Let f be a differentiable function with f(1) = 2, f'(1) = 3, f(-4)= -3, and
f'(-4)= 4. Let the function g(x) = f(2x - 6). Write the equation of the line
tangent to the graph of g at the point where x = 1.
Answers
The equation of the line tangent to the graph of g at the point where x = 1 y + 10x + 44 =0.
What is line tangent?
A line that touches a curve at one point is said to be tangent. A point of tangency is the location where a curve and a line intersect. Y = mx + b is the slope-intercept formula for a line, where m is the line's slope. The straight line that "just touches" the curve at a particular location is referred to as the tangent line to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.
Given g(x)=f(2x)
Differentiate it on both side with respect to x.
[tex]\begin{aligned}& \frac{d g(x)}{d x}=2 * \frac{d f(2 x)}{d x} \\& \frac{d g(-1)}{d x}=2 * \frac{d f(-8)}{d x}=-5^* 2=-10\end{aligned}[/tex]
Slope =-10
Here x coordinate = -4
g(-4)=f(-8)=-4 = y coordinate
Thus point of tangency on function g is (-4,-4)
Thus equation of tangent is
y + 4= -10(x+4)
y + 10x + 44 =0
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Answer:
y = 8x -11
Step-by-step explanation:
You want the equation of the line tangent to g(x) = f(2x-6) at x=1, where f is a differentiable function with f(1) = 2, f(-4) = -3, f'(1) = 3, f'(-4) = 4.
Tangent lineThe equation of the tangent line at x=1 can be written ...
y = g'(1)(x -1) +g(1)
The necessary function values are ...
g(1) = f(2·1 -6) = f(-4) = -3
and
g'(x) = f'(2x -6)·(2x -6)' = 2f'(2x -6)
g'(1) = 2f'(2·1 -6) = 2f'(-4) = 8
Then the equation of the line is ...
y = 8(x -1) +(-3) = 8x -8 -3
y = 8x -11 . . . . . . tangent to g(x) at x=1
__
Additional comment
The minimum polynomial function f(x) that can have the desired values and derivatives is a cubic. The attached graph shows g(x) and the tangent at x=1 using that cubic for f(x).
Related Questions
PLEASE HELP ASAP!!!!!! I WILL GIVE BRAINIEST!!!!! I only need 2 and 3. Please explain your answer so I can understand this!!
Answers
The least expensive per pound is Customer A.
How to illustrate the expression?It should be noted that expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
The rate for the first customer will be:
= $14.50 / 1.75
= $8.29 per pound.
The second Customer rate will be:
= $26.25 / 2.5
= $10.5 per pound
The third Customer will be:
= $5.50 / 0.375
= $14.47 per pound.
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Simplify the expression below
7/2h - 3(5h - 1/2)
step by step please
Answers
Answer: [tex]-\frac{23}{2}h+\frac{3}{2}[/tex]
Step-by-step explanation:
[tex]\frac{7}{2}h-15h+\frac{3}{2}\\\\\frac{7}{2}h-\frac{30}{2}h+\frac{3}{2}\\\\-\frac{23}{2}h+\frac{3}{2}[/tex]
Graph the solution to this inequality on the number line. 1/2x−3<−1 3/8
Answers
The solution to the inequality, 1/2x - 3 < -1 3/8, is x < 13/4. See the graph below.
How to Graph the Solution of an Inequality on a Number Line?Given the inequality, 1/2x - 3 < -1 3/8, solve to find the value of x, which is the solution to the inequality.
1/2x - 3 < -1 3/8 [given]
1/2x - 3 < -11/8
Add 3 to both sides of the equation:
1/2x - 3 + 3 < -11/8 + 3 [addition property of equality]
1/2x < 13/8
Multiply both sides by 2:
1/2x * 2 < 13/8 * 2 [multiplication property of equality]
x < 13/4
The solution to this inequality, x < 13/4 is given in the graph below.
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Jimmy, Johny, and Jolly worked part-time on the weekend to earn some extra money. Three of them together earned $57. If Johny earned twice as much as Jolly did and Jimmy earned $3 less than Johny did, how much did Jimmy earn?
Answers
On solving the provided linear equation question - Jolly = $17.4, Jimmy =2x-30 =4.8 and Johnny = 2x=34.8
What is a linear equation?A linear equation has the algebraic form y=mx+b. where m is the slope and b is the y-intercept, consisting of a first-order (linear) term and a constant. If x and y are variables, the above is sometimes called a "two-variable linear equation".
