Which exponential expressions are equivalent to the one below? Check allthat apply.(3.7) 10A. 310 + 710B. (3:7)10O .C. 2110O d. 310.710
Answers
Given the exponential expression:
[tex](3\cdot7)^{10}[/tex]The equivalent expressions are:
[tex]\begin{gathered} (3\cdot7)^{10}=3^{10}\cdot7^{10} \\ (3\cdot7)^{10}=21^{10} \end{gathered}[/tex]So, the answer will be options C, D
Related Questions
Every day the ocean has two low tides and two high tides. Function g represents the height, in feet, of the water level in a cove relative to theaverage sea level. Let t represent the number of hours elapsed since the water height was equal to the average sea level after a low tide.s(e) = ssin(}t)Plot the points where s(4) is equal to the average sea level.
Answers
We can see from the question that we have the sine function, which is modeling the water level in a cove relative to the average sea level, and this function is given by:
[tex]g(t)=4sin(\frac{\pi}{6}t)[/tex]And we need to find the points where g(t) is equal to the average sea level.
1. To find it, we need to analyze the given function as follows:
2. Then we can say that the function has:
• An amplitude (the value from the ,midline of the function, in this case, x = 0,).
,• The period of the function is given by:
[tex]\begin{gathered} \text{ Period=}\frac{2\pi}{B} \\ \\ \text{ Period=}\frac{2\pi}{\frac{\pi}{6}}=2\pi(\frac{6}{\pi})=12 \\ \\ \text{ Period=}12 \end{gathered}[/tex]3. These values can be seen as follows:
4. To find the points where g(t) is equal to the average sea level, we can see that the average sea level is represented by the midline, x = 0, and from the graph, we can see that these points are points on the x-axis, and they are (6, 0), and (12, 0) for the given graph:
Mia is painting a fence that is 1625 meters long In the morning she painted 245 meter of the fence how can Mia figure out how much more she has left to paint
Answers
If Mia is painting a fence that is 1625 meters long In the morning she painted 245 meter of the fence then she 1380 more she has left to paint
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Mia is painting a fence that is 1625 meters long
Morning she painted 245 meter of the fence
We need to find how much more she has left to paint
To find this we need to subtract 245 from 1625
1625-245
1380
Hence 1380 more she has left to paint
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Unit 5 Project 1. A projectile is fired upward from the ground with an initial velocity of 300 feet per second. Neglecting air resistance, the height of the projectile at any time I can be described by the polynomial function P(t) = -16ť + 3000 a. Find the height of the projectile when t = 1 second. b. Find the height of the projectile when t = 5 seconds. c. How long will it be until the object hits the ground? 2. A board has length (3x + 6x - 18) meters and width of 2x + 1 meters. The board is cut into three pieces of the same length a. Find the length of each piece. b. Find the area of each piece. c. Find the area of the board before it is cut. d. How is the area of each piece of the board related to the area of the board before it is cut? 3. A cubic equation has zeros at -2, 1, and 3. a. Write an equation for a polynomial function that meets the given conditions. b. Draw the graph of a polynomial function that meets the given conditions. 4. Alice was having a conversation with her friend Trina, who had a discovery to share: 10
Answers
1)
The polynomial modelling this scenario is expressed as
P(t) = - 16t^2 + 300t
where
P(t) represents the height at time t
a) To find the height of the projectile when t = 1 second, we would substitute
t = 1 into the equation. Thus,
P(1) = - 16(1)^2 + 300(1)
P(1) = - 16 + 300 = 284
Height of projectile when t = 1 second is 284 feet
b) To find the height of the projectile when t = 5 second, we would substitute
t = 5 into the equation. Thus,
P(1) = - 16(5)^2 + 300(5)
P(1) = - 400 + 1500
Height of projectile when t = 5 second is 1100 feet
c) At the time when the object hits the ground, the height would be zero. This means that p(t) = 0
Thus, the equation would be
0 = - 16t^2 + 300t
Factoring out 4t from the right, we have
0 = - 4t(4t - 75)
- 4t = 0 or 4t - 75 = 0
t = 0/-4 or 4t = 75
t = 0 or t = 75/4
t = 0 or t = 18.75
It will take 18.75 seconds until the object hits the ground
26. Find the area of the figure to the nearest tenth,165°7 inA. 13.5 in.B. 7.1 in 2C. 84.8 in 2D. 42.4 in?
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To find the area of the segment of the circle, use the following formula:
[tex]A=\frac{a}{360}\pi r^2[/tex]Where a is the angle of the segment and r is the radius of it. Replace for the given values and find the area of the segment:
[tex]\begin{gathered} A=\frac{165}{360}\pi\cdot(7)^2 \\ A=70.55 \end{gathered}[/tex]please help i dont know to do it please help
Answers
Given:
0.5
Let's write the decimal in form of a fraction a/b using integers.
