The instantaneous rate of change of g with respect to x at x = π/3 is 1/2.
How to determine the instantaneous rate of change of a given functionThe instantaneous rate of change at a given value of [tex]x[/tex] can be found by concept of derivative, which is described below:
[tex]g(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]
Where [tex]h[/tex] is the difference rate.
In this question we must find an expression for the instantaneous rate of change of [tex]g[/tex] if [tex]f(x) = \sin x[/tex] and evaluate the resulting expression for [tex]x = \frac{\pi}{3}[/tex]. Then, we have the following procedure below:
[tex]g(x) = \lim_{h \to 0} \frac{\sin (x+h)-\sin x}{h}[/tex]
[tex]g(x) = \lim_{h \to 0} \frac{\sin x\cdot \cos h +\sin h\cdot \cos x -\sin x}{h}[/tex]
[tex]g(x) = \lim_{h \to 0} \frac{\sin h}{h}\cdot \lim_{h \to 0} \cos x[/tex]
[tex]g(x) = \cos x[/tex]
Now we evaluate [tex]g(x)[/tex] for [tex]x = \frac{\pi}{3}[/tex]:
[tex]g\left(\frac{\pi}{3} \right) = \cos \frac{\pi}{3} = \frac{1}{2}[/tex]
The instantaneous rate of change of g with respect to x at x = π/3 is 1/2. [tex]\blacksquare[/tex]
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The instantaneous rate of change of g with respect to x at x = π/3 is 1/2.
What is the instantaneous rate of change?The instantaneous rate of change is the change in the rate at a particular instant, and it is the same as the change in the derivative value at a specific point.
The instantaneous rate of change is given by the following formula;
[tex]\rm g(x)=lim_{h\rightarrow 0}\dfrac{f(x+h)-f(x)}{h}[/tex]
The given function is;
[tex]\rm f(x)=sinx[/tex]
The function is also written as;
[tex]\rm g(x)=lim_{h\rightarrow 0}\dfrac{sin(x+h)-sin(x)}{h}\\\\g(x)=lim_{h\rightarrow 0}\dfrac{sinx cosh +cosx sinh-sinx}{h}\\\\g(x)=lim_{h\rightarrow 0}\dfrac{sinh}{h}. \ lim_{h\rightarrow 0} cosx\\\\g(x)=cosx[/tex]
Substitute the value of x in the function
[tex]\rm g(\pi /3)= cos(\pi /3)=1/2\\[/tex]
Hence, the instantaneous rate of change of g with respect to x at x = π/3 is 1/2.
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Kathy was building a bed for her dollhouse. She used her bed, which is 3 feet × 5 feet, as a guide. She scaled down the dimensions of her bed by a factor 1 over 5 . What are the dimensions of the model bed she built? (1 point) 0.06 ft × 0.1 ft 0.3 ft × 0.5 ft 0.03 ft × 0.05 ft 0.6 ft × 01 ft
Answer:
0.6 x 0.1
Step-by-step explanation:
Is the following relation a function yes or no
It's function of sinus
...........
answer quickly please
The line TU is tangent to the circle whose center is at point S
The measure of angle U is 84 degrees
How to determine angle U?From the question, we understand that:
Angle STV = 84 degreesTU is tangent to circle SThis second highlight means that:
Angle STU = 90 degrees
And:
Angle STU = Angle STV + Angle VTU
This gives
90 = 84 + Angle VTU
Subtract 84 from both sides
Angle VTU = 6
The measure of angle U is then calculated as:
U + Angle VTU + Angle UVT = 180 ------ sum of angles in a triangle
This gives
U + 6 + 90= 180
Evaluate the sum
U + 96 = 180
Subtract 96 from both sides
U = 84
Hence, the measure of angle U is 84 degrees
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Jacob and his father measured the lengths of scrap wood in their yard. Make a line plot of their data.