Take Jolly's expenditure as x.
Jimmy would have spent twice as much as Jolly.
Johnny Equals 2x-30 if Johnny spent $30 less than Johnny.
Total amount spent: $57
Therefore,
[tex]x+ (2x-30) + 2x = 57\\ x+ 2x -30 +2x =57.\\ 5x = 57+ 30\\[/tex]
x = 87/5
x= 17.4
Now take is that - X= 17.4.
Jolly is that - x= $17.4
Jimmy is that - =4.8
Johnny is that = =34.8
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What is the slope of line a?
13
12
11
10
6
do
9
is
-
(5.7)
(x,y)
11
a
Answers
Answer:
Your question choices are messed up fix and I can help
Step-by-step explanation:
:)
Harmony pays $64.00 per month for a base cable package and an additional amount for on-demand programming. Last month, Harmony received a $67.36 cable bill.
$64.00 + x = $67.36
Ignoring sales tax and additional fees, how much did she spend for on-demand programming?
A) $3.36
B) $6.36
C) $70.72
D.) $131.36
Answers
Danny opened a savings account and deposited $100.00. The account earns 2% interest,
compounded annually. If he wants to use the money to buy a new bicycle in 3 years, how
much will he be able to spend on the bike?
nt
P(1 + 1)^²₁. where A is the balance (final amount), P is the principal
Use the formula A = P 1 +
(starting amount), r is the interest rate expressed as a decimal, n is the number of times per
year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.
Answers
Answer: f = p * (1 + r) ^ n
f is the future value.
p is the present value.
r is the interest rate per time period.
n is the number of time periods.
time periods are months.
rate is the percent divided by 100.
p = 100
r = 6% per year / 12 = .5% per month / 100 = .005 per month.
n = 2 years * 12 = 24 months.
formula becomes f = 100 * (1 + .005) ^ 24
solve for f to get:
f = 112.7159776 = 112.72
that's how much Danny will be able to spend on the bike in 2 years.
Step-by-step explanation:
Josefina ate 3/8 of the pizza and Leando ate 4/16. How much did they eat between the two of them?
Answers
To calculate how much they ate between the two of them, the amounts each ate must be added:
[tex]\begin{gathered} \sf \frac{3}{8} + \frac{4}{16} = \\ \\ \sf\frac{16 \div 8 \times 3 + 16 \div 16 \times 4}{16} = \\ \\ \sf\frac{6 + 4}{16} = \\ \\ \sf \frac{10}{16} = \red {\boxed{ \sf \frac{ \green5}{ \green8} }}\end{gathered}[/tex]
Therefore, between the two of them they ate five eighths of pizza.
To add heterogeneous fractions, fractions with different denominators, follow these steps:
Find the common denominator, which is the least common multiple of the denominators.Divide the common denominator by the other denominator and multiply by the numerator.Write the results obtained above as numerators with the sign of the sum between them.Add the numerators.Simplify the result if possible.Merry Christmas and Happy New Year
The Alpha.To calculate how much they ate between the two of them, the amounts each ate must be added:
[tex]\begin{gathered}\begin{gathered} \bold{ \frac{3}{8} + \frac{4}{16}} \\ \\ \bold{\frac{16 \div 8 \times 3 + 16 \div 16 \times 4}{16}} \\ \\ \bold{\frac{6 + 4}{16}} \\ \\ \bold{ \frac{10}{16} }= {\boxed{ \sf \frac{ \bold5}{ \bold8} }}\end{gathered}\end{gathered} [/tex]
[tex]\therefore[/tex] Between the two of them they ate five eighths of pizza.
To add heterogeneous fractions, fractions with different denominators, follow these steps:
Find the common denominator, which is the least common multiple of the denominators.
Divide the common denominator by the other denominator and multiply by the numerator.
Write the results obtained above as numerators with the Sign of the sum between them.
Add the numerators.Simplify the result if possible.The average mass of 5 boys is 50 kilograms. Another boy’s mass is added and the average goes to 40 kilograms. What was the mass of the sixth boy?
Answers
The mass of the sixth boy is 80 kilograms.
What was the mass of the sixth boy?It's important to note that a mean simply means the average of a set of numbers that are given. In this situation, the average mass of 5 boys is 50 kilograms. The total mass will be:
= 50 × 5
= 250 kilograms
In this case, when another boy’s mass is added and the average goes to 55 kilograms. The total mass will be:
= 55 × 6
= 330 kilograms.
