30 POINTS:
Function f satisfies f(0) = 2 and f ′(0) = −2. Use this information to compute f^−1′(2).
Answers
Answer:
-1/2
Step-by-step explanation:
The relevant relationship is ...
f^-1'(x) = 1/f'(f^-1(x))
f^-1'(2) = 1/f'(f^-1(2)) = 1/f'(0) = 1/-2
f^-1'(2) = -1/2
_____
The attached graph shows the tangent lines at the relevant points. The red line is the tangent to f(0); the blue line is the tangent to f^-1(2).
The inverse function is the function reflected across the line y=x. So, too, for the tangent lines to the function. Each is a reflection of the other across the line y=x. For the purpose here, the tangent line is a suitable representation of the function at the point(s) of interest.
Related Questions
find all of the remaining angles
Answers
Step-by-step explanation:
angle 1 = 73°
angle 2 = 107°
angle 3 = 73°
angle 4 = 107°
angle 5 = 73°.
hope this helps you.
Write 1 over 9 as a decimal and round it to 2 decimal places
Answers
Answer:
0.111
Step-by-step explanation:
1/9 as a decimal is 0.11111111 but rounded to 2 decimal places is 0.111.
Hope this helps :)
Have a good day / night
Step-by-step explanation:
1/9 converted to a decimal is 0.11111111111 to round it to any place if it is 5 or greater like this 0.55 rounded would be 0.6 because the second five is greater than four if not greater than four like this: 0.44 the rounded form will be 0.4 then get your answer!
The price of a stock was $24.56 per share. An investor decided to spend $5,000 to buy shares of the stock. To the nearest whole number, what is the maximum number of shares of stock that the investor can buy
Answers
Answer:
203 i just did it
Step-by-step explanation:
Answer:
the answer is 203
Step-by-step explanation:
Just got it right on edge 22
A box contains 6 black pens, 4 blue pens, and 7 red pens. Without looking, Clarissa randomly picks a black pen out of the box. If she chooses another pen out of the box without replacing the first one, what is the probability that she will pick a black pen both times? Write your answer as a percent.
Group of answer choices
Answers
Answer:
31.35%
Step-by-step explanation:
Initial reading:In the box, there are:
6 Black pens4 blue pens7 red pensTotal number of pens in the box = 6 + 4 + 7
= 17
If we count pens as outcomes the total number of possible outcomes are 17.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
New reading:Clarissa takes out a black pen from the box.
That reduces the number of black pens by 1 which increases the total number of pens by 1 as well.
So now:
Number of black pens = 6 - 1 = 5 Total number of pens = 17 - 1 = 16- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Probability:[tex] \boxed{ \mathsf{probability = \frac{favorable \: outcomes}{total \: outcomes} }}[/tex]
If we want her to pick up a black pen, and she ends up picking one. So, we can say that the outcome is in our favor.
That makes it,
the number of favorable outcomes = number of black pens= 5
and total outcomes = Total number of pens= 16
[tex] \implies\mathsf{probability = \frac{5}{16} }[/tex]
For showing it as some percent we'll just multiply the fraction by 100
[tex] \implies \mathsf{ \frac{5}{16} \times 100 }[/tex]
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
As a percent:[tex] \implies \mathsf{ \underline{ 31.25 \: \% } }[/tex]
Kardal used the line of best fit to predict that a man 80 inches tall would wear about a size 16 shoe. What can be concluded about this prediction? Check all that apply. The prediction is reasonable. The prediction is an interpolation. No data is given in the scatterplot for a height of 80 inches, but a shoe size can still be predicted. A prediction cannot be made for a man who is 80 inches tall. A man who is 80 inches tall will likely wear a size 12. 5 shoe.
Answers
Answer:
A and C
Step-by-step explanation:
A. The prediction is reasonable.
C. No data is given in the scatterplot for a height of 80 inches, but a shoe size can still be predicted.
__________________________________________________________
Based on the average height-to-shoe size ratio, it is rational to predict that a man who is 80 inches tall would wear a size 16 shoe, even without there being a scatterplot for a height of 80 inches.
Can you write 8x=1 as a quadratic equation?
Answers
Answer:
yes
Step-by-step explanation:
The root of the given linear equation can be made to be a repeated root of a quadratic equation:
(8x -1)² = 0
The rectangle below has been enlarged by a scale of 3.5.
A rectangle with a length of 8 and width of 6.
Answers
Multiply the original dimensions by the scale:
8 x 3.5 = 28
6 x 3.5 = 21
New dimensions: length = 28, width = 21
Which equation matches the graph shown?