To write the number in fractional form, we have:
[tex]0.5=5\times10^{-1}[/tex]Since the exponent is the negative of 1, using the definition of negative exponent, we have:
[tex]5\times10^{-1}=\frac{5}{10^1}=\frac{5}{10}[/tex]Therefore, the correct fraction is:
[tex]\frac{5}{10}[/tex]ANSWER:
[tex]\frac{5}{10}[/tex]your dinner bill was $21.00 if you leave a 20% tip, how much will the tip be?
Answers
As given by the question,
There are given that the total bill was $21.00
Now,
If leave a 20% tip,
Then,
[tex]\begin{gathered} 21\times\frac{20}{100}=21\times\frac{1}{5} \\ =4.2 \end{gathered}[/tex]Hence, the tip
Which of these describes the function graphed below? 6 2 8 6 2 8 -2 -6 -8 There is a nonlinear relationship between x and y when x is less than 1 and a linear relationship when x is greater than 1 O There is a linear relationship between x and y when x is less than 1 and a nonlinear relationship when x is greater than 1 There is a linear relationship between x and y when x is less than 0 and a nonlinear relationship when x is greater than 0. There is a nonlinear relationship between x and y when x is less than 0 and a linear relationship when x is greater than 0
Answers
Answer
Option C is correct.
There is a linear relationship between x and y when x is less than 0 and a nonlinear relationship when x is greater than 0.
Explanation
From the graph, we can see that at values of x less than 0, the graph indicates a very straight line that translates to a linear relationship.
But at values of x greater than 0, the graph begins to curve showing that the relationship is no longer linear.
So, option C is correct.
Hope this Helps!!!
The answer is 139 ft provided by my teacher, I need help with the work
Answers
Answer:
139 ft
Explanation:
Given below is the diagram of the situation
the tangent ratio fo 24 degrees gives
[tex]\tan 24=\frac{h}{300}[/tex]multiplying both sides by 300 gives
[tex]300\cdot\tan 24=h[/tex][tex]h=133.57ft[/tex]We have to remember here that the measuring device was 5 ft above the ground; therefore,
[tex]\text{height}=133.57+5[/tex][tex]\text{height}=138.57ft[/tex]rounding to the nearest integer gives
[tex]\text{height}=139ft[/tex]which is our answer!
Can someone please help me with this I really need help
Please
Answers
The complete table is as follows:
x = 0, p(x) = 0x = 1, p(x) = 4x = 2, p(x) = 8x = 3, p(x) = 12x = 4, p(x) = 16x = 5, p(x) = 20x = 6, p(x) = 24The equation that represent the function is p(x) = 4x.
How to represent equation of a table?Function p represents the perimeter in inches of a square with side length x inches.
Therefore,
perimeter of a square = 4l
where
l = side lengthHence, x represent the side length and p(x) is the perimeter of the square.
Therefore, the equation that represent the situation is as follows;
p(x) = 4x
Let's fill the table as follows:
x = 0, p(x) = 0x = 1, p(x) = 4(1) = 4x = 2, p(x) = 4(2) = 8x = 3, p(x) = 4(3) = 12x = 4, p(x) = 4(4) = 16x = 5, p(x) = 4(5) = 20x = 6, p(x) = 4(6) = 24learn more on equation here: https://brainly.com/question/29326385
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please help me with this question and explain it so I can understand. thank you!
Answers
We can solve this question using trigonometric functions. Here, we use the tangent of the angle of elevation to find the height of the tree.
[tex]\begin{gathered} \tan 40^o=\frac{h}{35} \\ 0.839=\frac{h}{35} \\ 0.839\times35=h \\ 29.36=h \end{gathered}[/tex]Thus, the height of the tree is 29 feet (to the nearest foot).
ity is net ranges $% per ment plus a one time.
Answers
Answer
a) The equation that represents the amount to be paid to xinfinity for using the internet for m months is
f(m) = 75m + 50
b) If Jose uses the xinfinity internet for 10 months, then he has paid the company $800.
