Determine the values of the constants b and c so that the function given below is differentiable. f(x)={2xbx2+cxx≤1x>1
To make the function differentiable, we need to make it continuous at x = 1 by ensuring that both sides of the function have the same value. The values of the constants b and c are b = 1 - c, where c is any real number.
Explanation:The function given is:
f(x)={2xbx2+cxx ≤ 1 x > 1
To determine the values of the constants b and c such that the function is differentiable, we need to make sure that the function is continuous at x = 1 and both sides of the function have the same derivative at x = 1.
To do this, we need to find the limits of the function as x approaches 1 from both the left and the right sides.
From the given function, we can see that when x ≤ 1, the function is a polynomial and is differentiable for any value of b and c.
However, when x > 1, the function is not differentiable unless we choose the values of b and c such that the function becomes continuous at x = 1.
To make the function continuous, we need to make sure that both sides of the function have the same value at x = 1.
Substituting x = 1 into the given function, we have 2b(1)(1) + c(1) = b + c = 1 (since the function should be continuous at x = 1).
Therefore, the values of the constants b and c that make the function differentiable are b = 1 - c, where c is any real number.
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a tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an intial speed of 130 feet per second. What is the maximum height, in feet, the ball will attain? round to the nearest hundredth
Final answer:
Using the kinematic equation for vertical motion, the maximum height a tennis ball will reach when fired at an initial speed of 130 ft/s from a height of 2 feet is approximately 264.91 feet.
Explanation:
Calculating the Maximum Height of a Tennis Ball
The maximum height that a tennis ball will attain when fired vertically can be calculated using the kinematic equations that describe projectile motion. Given that the initial speed of the ball is 130 feet per second and it is launched from a height of 2 feet, we can use the equation for vertical motion:
v^2 = u^2 + 2gh
where v is the final velocity (0 ft/s at the highest point), u is the initial velocity (130 ft/s), g is the acceleration due to gravity (-32.2 ft/s^2, negative because it is directed downwards), and h is the height gained. Rearranging the formula to solve for h we get:
h = (v^2 - u^2) / (2g) = (0 - 130^2) / (2 * -32.2)
After calculating h, we add the initial launch height of 2 feet to find the maximum height above ground:
Maximum Height = h + 2 feet
By plugging in the values, we can find the maximum height to be:
Maximum Height = (0 - 16900) / (-64.4) + 2 ≈ 264.91 feet (rounded to the nearest hundredth).
Therefore, the maximum height attained by the tennis ball is approximately 264.91 feet.
A company has a minimum required rate of return of 9% and is considering investing in a project that costs $350,000 and is expected to generate cash inflows of $140,000 at the end of each year for three years. the net present value of this project is
Q # 17 please solve the figures
How do you solve this
what kinds of symmetry does the capital letter E have
Solve for x. Use the completing the squares method. Round decimals to the nearest tenth. 2x2+16x=−18 (
Answer:
[tex]x = -4 \frac{+}{-} 2\sqrt{5\\}[/tex]
Step-by-step explanation:
Juan is spinning a wheel with 4 unequal spaces marked with values of $200, $300, $400, and $600. The probability of landing on $200 is 2/9 . The probability of landing on $300 is 4/9 . The probability of landing on $400 is 2/9. The probability of landing on $600 is 1/9 . The expected value of spinning the wheel once is $, and the expected value of spinning the wheel three times is
Answer:
333 and 1000
Step-by-step explanation:
a marble is selected at random from a jar containing 6 red marbles 3 yellow Marbles and 2 green marbles what are the odds in favor of selecting a red marble
Christina goes to the market with $50. She buys one papaya for $20 and spends the rest of the money on bananas. Each banana cost $6. Write an inequality for the number of bananas purchased
please help!! I don't understand
Answer:
(4, 5)
Step-by-step explanation:
All the medians intersect at the same point. RU and PS are medians so they intersect at the same point that medians QT and PS intersect.
Which value of r indicates a stronger correlation: requals0.811 or requalsnegative 0.861? explain your reasoning?
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The height of a triangle is increasing at a rate of 2 2 centimeters/minute while the area of the triangle is increasing at a rate of 3.5 3.5 square centimeters per minute. at what rate is the base of the triangle changing when the height is 10 10 centimeters and the area is 80 80 square centimeters?
If we reject the null hypothesis, h0: ρ = 0 , what can we conclude about the population correlation coefficient?
A camera manufacturer spends $2,100 each day for overhead expenses plus $9 per camera for labor and materials. The cameras sell for $14 each. a. How many cameras must the company sell in one day to equal its daily costs? b. If the manufacturer can increase production by 50 cameras per day, what would their daily profit be?
Here, first we need to find the number of cameras that can be sold, so that total costs are equal to total revenues.
Let the number of cameras that can be sold be "x".