Answers
Answer:
Vertex form: y = -2(x - 1)²
Standard form: y = -2x² + 4x - 2
Step-by-step explanation:
Given the x-intercept as the vertex, (1, 0), and the y-intercept, (0, -2) as the two points on the graph of a parabola:
We can determine the equation by substituting these given values into the vertex form of the quadratic equation:
y = a(x - h)² + k
where:
a = determines the direction of where the graph opens, and the wideness or narrowness of the parabola.
(h, k) = vertex
Solve for the value of a:Use vertex: (1, 0) and y-intercept, (0, -2):
y = a(x - h)² + k
-2 = a(0 - 1)² + 0
-2 = a(-1)²
-2 = a(1)
-2 = a
Quadratic Equation:Vertex form:The quadratic equation in vertex form that matches the graph is:
y = -2(x - 1)² + 0 or y = -2(x - 1)² ⇒ This is the quadratic equation in vertex form.
Standard form:To transform the vertex form into the standard form, y = ax² + bx + c:
Simply expand the perfect square, (x - 1)², through FOIL method before distributing -2:
y = -2(x - 1)²
y = -2(x - 1)(x - 1)
y = -2(x² -2x + 1)
y = -2x² + 4x - 2 ⇒ This is the quadratic equation in standard form.
Please help me quickly
Answers
Step-by-step explanation:
a full circle (turning around a point a full turn) is 360°.
so, all these angles together must be 360°.
90 + 33 + 165 + 20 + x = 360
308 + x = 360
x = 52°
ABCD is a rectangle. Its diagonals meet at O. Find the value of x if BO = 3x + 4 andOC = x + 8 .Also find the length of its diagonals.(Lengths are in cm).
pls help will mark as brainlist
Answers
Step-by-step explanation:
the lengths OB, OC & BC together forms a isosceles triangle.
therefore,
OB=OC
3x+4=x+8
2x=4
x=2.
OB = 3x+4= 3.2+4=10cm.
OC= x+8= 2+8=10cm.
therefore, the diagonals are : 20cm each.
hope this helps you.
Anrnav was 1.5m tall in the last couple years his height increased by 20%
How tall is anrav today?
Answers
Answer:
1.8 meters
Step-by-step explanation:
It was easy for me
PLS SOMEONE HELP PLSSS
Answers
Answer:
x=17
Step-by-step explanation:
ok so since lines PR and RQ are congruent (we know because of the lines on them), that means angles P and Q are also equal.
now we can set up the equation to find x like this:
29+29+(8x-14)=180 (180 because the three angles of a triangle always equal 180)
x=17
I have an exercise that asks me: answer true or false, are the Italian regions washed by the sea a whole?
Answers
Answer:
Select an answer for each item. If you do not know the answer, you should make an educated guess. At the bottom of the test, you will be given your results. Questions 1-5. Read the following early draft of an essay and then choose the best answer to the question or the best completion of the statement. (1) Seaweed-based fuel could one day power ...
Step-by-step explanation:
Answer:
Is false because the Italian regions are partly bathed by the sea
Step-by-step explanation:
What is 93x43 please show your work.
Answers
Answer:
The answer is 3,999
Step-by-step explanation:
93 x 43 = 3,999
brainliest :)
3 less than the quotient of a number and 5 is -7
Answers
Answer: The number is -20
Step-by-step explanation:
Take each part of the sentence and write what it is telling us:
3 less than the quotient of a number and 5 is -7
The quotient of a number and 5 is (X/5), where X is the "number."
3 less than is (X/5) - 3
is -7 is = -7
Therefore:
3 less than the quotient of a number and 5 is -7 is: (X/5) - 3 = -7
---
(X/5) - 3 = -7
(X/5) = -4
X = -20
===
See if this works:
3 less than the quotient of -20 and 5 is -7
(-20/5) = -4
Three kless than -4 is -7: It works
another mathh question
Answers
where is the Question!!!
can you plz give me brainliest I really need it
Your question is incomplete.
Please if you need help I will try to help you :)
Have a Good Day.
Help me pls I don't get it
Answers
Answer:
maybe A
Step-by-step explanation:
the product of two irrational numbers is _____ rational
1.always
2.never
3.sometimes
Answers
Answer:
3. sometimes
Step-by-step explanation:
The product of two irrational numbers is sometimes rational. It depends on the two given numbers.
the total surface area of an cube is 294cm2 work out the volume of the cube
Answers
Answer:
343 cm³
Step-by-step explanation:
V = 343 cm³
Surface A = 294 cm²
A baker baked some loaves of bread. 240 loaves were sold by the end of the day. The baker was left with 9/25 of the number of loaves that were baked. How many loaves of bread did the baker bake on that day?
Please do this in a easy way and explain no algebra
Answers
Answer:
The baker baked 375 loaves of bread that day.
Step-by-step explanation:
The baker baked a total of x loaves of bread.
240 loaves were sold by the end of the day.
The baker was then left with 9/25 of the number of loaves that were baked.
We get the equation:
x-240 = 9x/25
When you solve the equation, you will see that x=375.
Therefore, the baker baked 375 loaves of bread that day.
Can you please answer this world problem? And please don't mind the numbers on top.
Answers
Answer: 5 1/15 feet
Step-by-step explanation:
For this you have to add fractions.
First find a common denominator between the factions which can be will turn into 15.
The fraction is now: 1 10/15 + 3 6/15
Now that the denominator is the same add the fractions.
1 10/15 + 3 6/15 = 5 1/15
Make the answer negative since its under sea level
Answer = -5 1/15 feet
Graph the line passing though (-6,-1) whose slope is m= -4/3
Answers
y=-4/3x-9
hope it helps
If 7 > 2, then explain why -7 < -2.
A. The above statement is false.
B. Because the sign changed.
C. Because -7 is more negative and further to the left on the numberline than
-2.
D. Because 7 is an odd number and 2 is even, which flips when they become
negative, where -7 becomes even and -2 becomes odd.
Answers
Answer:
C
Step-by-step explanation:
Hope it can help you lovelots
If 7 > 2, then explain why -7 < -2.
Answer =》C. Because -7 is more negative and further to the left on the numberline than
-2.
______
RainbowSalt2222 ☔
Helppppppppppp asapppppppppppp
Answers
Answer:
Step-by-step explanation:
First, you have to use the law of cosines which is c² = a² + b² - 2abcosФ where Ф is the angle measure between sides a and b. So, just plug-in a = 10, b = 12, and Ф = 72 into the equation and you will get (I won't show all the calculations):
c = 13.0321
Then plug that into the area formula to get:
(0.5)(10)(12)(0.225496911)
Which is about:
13.53
800 students were surveyed to find out their favorite subject. 35% chose math. How many students chose math.
Answers
Evaluate the function.
f(x) = 2x2 – 15
Find f(-2)
Answers
Answer:
[tex]f(-2)=-17[/tex]
Step-by-step explanation:
[tex]f(-2)=2(-2)^2-25\\\\f(-2)=2(4)-25\\\\f(-2)=8-25\\\\f(-2)=-17[/tex]
f(x) = 2x² - 15
f(-2) = ?
Substitute -2 in the place of x.
f(x) = 2x² - 15
f(-2) = 2(-2)² - 15
f(-2) = 8 - 15
f(-2) = -7
______
Hope it helps :)) ⚜
At Fenway park, they can sell 5000 hot dogs at $4 per dog. They also know that for each quarter (25 cents) they raise the price, they will sell 200 less hot dogs. How many hot dogs should they sell to make profit? Please I need this question by 11:30 pm I’ve been looking everywhere but can’t find answers.
Answers
2500 hot dogs must be sold to make a profit
If they can sell 5000 hot dogs at $4 per dog, the selling price for the 5000dogs will be expressed as:
SP= 4 * 5000
SP = 4 + 0.25x
Total number hot dog sold = 5000 - 200x
Revenue = Sales price*Total number hot dog sold
When the price is increased by $0.25 then the revenue will be expressed as [tex]g(x) = (4+0.25x) (5000 - 200x)[/tex]
Taking the product, the resulting function will be;
[tex]g(x) = -50x^2 + 1250x + 20000[/tex]
To get the maximum profit, we need to maximize the revenue by differentiating the function and equating it to zero to have:
[tex]g'(x) = -100x + 450\\0=-100x + 1250\\100x = 1250\\x = 12.5[/tex]
Substittute x = 12.5 into the total number hot dog sold function
Recall that n = 5000 - 200x
n = 5000 - 200(12.5)
n = 5000 - 2500
n = 2500
Hence 2500 hot dogs must be sold to make a profit
Learn more here: https://brainly.com/question/19594550
using oliver's table, how can you find the unit rate
Answers
The unit rate of the distance covered per unit stride taken is; 3.5 ft per stride.
How to find the unit rate?From the given table and graph, we see that;
Number of strides taken is on the x-axis.
Distance covered for each respective number of strides is on the y-axis.
Now, the rate will be;
Rate = Change in Distance covered/Change in number of strides
Thus;
Rate = (14 - 7)/(4 - 2)
Rate = 7/2
Rate = 3.5 ft per strides
Read more about Unit Rate at; https://brainly.com/question/19493296
#SPJ1
Answer:
Oliver’s table indicates that for every increase of 2 strides, the distance he travels increases by 7 feet. So, the change in distance divided by the change in stride gives the unit rate.
Step-by-step explanation:
Urgently please it is due today
Answers
Answer:
1/4.
Step-by-step explanation:
There are 12 possible outcomes.
There are are 3 outcomes represented by 4B.
So required probability = 3/12 = 1/4.
Simplyfy (4^7/5^2)^3