Find the average rate of change of f(x) = 6x² - 3 on the interval [3, t]. Your answer will be an expression involving t.
Answers
To find the average rate of change of a function on an interval, we need to calculate the difference in function values divided by the difference in x-values.
Given the function f(x) = 6x^2 - 3, we want to find the average rate of change on the interval [3, t].
Let's evaluate the function at the endpoints of the interval:
f(3) = 6(3)^2 - 3 = 54 - 3 = 51
f(t) = 6(t)^2 - 3
The difference in function values is f(t) - f(3) = (6t^2 - 3) - 51 = 6t^2 - 54.
The difference in x-values is t - 3.
Therefore, the average rate of change of f(x) on the interval [3, t] is (6t^2 - 54)/(t - 3).
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Related Questions
What is 3 1/4 x 2/5 x1/2
Answers
Answer: 0.65
Step-by-step explanation:
Answer:
\(\frac{13}{20}\)
Explanation:
\(3 \frac{1}{4}\) × \(\frac{2}{5}\) × \(\frac{1}{2}\)
First, you want to remove any coefficient in front of the fraction.
\(3\frac{1}{4} = \frac{13}{4}\)
To change \(3\frac{1}{4}\), first you multiply the coefficient 3 to 4, which equals 12. Then add 12 to 1, which equals 13.
Now multiply:
\(\frac{13}{4}\) × \(\frac{2}{5}\) × \(\frac{1}{2}\)
\(13\) × \(2\) × \(1\) = \(26\)
\(4\) × \(5\) × \(2\) = \(40\)
\(\frac{13}{4}\) × \(\frac{2}{5}\) × \(\frac{1}{2}\) = \(\frac{26}{40}\)
Simplify:
\(\frac{26}{40}\) = \(\frac{13}{20}\)
add (4x + 8) + (7x + 3)
Answers
Answer:
11x+11
Step-by-step explanation:
(4x+8)+(7x+3)=4x+7x+8+3=11x+11=11(x+1)
Answer:
11x + 11
Step-by-step explanation:
(4x + 8) + (7x + 3)
add 4x and 7x
then add 8 and 3
Which is the best estimate of the difference between 6 7 8 678 and 2 1 8 218
Answers
Answer: C.5
Step-by-step explanation:
researcher records the following scores for an Olympic gymnast following her routine: 9.9, 9.8, 9.6, 9.5, 9.7, 9.1, 8.9, and 9.8. What is the range for the scores?
1.0 (9.9 to 8.9)
0.3 (9.8 to 9.5)
0.5 (9.6 to 9.1)
It is not possible to compute a range with an even number of scores.
Answers
The range for the scores is 1.0 (from 9.9 to 8.9). The range is the difference between the highest and lowest numbers in a set of numbers. In this case, the highest score is 9.9 and the lowest score is 8.9, so the range is 1.0.
In mathematics, the range of a function can refer to one of two similar terms:
the common area of the function
The image of the function
Given two groups X and Y, the binary relation f between X and Y is a (exact) function (X to Y), if there is a y in Y for every x in X, so f is associated with y. The sets X and Y are called the area of f and the common domain, respectively.
The range is a measure of dispersion in a set of numbers. To find the range, you need to subtract the lowest score from the highest score. In this case, the scores for the Olympic gymnast are: 9.9, 9.8, 9.6, 9.5, 9.7, 9.1, 8.9, and 9.8.
First, identify the highest and lowest scores:
Highest score: 9.9
Lowest score: 8.9
Next, subtract the lowest score from the highest score:
Range = 9.9 - 8.9
The range for the scores is 1.0 (9.9 to 8.9).
Your answer: 1.0 (9.9 to 8.9)
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what does the equation x 2 y 2 = 4 correspond to if a) x, y are the only variables being considered, b) x, y, z are the only variables being considered.
Answers
The equation x² y² = 4 corresponds to a hyperbola when only considering x and y as variables. When considering x, y, and z as variables, the equation corresponds to a two-sheeted hyperboloid.
a) When only x and y are the variables being considered, the equation x² y² = 4 corresponds to a circle in the xy-plane. The circle has a center at the origin (0,0) and a radius of 2.
b) If x, y, and z are the only variables being considered, the equation x² y² = 4 still represents a circle in the xy-plane, but it becomes a cylinder along the z-axis. This cylinder has a center on the z-axis and a radius of 2, extending infinitely along the z-axis.
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Joseph has a bag filled with 3 red, 3 green, 9 yellow, and 10 purple marbles. Determine P(not green) when choosing one marble from the bag.
92%
88%
24%
12%
Answers
The probability, P(not green) when choosing one marble from the bag is 88%.
