Answer:
[tex]y(t) = 3x+8e^{-3x} -1[/tex]
Step-by-step explanation:
Recall that the following laplace transforms
[tex]L(y') = sY(s)-y(0)[/tex]
[tex]L(t) = \frac{1}{s^2}[/tex]
The laplace transform is linear, so, applying the laplace transform to the equation we get
[tex]L(y'+3y) = sY(s)-7+3Y(s) = L(9t) = \frac{9}{s^2}[/tex]
By some algebraic manipulations, we get
[tex] Y(s)(s+3) = \frac{9+7s^2}{s^2}[/tex]
which is equivalent to
[tex] Y(s) = \frac{9+7s^2}{s^2(s+3)} = \frac{9}{s^2(s+3)}+\frac{7}{s+3}[/tex]
By using the partial fraction decomposition, we get
[tex] \frac{9}{s^2(s+3)} = \frac{-1}{s} + \frac{3}{s^2} + \frac{1}{s+3}[/tex]
then
[tex]Y(s) = \frac{-1}{s} + \frac{3}{s^2} + \frac{1}{s+3} + \frac{7}{s+3} = \frac{8}{s+3} + \frac{3}{s^2}-\frac{1}{s}[/tex]
Using that
[tex] L(e^{-ax}) = \frac{1}{s+a}[/tex]
[tex]L(1) = \frac{1}{s}[/tex]
by taking the inverse on both sides we get
[tex] y(t) = L^{-1}(\frac{8}{s+3})+L^{-1}(\frac{3}{s^2})+L^{-1}(-\frac{1}{s}) = 8e^{-3x} + 3x-1[/tex]
Consider it this cone with a diameter of 19 cm use the drop-down menus to describe the con measurements
Answer:
1) Radius of the cone = 9.5 cm
2) BA = 90.25 π cm²
3) SA = 384.7 π cm²
Step-by-step explanation:
1) Radius of the cone = 9.5 cm
2) Base Area of the cone = [tex]\pi r^2[/tex]
BA = (π)(9.5)²
BA = 90.25 π cm²
3) Surface Area of Cone = [tex]\pi r(r+\sqrt{h^2+r^2)}[/tex]
SA = π(9.5)(9.5 + √(29.5)²+(9.5)²)
SA = 9.5π(9.5 + 31)
SA = 9.5π(40.5)
SA = 384.7 π cm²
Do Audience Ratings Differ Based on the Genre of the Movie? The dataset HollywoodMovies includes a quantitative variable on the Audience-Score of the movie as well as a categorical variable classifying each movie by its Genre. The computer output above gives summary statistics for audience ratings based on genre for a sample of the movies, using four of the possible genres. Variable Genre N Mean StDev Minimum Qi Median Q3 Maximum Audience Score Action 32 58.63 18.39 32.00 44.50 51.00 78.00 93.00 Comedy 27 59.11 15.68 31.00 48.00 58.00 71.00 93.00 Drama 21 72.10 14.55 46.00 59.00 72.00 84.50 91.00 Horror 17 48.65 15.88 25.00 34.00 52.00 60.50 78.00 (a) Which genre has the highest mean audience score? The lowest mean audience score? (b) Which genre has the highest median score? The lowest median score? (c) In which genre is the lowest score, and what is that score? In which genre is the highest score, and what is that score? (d) Which genre has the largest number of movies in that category? (e) Calculate the difference in mean score between comedies and horror movies, and give notation with your answer, using i, for the mean comedy score and , for the mean horror score.
Answer:
Step-by-step explanation:
Hello!
(a) Which genre has the highest mean audience score? The lowest mean audience score?
1) Action [tex]\frac{}{X}_1[/tex]= 58.63
2) Comedy [tex]\frac{}{X}_2[/tex]= 59.11
3) Drama [tex]\frac{}{X} _3[/tex] = 72.10
4) Horror [tex]\frac{}{X}_4[/tex]= 48.65
The lowest mean score is [tex]\frac{}{X}_4[/tex]= 48.65
The highest mean score is [tex]\frac{}{X} _3[/tex] = 72.10
(b) Which genre has the highest median score? The lowest median score?
