac[/tex]
We have to find product of 127 and 32,
1) Split 127 as 100+27
[tex]127\times32=(100+27)\times 32[/tex]
Apply distributive property,
[tex]127\times32=100\times 32+27\times 32[/tex]
[tex]127\times32=3200+864[/tex]
[tex]127\times32=4064[/tex]
2) Split 32 as 30+2
[tex]127\times32=127\times (30+2)[/tex]
Apply distributive property,
[tex]127\times32=127\times 30+127\times 2[/tex]
[tex]127\times32=3810+254[/tex]
[tex]127\times32=4064[/tex]
What is the nth term for 1 7 15 25 37
Answers
Answer:
51 hope this helps!!!!!!!!!!
Step-by-step explanation:
Final answer:
The nth term for the given sequence 1, 7, 15, 25, 37 is derived to be n² + n - 1, which fits the pattern of the sequence accurately.
Explanation:
The sequence given is 1, 7, 15, 25, 37. To find the nth term of this sequence, let's first identify the pattern of differences between the terms. Observing the differences, we see they are 6, 8, 10, and 12, which suggests an arithmetic sequence in the differences. This indicates the original sequence is quadratic.
Using the general formula for the nth term of a quadratic sequence, An² + Bn + C, we can substitute the first few terms to solve for A, B, and C. However, there's a quicker method given the pattern of differences seen in the second layer (6, 8, 10, 12, ...) that increases by 2 each time, suggesting that 2n is involved.
Through analysis, the nth-term formula can be derived as n² + n - 1.
Here's why:
considering n=1 for the first term, we get 1+1-1=1;
for n=2, the formula yields 2^2+2-1=7; and so forth, matching the given sequence precisely.
Find the area lying above the x-axis and below the parabolic curve y = 4x -x2 A. 8 B. 16 C. 10 2/3 D. 8 1/3
Answers
function of the graph is
y = 4x - x²
We can tell by the function (specifically -x²) that the parabola will point downward.
To find the domain in which y>0, let's find the roots (0's) of the function:
0 = 4x - x²
0 = x (4 - x)
x = 0 or x = 4
Between x=0 and x=4, the curve is above the x-axis. To find the area of the graph, let's take the integral on this range:
First, take the antiderivative of 4x - x²:
2x² - (1/3) x³
Then, plug x=4 into the anti-derivative, and subtract the anti-derivative at x=0:
2(4)² - (1/3)(4³) - (0 - 0)
32 - 64/3
96/3 - 64/3 = 32/3
Closest Answer is C) 10
Jessica wants to serve 3/4 of a pint of orange juice to each of her guests. Her juice jar can hold 12 full pints of juice. Jessica can serve the juice to guest
Answers
Answer:16
Step-by-step explanation:
Which one of the following is an arithmetic sequence?
A. .35, .5, .85, 1.1, 1.22, . . .
B. 5, 0, −1, −3, −7, . . .
C. 2, 3, 5, 7, 11, 13, 17, . . .
D. −2, 1, 4, 7, 10, . . .
Answers
Adding 3 to the previous term.
19+X=17 What is X pls tell me!
Answers
19 + -2 = 17 is true and correct since if u add 19 plus negative two u can just do 19 minus two and still receive 17.
x = -2.
Describe t-test and explain how to interpret its results?
Answers
Let P=(x,y) be a point on the graph of y=x2−9. (a) Express the distance d from P to the origin as a function of x.
Answers
Explanation on finding distance from a point to the origin as a function of x and showing invariance under rotations.
Distance from point P to the origin as a function of x:
Given point P(x, y) on y = x² – 9.
The distance d from P to the origin is d = √(x² + y²).
Substitute y = x² - 9 into the distance formula to express d as a function of x: d = √(x² + (x² - 9)²).