The average mass of the last boy will be:
= 330 - 250
= 80 kilograms
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Complete questions
The average mass of 5 boys is 50 kilograms. Another boy’s mass is added and the average goes to 55 kilograms. What was the mass of the sixth boy?
Select yes or no to state if the expression is equivalent to -2 + 5
A. 5 - 2 yes or no
B. -2 - (-5) yes or no
C. -2 - 5 yes or no
D. 5 + (-2) yes or no
Answers
Answer:
a) yes
b) yes
c) no
d) yes
Step-by-step explanation:
-2 + 5 = 3
5-2 = 3
-2 - (-5) = -2 + 5 = 3
-2 - 5 = -7
5 + (-2) = 5-2 = 3
Which equation represents how to determine the speed of an object?
Answers
The equation that the speed of an object is speed = distance/time
How to determine the equation of an objectFrom the question, we have the following parameters that can be used in our computation:
Parameter = Object
Argument = Speed
By definition, the speed of an object is the ratio of the distance moved by the object and the time travelled by the object
Mathematically, this can be represented as
Speed = Distance : Time
Express as fraction
Speed = Distance/Time
Hence, the equation is Speed = Distance/Time
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If Harry travels 4 and 6/8 of a mile in 5 hours on his broomstick. How far will he travel in 1 hour?
Answers
Answer:
Step-by-step explanation:
Use the given functions to set up and simplify 6/8.
4 =
6/8 = 3/4
1/5 mi/hr mulitplied by 1 hr = 1/5 mi
for every 8chin ups Melanie can do Theresa can do 5. If Melanie did 48 chin ups, how many fewer did Theresa do
Answers
Answer: Theresa did 18 fewer chin-ups.
Step-by-step explanation:
Melanie 8,16,24,32,40,48
Theresa 5,10,15,20,25,30
48-30=18
Write an equation for (k) and (t)
Answers
Required equation of points plotted on graph relating range gain(k) and charging time(t) is k=4t.
What is linear equation in two variables?A two-variable linear equation is one in which both variables have exponent 1.
What is straight line?An object in geometry known as a line is simply one that is described as being straight, thin, one-dimensional, zero width, and extending on both sides to infinity.
In essence, a straight line is just a line devoid of any bends.
Additionally, we can state that any line that crosses two certain points on the same plane will be singular.
Straight line form
m= y 2. – y 1/x 2-x 1
y-y 1=m (x-x 2)
A (0,0) and B (5,20)
([tex]x_{1}[/tex],[tex]y_{1}[/tex] ) = (0,0) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]) = (5,20)
m = 20-0/5-0
= 20/5
= 4
([tex]x_{1}[/tex],[tex]y_{1}[/tex] ) =(0,0)
y-0=4(x-0)
y=4x
Replace y with k and x with t
k=4t
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Jaylen bought 5 pounds of apples for 12.99 and 4 cupcakes for 2.99 each. He went to the store with $48. How much did Jaylen have left after his shopping trip?
23.05
37.94
10.06
24.95
Answers
Answer:
$24.95
Step-by-step explanation:
2.99 times 4 is 11.96, and you would add that with 12.99 to get 24.95.
Answer:
Jaylen have left 23.05 $
Step-by-step explanation:
5 pounds of apples = 12.99 $
4 cupcakes = 2.99 $/apple
Total money = 48 $
All the cupcakes costs = 4*2.99 = 11.96 $
Then she bought in total:
48 -(12.99 + 11.96)
48 - 24.95 = 23.05
4. The chart below represents the kinematics of a freely falling body.
Time
(seconds t)
Total Distance
meters d (t)
1
5
2
20
45
80
125
3
4
5
a. Is the relationship between time and distance an arithmetic sequence?
Explain.
b. The total distance a freely falling body covers in time, t, is given by the equation d(t)=1/2 gt2, where g is constant at 10 m/s². Show, in terms of n, the distance a falling body covers in t = n seconds of movement.
Answers
a. The given sequence is not an arithmetic sequence.
b. The distance a falling body covered in t = n seconds of movement is 5n²meters.
What is the distance?
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.
Here, we have
a. A sequence can be said arithmetic sequence if the difference between any two consecutive terms remains the same.
In this case, the difference between 20 and 5 is 15, and the difference between 45 and 20 is 25, this shows that the difference between two consecutive terms is not the same.