1) Action Me₁= 51.00
2) Comedy Me₂= 58.00
3) Drama Me₃= 72.00
4) Horror Me₄= 52.00
The Lowest median is Me₁= 51.00
The Highest median is Me₃= 72.00
(c) In which genre is the lowest score, and what is that score? In which genre is the highest score, and what is that score?
Lowest or minimum scores:
1) Action 32.00
2) Comedy 31.00
3) Drama 46.00
4) Horror 25.00
The genre with the lowest score is "Comedy"
Highest or maximum scores:
1) Action 93.00
2) Comedy 93.00
3) Drama 91.00
4) Horror 78.00
There are two genres with the highest score "Action" and "Comedy"
(d) Which genre has the largest number of movies in that category?
The number of movies for each category corresponds to the sample sizes:
1) Action n₁= 32
2) Comedy n₂= 27
3) Drama n₃= 21
4) Horror n₄= 17
The largest number of movies sampled was for the genre "Action"
(e) Calculate the difference in mean score between comedies and horror movies, and give notation with your answer, using i, for the mean comedy score and, for the mean horror score.
Comedy [tex]\frac{}{X}_C[/tex]= 59.11
Horror [tex]\frac{}{X}_H[/tex]= 48.65
[tex]\frac{}{X}_C[/tex] - [tex]\frac{}{X}_H[/tex]= 59.11 - 48.65= 10.46
I hope this helps!
The figure below is made of 2 rectangular prisms. What is the volume of this figure?
_____ cubic units.
Answer:
100
Step-by-step explanation:
The Volume of the Rectangular prism on the left is 60
The Volume of the Rectangular prism on the right is 40
Answer:
Your correct answer is 40
Step-by-step explanation:
Multiply 8 x 5.
8 x 5 = 40
MUltiply 40 x 1.
40 x 1 = 40
So, it stays the same. Anything multiplied by 1 stays the same.
Therefore, your correct answer is 40.
Buchtal, a manufacturer of ceramic tiles, reports on average 2.3 job-related accidents per year. Accident categories include trip, fall, struck by equipment, transportation, and handling. The number of accidents is approximately Poisson. Please upload your work for all of the parts at the end. a) What is the probability that more than one accident occurs per year? Include at least 3 decimal places in your answer. Submit Answer Tries 0/5 b) Suppose that 5 years are randomly selected. What is the expected number of accidents in this time period? Submit Answer Tries 0/5 c) What is the standard deviation of the number of accidents in 5 years? Submit Answer Tries 0/5 d) What is the probability that exactly 8 accidents occur in 5 years? Include at least 3 decimal places in your answer. If you get an error on your calculator, please use an online source like Wolfram Alpha to calculate the number. Submit Answer Tries 0/5
Answereippcb.jrc.ec.europa.eu
Step-by-step explanation:
this I the wed go on it and you will get your answer
A division problem is shown below. 4 and one-third divided by 5 and StartFraction 1 over 6 EndFraction The reciprocal of a fraction must be found to solve the problem. What is the reciprocal fraction that is required?
Answer:
6/5
Step-by-step explanation:
you have to flip the numerator and denominator. If it is 5/6 then it would be 6/5.
The reciprocal fraction that is required will be 31/26.
What is a fraction?A fraction is a numerical number that is represented in the numerator and denominator form.
We have Two mixed fractions, the First fraction = 4(1/3) and the Second fraction = 5(1/6).
Now,First, convert mixed fractions into simple fractions,i.e.First fraction = 4(1/3) = 13/3And,Second fraction = 5(1/6) = 31/6
Now, According to the question,
Divide First fraction by Second fraction;i.e.= (13/3) / (31/6)Now simplify,= ( 13 × 6) / (31 × 3)
Now, We get,= 26/31
So, the reciprocal fraction = 31/26.
Hence we can say that the reciprocal fraction that is required will be 31/26.
To learn more about fractions click here,https://brainly.com/question/10354322
#SPJ2
0.006772 to 1 significant number
Answer:
0.006772
If the last dropping digit is less than 5 then it will be ignored
0.00677
if the last dropping digit is greater than 5 than the the last retained digit increases by 1
0.0068
if the last dropping digit is greater than 5 than the the last retained digit increases by 1
0.007
if the last dropping digit is greater than 5 than the the last retained digit increases by 1
0.01
if the last digit is less than 5 so it will be ignored
0.0 is significant figure because zero to the right of decimal point are significant
Step-by-step explanation:
i hope this will help you :)
Answer:
0.007
Step-by-step explanation:
Rounding off 0.006772 to 1 significant figures:
=> 0.007
There is only 1 significant figure in this , since the zeroes on the left are not counted as significant figures.
The given function is analytic at a = 0. Use appropriate series in (2) and long division to find the first four nonzero terms of the Maclaurin series of the given function.
Sec x.
Answer:
[tex]\mathbf{1 + \dfrac{x^2}{2!}+ \dfrac{5}{24}x^4+\dfrac{61}{720}x^6}[/tex]
Step-by-step explanation:
From the given information:
we are to find the first four nonzero terms of the Maclaurin series of the given function.
Sec x.
If we recall ; we will realize that the derivative of sec x = [tex]\dfrac{1 }{cos \ x}[/tex]
Also; for cos x ; the first four terms of its Maclaurin Series can be expressed as ;
=[tex]1- \dfrac{x^2}{2!}+\dfrac{x^4}{4!}- \dfrac{x^6}{6!}+...[/tex]
However, using the long division method: we have;
[tex]\dfrac{1}{1- \dfrac{x^2}{2!}+\dfrac{x^4}{4!}- \dfrac{x^6}{6!}}[/tex]
the rule of the long division method is to first use the 1 from the denominator to divide the 1 from the numerator. the multiply it with the answer we get which is (1) before subtracting it from that answer (1).
i.e
1/1 = 1
1 × 1 = 1
1 - 1 = 0
Afterwards; we will subtract the remaining integers from this numerator.
So, we have:
[tex]\dfrac{-(1 - \dfrac{x^2}{2!}+\dfrac{x^4}{4!}- \dfrac{x^6}{6!} )}{0+ \dfrac{x^2}{2!}-\dfrac{x^4}{4!}+ \dfrac{x^6}{6!}}[/tex]
We are going to apply the same process to the remainder [tex]\dfrac{x^2}{2!}[/tex];
which is to divide the second integer with 1
[tex]\dfrac{\dfrac{x^2}{2!}}{1}= \dfrac{x^2}{2!}[/tex]
Then we will multiply the numerator with [tex]\dfrac{x^2}{2!}[/tex] ; the result will then be subtracted from the polynomial.
[tex]= \dfrac{-( \dfrac{x^2}{2!} - \dfrac{x^4}{2! 2!} + \dfrac{x^6}{2! 4!}- \dfrac{x^8}{2! 6!}) }{0 + \dfrac{5}{24}x^4 - \dfrac{7}{360}x^6- \dfrac{x^8}{2!6!} }[/tex]
Repeating the same process for remainder [tex]\dfrac{5}{24}x^4[/tex]; we have:
[tex]\dfrac{ \dfrac{5}{24}x^4 }{1}= \dfrac{5}{24}x^4[/tex]
so; we will need to multiply 1 with [tex]\dfrac{5}{24}x^4[/tex] and subtract it from the rest of the polynomial
[tex]=\dfrac{{0 + \dfrac{5}{24}x^4 - \dfrac{7}{360}x^6- \dfrac{x^8}{2!6!} }}{ 1-x^2+ \dfrac{x^4}{4!} - \dfrac{x^6}{6!} }[/tex]
[tex]= \dfrac {- ( \dfrac{5}{24}x^4 -\dfrac{5}{2!4!}x^6 - \dfrac{5x^8}{4!4!} - \dfrac{5x^{10}}{6!4!} } {0+ \dfrac{61}{720}x^6}[/tex]
Here ; the final remainder is [tex]\dfrac{61}{720}x^6}[/tex]; repeating the usual process for long division method; we have:
[tex]\dfrac{\dfrac{61}{720}x^6}{1}= \dfrac{61}{720}x^6}[/tex]
So;
[tex]= \dfrac{0+ \dfrac{61}{720}x^6}{1-x^2+ \dfrac{x^4}{4!} - \dfrac{x^6}{6!} }[/tex]
[tex]= \dfrac{-( \dfrac{61}{720}x^6)}{0 }[/tex]
Now the first four nonzero terms of the Maclaurin series is the addition of all the integers used as remainders ; i.e
[tex]\mathbf{1 + \dfrac{x^2}{2!}+ \dfrac{5}{24}x^4+\dfrac{61}{720}x^6}[/tex]
Solve 6 + 5 √ 2 4 9 − 2 x = 7
[tex]
6+5\sqrt{249}-2x=7 \\
-2x=7-6-5\sqrt{249} \\
-2x\approx-77.9 \\
x\approx\frac{-77.9}{2}\approx38.95
[/tex]
Hope this helps.
A LINE PASSES THROUGH THE POINTS. what is the EQUATION OF THE LINE? (2,-4) and (6,10)?
Hey there! :)
Answer:
y = 7/2x - 11
Step-by-step explanation:
Use the slope formula to calculate the slope:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in the coordinates:
[tex]m = \frac{10-(-4)}{6-2}[/tex]
Simplify:
[tex]m= \frac{14}{4}[/tex]
[tex]m = \frac{7}{2}[/tex]
Slope-intercept form is y = mx + b. Plug in the slope, as well as the coordinates of a point given to solve for b:
10 = 7/2(6) + b
10 = 42/2 + b
10 = 21 + b
10 - 21 = b
b = -11.
Write the equation:
y = 7/2x - 11
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.y=-6x+6 y=-3x-3
Hey there! :)
Answer:
Has one solution.
(Graphed below)
Step-by-step explanation:
***The equations are graphed below, but this can also be solved algebraically.***
Set each equation equal to each other:
-6x + 6 = -3x - 3
Add 6x to both sides:
6 = 3x - 3
Add 3 to both sides:
9 = 3x
x = 3.
Plug in the value of x into an equation to solve for y:
y = -6(3) + 6
y = -18 + 6
y = -12.
The system of equations only has ONE solution at (3, -12).
On the graph, as well, the point of intersection is at (3, -12). This is the solution.
Please answer this question fast in two muintues
Answer:
W
Step-by-step explanation:
W is the vertex, you can see the letter above the angle
Answer:
W
Step-by-step explanation:
The vertex is where the 2 rays meet, or the corner of the angle
The vertex is W
PLEASE HELP ME!!! FIRST ANSWER GETS BRAINLIEST ANSWER!!!
Jamie wants to know the volume of his gold ring in cubic centimeters. He gets a rectangular glass with a base 3 cm by 2 cm and fills the glass 4 cm high with water. Jamie drops his gold ring in the glass and measures the new height of the water to be 4.25 cm. What is the volume of Jamie's ring in cubic centimeters?
Volume before the gold:
3 x 2 x 4 = 24 cubic cm.
Volume after gold:
3 x 2 x 4.25 = 25.5 cubic cm
Volume of gold is the difference:
25.5 - 24 = 1.5 cubic cm.
10.
AA'B'C' is a dilation image of AABC. Which is the correct description of the dilation?
12
of a
А)
6
B' =B
С
Answer:
Option (2)
Step-by-step explanation:
In the figure attached,
ΔA'B'C' is a dilation image of ΔABC or both the triangle are similar.
Therefore, by the property of similarity of two similar triangles, corresponding sides these similar triangles will be proportional.
Scale factor = [tex]\frac{\text{Side of image triangle}}{\text{Side of the pre-image}}[/tex]
= [tex]\frac{\text{B'A'}}{\text{B'A}}[/tex]
= [tex]\frac{\text{(B'A+AA')}}{\text{B'A}}[/tex]
= [tex]\frac{(6+12)}{6}[/tex]
= 3
Therefore, scale factor is 3 when center of dilation is B.
Option (2) will be the answer.
Find the height of cylinder when volume is 154 cm^3 volume and radius is 3 cm
Answer:
Volume of a cylinder is πr²h
Where
r is the radius
h is the height
Volume = 154cm³
radius = 3cm
height = ? cm
154 = π × 3² × h
154 = π × 9 × h
154 = 9πh
divide both sides by 9π
h = 154/9π
h = 5.4cm
Height is 5.4cm
Hope this helps
Suppose that a high school marching band has 97 members. Of these 97 band members, 31 are seniors, 18 play the trumpet, and 6 are seniors who play the trumpet.What is the probability that a randomly selected band member is a senior given that he or she plays the trumpet? Give your answer as a percentage, rounded to one decimal place.___%What is the probability that a randomly selected band member plays the trumpet given that he or she is a senior?___%
Answer:
Step-by-step explanation:
33.3%
19.4%
Identify the glide reflection rule in the given figure
Answer:
Option (3)
Step-by-step explanation:
Glide reflection of a figure is defined by the translation and reflection across a line.
To understand the glide rule in the figure attached we will take a point A.
Coordinates of the points A and A' are (2, -1) and (-2, 4).
Translation of pint A by 5 units upwards,
Rule to be followed,
A(x, y) → A"[x, (y + 5)]
A(2, -1) → A"(2, 4)
Followed by the reflection across y-axis,
Rule to be followed,
A"(x, y) → A'(-x, y)
A"(2, 4) → A'(-2, 4)
Therefore, by combining these rules in this glide reflections of point A we get the coordinates of the point point A'.
Option (3) will be the answer.
Answer:Reflection along the line y= -1
Step-by-step explanation:
took test
Two dice are rolled. What is the probability that the sum of the numbers rolled is either 6 or 9? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answer:
1/4
Step-by-step explanation:
There are 36 possible combinations. Of those 36, the ones that add up to either 6 or 9 are:
1+5, 2+4, 3+3, 4+2, 5+1, 3+6, 4+5, 5+4, 6+3
There are 9 combinations that add up to either 6 or 9. So the probability is 9/36, or 1/4.
The probability that the sum of the numbers rolled is either 6 or 9 is [tex]\frac{1}{4}[/tex] . In rounded to the nearest millionth, the probability is 0.25.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.
Possible outcomes are
1+5, 2+4, 3+3, 4+2, 5+1, 3+6, 4+5, 5+4, 6+3.
The number of possible outcomes is 9.
Each dice has 6 possible outcomes.
Total number of outcomes = 6 × 6 =36
The probability is the ratio of total number of outcomes to possible outcomes.
The probability is 9/ 36 = 1/4 = 0.25
Hence, required probability is 1/4 or 0.25.
Learn more about probability from the given link.
https://brainly.com/question/251701
#SPJ2
A theater group made appearances in two cities. The hotel charge before tax in the second city was $ 1500 higher than in the first. The tax in the first city was 5 % , and the tax in the second city was 8.5 % . The total hotel tax paid for the two cities was $ 836.25 . How much was the hotel charge in each city before tax?
Answer:
In city one, the hotel charges before taxes were $5,250.
In city two, the hotel charges before taxes were $6,750.
Step-by-step explanation:
Let the hotel charge in the first city be x and in the second city be y.
Given that the hotel charge before tax in the second city was $ 1500 higher than in the first. That can be written as:
[tex]y - x = \$1500[/tex] ...[1]
The tax in the first city was 5 %, and the tax in the second city was 8.5 %.
The total hotel tax paid for the two cities was $ 836.25
5% of x + 8.5% of y = $836.25
[tex]0.05x+0.085y=\$836.25[/tex]...[2]
Now putting value of y from [1] in to [2]:
[tex]y = \$1500+x[/tex]
[tex]0.05x+0.085\times (\$1500+x)=\$836.25[/tex]
On solving we get :
x = $5,250
Using vakue of x in [1] to find y:
[tex]y=\$1500+\$5,250=\$ 6,750[/tex]
In city one, the hotel charges before taxes were $5,250.
In city two, the hotel charges before taxes were $6,750.
In 1990, the profit of the Gamma company was $11.900,848. Each year after 1990profits fell by \$48,263 on average Construct a linear model for this scenario and use it to solve for the profits in the year 2020. Round your answer to a whole dollar
Answer:
$10452958
Step-by-step explanation:
Initial profit = $11900848
Fall rate= $48263 per year
Equation:
P(x)= 11900848 - (x-1990)*48263,where P(x)= profit at year of x, and 1990<x<2020
P(2020)= 11900848- 30*48263= $10452958pls help i give brainliest
Answer:
Step-by-step explanation:
Area of triangle = 1/2 × b × h
69.3 = 8.4 × h
h = 69.3 / 8.4
h = 8.25 mm
hope this helps
plz mark as brainliest!!!!!!
Answer:
16.5mm
Step-by-step explanation:
1. 69.3 x 2
2. 138.6 divided by 8.4
3. solve which equals 16.5mm
Hope this helps you:)
What angle is included by AB and BC ?
B
A
O A. ZB
OB. ZA
O c. Zc
Answer:
[tex] \angle B[/tex]
Step-by-step explanation:
[tex] \angle B[/tex] is included by AB and BC, because B is the common vertex in AB and BC,
A rocket is stopped 34 feet from a satellite when it begins accelerating away from the satellite at a constant rate of 18 feet per second per second. The distance between the rocket and the satellite is given by the polynomial P(t) = 9t2 + 34. Find the distance between the rocket and the satellite 10 seconds after the rocket started moving.
Answer:
The distance between the rocket and the satellite 10 seconds after the rocket started moving is of 934 feet.
Step-by-step explanation:
The distance between the rocket and the satellite, in feet, after t seconds, is given by the following equation:
[tex]P(t) = 9t^{2} + 34[/tex]
Find the distance between the rocket and the satellite 10 seconds after the rocket started moving.
This is P(10).
[tex]P(t) = 9t^{2} + 34[/tex]
[tex]P(10) = 9*(10)^{2} + 34 = 934[/tex]
The distance between the rocket and the satellite 10 seconds after the rocket started moving is of 934 feet.
A population has a known standard deviation of 1.27 and a sample space contains 85 values find the margin of error needed to create a 99% confidence interval estimate of the mean of the population
Answer:
The margin of error needed to create a 99% confidence interval estimate of the mean of the population is of 0.3547
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
In this question:
[tex]\sigma = 1.27, n = 85[/tex]
So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]M = 2.575*\frac{1.27}{\sqrt{85}}[/tex]
[tex]M = 0.3547[/tex]
The margin of error needed to create a 99% confidence interval estimate of the mean of the population is of 0.3547
PLEASE HELP Kelly wants to join an aerobics class. The initial membership fee is $25.00, and each clas costs $10.00. She pays a total of $115.00 to register for a certain number of classes. Create an equation to find the number of classes Kelly registered for.
Answer:
$25.00 + $10x = $115.00
Step-by-step explanation:
We know that the initial charge of joining is $25. Each class costs $10 each. She spent a total of $115. What we don't know is how many classes she took. With this equation, we can easily find out how many classes she took.
HELP PLS!!! ITS DUE ASAP AND I NEED HELP ITS THE LAST QUESTION
Answer:
See below.
Step-by-step explanation:
Recall the volume of a sphere: [tex]V=\frac{4}{3}\pi r^3[/tex]
We know that the diameter is 14, so the radius is 7.
Plug it into the equation:
[tex]V=\frac{4}{3}(3.14)(7^3)\approx 1436.03cm^3[/tex]
QUESTION 4
In a class. 30 students read English, 25 read Mathematics, 5 read both subjects and 6 were
allowed to read both subjects. How many students are in the class?
CH
Answer:
66
Step-by-step explanation:
30+25+5+6 = 66.
There are 66 students in the class.
Use the 4 step process to find the f'(x) of the function f(x)=x^2-3/2
Answer:
see below
Step-by-step explanation:
Modified problem
(x)^2-3/x
Step 1: Find f(x+h)
(x+h)^2-3/(x+h)
x^2 +2hx + h^2 -3/(x+h)
Step 2: Find f(x + h) − f(x)
x^2 +2hx + h^2 -3/(x+h) - ( x^2-3/x)
Distribute the minus sign
x^2 +2hx + h^2 -3/(x+h) - x^2+3/x
Combine like terms and get a common denominator
2hx + h^2 -3x/(x(x+h)) +3(x+h)/(x(x+h)
2hx + h^2 +3h/(x(x+h))
Step 3: Find (f(x + h) − f(x))/h
(2hx + h^2+3h/(x(x+h)) )/h
2hx/h + h^2/h+3h/(x(x+h)) /h
2x +h +3/(x(x+h))
Step 4: Find lim h→0 (f(x + h) − f(x))/h
2x+0 +3/(x(x+0))
2x +3/x^2
Find the first, fourth, and eighth terms of the sequence A(n)=-3 X 2^n-1
1; –216; –279,936
–6; –48; –768
–12; –96; –1,536
–3; –24; –384
Answer:
The answer is
3, 24, 384Step-by-step explanation:
Usng the formula
[tex]A(n) = 3(2) ^{n - 1} [/tex]
Where n is the number of terms
For the first term
[tex]A(1) = 3(2)^{1 - 1} \\ = 3(2) ^{0} \\ = 3(1) \\ \\ = 3[/tex]
For the fourth term
[tex]A(4) = 3(2)^{4 - 1} \\ = 3 ({2})^{3} \\ = 3 \times 8 \\ \\ = 24[/tex]
For the eighth term
[tex]A(8) = 3 ({2})^{8 - 1} \\ = 3 ({2})^{7} \\ = 3(128) \\ \\ = 384[/tex]
Hope this helps you
Answer: –3; –24; –384
Step-by-step explanation:
How to calculate a circumference of a circle?
Answer:
πd or 2πr
Step-by-step explanation:
To calculate the circumference of a circle, multiply the diameter of the circle by pi or multiply 2 times the radius times pi.
Hope that helps.
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Write down the formula for finding the circumference of a circle using the diameter. The formula is simply this: C = πd. In this equation, "C" represents the circumference of the circle, and "d" represents its diameter. That is to say, you can find the circumference of a circle just by multiplying the diameter by pi. Plugging π into your calculator will give you its numerical value, which is a closer approximation of 3.14 or 22/7.
` OR `
Plug the given value of the diameter into the formula and solve.[2]
Example problem: You have a circle tub with a diameter of 8 feet, and you want to build a white fence that creates a 6-foot wide space around the tub. To find the circumference of the fence that has to be created, you should first find the diameter of the tub and the fence which will be 8 feet + 6 feet + 6 feet, which will account for the entire diameter of the tub and fence. The diameter is 8 + 6 + 6, or 20 feet. Now plug it into the formula, plug π into your calculator for its numerical value, and solve for the circumference:
C = πd
C = π x 20
C = 62.8 feet
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
Which equation can be used to solve for x in the following diagram?
Answer:
x + (4x-85) = 90
Step-by-step explanation:
The two angles are complementary which means they add to 90 degrees
x + (4x-85) = 90
Answer: A
Step-by-step explanation:
Both angles are makes a right angle which adds up to 90 degrees so they both have to add up to 90 degrees.