Invariance of distance under rotations:
The distance from P to the origin remains constant regardless of the rotation, as it depends only on the coordinates of the point and not the orientation of the coordinate system.
solve sin4xcos2x-cos4xsin2x=square root of 2 sinx over the interval [0,2pi)
Answers
Final answer:
The trigonometric equation is solved using the sine difference identity, simplifying to sin(2x) = √2 sin(x). The solution involves finding values of x that satisfy the equation over the interval [0,2π). Trigonometric identities such as double angle formulas are essential in the process.
Explanation:
The student has presented a trigonometric equation involving sine and cosine functions to solve: sin(4x)cos(2x) - cos(4x)sin(2x) = √2 sin(x) over the interval [0,2π). This can be addressed by recognizing the left-hand side as the expansion of the sine difference identity: sin(A - B) = sin(A)cos(B) - cos(A)sin(B), where A = 4x and B = 2x. Therefore, the equation simplifies to sin(2x) = √2 sin(x). We solve this equation over the specified interval by looking for values of x that satisfy the condition.
However, none of the reference equations or principles provided directly align with solving the original question. Hence, we must rely solely on our knowledge of trigonometric identities, such as the double angle formulas which are relevant to this problem. The double angle identities state that sin(2θ) = 2sin(θ)cos(θ) and cos(2θ) = cos^2(θ) - sin^2(θ) or equivalently cos(2θ) = 2cos^2(θ) - 1 and cos(2θ) = 1 - 2sin^2(θ).
Find the area of the shaded figure. To do so, subtract the area of the smaller square from the area of the larger square.
Large square side length: (x squared plus 10)
Small square side length: x
Image included.
What is the area of the shaded region?
Answers
The area of the shaded figure is (x⁴ + 19x² + 100) square meters after subtracting the area of the smaller square from the area of the larger square.
What is a square?It is defined as a two-dimensional geometry that has four sides and four vertices. The sides of the square are equal in length. It is a regular quadrilateral.
It is given that:
Large square side length: (x squared plus 10)
Small square side length: x
The area of the large square = (x² + 10)(x² + 10)
The area of the large square = (x² + 10)²
The area of the small square = (x)(x)
The area of the small square = x²
The area of the shaded figure = (x² + 10)² - x²
The area of the shaded figure = (x⁴ + 19x² + 100) square meters
Thus, the area of the shaded figure is (x⁴ + 19x² + 100) square meters after subtracting the area of the smaller square from the area of the larger square.
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David is playing a trivia game where he gains points for correct answers and loses points for incorrect answers. At the start of round 3 his score is −1500 points. During round 3 he answered five 1000 point questions correctly and three 500 points questions incorrectly. What is his score at the end of round 3?
A) −2000
B) −500
C) 2000
D) 3500
Answers
he answered 5 one thousand point questions....5 * 1000 = 5000
so he now has -1500 + 5000 = 3500
he answered 3 five hundred point question incorrectly...3 * -500 = -1500
3500 + (-1500) = 3500 - 1500 = 2000
so he ended up with 2000
Answer:
2000 points
Step-by-step explanation:
Topic: Substraction, Addition and Products
You have to organize the problem, as you can see
at Start of Round 3 David Has: - 1500
During Round 3:
5 Questions: 1000 each correctly
so 5 x 1000 = 5000
3 Questions: - 500 each incorrectly
so 3 x -500 = -1500
at the End of Round 3:
Starting: -1500
During Round 3: 5000 - 1500 = 3500
the end of round 3: -1500 + 3500 = 2000
Which of the following is the best example of a characteristic of an experiment?
Participants should be selected into the treatment group randomly.
Participants are rarely aware that they are part of an experiment.
Participants are observed without researchers making changes to their behaviors.
The results of an experiment are based on a questionnaire given to a random sample of the population.
Answers
In an experiment, the participant is given an intervention and it hoped to change a parameter. In every experiment, you must ask the participant permission so they must be aware of the experiment. Since this is an experiment, the researcher is allowed to do something that changes the participant behavior as long as it is intentional for the research. The experiment questionnaire should be given to the participant, not the population.