What is probability?The probability of an event is a number that indicates how likely the event is to occur.
Given is that Joseph has a bag filled with 3 red, 3 green, 9 yellow, and 10 purple marbles
We can write -
P(not green) = 1 - P(green)
So, we can write -
P(green) = n{g}/n{s}
P(green) = 3/25
So, we can write -
P(not green) = 1 - P(green)
P(not green) = 1 - 3/25
P(not green) = 22/25
Now -
Let -
22 is x% of 25
22 = x/100 x 25
x/4 = 22
x = 88%
Therefore, the probability, P(not green) when choosing one marble from the bag is 88%.
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Is the curve r(t) = parametrized by its arc length? Explain.
choose the correct answer below.
1- no. the curve is not parametrized by its arc length because (v(t))= cos t- sin t.
2- yes. the curve is parametrized by its arc length because (v(t))= t for all t. Thus, (v(t))= 1 for t=1.
3- no. the curve is not parametrized by its arc length because(v(t))=(r(t)) for all t.
4- yes. the curve is parametrized by its arc length because (v(t))=1 for all t.
Answers
The correct answer is 4 - yes. The curve r(t) is parametrized by its arc length, because the speed or magnitude of the velocity vector (v(t)) is constant and equal to 1 for all t.
When a curve is parametrized by its arc length, it means that the parameter t represents the distance traveled along the curve starting from some fixed point. In other words, if we take any two values of the parameter, say t1 and t2, then the distance between the corresponding points on the curve will be |r(t2) - r(t1)| = t2 - t1.
To see why the given curve is parametrized by its arc length, we can calculate the speed or magnitude of its velocity vector:
|v(t)| = sqrt((dx/dt)^2 + (dy/dt)^2)
= sqrt((-sin(t))^2 + (cos(t))^2)
= sqrt(sin^2(t) + cos^2(t))
= sqrt(1)
= 1
Since the speed is constant and equal to 1, we can interpret the parameter t as the arc length traveled along the curve starting from some fixed point. Therefore, the curve r(t) is indeed parametrized by its arc length.
In summary, the key idea here is that when the speed of a curve is constant and equal to 1, the parameter can be interpreted as the arc length traveled along the curve, and hence the curve is parametrized by its arc length.
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Consider the quadratic function f(x) =x - 5x + 6.
What are the values of the coefficients and constant in the function?
Answers
The values of the coefficients and constant in the quadratic function are a = 1, b = -5, and c = 6, where a and b are coefficients and c is the constant.
What are quadratic functions?A polynomial function with one or more variables, where the greatest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the highest degree term in a quadratic function is of the second degree. The formula for a quadratic equation is ax² + bx + c = 0, where a and b are referred to as the coefficients of x² and x, respectively. The function's constant is the c term.Given quadratic function f(x) = x² - 5x + 6.
The values of the coefficients and constant in the function are
a = 1
b = -5
c = 6
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The ratio of green apples to red apples in a bucket is 5 to 9. For every 10 green apples there are __ red apples.
plz help
Answers
Your hospital has just reset the safety stock level for sleeping pills to be 220 pills.
If your hospital consumes an average of 1,155 per day with a standard deviation of 81 pills, what is the chance that your hospital will run out of sleeping pills on any day? (Keep four decimal places in your answer, which should be a number not a percentage)
Answers
The chance that the hospital will run out of sleeping pills on any given day is 0.5000 (or 0.5000 with four decimal places).
To calculate the chance that the hospital will run out of sleeping pills on any given day, we can use the normal distribution and Z-score.
First, let's calculate the Z-score using the formula:
Z = (X - μ) / σ
Where:
X = consumption rate per day (1,155 pills)
μ = average consumption rate per day (1,155 pills)
σ = standard deviation (81 pills)
Z = (1,155 - 1,155) / 81
Z = 0
Now, we need to find the probability associated with this Z-score. However, since the demand for sleeping pills can be considered continuous and not discrete, we need to calculate the area under the curve from negative infinity up to the Z-score. This represents the probability of not running out of sleeping pills.
We discover that the region to the left of a Z-score of 0 is 0.5000 using a basic normal distribution table or statistical software.
To find the probability of running out of sleeping pills, we subtract this probability from 1:
Probability of running out of sleeping pills = 1 - 0.5000
Probability of running out of sleeping pills = 0.5000
Therefore, on any given day, the hospital has a 0.5000 (or 0.5000 with four decimal places) chance of running out of sleeping tablets.
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Danica has 15 stickers. She gives 3 to one friend
and gets 4 from another friend. What expression
would match the words?