Total revenue = $ 14x
Total costs will be = $ 2100 + $9x
So, the equation that will be formed ⇒
14 x = 2100 + 9x
5x = 2100
x = 420
Thus, in order to make total costs equal to total revenues, 420 cameras are required to be sold.
If instead of 420, 470 cameras are sold, the daily profit will be calculated as under -
Total revenue = $ 14 × 470 cameras = $ 6,580
Total costs = $ 2100 + ( $ 9 × 470 cameras) = $ 6,330
Daily profit = Total revenue - Total costs = $ 6,580 - $ 6,330 = $ 250
Unit rate of 3 1/2 and 1/4
what is the difference between the greatest amount and least amount of gasoline used to mow lawns?
1/8 2/8 3/8/4/8 5/8
which statement describes the ratio of weight to mass and the value of x in the table?
At the sandwich shop, there are four different types of meat and three different types of cheese. If you select a sandwich without looking, what is the probability that it has your favorite type of meat on it?
give answer as a fraction
The solution is : 1/4 is the probability that it has your favorite type of meat on it.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Here, we have,
given that,
At the sandwich shop, there are four different types of meat and three different types of cheese.
If you select a sandwich without looking,
then we need to find the probability.
Solution
There are four different types of meat and three different types of cheese
Probability = number of required outcome / number of possible outcome
Total amount of meat = number of possible meat = 4
If you only have one favorite type of meat the probability 1/4
Hence, the correct answer is Option B.
The solution is : 1/4 is the probability that it has your favorite type of meat on it.
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The first term in a sequence is -2 and the common ratio is 3. What is the sixth term of the sequence?
Jim picked a card from a standard deck. What is the probability that Jim picked a heart or an ace?
Answer:
The answer is actually 16/52.
Step-by-step explanation:
There are 13 hearts and 4 aces. However, one of the 4 aces is a heart, so there would only be 3 other aces.
13 hearts + 3 other aces = 16
There are 52 cards in a deck, so the probability would be 16/52.
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Choose the correct conic section to fit the equation. x^2/36-y^2=1 Circle Ellipse Parabola Hyperbola
Choose the correct conic section to fit the equation. x^2/36-y^2=1 Circle Ellipse Parabola Hyperbola
Solution:
The general equation of circle is:-
(x-h)²+(y-k)=r²
The general equation of ellipse is:-
[tex] \frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{{b^{2}}}=1 [/tex]
The general equation of parabola is:-
y = a(x-h)²+k
The general equation of hyperbola is:-
[tex]\frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{{b^{2}}}=1[/tex]
The equation of conic section is: x^2/36-y^2=1
[tex]\frac{(x-0)^{2}}{36}-\frac{(y-0)^{2}}{1}}=1[/tex]
[tex]\frac{(x-0)^{2}}{6^{2}}-\frac{(y-0)^{2}}{{1^{2}}}=1[/tex]
Hence, this is hyperbola.
Answer: Hyperbola Option (D)
10) Given that two tangent lines are constructed from the shared point A outside a circle with the center O and points of tangency B and C, what is the relationship between ∠OAB and ∠OAC?
a customer buys three bottles of water at ninety nine cents each. there is seven percent tax on each bottle. what is the total bill?
Volume and Surface Area
Math help 100 points
Answer:
1 - V = Smaller solid=512 cm³
V = Larger solid=2197 cm³
2- 1.625² = 2.64
3 - SA of big solid is found 2535 cm²
The balance on a car loan after 4 years is $8,996.32. The interest rate is 5.6% compounding annually. What was the initial value of the loan?
Write the related series for the finite sequence –7, –10, –13, . . ., –22. then find the sum.–7 + (–10) + (–13) + (–16) + (–19) + (–22) = –87
–7 + (–10) + (–13) + (–15) + (–18) + (–22) = –85
–7 + (–10) + (–13) + (–14) + (–18) + (–22) = –84
–7 + (–10) + (–13) + (–17) + (–20) + (–22) = –89
Answer: [tex]-7+(-10)+(-13)+(-16)+(-19)+(-22)=-87[/tex]
Step-by-step explanation:
Given finite sequence : -7, -10, -13, . . ., -22.
Difference between first and second term=[tex]-10-(-7)=-10+7=-3[/tex]
Difference between second and third term =[tex]-13-(-10)=-13+10=-3[/tex]
Hence, the common difference = -3
The next term after -13 =[tex]-13+(-3)=-13-3=-16[/tex]
The next term after -16 =[tex]-16+(-3)=-16-3=-19[/tex]
The next term after -19 =[tex]-19+(-3)=-19-3=-22[/tex].........which is the last term of the sequence.
Now, the sum of the given sequence =[tex]-7+(-10)+ (-13) + (-16) + (-19) + (-22) [/tex]
[tex]=-7-10-13-16-19-22= -87[/tex]