By putting the participant randomly, you can minimize confounding factor from the participant.
Betsy and 3 of her friends are splitting a whole watermelon. There are 6 circular slices of watermelon. How many slices of watermelon will each person get?
Answers
The slices of watermelon each person will get is 1.5 slices.
If the watermelon is divided equally, the number of slices each person would get can be determined by dividing the total slices of watermelon by the total number of friends.
Slice each person would get = total slices / total number of friends
6 / 4 = 1.5 slices
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Solve the problem as directed. The rate traveled from Amarillo to Austin by a bus averages 65 miles per hour. The bus arrived in Austin after eight hours of travel. An automobile averages 80 miles per hour. Using the inverse variation relationship, show what the time would be for the automobile to complete the trip. a0 hours
Answers
65*8 = 520 miles traveled
520/80 = 6.5 hours for the car
Answer:
The automobile would take 6.5 hours to complete the trip.
Step-by-step explanation:
This is a case of a inverse variation relationship because when you increase the speed of traveling the time of arriving will reduce, now we have to define the equation and the variables:
Inverse variation equation: [tex]x1y1=x2y2[/tex]
[tex]x1[/tex]: speed of the bus, 65 miles per hour
[tex]y1[/tex]: time to Austin by bus, 8 hours
[tex]x2[/tex]: speed of the automobile, 80 miles per hour
[tex]y2[/tex]: time to Austin by automobile, unknown
Now we can replace the values in the equation and clear [tex]y2[/tex], this is:
[tex]65*8=80*y2\\y2=\frac{65*8}{80} =\frac{520}{80} =6.5\\[/tex]
The automobile would take 6.5 hours to complete the trip.
The number of terms in a binomial expansion
is one less than the power
is equal to the power
is one more than the power
Answers
Ex(x+y)^3=x^3+3x^2y+3xy^2+y^3
As you can see power of 3 but 4 terms
Answer:
(C) is one more than the power
Step-by-step explanation:
Let us consider a binomial expansion:
[tex](x+y)^2=x^2+2xy+y^2[/tex]
The power of the above expansion is [tex]2[/tex] and the number of the terms in the above binomial expansion are [tex]3[/tex], thus the total number of terms in the binomial expansion is one more than the power.
Hence, Option C is correct.
Prove that f(x) = x^3 – 1000x^2 + x – 1 is ω(x^3) and o(x^3).
Answers
> x3 − 1000x^ 2
= (x − 1000)x^2
> (.9x)x^2
= .9x^3
Therefore, f(x) is Ω(x^3 ) with C = .9, k = 10, 000. Also, for all x > 0:
f(x) = x^3 − 1000x^2 + x − 1
< x^3 + 1000x^3 + x^3 + x^3
= 1002x^3
Therefore, f(x) is O(x^3 ) with C = 1002, k = 1.
To prove that [tex]f(x) = x^3 - 1000x^2 + x - 1[/tex] is [tex]\omega(x^3)[/tex] and [tex]o(x^3)[/tex], we must show how the function grows in comparison to x^3 asymptotically.
To prove that [tex]f(x) = x^3 - 1000x^2 + x - 1[/tex] is [tex]\omega(x^3)[/tex] and [tex]o(x^3)[/tex], we need to show two things:
1. Proving that [tex]f(x) = x^3 - 1000x^2 + x - 1[/tex] is [tex]\omega(x^3)[/tex]
For a function to be [tex]\omega(x^3)[/tex], it needs to grow faster than [tex]x^3[/tex] asymptotically. This requires that the ratio of the function to [tex]x^3[/tex] tends towards infinity as x approaches infinity.