Answers
Answer:
(15-3)+4 = x (amount of stickers)
Step-by-step explanation:
She has fifteen but gives three to a friend, giving you the first amount and then you add the four she later gets from someone else into the total to get your final number.
Drag each label to the correct location on the equation. Each label can be used more than once, but not all labels will be used. A company has two packaging machines in a unit, each with a different daily capacity. The capacity of machine 1 is defined by the function f(m) = (m + 4)2 + 100, and the capacity of machine 2 is defined by the function g(m) = (m + 12)2 − 50, where m is the number of minutes the packaging machine operates. Create the function C(m) that represents the combined capacity of the two machines
Answers
The combined capacity is given by (f+g) m = 2m² +32 m +210
What is an Equation ?An equation is defined as a mathematical statement used to relate a dependent and an independent variable.
The equation that gives the capacity of machine 1 is
f(m) = (m+4)² +100
and
The equation that gives the capacity of machine 2 is
g(m) = (m + 12)² -50
The total capacity of both the machine is given by
f(m) + g(m) = (m+4)² +100 +(m + 12)² -50
(f+g) m = 2m² +32 m +210
Therefore the combined capacity is given by (f+g) m = 2m² +32 m +210
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On a test that has a normal distribution, a score of 54 falls two standard deviations
above the mean, and a score of 42 falls one standard deviation below the mean.
Determine the mean of this test.
Answers
Let μ be the mean of the distribution and let σ be its standard deviation.
We know that 54 falls two standard deviations above the mean, this can be express as:
\(\mu+2\sigma=54\)We also know that 42 falls one standard deviation below the mean, this can be express as:
\(\mu-\sigma=42\)Hence, we have the system of equations:
\(\begin{gathered} \mu+2\sigma=54 \\ \mu-\sigma=42 \end{gathered}\)To find the mean we solve the second equation for the standard deviation:
\(\sigma=\mu-42\)Now we plug this value in the first equation:
\(\begin{gathered} \mu+2(\mu-42)=54 \\ \mu+2\mu-84=54 \\ 3\mu=138 \\ \mu=\frac{138}{3} \\ \mu=46 \end{gathered}\)Therefore, the mean of the distribution is 46
pls help im failing i need help ASAP
Answers
The answer is choice 1 because when you divide 2 numbers with the same base and different exponents you subtract the second exponent from the first.
p^-m / p^-n = p^(-m - (-n))
CHOICE 1
Hope this helps
Two parallel tangents 12m apart are connected by a reversed curve. The chord length from
the PC to the PT is 100m long. If the reversed curve has equal radii, determine the following
The equal radius of the reversed curve.
Answers
The radius of the reversed curve is approximately 50.72m.
Given data: Two parallel tangents 12m apart are connected by a reversed curve. The chord length from the PC to the PT is 100m long. If the reversed curve has equal radii.
To determine the equal radius of the reversed curve we will use the following formula
R = [(L/2)²+ (C/2)²]/2(C/2)
Where R = radius of the reversed curve
L = length of curve
C = chord length
For this problem, we have C = 100mL = 12m
Now, substituting these values into the formula, we get
R = [(L/2)²+ (C/2)²]/2(C/2)
R = [(12/2)² + (100/2)²]/2(100/2)
R = [6² + 50²]/50R = (36 + 2500)/50
R = 2536/50R = 50.72m
Hence, the radius of the reversed curve is approximately 50.72m.
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Which of the following is NOT a guideline for finding the best multiple regression equation? Choose the correct answer below. A. If two predictor values have a very high linear correlation coefficient, both should be included in finding the multiple regression equation. B. Consider equations with high values of adjusted R2, and try to include only a few variables C. Consider the P-value to select an equation having overall significance. D. Use common sense and practical considerations to include or exclude variables.
Answers
Answer: Answer A is correct :)
Step-by-step explanation:
If two predictor values have a very high linear correlation coefficient, both should be included in finding the multiple regression equation.
5. An online music streaming company, iTunez, charges Alex $8.99 each month for unlimited
music downloads. Another company, Beatz On Demand, charges him a one-time fee plus a
monthly charge as shown in the table. Which company charges the smallest monthly rate?
0
1
2.
3
Number of Months
$25
$30.99
$36.98
Total Cost
$42.97
Answers
Answer:
Beatz on demand
Step-by-step explanation:
because...
40,000 + 6,000 + 200 + 80 + 8 written in standard form?