Explanation
If the amount paid in total fir using the xinfinity internet for m months onths is f(m),
And xinfinity internet charges a $75 per month fee plus a one-time activation fee of $50.
a) So, if one really does use the xinfinity internet for m months, the total charge is
f(m) = (75 × m) + 50
f(m) = 75m + 50
b) If Jose uses the xinfinity internet for 10 months, we cam calculate how much he pays the xinfinity.
m = 10 months
f(m = 10) = 75 (10) + 50
= 750 + 50
= 800 dollars.
If Jose uses the xinfinity internet for 10 months, then he has paid the company $800.
Hope this Helps!!!is f(m),
And
A=16xx-6use the given area to find the missing sides of the rectangle
Answers
The area of the rectangle is given as 16 units squared
The length = x
The width = x-6
The area of a rectangle is given by the formula;
A= l * w
A= x {x-6}
16 = x^2 -6x -----------form a quadratic equation as;
[tex]x^2-6x-16\text{ =0}[/tex]Find the factors of -16 that can add or subtract to give -6
The factors will be -8 and 2
Factorize the equation as ;
[tex]x^2+2x-8x-16=0[/tex][tex]x(x+2)-8(x+2)=0[/tex][tex](x+2)(x-8)=0[/tex]Finding the real values of x , take that which will result to a positive length
( x-8) = 0
x-8 = 0
x= 8 units
So ; Length = x = 8 units
Width = x- 6 = 8-6 = 2 units
Answers
Length = 8 units
Width = 2 units
It takes 3/4 of an hour for an automated sprinkler to cover 2/7 of a lawn after an hour has passed what fraction of the lawn has been covered
Answers
Answer:
x=8/21
Step-by-step explanation:
(3/4)/(2/7) = 1/x
(3/4)x = (2/7)
x = (2/7) / (3/4)
x = (2/7) * (4/3)
x = 8/21
Write T for true or F for false. 6. The number 14 is a multiple of 4. 7. The Identity Property says that any number times 1 equals the number itself. 8. A bar diagram can be used to show 3 X 6.
Answers
In the number 6, it says the number 14 is a multiple of 4. It means there would be an integer number X which when multiplied by 4 would result in the number 14. To check it, we can perform the following calculation.
[tex]14=X\times4\to X=\frac{14}{4}=3.5[/tex]Because the value of X found is not an integer, 6. is FALSE
In the number 7, it says the Identity Property rays that any number times 1 equals the number itself. This property says that there is a number that, when multiplied by any number will always equal the number itself, and this is the number 1. From this, 7 is TRUE
Number 8 says a bar diagram can be used to show 3X6. This technique can be used to show any multiplication by an integer number. Because both. 3 and 6, are integer, 8 is TRUE
what digit is in the
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Given:
[tex]\frac{13}{7}+\frac{9}{14}[/tex]Find LCM of the denominators.
LCM (7, 14)=14.
Multiply the numerator of each fraction by the LCM 14 and divide by 14.
[tex]\begin{gathered} \frac{1}{14}(\frac{14\times13}{7}+\frac{9\times14}{14}) \\ =\frac{1}{14}(2\times13+9) \\ =\frac{1}{14}(26+9) \\ =\frac{35}{14} \\ =\frac{5}{2} \end{gathered}[/tex]Therefore, the result of the sum is 5/2.
The table shows the diameters in volume certain balls used for different sports. A bowling ball has an approximate volume of 5200 cm³ what is the best estimate for the diameter of a bowling ball
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From the table, the value V = 5200 cm³ is between x = 21 cm and x = 22 cm.
Computing the average of the volumes associated to these x-values, we get:
V = (4,849.1 + 5,575.3)/2
V = 5212.2
which is near V = 5200 cm³. Then, the x-value related to V = 5200 cm³ is approximately the average between x = 21 and x = 22, that is:
x = (21 + 22)/2
x = 21.5 cm
Peyton go shopping she finds two shirts one cost $24.97 the other cost $13.75 she needs to know if she has enough money to buy both shirt using mental math she rounds $24.97 to $25 and add that to $13.75 to get $38.75 how does Peyton need to say to find the exact a total of 2 shirts
Answers
We know that Peyton wants to buy two shirts.
• First shirt cost $24.97.
,• Second shirt cost $13.75.
To do the mental math is ok to round $24.97 to $25, and them sum with $13.75.