Hence, it can be said that the given sequence is not an arithmetic sequence.
b. To evaluate the distance covered by the body in “n” seconds, Substitute t=n in d(t) then d(n) will represent the distance covered by the body in “n” seconds
d(n)=1/2 g(n)²
d(n) = 1/2(10)(n)²
d(n) = 5n²meters
Hence, the distance a falling body covered in t = n seconds of movement is 5n²meters.
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The square root of (-2x)^2 for which values of x does the expression makes sense?
Answers
Answer: [tex]x\leq 0[/tex]
Step-by-step explanation:
The first thing we need to do is to make the argument or the number inside the square root equal or larger than zero:
-2x ≥ 0
x ≤ 0/-2
x ≤ 0
So the given expression only makes sense for x that is less than or equal to zero.
-8p^4 +12p^3 +4p^4 -8p^2 +3p^2
Answers
Answer:
-4[tex]p^{4}[/tex] + [tex]12p^{3}[/tex] - 5[tex]p^{2}[/tex]
Step-by-step explanation:
[tex]-8p^{4}[/tex] + [tex]12p^{3}[/tex] + [tex]4p^{4}[/tex] - [tex]8p^{2}[/tex] + [tex]3p^{2}[/tex] Combine the terms with the same exponents
([tex]-8p^{4}[/tex] + [tex]4p^{4[/tex]) + [tex]12p^{3}[/tex] + ([tex]-8p^{2}[/tex] + [tex]3p^{2}[/tex])
[tex]-4p^{4}[/tex] + [tex]12p^{3}[/tex] - [tex]5p^{2}[/tex]
choose the best graph to match the given expression.
F(x)= [x+1]
Answers
Answer:
Step-by-step explanation:
I don't see a graph from which to choose. Are the brackets in "[x+1]" supposed to be parentheses, or are they absolute value signs?
The graph of functions
(F(x) = (x+1), and
(F(x) = |x+1| are both attached.
There are 75 fifth graders and 125 fourth graders. They are going to be grouped in teams for Field Day with the same number of students on each team. If there must be the same number of fifth graders on each team, how many teams can there be at most?
Answers
3 fifth graders each
5 fourth graders each
Answer:25
Step-by-step explanation:
3
5
Show the work please! Thanks!!
Answers
Simplifying
2x + 5y = 2
Solving
2x + 5y = 2
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-5y' to each side of the equation.
2x + 5y + -5y = 2 + -5y
Combine like terms: 5y + -5y = 0
2x + 0 = 2 + -5y
2x = 2 + -5y
Divide each side by '2'.
x = 1 + -2.5y
Simplifying
x = 1 + -2.5y
Simplifying
5X + 10y = 17
Solving
5X + 10y = 17
Solving for variable 'X'.
Move all terms containing X to the left, all other terms to the right.
Add '-10y' to each side of the equation.
5X + 10y + -10y = 17 + -10y
Combine like terms: 10y + -10y = 0
5X + 0 = 17 + -10y
5X = 17 + -10y
Divide each side by '5'.
X = 3.4 + -2y
Simplifying
X = 3.4 + -2y
A package of 6 pair of inulated glove cot $47. 94 what i the unit price of the pair of glove?
Answers
Therefore the solution for this question is the unit price of each pair of gloves is $7.99.
What is division?One of the four fundamental arithmetic operations, or the process by which two or more numbers are added together to create a new number, is division. Multiplication, addition, and subtraction round out the list of operations.
Here,
The cost of 6 pairs of gloves = $47.94
Now, the unit price = Price per unit of the given item
Let x be the unit price of the glove
thus
x=47.94/6
x=7.99
or it can be written as price of glove=$7.99
Therefore, Unit price of the glove = $7.99
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if you have a learner's license, how many hours of driving experience are required to earn the class e license?
Answers
If you currently hold a learner's permit, you must complete 50 hours of practice driving under supervision, including at least 15 hours after dusk, before you may take a road test to get a class e license.
Explain the term learner's license?The candidate receives a learner's license after passing a written or online exam that assesses his understanding of traffic laws.
You may practice driving the public roads after receiving a learner's permit as long as you are supervised by someone who has a valid driving license.Before being permitted to receive a full driver's license, first-time drivers must first obtain a driver's permit, sometimes referred to as a learner's permit, driver's licence license, or provisional license. Prior to passing your driving test, you are able to drive (with some restrictions) if you obtain a driver's permit. Each state has a different minimum age requirement for obtaining a driver's license.Thus, if you currently hold a learner's permit, you must complete 50 hours of practice driving under supervision, including at least 15 hours after dusk, before you may take a road test to get a class e license.
