Answer: See below
Step-by-step explanation:
The function of the seat’s height from the ground level is given as,
[tex]h(t)=-1.1 \cos \left(\frac{2 \pi}{3} t\right)+3.1[/tex]
Here, t denotes the time.
(a) The height will be maximum or minimum when the derivative of the function of height is equal to zero.
[tex]\begin{aligned}h^{\prime}(t) &=0 \\\frac{d}{d t}\left(-1.1 \cos \left(\frac{2 \pi}{3} t\right)+3.1\right) &=0 \\-1.1 \times \frac{2 \pi}{3}\left(-\sin \left(\frac{2 \pi}{3} t\right)\right) &=0 \\t &=0,1.5\end{aligned}[/tex]
The height of the seat at time t = 0 s can be determined as,
[tex]\begin{aligned}h(0) &=-1.1 \cos \left(\frac{2 \pi}{3}(0)\right)+3.1 \\&=2 \mathrm{ft}\end{aligned}[/tex]
Therefore, the maximum height of the swing is 4.2 ft and the minimum height of the swing is 2 ft.
(b) The height of the swing is given as,
[tex]\begin{aligned}h &=3 \mathrm{ft} \\-1.1 \cos \left(\frac{2 \pi}{3} t\right)+3.1 &=3 \\t &=0.7 \mathrm{~s}\end{aligned}[/tex]
Therefore, the first time after t = 0 s that the swing’s height of 3 ft is 0.7 s.
(c) The height of the swing is given as,
[tex]\begin{aligned}h &=3 \mathrm{ft} \\-1.1 \cos \left(\frac{2 \pi}{3} t\right)+3.1 &=3 \\\frac{2 \pi}{3} t &=1.47976+2 \pi \\t &=3.7 \mathrm{~s}\end{aligned}[/tex]
Therefore, the second time after t = 0 s that the swing’s height of 3 ft is 3.7 s.
Billy had 55 stamps in his collection. Billy’s older brother Tommy had 73 stamps in his collection. How many stamps did the two brothers have together?
Answer:
128
Step-by-step explanation:
Billy has 55 stamps and his brother Tommy has 73. Add 73 and 55 together. 55+73=128
Calculus hw, need help asap with steps.
Answers are in bold
S1 = 1
S2 = 0.5
S3 = 0.6667
S4 = 0.625
S5 = 0.6333
=========================================================
Explanation:
Let [tex]f(n) = \frac{(-1)^{n+1}}{n!}[/tex]
The summation given to us represents the following
[tex]\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n!}=\sum_{n=1}^{\infty} f(n)\\\\\\\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n!}=f(1) + f(2)+f(3)+\ldots\\\\[/tex]
There are infinitely many terms to be added.
-------------------
The partial sums only care about adding a finite amount of terms.
The partial sum [tex]S_1[/tex] is the sum of the first term and nothing else. Technically it's not really a sum because it doesn't have any other thing to add to. So we simply say [tex]S_1 = f(1) = 1[/tex]
I'm skipping the steps to compute f(1) since you already have done so.
-------------------
The second partial sum is when things get a bit more interesting.
We add the first two terms.
[tex]S_2 = f(1)+f(2)\\\\S_2 = 1+(-\frac{1}{2})\\\\S_2 = \frac{1}{2}\\\\S_2 = 0.5\\\\\\[/tex]
The scratch work for computing f(2) is shown in the diagram below.
-------------------
We do the same type of steps for the third partial sum.
[tex]S_3 = f(1)+f(2)+f(3)\\\\S_3 = 1+(-\frac{1}{2})+\frac{1}{6}\\\\S_3 = \frac{2}{3}\\\\S_3 \approx 0.6667\\\\\\[/tex]
The scratch work for computing f(3) is shown in the diagram below.
-------------------
Now add the first four terms to get the fourth partial sum.
[tex]S_4 = f(1)+f(2)+f(3)+f(4)\\\\S_4 = 1+(-\frac{1}{2})+\frac{1}{6}-\frac{1}{24}\\\\S_4 = \frac{5}{8}\\\\S_4 \approx 0.625\\\\\\[/tex]
As before, the scratch work for f(4) is shown below.
I'm sure you can notice by now, but the partial sums are recursive. Each new partial sum builds upon what is already added up so far.
This means something like [tex]S_3 = S_2 + f(3)[/tex] and [tex]S_4 = S_3 + f(4)[/tex]
In general, [tex]S_{n+1} = S_{n} + f(n+1)[/tex] so you don't have to add up all the first n terms. Simply add the last term to the previous partial sum.
-------------------
Let's use that recursive trick to find [tex]S_5[/tex]
[tex]S_5 = [f(1)+f(2)+f(3)+f(4)]+f(5)\\\\S_5 = S_4 + f(5)\\\\S_5 = \frac{5}{8} + \frac{1}{120}\\\\S_5 = \frac{19}{30}\\\\S_5 \approx 0.6333[/tex]
The scratch work for f(5) is shown below.
train covers 20 km in one hour then how much distance will it cover in 1 min?
[tex]\sf\large\underline{Given:-}[/tex]
Speed of the train = 20km / 1hr.
[tex]\rightarrow[/tex] 1 hour = 60 minutes.
So, speed of the train = 20km/60min.
[tex]\sf\large\underline{To\: Find:-}[/tex]
[tex]\rightarrow[/tex]Distance covered by train in 1min.
[tex]\sf\large\underline{Solution:-}[/tex]
Let the distance covered by train in 1 min be [tex]\sf{x}[/tex] m.
So, if train covers 20 km in 60min then it covers [tex]\sf{x}[/tex] m in 1 min.
It can be written as,
[tex]\rightarrow[/tex] [tex]\sf{\frac{20}{60}}[/tex] [tex]\sf{=\frac{x}{1}}[/tex](by cross multiplication)
[tex]\rightarrow[/tex][tex]\sf{20\: = \: 60x}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{\frac{20}{60}= x}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{\frac{1}{3}= x}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{0.33= x}[/tex](approx)
Therefore, distance covered by train in 1 min= 0.33km (approx).
_______________________________
Hope it helps you:)
The roof of a tower in a castle is shaped like a cone. The height of the roof is 30 ft, and the radius of the base is 15 ft. What is the surface area of the roof?
Answer:
area=2πr
= 22/7*15
= 47.142
The principal P is borrowed at simple interest rate r for a period of time t. Find the loan's future value, A, or the total amount due at time t. Round answer to the nearest cent. P = $11,000.00, r = 9%, t = 150 days
well, if take a year to be 365 days so hmmm 150 days is really just 150/365 of a year, so let's use that.
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$11000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years\to \frac{150}{365}\dotfill &\frac{30}{73} \end{cases} \\\\\\ A=11000[1+(0.09)(\frac{30}{73})]\implies A=11000\left( \frac{757}{730} \right)\implies A\approx 11406.85[/tex]
A student could run 2 miles. After extensive training, the student could run five times as far as she could before the training. How far can the student run now?
Answer:
10 miles
Step-by-step explanation:
He could run 2 miles.
Now he can run 5 times as far.
Now he can run 5 times 2 miles.
5 × 2 miles = 10 miles
Louisa is 5 feet 4 inches tall.
How tall is she in inches?
Answer: 64 inches
Step-by-step explanation:
What is the measure of angle x?
Enter your answer in the box.
X=
Answer:
Step-by-step explanation:
y + 47° = 90° {Complementary angles}
y = 90° - 47°
y = 43°
x = y {Vertically opposite angles}
x = 43°
Answer:
x = 43°
Step-by-step explanation:
[tex] \sf{Y + 47° = 90° } [/tex]Substract 47° from both sides
[tex] \sf{Y + 47° - 47° = 90° - 47°} [/tex][tex] \sf{Y = 43°} [/tex]since X and y are vertically opposite angles
[tex] \sf{x = 43°} [/tex]What is the value of x?
Enter your answer in the box.
X =
Answer: x=20
Step-by-step explanation:
(6x-10)=(3x+50) (subtract both sides by 3x)
3x-10=50(add ten to both sides)
3x=60(divide both sides by 3)
x=20
Solve for x.
7.5x11=4.85
Enter your answer as a decimal in the box.
x =
7.5x11 = 4.85
82.5x = 4.85
*divide 82.5 on both sides*
x = 4.85 ÷ 82.5
x = 0.058788
Answer:
0.058787879
Step-by-step explanation:
(7.5)(x)(11)=4.85
82.5(x)=4.85
x=4.85÷82.5
x= 0.058787879
Ms. Bassie bikes a total of 11/12 mile to get to and from work each day. Write
an expression that can be used to find the total number of miles that Ms.
Bassie bikes to and from work over 5 days. Then evaluate the expression.
Answer:
Step-by-step explanation:
1 day, she travels 11/12 of a mile.
5 days, she travels 5 * 11/12 miles
5*11/12 = 55/12 = 4 7/12 miles.
Pls help this my last question!
Answer:
Step-by-step explanati
- |10+8l=-2
Fastest answer gets brainliest (must provide an explanation and steps for proof)
Answer:
[tex]\sf g(x+5) = \dfrac{x+6}{4x+17}[/tex]
explanation:
g(x + 5) || this function refers to x = x + 5
solving steps:
[tex]\sf g(x) = \dfrac{1+x}{-3+4x}[/tex]
[tex]\rightarrow \sf g(x+5) = \dfrac{1+(x+5)}{-3+4(x+5)}[/tex]
[tex]\rightarrow \sf g(x+5) = \dfrac{6+x}{-3+4x+20}[/tex]
[tex]\rightarrow \sf g(x+5) = \dfrac{x+6}{4x+17}[/tex]
Answer:
Given function:
[tex]g(x)=\dfrac{1+x}{-3+4x}[/tex]
To find [tex]g(x+5)[/tex], substitute [tex]x+5[/tex] into the function in place of [tex]x[/tex]:
[tex]\implies g(x+5)=\dfrac{1+(x+5)}{-3+4(x+5)}[/tex]
[tex]=\dfrac{1+x+5}{-3+4x+20}[/tex]
[tex]=\dfrac{x+6}{4x+17}[/tex]
A garden table and a bench cost $668 combined. The garden table costs $82 less than the bench. What is the cost of the bench?
Step-by-step explanation:
let the cost of the bench = x
the cost of the garden table = x + 82
x + (x + 82) = 668
2x + 82 = 668
2x = 586
x = 293
The bench costs $293 and the garden table costs 293 + 82 = $375
can you mark me as brainliest, it will help me a lot. thank you in advance
For f(x) = 2x+1 and g(x) = y2 - 7, find (f+ g)(x).
Answer:
D
Step-by-step explanation:
When you look for (f+g)(x), we are in essence say that we're looking for f(x)+g(x)
=(2x+1)+(x^2-7). (substitute for f(x) and g(x))
=2x+1+x^2-7. (remove the brackets by substituting positive 1 into g(x))
=2x+x^2-6 (add like terms- in this case 1-7=6)
=x^2+2x-6 (rearrange the equation)
Lily is 90 cm tall. If Anika is 3/5 of the height of Lily, and Sadaf is 4/3 of the height of Anika, how tall is Sadaf?
Mindy has already saved $20 and plans to save $8 each month.Georgette has no money saved yet but plans to to save $5 each month.Will the girls ever have saved the same amount?
Answer:
no
Step-by-step explanation:
because mindy has already saved $20 and is putting $8 which is more than the amount georgette is putting (monthly) and plus georgette has no money saved so basically mindy will have more money saved
Did i do this right?
Answer:
yes
Step-by-step explanation:
A car is traveling at a constant speed of 45 miles per hour. How many feet does it travel in 6 seconds?
Answer:
The car will travel at 198 feet in 3 seconds. The speed of the car = 45miles/ hour. To convert miles to feet;. 1 mile = 5280 feet.
Step-by-step explanation:
The car will travel at 198 feet in 3 seconds. The speed of the car = 45miles/ hour. To convert miles to feet;. 1 mile = 5280 feet.
I need HELP with this question!
Answer:
It will be C
Step-by-step explanation:
Because it says least to greatest and C says 1/2 3/8 5/16 7/16 9/32 15/32 and that is least to greatest there you go
2. An object of mass 20kg is released from a height of 10m above the ground level. The kinetic energy of the object just before it hits the ground is (g=10ms-²
Answer:
2000j
Step-by-step explanation:
Kinetic Energy = mgh
= 20 x 10 x 10 J
= 2000J
Mrs. Reynolds has $153. She buys a bicycle for $105.
Then, she finds $20 at the bottom of her purse.
How much money does she have now? Use the bar diagrams to help you.
Step 1:
Step 1: a bar diagram shows 105 and m, the money left after buying a bike. Together 105 and m are equal to 153.
Step 2:
Step 2: a bar diagram shows that 20 and m is equal to s, the money now.
Enter your answer in the box.
Mrs. Reynolds has $
now.
Answer:
$68
m=48 s=68
Step-by-step explanation:
153-105=48+20=68
the average car on the highway travels 65 miles per hour. if someone has been driving for 4.5 hours how many miles have they driven (Help)
Answer:
292.5
Step-by-step explanation:
Since they are driving 65 miles for every hour, you can multiply the 65 miles by 4.5
So:
65 * 4.5 = 292.5
Find the missing factor.
200 x ____ = 600
A) 2
B) 3
C) 4
D) 5
Answer:
B. 3
Step-by-step explanation:
we know 2x3 = 6 soo just add 2 zeros = 600
Which rule(s) represents a linear function?
Answer:
f(x) = ax + b, where a and b are real numbers.
Four friends are order pizza from a take away.
The amount of pizza each person eats is shown as a fraction below
Matthew eats 0.8of a pizza
Lily eats 3/4of a pizza
George eats 77%opizzas f a pizza
Sam eats 82%of a pizza
Which person eats the most pizza?
You must show your workings
Answer:
Sam ate the most pizza.
Step-by-step explanation:
Mathew: 0.8 is equal to 80%
To get a percentage, you need to move the decimal two places to the right.
Lily: 3/4 = 75%
George: 77%
Sam: 82%
ik it's a bit Blurry but Can someone help me Please best answer will be brainliest<33
Sita saves Rs. 1 today, Rs. 2 the next day, Rs. 4 the succeeding day and so on (each saving being twice of the preceding one). What will be total saving in two weeks time?
a
Answer:
Rs. 32767
Step-by-step explanation:
Because the amount is doubling every day, we can use the expression 1*2^15-1 because there is 1 to start with. Also cool trick! if you need to do 2^1+2^2+2^3+....+2^x, it will be equal to 2^(x+1)-1. So:
2^15-1
32768-1
32767
Complete the net worth statement. What is the net worth of the individual?
A) $171,645
B) $19,950
C) $21,000
D) $26,595
Considering it's concept, it is found that the net worth of the individual is given by:
D) $26,595.
What is the net worth of an individual?It is given by the sum of the individual assets subtracted by the sum of it's liabilities.
Researching the problem on the internet, we have that:
The sum of the assets, in dollars, is of 545 + 165000 + 6100 = 171645.The sum of the liabilities, in dollars, is of 144000 + 1050 = 145050.Hence, his net worth is given by:
N = 171645 - 145050 = $26,595.
More can be learned about net worth at https://brainly.com/question/12371230
The net worth of the individual with assets worth $171,645 and liabilities of $145,050 is D) $26,595.
What is the net worth?The net worth is the value of assets less the value of liabilities.
The net worth shows the amount by which the assets have increased or decreased in value versus the liabilities.
Data and Calculations:Assets = $171,645
Liabilities = $145,050
Net worth = $26,595 ($171,645 - $145,050)
Thus, the net worth of the individual with assets worth $171,645 and liabilities of $145,050 is D) $26,595.
Learn more about net worth at https://brainly.com/question/12371230
-
Using the GCF factor the given expression 4m - 20
4(m - 5)
2(2m - 10)
4m - 20)
2(2m - 20)
Hey there!
Finding something that’s equivalent to: 4m - 20
Option A.
4(m - 5)
= 4(m) + 4(-5)
= 4m - 20
Possibly Option A. is your answer.
Option B.
2(2m - 10)
= 2(2m) + 2(-10)
= 4m - 20
Possibly Option B. could be your answer
Option C.
4(m - 20)
= 4(m) + 4(-20)
= 4m - 80
Optipn C. isn’t your answer
Option D.
2(2m - 20)
= 2(2m) + 2(-20)
= 4m - 40
Option D. also isn’t your answer just like Option C.
FACTORS OF: 4m - 20
4: 1,2,4, & m
20: 1,2,4,5,10,& 20
LIKE TERMS: 1,2,4
GCF: 4
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)