However, to get the exact number, Peyton needs to subtract 3 pennies from the last amount $38.75, becuase she rounded before.
Therefore, to find the exact amount she needs to subtract 3 pennies.
Which statement(s) can be interpreted from the equation for an automobile cost, C(t)= 28,000(0.73) *where C(t) represents the costand t represents the time in years?Select all correct statements.A. $28,000 represents the initial cost of an automobile that appreciates 73% per year over the course of t years.B. The equation is an exponential decay equation.OC. The equation is an exponential growth equation.D. $28,000 represents the initial cost of an automobile that depreciates 27% per year over the course of t years.E. The equation is neither exponential decay nor exponential growthF. $28,000 represents the initial cost of an automobile that appreciates 27% per year over the course of years.OG $28,000 represents the initial cost of an automobile that depreciates 73% per year over the course of t years.
Answers
1) Since the value in the bracket is below 1, that indicates it is a decay exponential equation if it is greater than one, it is a growth equation
Therefore option b is correct.
2) Also, since the value in the bracket is 0.73 this implies the automobile that depreciates 27% per year over the course of t years.
Therefore option d is also correct.
4-Which turkey is the better deal? * Sarah Lee Turkey $6.58 per lb O Butterball Turkey $11.16 for 2 lbs 4b-What is the Unit Price for the better deal? Round to the nearest hundredth) Put your answer in the form 0.00 or .00, so if answer is 43 cents, its 0.43 or.43, if there is a dollar amount like 1.50, do not add zeros in front).
Answers
We will determine the best deal as follows:
We divide 11.16 by 2 to obtain the value per Lb, and we get that for each Lb the price is $ 5.58.
So, the best deal is Butterball Turkey at a price of $5.58 per Lb.
10. The graph of y=f(x) is given below.y!24168848 xWhat is the possible degree of f?A. 4IB. -3C. 2D. 3E. -1
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Answer:
The degree of the function is;
[tex]3[/tex]Explanation:
From the given graph, we can observe that the function has two extremum (one minima and one maxima).
The degree of the function will be the number of extremum plus 1;
[tex]\text{degree}=n+1[/tex]Since there are two extremum on the graph then;
[tex]\begin{gathered} \text{degree}=2+1 \\ \text{degree}=3 \end{gathered}[/tex]Therefore, the degree of the function is;
[tex]3[/tex]What is (a+b) (a+b) =?What is (a+1) (a+1) = ?What is (a+3) (a+3)=?What is (x+5) ^2=?
Answers
SOLUTION:
Case: Expansion
Method:
[tex]\begin{gathered} a^2+b^2=(a+b)^2 \\ R.H.S\text{ }expansion \\ (a+b)^2 \\ (a+b)(a+b) \\ a(a+b)+b(a+b) \\ a^2+ab+ab+b^2 \\ a^2+2ab+b^2 \end{gathered}[/tex]Final answer:
FALSE
[tex]a^2+b^2\ne(a+b)^2[/tex]The scores of individual students on the American College Testing (ACT) composite college entrance examination have a normal distribution with mean 18.6 and standard deviation 5.9. What is the probability that the mean score of an SRS of 40 students chosen from all those taking the test is 21 or higher? Round your percentage to 2 decimals.
Answers
Given data
*The given mean is
[tex]\mu=18.6[/tex]*The given standard deviation is
[tex]\sigma=5.9[/tex]The value of the z score is calculated as
[tex]z=\frac{x-\mu}{\sigma}[/tex]Substitute the values in the above expression as
[tex]\begin{gathered} z=\frac{21-18.6}{5.9} \\ =0.41 \end{gathered}[/tex]The probability that the mean score of an SRS of 40 students chosen from all those taking the test is 21 or higher is given as
[tex]\begin{gathered} P(Z\ge21)=P(X\ge0.41) \\ =1-P(X<0.41) \end{gathered}[/tex]The corresponding probability is evaluated by the table.
Substitute the values in the above expression as
[tex]\begin{gathered} P(Z\ge21)=1-0.6591 \\ =0.34 \end{gathered}[/tex]The question is in the image. Answer question 20 only.
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To convert radians to degrees we use the formula:
[tex]\theta\cdot\frac{180}{\pi}[/tex]In this case the angle is 12 radians, then we have:
[tex]12\cdot\frac{180\degree}{\pi}=687.55[/tex]Therefore, the angle in degrees is 687.55°
Which of the following are true about a one-to-one function? Select all that apply.1. It graph will pass the horizontal line test2. It will always have an inverse 3. It’s graph is symmetric about the y-axis 4. It will always have either a local or maximum but not both 5. The graph will pass through point (1,1).