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Ahmad jogged a distance of 3200 m on Saturday and a distance of 1.8 km on Sunday.
(a) Express the distance he jogged on Saturday as a percentage of the total distance jogged on both days.
(b) Find the percentage decrease in the distance he jogged from Saturday to
Sunday.
Answers
Answer:
a) 4,000 meters
b) - 56.25% (or -56% with 2 sig figs
Step-by-step explanation:
Calculate the total distance Ahmad jogged on both days. This will require a conversion unit to make the distances the same units.
Sat.: 3200 m
Sun: 1.8 km
(1,000m/km)
(1.8km)*(1,000 m/km) = 1,800 m jogged on Sunday
Total distance jogged = 3,200 m + 1,800 m = 4,000 meters total jogged
a) Percentage jogged on Saturday:
(3,200 m)/(4,000 m) = 0.80 or 80%
b) Percentage Decrease (From Saturday to Sunday):
Sat: 3200 m
Sun: 1800 m
Difference = 1400 m (decrease)
Percentage Decrease = (1800/3200) = 56.25%
Ahmad's distance on Sunday was a 56.25% decrease from Saturday.
At a football stadium, 25% of the fans in attendance were teenagers. If there were 10 teenagers at the football stadium, what was the total number of people at the stadium?
Answers
Answer:
40 people
Step-by-step explanation:
25% = 10
50% = 20
100% = 40
Using the unit circle, on what interval is the cosine function increasing? (0, startfraction pi over 2 endfraction) (0, pi) (startfraction pi over 2 endfraction, startfraction 3 pi over 2 endfraction) (pi, 2 pi)
Answers
The interval where the cosine function is increasing is (π, 2π).
Finding the value of the cosine function in different intervals:The cosine function for the interval (0, π/2) gives
cos(x) = cos(0) = 1
cos(x) = cos(π/2) = 0
So, the value of the function is decreasing in this interval.
Then, for the interval (0, π), it gives
cos(0) = 1; cos(π) = -1
So, the value of the cosine function is decreasing in this interval.
Then, for the interval (π/2, 3π/2), it gives
cos(π/2) = 0
cos(π) = -1
cos(3π/2) = 0
So, the value of the function decreases up to x = π and then increases up to the same value as before i.e., cos(π/2) = cos(3π/2).
Then, for the interval (π, 2π), the cosine function gives
cos(π) = -1
cos(2π) = 1
Thus, the cosine function in this interval increase from -1 to 1.
Therefore, in the interval (π, 2π), the cosine function is increasing.
This is explained by using a unit circle below:
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Answer:
D
Step-by-step explanation:
got it right
A store ships books by weight a small box can hold 4 to 6 pounds while a large box can hold 8 to 9 pounds how much can each box hold
Small box= 4 to 6 lbs
Large box= 8 to 9 lbs
Book weights large 3.1 lbs
Small 2.4 lbs
Answers
Answer:
The small box can hold 4 to 6 lbs, so it can hold the 3.1 lb book and 2.4 lb book. The large box can hold 8 to 9 lbs, so it can hold the 3.1 lb book, but not the 2.4 lb book.
Step-by-step explanation:
Find the slope (rate of change) of a line that passes through (-2, -3) and (1, 1).
1. 1/3
2. 1
3. 2
4. 4/3
Answers
Answer:
4. 4/3
Step-by-step explanation:
(-2, -3) (1,1)
1+3/1+2=
4/3
standard equation of a parabola with a vertex of (0,0) and a focus of (-8,0)
Answers
Answer:
(x + 8)^2 + y^2 = (x - 8)^2
Step-by-step explanation:
when $n$ is divided by $8$, the result is greater than $5$. what is the least possible integer value of $n$?
Answers
when N is divided by 8, the result is greater than 5 the least possible integer value of N is 48.
Zero, a positive natural number, or a negative integer with a minus sign are all examples of integers. The additive inverses of the positive numbers are the negative numbers. The boldface Z is frequently used in mathematics to denote the set of integers.
Positive integers: If a number is greater than zero, it is positive. Example: 1, 2, 3 . . .Negative integers: If a number is less than zero, it is negative. Example: -1, -2, -3 . . .Zero cannot be thought of as either a negative or a positive integer. It's an entire number.the least possible integer greater than 5 is 6,
and when 6 × 8 = 48 thus,
the least possible integer value of N is 48.
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