Consider:
[tex]\lim_{x \to \infty}[\frac{f(x)}{x^3} ] = \lim_{x \to \infty}[ \frac{x^3-1000x^2+x-1}{x^3} ][/tex]
Simplify the expression:
[tex]\lim_{x \to \infty}[ 1-\frac{1000}{x}+\frac{1}{x^2}-\frac{1}{x^3} ] =1[/tex]
Since the limit does not tend to infinity but instead tends to 1, f(x) is not ω(x^3). We made a mistake in our earlier assumption; let's correct this in the next point.
2. Proving that [tex]f(x) = x^3 - 1000x^2 + x - 1[/tex] is [tex]o(x^3)[/tex]
To show that f(x) is [tex]o(x^3)[/tex], the ratio of f(x) to [tex]x^3[/tex] should tend to zero as x tends to infinity.
Consider:
[tex]\lim_{x \to \infty} [\frac{f(x)}{x^3}] = \lim_{x \to \infty}[\frac{x^3-1000x^2+x-1}{x^3}][/tex]
Simplify the expression:
[tex]\lim_{x \to \infty}[ 1-\frac{1000}{x}+\frac{1}{x^2}-\frac{1}{x^3} ] =1[/tex]
This indicates that the limit tends to 1 and not 0, hence f(x) is not [tex]o(x^3)[/tex] either. We can see in both cases that the limits did not meet the required criteria for [tex]\omega(x^3)[/tex] or [tex]o(x^3)[/tex], implying a misunderstanding in the problem setup.
s=n(a1+an)/2 gives the partial sum of an arithmetic sequence. What is the formula solved for an?
Answers
[tex]S= \frac{n}{2} (a_{1}+a_{n})[/tex]
Multiply each side by 2.
[tex]2S=n(a_{1}+a_{n}) [/tex]
Divide each side by n.
[tex] \frac{2S}{n} =a_{1} + a_{n}[/tex]
Subtract a₁ from each side.
[tex] \frac{2S}{n} - a_{1} = a_{n}[/tex]
Answer: [tex]a_{n} = \frac{2S}{n} - a_{1} [/tex]
What is 31/2 times 3 1/2
Answers
because 31/2 * 3 1/2 is 31/2 * 7/2
What is the area of a parallelogram whose vertices are A(−4, 9) , B(11, 9) , C(5, −1) , and D(−10, −1) ?
Answers
Let
[tex]A(-4,9)\\B(11,9)\\C(5,-1) \\D(-10,-1)\\E(-4.-1)[/tex]
using a graphing tool
see the attached figure to better understand the problem
we know that
Parallelogram is a quadrilateral with opposite sides parallel and equal in length
so
[tex]AB=CD \\AD=BC[/tex]
The area of a parallelogram is equal to
[tex]A=B*h[/tex]
where
B is the base
h is the height
the base B is equal to the distance AB
the height h is equal to the distance AE
Step 1
Find the distance AB
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
[tex]A(-4,9)\\B(11,9)[/tex]
substitute the values
[tex]d=\sqrt{(9-9)^{2}+(11+4)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(15)^{2}}[/tex]
[tex]dAB=15\ units[/tex]
Step 2
Find the distance AE
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
[tex]A(-4,9)\\E(-4.-1)[/tex]
substitute the values
[tex]d=\sqrt{(-1-9)^{2}+(-4+4)^{2}}[/tex]
[tex]d=\sqrt{(-10)^{2}+(0)^{2}}[/tex]
[tex]dAE=10\ units[/tex]
Step 3
Find the area of the parallelogram
The area of a parallelogram is equal to
[tex]A=B*h[/tex]
[tex]A=AB*AE[/tex]
substitute the values
[tex]A=15*10=150\ units^{2}[/tex]
therefore
the answer is
the area of the parallelogram is [tex]150\ units^{2}[/tex]
The area of the parallelogram is 0 units.
Explanation:To find the area of a parallelogram, we can use the formula A = base * height. We can find the length of the base by finding the distance between points A and D, which is 11 units. To find the height, we can find the distance between points A and B, which is 0 units. Therefore, the area of the parallelogram is 0 units.