Let f be the continuous function defined on [-6,6]. Let g be the function given by g(x) = [tex]\int\limits^x_{-1} {f(t)} \, dt[/tex] . Write an equation for the tangent to the graph of g at x=4
![Let F Be The Continuous Function Defined On [-6,6]. Let G Be The Function Given By G(x) = [tex]\int\limits^x_{-1}](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/nnsxxNAcZzTm6sl1gR1lg8XSZMnLVCoN.jpeg)
Answers
Answer:
[tex]\displaystyle h(x) = x-\frac{13}{2}[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle g(x) = \int_{-1}^x f(t)\, dt[/tex]
And we want to write the equation for the tangent to the graph of g at x = 4.
First, determine g(4):
[tex]\displaystyle \begin{aligned} g(4) & = \int_{-1}^{(4)} f(t)\, dt \end{aligned}[/tex]
This is equivalent to the area of f from -1 to 4:
[tex]\displaystyle \begin{aligned} g(4) & = \frac{1}{2}(2)(3) + \frac{1}{2}(2)(-3)+\frac{1}{2}(-3+(-2))(1) \\ \\ & = \frac{1}{2}(6-6-5) \\ \\ & = -\frac{5}{2}\end{aligned}[/tex]
Note that areas under the x-axis are negative.
Find g'(4):
[tex]\displaystyle \begin{aligned} g'(x) = \frac{d}{dx}\left[ \int_{-1}^x f(t)\, dt\right]\end{aligned}[/tex]
By the Fundamental Theorem of Calculus:
[tex]\displaystyle \begin{aligned} g'(x) & = f'(x) \\ \\ g'(4) & = f'(4) \\ \\ & =1 \end{aligned}[/tex]
Note f is a line for 3 < x < 6 with a slope of 1.
Therefore:
[tex]\displaystyle \begin{aligned} h(x) -g(x_1) & = g'(x_1)(x-x_1) \\ \\ h(x) - \left(-\frac{5}{2}\right) & = (1)(x-(4)) \\ \\ h(x)& = (x-4) - \frac{5}{2} \\ \\ & = x - \frac{13}{2}\end{aligned}[/tex]
In conclusion, the equation of the tangent line is:
[tex]\displaystyle h(x) = x-\frac{13}{2}[/tex]
Related Questions
If x = 7-p and y = 3p + 4, which of the following
expresses y in terms of x ?
step by step please !!
Answers
Answer:
Step-by-step explanation:
Answer:
y = -3x + 25
Step-by-step explanation:
You have to find p first.
You can do this by using the x equation and moving the p to the right by adding p to each side to get p + x = 7.
Now, move the x to the left by subtracting x on both sides to get a final answer of p = 7 - x
Then, you can substitute p into the y equation.
So, y = 3(7 - x) + 4.
Distribute to get y = 21 - 3x + 4
Combine like factors to get y = -3x + 25
Hope this helps! :)
m TMN = x + 72, m LMN = 166°, and m LMT = 96 + x. Find m LMT. what is the answer to this? ill make you the brainly
Answers
Answer: LMT=95
Step-by-step explanation:
combine both problems to equal 166
x+x+72+96=166
Combine like terms
2x+168=166
Subtract 168 from 166
2x=168-166
Divide
X=-2/2
X=-1
Plug in -1 for x
96-1=95
72-1=71
71+95=166
LMT=95
Mitchell has been given the option of either paying his $200 bill now or settling it for $204 after 1 month (30 days). If he chooses to pay after 1 month, find the simple interest rate at which he would be charged.
Answers
The simple interest rate that he would be of 24.33% a year.
Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of money after t years in is modeled by:
[tex]A(t) = A(0)(1 + rt)[/tex]
In which:
A(0) is the initial amount.r is the interest rate, as a decimal.In this problem, considering than an year has 365 days, the parameters are as follows:
[tex]A(t) = 204, A(0) = 200, t = \frac{30}{365}[/tex]
Hence:
[tex]A(t) = A(0)(1 + rt)[/tex]
[tex]204 = 200\left(1 + \frac{30}{365}r\right)[/tex]
[tex]1 + \frac{30}{365}r = \frac{204}{200}[/tex]
[tex]\frac{30}{365}r = 0.02[/tex]
[tex]r = \frac{365}{30} \times 0.02[/tex]
[tex]r = 0.2433[/tex]
The simple interest rate that he would be of 24.33% a year.
More can be learned about simple interest at https://brainly.com/question/25296782
The function f is defined by f(x)= - 1/2x^2
Write down the expression for h(x).
Answers
Answer: -1/2 (x-4)^2 + 3
Step-by-step explanation:
Since the graphs both have the same stretch of -1/2x^2, you just need to see how much they were shifted up, down, left, or right. h(x) is shifted up 3 and right 4 of f(x) so h(x) = -1/2 (x-4)^2 + 3
Answer:
[tex]h(x)=-\dfrac12(x-4)^2+3[/tex]
Step-by-step explanation:
Given:
[tex]f(x)= - \dfrac12x^2[/tex]
From inspection of the graph, [tex]f(x)[/tex] has been translated 4 units to the right and 3 units up.
Therefore, [tex]h(x)=f(x-4)+3[/tex]
[tex]\implies h(x)=-\dfrac12(x-4)^2+3[/tex]
Maria buys 15 sarees. Each saree cost Rs. 525.50 Money spent by Maria is
Answers
Answer:
Rs. 7882.5
Step-by-step explanation:
if 1 saree ----->525.50
what about 15------>?
15×525.50÷1 = 7882.5.
I hope this helps
Answer:
Rs 7882.50
Step-by-step explanation:
525.50 x 15 = 7882.50
if you have a favorite subject in school what is it
Answers
Answer:
My favorite subject in school is ELA because I love to read. Please don't judge I am not a nerd. I just like a good book every once and a while.
Step-by-step explanation:
PLEASE MARK ME AS BRAINLIEST I REALLY WANT TO LEVEL UP
_____________Gym_______________
Vivian surveyed bicyclists in her community to see the average number of miles they biked per day. Her results are shown below.
7, 10, 13, 4, 12, 21, 10, 3
What is the MAD of her data set? What does this tell you about the number of miles biked each day by the bicyclists?
Answers
Step-by-step explanation:
4
data-mean/total =4
2. Find the rank of 4 1 3 3 3
7 -1 6 0 6
2 3 8 2 8
Answers
Step-by-step explanation:
please mark me as brainlest
Arc and sector area question please help
Answers
Answer:
A. x = 14Step-by-step explanation:
Angle formed by intersecting chords half the sum of intercepted arc measures.Apply this to the given measures:
56 = 1/2(3x + 10 + 5x - 10)56 = 4xx = 56/4x = 14Correct choice is A
I WILL GIVE BRAINLIEST IF YOU ANSWER CORRECTLY! I NEED THIS ASAP (15 POINTS)
Answers
Represent 0.7 pictorially
Answers
Refer to the attachment .
An artist makes a scale drawing of a parallelogram-shaped sculpture. The scale is 10 cm on the drawing for every 8 meters on the sculpture. What is the area of the scale drawing? Show your work.
Answers
Answer:
10 × 8
=80
therefore it takes 80 metre area
If Olivia makes a smoothie with a ratio 7 strawberries to 2 bananas, how many strawberries would she use with 3 bananas?
Answers
Answer:
13
Step-by-step explanation:
7strawberries 2 bananas 3 and she use the 3 bananas
and answer is.13
Answer:
The answer is 13 this is because idek
17. Mia has 4 inches of red yard and 2 inches of blue yarn. How many inches of yarn does she
have?
Answers
Answer:
6 inches
Step-by-step explanation:
Given:
length of red yarn = 4 inlength of blue yarn = 2 inTo find the total amount of yarn Mia has, add the two lengths together:
total yarn = red yarn + blue yard
= 4 in + 2 in
= 6 in
Vertical angles measure (x-28) degrees and (0.5x-13) degrees. What is the value of x?
Answers
Answer:
x = -30
Step-by-step explanation:
Ok remember this because its important vertical angles means the two angles are congruent and congruent means when two things are the same
if those two angles are vertical angles what does that mean?
They both equal each other because they are the CONGRUENT!
x-28 = 0.5x -13
combine like terms so add 28 to both sides
x = 0.5x + 15
then subtract - 0.5x on both sides
- 0.5x = 15
then get x by itself by dividing - 0.5 on both sides
x = -30
Enter the first 4 terms of the sequence defined by the given rule. Assume that the domain of each function is the set of whole numbers greater than 0.
[tex]f(n) =3 {n}^{2} + 1[/tex]
Answers
Given:
The rule for the sequence is
[tex]f(n)=3n^2+1[/tex]
Domain of the function is the set of whole numbers greater than 0.
To find:
The first 4 terms of the sequence defined by the given rule.
Solution:
We have,
[tex]f(n)=3n^2+1[/tex]
Domain of the function is the set of whole numbers greater than 0. So, domain for first four terms are 1, 2, 3 and 4 respectively.
For n=1,
[tex]f(1)=3(1)^2+1[/tex]
[tex]f(1)=3(1)+1[/tex]
[tex]f(1)=3+1[/tex]
[tex]f(1)=4[/tex]
For n=2,
[tex]f(2)=3(2)^2+1[/tex]
[tex]f(2)=3(4)+1[/tex]
[tex]f(2)=12+1[/tex]
[tex]f(2)=13[/tex]
For n=3,
[tex]f(3)=3(3)^2+1[/tex]
[tex]f(3)=3(9)+1[/tex]
[tex]f(3)=27+1[/tex]
[tex]f(3)=28[/tex]
For n=4,
[tex]f(4)=3(4)^2+1[/tex]
[tex]f(4)=3(16)+1[/tex]
[tex]f(4)=48+1[/tex]
[tex]f(4)=49[/tex]
Therefore, the first 4 terms of the sequence defined by the given rule are 4, 13, 28 and 49 respectively.