The line plot is used to show the lengths of the scrap woods using check marks above the line
How to draw the line plotFrom the question, we have the following frequency table
Lengths Frequency
[tex]4\frac 18[/tex] 2
[tex]4\frac 14[/tex] 3
[tex]4\frac 38[/tex] 1
[tex]4\frac 12[/tex] 6
[tex]4\frac 58\\[/tex] 1
[tex]4\frac 34[/tex] 2
[tex]4\frac 78[/tex] 2
[tex]5[/tex] 1
Next, we plot the number line.
Such that the lengths of the scrap woods are on the x-axis while their frequencies are on the y-axis
See attachment for the line plot
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Answer:
Step-by-step explanation:
Write the expression. Then, complete the statements.
twice the difference of a number and seven
The word "twice" means
.
The words "the difference of" indicate
.
The expression is written as
Answer:
The equation is 2(x-7)
Hope it is correct
Answer: Write the expression. Then, Complete the statements.
.
.
twice the difference of a number and seven
Step-by-step explanation:
1. multiplication by 2
2. subtraction in parentheses
3. 2(n-7)
can someone help me fast -2 1/3 - (-5
Answer:
your answer is positive 8/3
Step-by-step explanation:
When you are subtracting something by a negative number, it is the same as adding by a positive. For example, this equation would be solved like:
-2 1/3 + 5
Instead of -2 1/3 - (-5)
Hope that helps!
 Order these numbers least to greatest
Answer:
1. -83/7
2. -11.6666666
3. - square root of 133
4. 11 5/10
(PLS HELPP EASYY POINTS )
A company makes piñatas for special events such as birthday parties. One of their piñatas is in the form of a cone shaped hat. How much space do they have inside the piñata for candy if the piñata is 2 feet tall and 1.5 feet wide? Round to the nearest hundredth
I don't recognize this problem, please make sure the input is complete.
Jesse is helping her grandmother plant a garden in the shape of a trapzoid
Base one is 12.5
base two 0.5 times length of base one
the height is 10 feet
I need helppppppppppppppppppp
Answer:
See explanation
Step-by-step explanation:
look at the photo
I hope it will help you <3
Answer:
Step-by-step explanation:
*The other person that answered may be correct, but this was my way of solving the functions.
What is the measure of the
missing angle?
64°
97°
?
116°
O
o
78°
72°
80°
83°
Answer:
? = 83°
Step-by-step explanation:
the sum of the interior angles of a quadrilateral = 360°
sum the angles and equate to 360°
? + 116° + 97° + 64° = 360° , that is
? + 277° = 360° ( subtract 277° from both sides )
? = 83°
Answer:
it is an obtuse angle so that should get rid of some of the answer choices
Step-by-step explanation:
Find the area of the parallelogram
Answer:
30.42 in^2.
Step-by-step explanation:
Find the height:
sin 45 = 1/√2 = h/7.8
h = 7.8 /√2
the base = height = 7.8 /√2
Area = h * b
= (7.8 /√2)2
= 30.42.
The values in the table below represent function B, which is linear function (-3,-7) (-1,-1) (1,5) (3,11)
Answer:
I don't see the picture of the problem
Geometry shapes I need help asap
Question
Without looking, Luke picks necklace beads from a bag of 52 beads. Half the beads are rough. The other half are smooth. There are 13 red beads, 13 blue beads, 13 green beads, and 13 black beads.
What is the theoretical probability of selecting a blue bead? Write the probability as a fraction in simplest form.
Enter the correct answer in the boxes.
Answer:
1/4
Step-by-step explanation:
This question is asking for the probability of just picking a blue bead
It does NOT say anything about picking a smooth or rough!
This means you don't have to worry about it being smooth or rough (it is just extra information to throw you off)
So to find just picking one blue bead, you want to have the amount of blue beads divided by the total amount of beads
the amount of blue beads is 13
and the total is 52
So:
13/52 is your probability, but you want to simplify
Which comes out to
1/4
A rectangular red sticker has a perimeter of 40 millimeters and an area of 64 square
millimeters. What are the dimensions of the sticker?
millimeters by millimeters
Submit
Answer:
16 x 4.