Answers
SOLUTION
Recall the definition of a one-to-one function
one to one function or one to one mapping states that each element of one set, say Set (A) is mapped with a unique element of another set, say, Set (B), where A and B are two different sets
There, the correct answers are
1. It graph will pass the horizontal line test
2. It will always have an inverse
The measures of the angles of a triangle are shown in the figure below. Find the
measure of the smallest angle.
Answers
The smallest measure of the angle in the given triangle is 3x - 15 which is 33°.
What are triangles?A triangle is a polygon with three edges and three vertices. It belongs to the basic geometric shapes. A triangle having vertices A, B, and C is known as triangle ABC. Any three locations in Euclidean geometry that are not collinear result in a distinct triangle and a distinct plane.So, the measure of the smallest angle in the triangle is:
90 + 4x - 7 + 3x - 15 = 1807x + 68 = 1807x = 180 - 68x = 112/7x = 16Now,
4x - 7 = 4(16) - 7 = 57°3x - 15 = 3(16) - 15 = 33°Therefore, the smallest measure of the angle in the given triangle is 3x - 15 which is 33°.
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how do I find the value of x so f(x)=7
Answers
We have a function for which we only have the chart.
We need to find the value of x so that f(x)=7.
NOTE: As we are lookin for the value of x that makes the value of f(x) = 7, we are able to see it in the graph directly:
If we start at y=7, we can draw a line until we intersect the line for f(x). When this happens we draw a vertical line towards the x-axis until we intersect it.
The value of x at that point is the one that makes f(x)=7.
If we can not find the solution by graph, we have to find the equation of the line and clear x for f(x)=7.
SOLUTION WITH EQUATION:
With the information from the chart we have to find the equation.
We can identify two points in the function: (2,0) and (5,7).
Using the 2 known points, we calculate the slope of the line as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{7-0}{5-2}=\frac{7}{3}[/tex]Then, we can write the slope-point equation as:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-0=\frac{7}{3}(x-2) \\ y=\frac{7}{3}x-\frac{14}{3} \end{gathered}[/tex]Then, if we know that y=7, we can replace y with this value and calculate x as:
[tex]\begin{gathered} y=7=\frac{7}{3}x-\frac{14}{3} \\ 7\cdot3=7x-14 \\ 21=7x-14 \\ 7x=21+14 \\ 7x=35 \\ x=\frac{35}{7} \\ x=5 \end{gathered}[/tex]Answer: the value of x so that f(x)=7 is x=5.
a regular square pyramid has base whose area is 250 cm^2. a section parallel to the base and 31.8 cm above it has an area of 40 cm^2 . find the ratio of the volume of the frustum to the volume of the pyramid.
Answers
We are given that the area of the base of a pyramid is 250 cm^2. We are asked to determine the ratio of the volumes of the frustum and the volume of the pyramid. To do that, let's remember that the volume of a pyramid is given by:
[tex]V=\frac{1}{3}A_bh[/tex]Where:
[tex]\begin{gathered} A_b=\text{ area of the base} \\ h=\text{ height} \end{gathered}[/tex]Now, the volume of the frustum is given by:
[tex]V_f=\frac{1}{3}h_f(A_b+A_f+\sqrt[]{A_bA_f})[/tex]Where:
[tex]\begin{gathered} h_f=\text{ height of the frustum} \\ A_f=\text{ area of the base of the frustum} \end{gathered}[/tex]Now, the ratio of between the volume of the frustum and the volume of the pyramid is:
[tex]\frac{V_f}{V_{}}=\frac{\frac{1}{3}h_f(A_b+A_f+\sqrt[]{A_bA_f})}{\frac{1}{3}A_bh_{}}[/tex]We can cancel out the 1/3 and we get:
[tex]\frac{V_f}{V_{}}=\frac{h_f(A_b+A_f+\sqrt[]{A_bA_f})}{A_bh}[/tex]Now, we need to determine the heights. To do that we will use the fact that the ratio of the squares of the height of the pyramid and the height to the top of the pyramid is equivalent to the ratio of the areas, therefore, we have:
[tex](\frac{h}{h_t})^2=\frac{A_b}{A_f}[/tex]Now we substitute the areas:
[tex](\frac{h}{h_t})^2=\frac{250}{40}[/tex]Taking square root we get:
[tex]\frac{h}{h_t}=\sqrt[]{\frac{250}{40}}[/tex]Solving the operations:
[tex]\frac{h}{h_f}=2.5[/tex]Now we multiply by the height of the frustum on both sides:
[tex]h=2.5h_t[/tex]Now, let's look at the following diagram:
This shows us that the height of the frustum plus the height to the top must be equal to the height of the pyramid, therefore:
[tex]h=h_t+31.8[/tex]Substituting the relationship we determined for the height to the top we get:
[tex]h=\frac{h}{2.5}+31.8[/tex]Now we solve form the height "h" first by subtracting h/2.5 from both sides:
[tex]\begin{gathered} h-\frac{h}{2.5}=31.8 \\ \end{gathered}[/tex]Solving the operations:
[tex]\frac{1.5h}{2.5}=31.8[/tex]Now we multiply both sides by 2.5:
[tex]\begin{gathered} 1.5h=31.8\times2.5 \\ 1.5h=79.5 \end{gathered}[/tex]Now we divide by 1.5:
[tex]h=\frac{79.5}{1.5}=53[/tex]Therefore, the height of the pyramid is 53 cm. Now we substitute in the ratio of the volumes and we get:
[tex]\frac{V_f}{V_{}}=\frac{h_f(A_b+A_f+\sqrt[]{A_bA_f})}{A_bh}[/tex]Substituting the values:
[tex]\frac{V_f}{V_{}}=\frac{(31.8)(250+40+\sqrt[]{(250)(40)})}{(250)(53)}[/tex]Solving the operations:
[tex]\frac{V_f}{V}=0.936_{}[/tex]Therefore, the ratio is 0.936
I don't even get like what a mean and a median is can you explain?
Answers
The mean is an average of a set of numbers, where in order to calculate it, we sum all the numbers and divide by the amount of numbers.
For example, in the set {2, 5, 7, 10}, the mean is:
[tex]\frac{2+5+7+10}{4}=\frac{24}{4}=6[/tex]The median is the middle term of the set when it's put in the crescent order.
For example, in the set {4, 7, 2, 10, 5}, the median is:
[tex]\begin{gathered} \text{crescent order}\to\mleft\lbrace2,4,5,7,10\mright\rbrace \\ \text{middle term}\to5 \end{gathered}[/tex]If the number of elements in the set is even, the median will be the average of the two middle terms. For example, in the set {4, 7, 2, 10, 5, 3}, the median is:
[tex]\begin{gathered} \text{crescent order}\to\mleft\lbrace2,3,4,5,7,10\mright\rbrace \\ \text{middle terms}\to4\text{ and 5} \\ \operatorname{median}\to\frac{4+5}{2}=4.5 \end{gathered}[/tex]there are 7 Red 3 blue and 5 green marbles in a bag what is the probability that the first three chosen will not be red?
Answers
Determine the total number of marble in the bag.
[tex]\begin{gathered} n(T)=7+3+5 \\ =15 \end{gathered}[/tex]Determine the probability for first three marbles be red.
[tex]\begin{gathered} P(R=3)=\frac{^7C_3^{}}{^{15}C_3} \\ =\frac{35}{455} \\ =\frac{7}{91} \end{gathered}[/tex]The probability for first three marble is not to be red is equal to one minus the probability for the first three marble be red.
[tex]\begin{gathered} P(R\ne3)=1-P(R=3) \\ =1-\frac{7}{91} \\ =\frac{91-7}{91} \\ =\frac{84}{91} \\ =\frac{12}{13} \end{gathered}[/tex]So answer is 12/13.
Let F(x) = f(f(x)) and G(x) = (F(x)) ^ 2 . You also know that f(3) = 2 , f(2)=3, f^ prime (2)=7 , f^ prime (3)=11
Answers
From the information given,
F(x) = f(f(x)
G(x) = (F(x))^2
F'(x) = f'(f(x)) * f'(x)
F'(3) = f'(f(3)) * f'(3)
f'(f(3)) = f'(2) = 7
f'(3) = 11
F'(3) = 7 * 11
F'(3) = 77
G'(x) = 2F(x) * F'(x) = 2f(f(x) * F'(x)
G'(3) = 2F(3) * F'(3) = 2f(f(3) * F'(3)
Given,
f(f(3) = f(2) = 3
G'(3) = 2 * 3 * 77
G'(3) = 462