Question 1
25 pts
Identify the applications that involve percentages. SELECT ALL THAT APPLY.
Sales Tax
Retirement
Income
Original Sale Price
Loans
Commission
Income Tax
Answers
The applications that will involve percentages include:
Sales TaxOriginal Sale PriceCommissionIncome TaxWhich applications involve percentages?Sales tax will involve percentage because the sales tax percentage will be needed to calculate the sales tax. The same goes for the income tax.
Commissions also involve percentages as the commission is a percentage of sales. The original sales price can only be acquired by using the discount or markup percentage applied to it to get the current sales price.
Find out examples of commission percentages at https://brainly.com/question/24951536.
Thom’s restaurant bill is $45 and he leaves a 20 percent tip. What is the total cost for Thom’s meal?
$20
$54
$65
$90
Answers
Answer:
$54
Step-by-step explanation:
[tex]\frac{x}{45} = \frac{20}{100}[/tex]
To get x which is the 20% tip
1. 45×20 = 900
2. 900÷100=9
3. 9 is the tip
To get the total cost, you would have to add $9 to $45 which is $54.
If someone is a chef, then he can cook well.
Jack is a terrible cook.
What us a valid conclusión?
Answers
Answer:
he is not a chef
Step-by-step explanation:
Answer: he a bad cook.
Step-by-step explanation:
Type the correct answer in the box.
x
The value of log,5
10828 15
Answers
Answer:
190.3
Step-by-step explanation:
190.3 I multiplied sorry if incorrect
Find the value of xxx, yyy, and zzz in the parallelogram below.
Answers
Answer:
Step-by-step explanation:
Opposite sides of a parallelogram are congruent, so:
[tex]8x+3=19 \longrightarrow x=2[/tex]
[tex]27=-y-5 \longrightarrow y=-32[/tex]
II. State the aditional information needed to prove each pair of triangles is congruent indicated by the theorem.
Answers
Answer:
Step-by-step explanation:
8) HL ---> Hypotenuse and Leg
It is already given legs are congruent
Hypotenuse: DE = IJ
9) LL -----> This SAS congruent ---> Both legs of the right angled traingle are congruent
AC = YX
10) LA ----> This is AAS congruent.
BE = EI
Help with equation please
Answers
9514 1404 393
Answer:
x = 120/17
Step-by-step explanation:
In this arrangement of right triangles, each is similar to any other. Then the ratio (long side)/(hypotenuse) is the same for all.
long side/hypotenuse = BD/BA = CB/CA
x/8 = 15/17
x = 8(15/17)
x = 120/17
Hugo began his science experiment with 22 grams of sugar crystals. During the experiment, the change in the mass of the sugar crystals was – 6 grams. What is the final mass of the sugar crystals?
Answers
Answer:
16
Step-by-step explanation:22 minus 6 is 16
The final mass of the sugar crystals is 16 grams if Hugo began his science experiment with 22 grams of sugar crystals.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
It is given that:
Hugo began his science experiment with 22 grams of sugar crystals.
During the experiment, the change in the mass of the sugar crystals was – 6 grams.
Let x be the final mass of the sugar crystals.
The value of the x can be found using:
x = 22 - 6
x = 16 grams
Thus, the final mass of the sugar crystals is 16 grams if Hugo began his science experiment with 22 grams of sugar crystals.
Learn more about the arithmetic operation here:
brainly.com/question/20595275
#SPJ2
plz help me will br
Answers
16x=320
X=20
what is the slope intercept equation of this line
Answers
Answer:
B
Step-by-step explanation:
One approach is to plug (2, -2) to every function and only B will work.
Choice A) y = 3x + 4
-2 = 3(2) + 4
-2 = 10
Does not work
Choice B) y = -3x + 4
-2 = -3(2) + 4
-2 = -2
Works
Choice C) y = -1/3x + 4
-2 = -1/3(2) + 4
-2 = -2/3 + 4
-2 = -2/3 + 12/3
-2 = 10/3
Does not work
Choice A) y = 4x - 3
-2 = 4(2) - 3
-2 = 5
Does not work
You can also just take a look at the function and see that its slope is downwards so it has to be negative. Then check the slope using rise/run.
For every 1 to the right it goes down 3, so -3/1 = -3. The only function with a slope of -3 is answer choice B.
Mrs. keys has 36 pens. Yesterday she had half that amount plus 2. How many pens did she have?
Answers
Answer:
20 pens
Step-by-step explanation:
Half of 36 is 18, along with 2 additional pens.
I need solution of 5
Answers
A= 16*8=128 (Hope this helps!)
| Find the total surface area of the prism.
3 cm
5 cm
8 cm
4 cm
6 cm
Answers
Answer:
8
Step-by-step explanation:
How do you know that the table and the equation represent the same proportional relationship between x and y
Answers
x. y
2. 3
4. 6
6. 9
in this example the x values are increasing by 2 every time while the y values are increasing by 3 every time. note that the increase or decrease of the x and y values dont have to be the same
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