Step-by-step explanation:
What multiplies into 64?
could be 16 and 4?
16 x 2 = 32
4 x 2 = 8
32 + 8 = 40, therefore, this is correct.
The rectangle graphed has a length of 5 and a width of 4. How does the perimeter change when the width is decreased by half?
A) The perimeter is decreased by 2.
B) The perimeter is decreased by 4.
The perimeter is decreased by 5.
C) The perimeter is decreased by 6.
D) The perimeter is decreased by half
sam
Answer:
B
Step-by-step explanation:
The perimeter is decreased by 4 because 2(5+2) = 14 when 2(5+4) = 18
line c has a slope of -9/2. line d is parallel to like c. what is the slope of line d?
Answer:
-9/2
Step-by-step explanation:
parallel lines have the same slope/gradient
Jasmine made a line plot to show the lengths of string in inches that the art teacher gave her for a craft project. A line plot named Which of the following statements that Jasmine made about the string lengths are true? Select the two that apply. A. The difference between the longest length and shortest length is 14 inches. B. I have twice as many 12-inch strings as I do 8-inch strings. C. The total length of string that I have is 84 inches. D. I cannot determine what the shortest string is by looking at my line plot. E. Since I need 100 total inches of string for my project, I have enough string.
The length of all the strings combined is 84 inches, while the length of the smallest string is 6 inches.
What is a line plot?
A line plot is a graph that shows the frequency of each value by displaying data as points or checkmarks above a number line.
In the given line plot, if we consider each of the options with the plot given to us, we will get to know which of the options are true or not.
A.) A. The difference between the longest length and shortest length is 14 inches.
As given in the plot, the longest string is 14 units while the smallest is 6 units, therefore, the first option is incorrect.
B.) I have twice as many 12-inch strings as I do 8-inch strings.
In the plot since the number of dots represents the number of strings of a particular length, therefore, the number of strings of length 12-inches is 4 and the number of strings of length 8-inches is 2. Thus, the given options are correct.
C.) The total length of string that I have is 84 inches.
As per the plot, the number of strings of length 6 inches is 1, the number of strings of length 8 inches is 2, the strings of length 12inches is 4, and the number of strings of length 14 inches is 1. Thus, the sum of the length of all the strings is 84 inches.
Hence, the statement is correct.
D.) I cannot determine what the shortest string is by looking at my line plot.
As given in the plot, the length of the smallest string is 6 inches, thus, the statement is incorrect.
E.) Since I need 100 total inches of string for my project, I have enough string.
As the length of all the strings combined is just 84 inches, thus, the statement is incorrect.
Hence, the only option that is correct is 'B' and 'C'.
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Starting at an initial height of 364 feet, an object is projected
upward at 60 feet per second. In how many seconds will it
reach the ground? I’m
Step-by-step explanation:
4.5 s, 324 ft
Explanation:
The object is projected upward with an initial velocity of
v_0 = 144 ft/sv
0
=144ft/s
The equation that describes its height at time t is
s(t) = -16t^2 + 144 ts(t)=−16t
2
+144t (1)
where t, the time, is measured in seconds.
In order to find the time it takes for the object to reach the maximum height, we must find an expression for its velocity at time t, which can be found by calculating the derivative of the position, s(t):
v(t) = s'(t) = -32t +144v(t)=s
′
(t)=−32t+144 (2)
At the maximum heigth, the vertical velocity is zero:
v(t) = 0
Substituting into the equation above, we find the corresponding time at which the object reaches the maximum height:
\begin{gathered}0=-32t+144\\t=\frac{144}{32}=4.5 s\end{gathered}
0=−32t+144
t=
32
144
=4.5s
And by substituting this value into eq.(1), we also find the maximum height:
s(t) = -16(4.5)^2+144(4.5)=324 fts(t)=−16(4.5)
2
+144(4.5)=324ft
used this way i even don't know sorry:))Abby is buying flower bulbs for her garden. She wants to buy the same number of tulips and daffodils. If tulip bulbs come in packs of 8 and daffodil bulbs come in packs of 4, what is the least number of each type of bulb Abby will need to buy?