Answers
Answer:
46,288
Step-by-step explanation:
40,000 + 6,000 + 200 + 80 + 8
46,288
Hope this helps :D
Solve the inequality:
11x+12≥45
Select one:
x>3
x≤3
x<3
x≥3
Answers
Answer:
ALL OF THEM
Step-by-step explanation:
Answer:
x≥3
Step-by-step explanation:
subtract 12 from each side
11x≥33
divide by 11
x≥3
at is the volume of this triangular prism? 7m, 24m, 22m
Answers
Answer:
3,696
Step-by-step explanation:
7x24x22 equals 3,696
24x7=168
168x22=3,696
In the circle, BC is a diameter. What is the measure of x?
Answers
The measure of the angle x is 22.5 degrees
Circle geometryCircle theorem includes the concept of tangents, sectors, angles, the chord of a circle and proofs.
A circle is the locus of all points in a plane which are equidistant from a fixed point
From the given diagram
arc AC = 180 - 135
arcAC = 45 degrees
Since the angle at the vertex is half the intercepted arc, hence;
x = 1/2(arc AC)
x = 1/2(45)
x = 22.5 degrees
Hence the measure of the angle x is 22.5 degrees
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When Alexis adopted her puppy, the puppy weighted 12 pounds. One year later, the puppy weighted 60 pounds. By what percent did the puppy's weight change in one year?
Answers
Answer:
400%
Step-by-step explanation:
Original wieght = 12
New weight = 60
Change = 60- 12= 48
Change percent = change / original x 100 = 48 / 12 x 100 = 400 %
I hope its right!!!! :)
A ____ should ALWAYS be representative of the general population.
A. Mode
B. Survey
C. Sample
D. Dot plot
(7th grade math)
Answers
125+25x = 50 I need a answer quickly
Answers
Answer:
-3
Step-by-step explanation:
Subtract 25x 125=-25x+50
Subtract 50 125-50= -25x
Simplify 75= -25x
Divided 75 by negatrive 25
work out 3a+b as a column vector
Answers
```
[3a + b]
```
This is a column vector with one element.
The school is 3.64 miles from Tonya's house and 1.27 miles from Jamal's house. How much farther from school is Tonya's house than Jamal's house? Complete the explanation on how you can use a quick picture to solve the problem.
Answers
Answer: Tonya's house is 2.37 miles farther from the school than Jamal's house.
Step-by-step explanation: To solve this problem using a quick picture, we can draw a line segment to represent the distance from the school to Tonya's house, and another line segment to represent the distance from the school to Jamal's house. We can then use a ruler to measure the length of each line segment and subtract the length of the line segment representing the distance to Jamal's house from the length of the line segment representing the distance to Tonya's house.
For example, if we draw a line segment that is 3.64 inches long to represent the distance from the school to Tonya's house and a line segment that is 1.27 inches long to represent the distance from the school to Jamal's house, then we can use a ruler to measure the lengths of the line segments and find that the line segment representing the distance to Tonya's house is 3.64 - 1.27 = 2.37 inches longer than the line segment representing the distance to Jamal's house. This means that Tonya's house is 2.37 miles farther from the school than Jamal's house.
Plot the ordered pairs on your grid paper, connect, and label them accordingly.
Line Segment A (0, 7); (0, 9)
Line Segment B (3, 9); (4.5, 9)
Line Segment C (4.5, 8); (4.5, 10)
Which line segment is 1.5 units long?
Answers
cot²3x - 3cot3x +2 = 0
cotx = t
what equation for t
Answers
Answer:
Step-by-step explanation:
cot²(3x)=y
y²-3y+2=0
y²-y-2y+2=0
y(y-1)-2(y-1)=0
(y-1)(y-2)=0
y=1,y=2
cot3x=1
tan 3x=1=tan (π/4)=tan (nπ+π/4)
3x=nπ+π/4=(4nπ+π)/4=(4n+1)π/4
x=(4nπ+1)π/12,n is an integer.
cot 3x=2
tan 3x=1/2
3x=tan^{-1}(1/2)≈26.57°+360n
x≈8.86°+120n
Given the points below, are the two lines parallel, perpendicular, or neither.
L1: (-4, 6) (-3,-1) L2: (8,9) (15, 10)
Answers
Answer:
perpendicular
Step-by-step explanation:
First we need to dtemine the slopes of the line
For line 1
L1: (-4, 6) (-3,-1)
m1 = y2-y1/x2-x1
m1= -1-6/-3+4
m1 = -7/1
m1 = -7
For line 2:
L2: (8,9) (15, 10)
m2 = 10-9/15-8
m2 = 1/8
Take their product
m1 * m2 = -7 * 1/7
m1m2 = -1
Since the product of their slopes is -1, hence they are perpendicular
456 milligrams equals how many grams
Answers
Answer:
0.456 :)
Step-by-step explanation: