For the following function y = f(x) = 4x^3 - 5
I worked out this Calculus problem, but I keep getting 1/-432 for part c. Can anyone work out the problem step-by-step so I can understand what I’m doing wrong? It would be greatly appreciated.
Answers
The answer for each of the differentiation are; f'(-6) = 432; f⁻¹(y) = ∛((y + 5)/4); df⁻¹/dy = 1/432
How to differentiate functions?
1) f(x) = 4x³ - 5
We will differentiate it to get;
f'(x) = df/dx = 12x²
f'(-6) = 12(-6)²
f'(-6) = 432
2) We are given the formula;
x = f⁻¹(y)
Thus;
y = 4x³ - 5
4x³ = y + 5
x³ = (y + 5)/4
x = ∛((y + 5)/4)
f⁻¹(y) = ∛((y + 5)/4)
c) f⁻¹(y) = ∛((y + 5)/4)
df⁻¹/dy = -1/12y²
At f(-6), we have;
df⁻¹/dy = 1/432
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Related Questions
Thalia, a quiz show contestant, answered 20 questions. She was awarded 2 points for every correct answer that she gave, but she was penalized 1 point for every incorrect answer. In the end, Thalia had a total of 28 points. In order to determine the number of correct and incorrect answers that she gave, a viewer at home used the system of linear equations x + y = 20 and 2 x + y = 28, with x being the number of correct answers and y being the number of incorrect answers. The viewer solved the system by using the linear combination method as shown.
x + y = 20. + StartFraction Negative 2 x minus y = negative 28 over Negative x = negative 8 EndFraction. StartFraction negative x Over negative 1 EndFraction = StartFraction negative 8 Over negative 1 EndFraction. X = 8.
8 + y = 20. 8 + y minus 8 = 20 minus 8. y = 12.
The viewer calculated that the contestant answered 8 questions correctly and 12 questions incorrectly. What went wrong?
The viewer mistakenly determined that one of the equations in the system should be x + y = 20.Instead modifications should have been made before applying the equation.
The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28. Instead modifications should have been made before applying the equation.
The viewer multiplied the equation 2 x + y = 28 by –1 incorrectly.
The viewer added the equations x + y = 20 and Negative 2 x minus y = negative 28 incorrectly.
Answers
The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28. Instead modifications should have been made before applying the equation.
What is an Equation ?An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.
Total Questions = 20
Total Points = 28
Correct Answers = +2 points
Incorrect Answers = -1 point
The viewer represents the correct answers with x and the incorrect ones with y.
x+y = 20
for every correct answers 2 points;
and for every incorrect answers, -1 point
This can be written as
2x-y = 28
The viewer's mistake is that; instead of subtracting total incorrect points from the correct points, the viewer added them together;
now
2x-y = 28
x+y = 20
On adding the equations
]3x = 48
x = 16
y = 4
This means that the contestant answered 16 questions correctly and 4 questions incorrectly
The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28.
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If anyone can help me to solve this.
Answers
Answer:
1) x + 96 = 90°
2) x + 89 = 80°
Step-by-step explanation:
Consecutive Interior Angles Theorem
When a transversal line intersects two parallel lines, it forms two pairs of consecutive angles on either side of the transversal line. Each pair of consecutive interior angles are supplementary (sum to 180°).
Question 1To find the measure of the angle circled on the diagram, find the value of x by using the Consecutive Interior Angle Theorem:
⇒ (x + 96)° + (x + 96)° = 180°
⇒ x + 96 + x + 96 = 180
⇒ 2x + 192 = 180
⇒ 2x + 192 - 192 = 180 - 192
⇒ 2x = -12
⇒ 2x ÷ 2 = -12 ÷ 2
⇒ x = -6
Substitute the found value of x into the expression to find the measure of the angle circled on the diagram:
⇒ x + 96 = -6 + 96 = 90°
⇒ x + 96 = 90°
Question 2To find the measure of the angle circled on the diagram, find the value of x by using the Consecutive Interior Angle Theorem:
⇒ (x + 109)° + (x + 89)° = 180°
⇒ x + 109 + x + 89 = 180
⇒ 2x + 198 = 180
⇒ 2x + 198 - 198 = 180 - 198
⇒ 2x = -18
⇒ 2x ÷ 2 = -18 ÷ 2
⇒ x = -9
Substitute the found value of x into the expression to find the measure of the angle circled on the diagram:
⇒ x + 89 = -9 + 89
⇒ x + 89 = 80°
Answer:
[tex]\boxed {1) 90^{o}}\\\boxed {2) 80^{o}}[/tex]
Step-by-step explanation:
Part 1 :
x + 96 + x + 96 = 180 (angle pairs of a line)2x + 192 = 1802x = -12x = -6∠ = -6 + 96∠ = 90°Part 2 :
x + 109 + x + 89 = 180 (same reason)2x + 198 = 1802x = -18x = -9∠ = -9 + 89∠ = 80°Which standard form of the equation of the hyperbola has vertices at (0, 5) and (0, –5), and asymptotes y equals plus or minus five twelfths times x question mark
y squared over 25 minus x squared over 144 equals 1
y squared over 144 minus x squared over 25 equals 1
x squared over 25 minus y squared over 144 equals 1
x squared over 144 minus y squared over 25 equals 1
Answers
The equation first represents the hyperbola has vertices at (0, 5) and (0, –5), and asymptotes y = ±(5/12)x option first is correct.
What is hyperbola?It's a two-dimensional geometry curve with two components that are both symmetric. In other words, the number of points in two-dimensional geometry that have a constant difference between them and two fixed points in the plane can be defined.
We have:
Vertices of the hyperbola = (0, 5) and (0, -5)
Asymptotes: y = ±(5/12)x
The equations we have:
[tex]\rm \dfrac{y^{2}}{25}-\dfrac{x^{2}}{144}=1[/tex]
[tex]\rm \dfrac{y^{2}}{144}-\dfrac{x^{2}}{25}=1[/tex]
[tex]\rm \dfrac{x^{2}}{25}-\dfrac{y^{2}}{144}=1[/tex]
[tex]\rm \dfrac{y^{2}}{144}-\dfrac{x^{2}}{25}=1[/tex]
From the equation first:
[tex]\rm \dfrac{y^{2}}{25}-\dfrac{x^{2}}{144}=1[/tex]
The value of a and b are:
a = 12
b = 5
Vertices of the hyperbola = (0, b) and (0, -b)
Vertices of the hyperbola = (0, 5) and (0, -5)
Asymptotes: y = ±(b/a)x
Asymptotes: y = ±(5/12)x
Thus, the equation first represents the hyperbola has vertices at (0, 5) and (0, –5), and asymptotes y = ±(5/12)x option first is correct.
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Answer:
A
Step-by-step explanation:
Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function G(t) = (- 8t ^ 2 + 56t)/(t ^ 2 + 3t + 2) where the time, t, is hours after injection. Part A: What is the domain of the function C(t) based on the context of the problem? Show all necessary calculations. Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body.
Answers
Graphs are used to show the relationship between variables, where the variables are represented by a pair of axes.
The domain of the function is t ≥ 0
The greatest concentration of the medication is 5mg/L
Given that:
C(t) = [tex]\frac{-8t^2 + 56t}{t^2 +3t + 2}[/tex]
(a): The domain of the function
Because the medication concentration C(t) is a function of time (t), the domain is the possible values t can take.
t, cannot take negative values (i.e. it is not possible to have a negative time).
The least possible value of t is 0
So, the domain of the function based on the context is: t ≥ 0
(b) The greatest concentration of the medication
From the graph (see attachment), the maximum y-value is 5.
Hence, the greatest concentration of the medication is 5 mg/L
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Find the value of d.
Answers
Answer:
Step-by-step explanation:
Comment
The rule that governs this situation is the average of arc d and 94 = the angle where the chords cross.
Givens
Arc 1 = 94
Arc2 = d
interior angle = 75
Formula
(d + 94)/2 = interior angle/1
Solution
(d + 94)/2 = interior angle/1 Cross Multiply
1*(d + 94) = 75 *2 Combine
d + 94 = 150 Subtract 94 from both sides
d + 94 - 94 = 150 - 94 Combine
d = 56
Answer: d = 56
forty percent of participants in a math contest were boys. fifty percent of the boys revived medals. the number of boys who received the medals was equal to the number of girls who received the medals. what percent of the participants were girls who received medal?
Answers
20% of the participants are girls and got a medal, and 33% of the girls got a medal.
What percent of the participants were girls who received medal?
First, we know that 40% of the participants were boys, so the other 60% were girls.
We know that 50% of the boys got a medal, so the percentage (in decimal form) of participants that are boys and got a medal is:
P = (0.4)*(0.5) = 0.2
So, 20% of the participants are boys and got a medal.
We know that the number of girls that got a medal is the same as the number of boys, then we also have that 20% of the participants are women who got a medal.
Then if the percentage of girls that got a medal is x (in decimal form), we must have that:
Q = (0.6)*(x) = 0.2
x = 0.2/0.6 = 0.33
x = 0.33
This means that 33% of the girls got a medal.
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only 1st main ,please do solve this asap
Answers
Answer:
(i) 8b-32
(ii) 7z^3+12z^2-20z
(iii) –q+p
(iv) a+ab
(v) 8x^2y+8xy^2-4x^2-7y^2
(vi) 4y^2-3y
Step-by-step explanation:
17, 18, 22, 31, 47 what is the next number
Answers
Answer:
the next number is 47+ 16 =63
What is the surface area of prism below?
Answers
Answer:
Aprism = 483.246 yd2
Step-by-step explanation:
The surface area is the sum of the 2 circles areas and the rectangle area.
Ac1 = PI*r2
Ac1 = (3.14)*(11.4/2)2
Ac1 = 102.0186 yd2
Ac1 = Ac2 then
Ac2 = 102.0186 yd2
Now the perimeter of the circle is one the sides of the rectangle:
Pc = 2PI*r
Pc = 2*3.14*(11.4/2)
Pc = 35.796 yd
Now the area of the rectangle is:
Ar = 7.8yd*35.796yd
Ar = 279.2088 yd2
Then, the surface area of prism is:
Aprism = Ac1 + Ac2 + ArAprism = 102.0186yd2 + 102.0186yd2 + 279.2088yd2Aprism = 483.246 yd2solve for a
(log(a-1))^2 =log10
Answers
A function assigns the values. The value a is 11.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The given logarithmic function can be solved as shown below.
[tex](\log(a-1))^2 =\log10\\\\(\log(a-1))^2 =1\\\\(\log(a-1)) =\sqrt1\\\\\log(a-1) = 1\\\\10^1 = a-1\\\\a = 11[/tex]
Hence, the value a is 11.
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Find the value of the function f(x) = x2 + 9x + 10, for x = -1.
Answers
Answer:
this is pretty easy we just replace the x with -1 so
(-1)^2+(-1)9+10
-1*-1=1
-1*9=-9
1+-9=-8
-8+10=2
f(-1)=2
Hope This Helps!!!
help please
what is
Answers
Answer:
sure how can I help you? please tell me
In formula P = 2L + 2W
A. solve for L
B. solve for W
C. Find P if L=12 and W=8
Answers
Answer:
P=2l+2W
if l=12 and W=8
then,
P=2L+2W
=2.18+2.8
=36+16
=52
On a coordinate plane, a parabola opens down with solid circles along the parabola at (negative 3, negative 5), (negative 2, 0), (negative 1, 3), (0, 4), (1, 3), (2, 0), (3, negative 5). Which statement is true regarding the intervals where the function is increasing and decreasing? The function is increasing from (–∞, 0). The function is increasing from (0, ∞). The function is decreasing from (–∞, 0). The function is decreasing from (–∞, ∞).
Answers
The true statement regarding the intervals where the function is increasing and decreasing is option A: The function is increasing from (–∞, 0).
What is a function?A function is defined as a relation between the set of inputs having exactly one output each.
On a coordinate plane, a parabola opens down with solid circles along the parabola at (-3, -5), (-2, 0), (-1, 3), (0, 4), (1, 3), (2, 0), (3, -5).
The domain is all real numbers.
The range is all real numbers.
If for an interval I, when x decreases meanwhile staying in interval I, the function's output increases (or can stay same), then we say that the function is increasing in the interval.
The true statement regarding the intervals where the function is increasing and decreasing is option A: The function is increasing from (–∞, 0).
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Answer:
A
Step-by-step explanation:
50% of 42 students are girls. How many of the students are girl's
Answers
Answer:
21 girls.
Step-by-step explanation:
50% of 42 students are girls.
So 42/2 = 21.
Therefore 21 of the students are girls.
Hope I helped
How much for $100 invested in 6% interest compounded monthly be worse after 20 years
Answers
Answer:
$331.02
Step-by-step explanation:
compound interest formula
A = P ( 1 + r/n)^nt
P = principal amount
r = rate decimal
n = number of times interest is compounded
t = time
A = 100 * (1 + .06/12)^(12*20)
A = 331.02
Suntract (7x-3x)-(5x-6).
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: final \:\:value = -x + 6 \degree[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: (7x - 3x) - (5x - 6)[/tex]
[tex]\qquad \tt \rightarrow \: (4x) - 5x - ( - 6)[/tex]
[tex]\qquad \tt \rightarrow \: 4x - 5x + 6[/tex]
[tex]\qquad \tt \rightarrow \: - x + 6[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:6-x
Step-by-step explanation:
The solution is in the image
Another quick geometry question! Thanks!
Answers
14/12=x/18
14 x 18 = 252
252/12= 21
so x=21
1) When the polynomial P(x) is divided by x+5, the remainder is 3. Which of the following is definitely true?
a) P(3) = 5
b) P(-5) = 3
c) P(5) = 3
d) P(-3) = 5
2) P is a degree 3 polynomial with real coefficients and three zeros. Two of the zeros are 5 and 3+4i. What is the other zero?
a) 4-3i
b) 4+3i
c) -5
d) 3-4i
Answers
1) The definitely true for the statement is b) P(-5) = 3.
2) The three roots are 5, 3 + 4i, and 3 - 4i. Option D is correct.
What is the remainder theorem for polynomials?If there is a polynomial p(x), and a constant number 'a', then
[tex]\dfrac{p(x)}{(x-a)} = g(x) + p(a)[/tex]
where g(x) is a factor of p(x)
Given;
1) When the polynomial P(x) is divided by x+5, the remainder is 3.
If a polynomial P(x) is divided by (x-a), then the remainder is P(a).
If the polynomial P(x) is divided by (x+5), then the remainder will be P(-5).
So, P(-5) = 3
Therefore, the definitely true for the statement is b) P(-5) = 3.
2) P is a 3 degree polynomial with real coefficients and three zeros. Two of the zeros are 5 and 3+4i.
The complex roots always exist in conjugate pairs so,
3 + 4i and 3 - 4i
Thus, the three roots are 5, 3 + 4i, and 3 - 4i. Option D is correct.
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The probability that the number of students who will take the mathematics exam is 40 out of 50. What is the expressed as a percentage
Answers
Answer:
I think it's 80%
Step-by-step explanation:
Method 1: (40/50)*100 = 80%
Method 2: [tex]\frac{40*2}{50*2} = \frac{80}{100}[/tex] = 80%
The table displays the scores of students on a recent exam. Find the mean of the
scores to the nearest 10th.
Score Number of Students
70
7
75
5
80
4
85
1
90
6
Answers
Answer:
78.7
Step-by-step explanation:
To find the mean, we can do the sum of all scores divided by the total amount of scores.
We see that there are 7 scores of 70, and 70*7=490.
We see that there are 5 scores of 75, and 75*5=375.
We see that there are 4 scores of 80, and 80*4=320.
We see that there is 1 score of 85, and 85*1=85.
We see that there are 6 scores of 90, and 90*6=540.
Now we can do [tex]\frac{490+375+320+85+540}{7+5+4+1+6} =\frac{1810}{23} =78.7[/tex]
What are m and b in the linear equation y=16+6x
Answers
Answer: B=16 and m=6
Step-by-step explanation:
in y=mx+b the number next to x is always the m/slope and the number without a variable is always the b.
Which of the function correctly expresses the exponential model f(x)=6(14)^x with base of e
Answers
The exponential equation with a base of e is:
[tex]f(x) = 6*e^{2.639*x}[/tex]
How to change the base?
We start with:
[tex]f(x) = 6*(14)^x[/tex]
We want to rewrite this to:
[tex]f(x) = 6*(e^n)^x[/tex]
So we only need to find the value of n such that:
[tex]e^n = 14[/tex]
If we apply the natural logarithm to both sides:
[tex]ln(e^n) = ln(14)\\n = ln(14) = 2.639[/tex]
Then the exponential equation with base of e is:
[tex]f(x) = 6*e^{2.639*x}[/tex]
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A cab company charges a $5 boarding rate in addition to its meter which is $3
for every mile. What is the equation of the line that represents this cab
company's total charge?
Re
co
Answers
Answer:
m3+5
Step-by-step explanation:
m is miles
take the number of miles multiply by3
take that answer add 5
The equation that represents the cab's total charge is y = 3x + 5 , Option A is the correct answer.
What is an Equation ?A statement that relate two expressions with an equal sign is called an Equation.
It is given that
A cab company charges a $5 boarding
Charges for every mile is $3 per mile
Let x be the mile travelled
The cab's total charge is represented by y
then y = 3x + 5
Therefore the equation that represents the cab's total charge is y = 3x + 5 , Option A is the correct answer.
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A bag contains 3 blue, 7 green and 1 purple counter. One counter is picked
at random. What is the probability that the counter is green or purple? Give
your answer as a fraction.
Answers
A bag contains 3 blue, 7 green and 1 purple counter. One counter is picked at random, the probability of selecting a green or purple counter is 8/11.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur.
There are a total of 11 counters in the bag, 3 of which are blue, 7 are green, and 1 is purple.
The probability of selecting a green or purple counter is the sum of the probabilities of selecting a green counter and a purple counter, since the events are mutually exclusive (a counter cannot be both green and purple at the same time).
So the probability of selecting a green or purple counter is:
Probability = (Number of green counters + Number of purple counters) / Total number of counters
Probability = (7 + 1) / 11
Probability = 8/11
Therefore, the probability of selecting a green or purple counter is 8/11.
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which law would you use to simplify the expression...
Answers
Answer:
Power of a quotient
The following confidence interval is'obtained for a population proportion p: 0.87 < p < 0.93 What is the margin error E. The following confidence interval is'obtained for a population proportion p : 0.87 < p < 0.93 What is the margin error E.
Answers
The margin error of the confidence interval 0.87<p<0.93 is 0.03.
Given confidence interval 0.87<p<0.93.
We have been given the confidence interval 0.87<p<0.93 and we have to find out the margin error E. The margin error is a statistic expressing the amount of random sampling error in the results of a survey. The margin error depends on whether the problem is two tailed or half tailed but in this question we have not given whether it is two tailed or one tailed. The margin error is the half of the width of the confidence interval.
Confidence interval is 0.87<p<0.93.
Width of the interval= 0.93-0.87
=0.06
=0.03
Hence the margin of error is equal to 0.03.
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Mark divided a basket of apples evenly into small bags. The number of bags was equal to the number of apples in each bag. Which could be the total number of apples?
A. 25 B. 27 C. 20 D. 18
Answers
There are 5 bags and each bag has 5 apples and total there are 25 apples , Option A is the correct answer.
What is a Perfect Square ?A perfect square is a number which can be written as the product of an integer with itself.
It is given that Mark divided a basket of apples evenly into small bags.
Let there be n no. of bags and therefore n number of apples in each bag
Then the total number of apples will be
n * n
n²
The value of total number of apples should be a perfect square,
In the option given only 25 is the perfect square
Therefore the equation can be made as
n² = 25
n = 5
There are 5 bags and each bag has 5 apples and total there are 25 apples.
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Need number 8 please!!
Answers
Using translation concepts, the graph of function g(x) = f(x) - 2 = x² - 2 is given at the end of the question.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the functions are given as follows:
f(x) = x².g(x) = f(x) - 2 = x² - 2.Which means that g(x) is a shift down of 2 units of f(x), as given by the graph in the end of the question.
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find the area for this pls
Answers
Answer:
3,36 in^2
Step-by-step explanation:
The geometric shape shown in image is called a trapezoid
to calculate the area of a trapezoid we use the following formula:
1/2*(a+b)*h (a and b are bases, h: height)
bases are 1.3 and 3.5 and height is 1.4
1/2(1.3 + 3.5)*(1.4) = 3,36 the area is stated in square units so the answer is
3,36 in^2