16
lcm : 4= 4, 8, 12 , 16
8= 8 , 16
The group is trying to determine what the price difference would be per passenger if 10 of them go on the trip versus if 16 of them go on the trip. what is the difference in price per passenger for a group of 16 versus a group of 10? $46.25 $36.25 $56.25 $26.25
The difference in price per passenger for a group of 16 versus a group of 10 for this condition is given by: Option D: $26.25
What does a graph of a function represents?A graph contains data of which input maps to which output.
For Cartesian plane, this includes inputs x-axis, and corresponding output on y axis and the highlighted point (x,y) shows that the x value is related to the specific y value.
For the considered case, the missing image is attached below.
From the image, we see that corresponding to the value of number of people 10, the corresponding point on the graph is connected with vertical axis at $1300
For number of people 16, it is $2500
The price per passenger for 10 people is: 1300/10 = $130 The price per passenger for 16 people is: 2500/16 = $156.25The difference in these prices is 156.25 - 130 = 26.25 (in dollars)
Thus, the difference in price per passenger for a group of 16 versus a group of 10 for this condition is given by: Option D: $26.25
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Answer:
D. $26.25
Step-by-step explanation:
edg
When solving, at what point do you know that your solutions are imaginary? Does x^2 +9 =0 have real or imaginary solutions? How do you know?
Answer:
Real solutions
Step-by-step explanation:
I know that because I am smart
To train for a marathon, Lily plans on running 4 miles per day for the first week and then increasing that daily distance by 1 mile each of the following weeks.
Which of these equations represent the problem.
The equation which represent the problem is given by an = 4 + 1.00(n - 1)
How to write equation?Number if miles Lily run per day first week = 4 miles
Additional miles per day each week = 1 mile
let
n = total miles
The equation:
an = 4 + 1.00(n - 1)
When n = week 2an = 4 + 1(n - 1)
= 4 + 1(2 - 1)
= 4 + 1(1)
= 4 + 1
= 5 miles
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How can you reduce the variability of a statistic?
Answer:
How can you reduce the variability of a statistic? By taking a larger sample. Larger samples give smaller spread. Also by better design, such as stratified sampling. What effect does the size of the population have on the variability (spread) of a statistic?
Step-by-step explanation:
The formula P = I-E is used to calculate profit.
P = Profit
I= Income
E = Expenses
The school bake sale earned $72 in sales and had
$125 in expenses.
Find the profit.
b. What does a negative profit mean?
Hey there!
P = I - E
Income = $72Expenses= $125P = I - E {Add values}
P = 72 - 125
= -53
Negative profit means loss, which means there was no gain
Hopes this helps
Rebecca has $128 to spend. She
spends $78 on a running shoes.
Tank tops cost $12.50 each. Write and
solve an inequality to find how many
tank tops she can buy.
Answer:
12.5x =10x+10
12.50x=x10+10
subtract 10x from both sides
2.5x=10
divide by 2.5
x=4
I need jelpsssssssss
Answer:
sum up all the sizes and multiple it by 2
help me please!! will choose brainlyest if you get it right
what are the features of function g if g(x)=f(x + 4) + 8?
vertical asymptote of x= -4
domain of (4, [infinity])
y-intercept at (0,10)
x-intercept at (1,0)
range of (8, [infinity])
The correct statement is that the range of the function is (8, [infinity])
How to find the intercept, domain and range of a functionGiven the function as shown below:
g(x) = √(x + 4) + 8
The domain of the function is the point here x + 4 ≥ 0
Domain = x ≥ -4
In interval form, the domain of the function is [-4, 0)
The range of the function is the real values from 8 and above. Hence the range of the function is (8, [infinity])
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