Answer:
The time [tex]t = \frac{3}{2}[/tex] seconds elapses between two consecutive times that the swing is at its maximum height 'h' = 2
Step-by-step explanation:
Explanation:-
Step(i):-
Given function [tex]h(t) = 3 cos (\frac{3\pi }{2 t} ) +5[/tex] ....(i)
By using derivative formulas
[tex]\frac{d cosx }{d x} = -sinx[/tex]
[tex]\frac{d x^{n} }{d x} = n x^{n-1}[/tex]
[tex]\frac{d t^{-1} }{d x} = -1 t^{-1-1} = - t^{-2} = \frac{-1}{t^{2} }[/tex]
Step(ii):-
Differentiating equation(i) with respective to 't'
[tex]h^{l} (t) = 3(-sin(\frac{3\pi }{2t})\frac{d}{dt} (\frac{3\pi }{2t } )+0[/tex] ...(ii)
[tex]h^{l} (t) = 3(-sin(\frac{3\pi }{2t})(\frac{-3\pi }{2t^{2} } )+0[/tex]
Equating zero
[tex]h^{l} (t) = 3(-sin(\frac{3\pi }{2t})(\frac{-3\pi }{2t^{2} } )=0[/tex]
[tex]3(-sin(\frac{3\pi }{2t})(\frac{-3\pi }{2t^{2} } ) = 0[/tex]
on simplification , we get
[tex](sin(\frac{3\pi }{2t}) = 0[/tex]
now we use formulas
sin 0 = 0 and sinπ = 0
General solution
[tex](sin(\frac{3\pi }{2t}) = sin\pi[/tex]
[tex](\frac{3\pi }{2t}) = \pi[/tex]
Cancellation 'π' on both sides, we get
[tex]3 = 2 t[/tex]
Dividing '2' on both sides , we get
[tex]t = \frac{3}{2}[/tex]
Again differentiating with respective to 't' , we get
[tex]h^{ll} (t) = 3(-cos(\frac{3\pi }{2t})(\frac{-3\pi }{2t^{2} } )+ (-3)(-sin(\frac{3\pi }{2t} )(\frac{6\pi }{2t^{3} }[/tex]
Put t= 3/2 and simplification
[tex]h^{ll} (t) < 0[/tex]
The maximum height
[tex]h(t) = 3 cos (\frac{3\pi }{2 t} ) +5[/tex]
[tex]h(\frac{3}{2} ) = 3 cos (\frac{3\pi }{2(\frac{3}{2} )} )+5[/tex]
[tex]h(\frac{3}{2} ) = 3 cos (\pi )+5 = -3+5 =2[/tex]
[tex]t = \frac{3}{2}[/tex] seconds elapses between two consecutive times that the swing is at its maximum height 'h' = 2
Conclusion:-
The time [tex]t = \frac{3}{2}[/tex] seconds elapses between two consecutive times that the swing is at its maximum height 'h' = 2
Select the best answer for the question.
15. Solve the inequality. Write the solution set in interval notation.
Answer:
answer is the first one
Answer:
A.
[tex]$\left[-\frac{13}{2},\infty \right)$[/tex]
Step-by-step explanation:
Inequality given:
[tex]11\leq 6(n+4)-4n[/tex]
[tex]11\leq 6n+24-4n[/tex]
[tex]11\leq 2n+24[/tex]
[tex]11-24\leq 2n+24-24[/tex]
[tex]-13\leq 2n[/tex]
[tex]$\frac{-13}{2} \leq n$[/tex]
Interval Notation:
[tex]$\left[-\frac{13}{2},\infty \right)$[/tex]
We have:
[tex]$\{n \in \mathbb{R}:n\geq \frac{-13}{2} \}$[/tex]
4(1 - x) + 3x = - 2(x + 1)
Answer:
X=-6
Step-by-step explanation:
4(1−x)+3x=−2(x+1)
(4)(1)+(4)(−x)+3x=(−2)(x)+(−2)(1)(Distribute)
4+−4x+3x=−2x+−2
(−4x+3x)+(4)=−2x−2(Combine Like Terms)
−x+4=−2x−2
−x+4=−2x−2
Step 2: Add 2x to both sides.
−x+4+2x=−2x−2+2x
x+4=−2
Step 3: Subtract 4 from both sides.
x+4−4=−2−4
x=−6
Answer:
x=−6
Answer:
x=-2
Step-by-step explanation:
4 - 4x + 3x=-2x -2
4 -1x=-2x -2
4= -1x -2
2=-1x
x=-2
In Pennsylvania, the state sales tax is 6%. A book costs $11.50 and a video game costs $65. Rounded to the nearest cent, how much more is the tax on the video game than the tax on the book?
A.$4.59
B.$3.90
C.$3.21
D.$0.69
Answer:
The answer is $4.59
Step-by-step explanation:
You have to add the two prices, divide by 100, and multiply by 6
Can someone help me with this question?
Answer:
Answer is D
Step-by-step explanation:
$12 x 4 = $48
$68 - $4 = $20
Y= $20(her bonus)
X= 4
20(y) - 68 = 12(x - 4)
Someone can u please help me, ill give u 25 points, :D
Answer:
I am pretty sure that it is the bottom left answer.
Step-by-step explanation:
Answer:
it would've been A the first one
can sales found in newspapers or online be referred to as offers?
Answer:
Yes
Step-by-step explanation:
Only if its sold by a person and not a company, most people refer to that as an offer.
Answer:
Yup, it can
Step-by-step explanation:
In newspapers or online people do many offers/sales to get you to buy something. For example, let's say you see Gardening Services, that would be considered as an offer, because the salesperson or company is selling you something. Online, you could be sold offers as well, like a new phone, a house, etc.
Hope this helps
39 calls in 6.5 days is ______ calls per day? *
Answer:
39/6.5=6 calls per day
Answer:
6
Step-by-step explanation:
6 ( 6.5)= 39
Simplify. 5y(4x-3z)
Answer:
20xy-15yzOption D is the right option.
Solution,
[tex]5y(4x - 3z) \\ = 5y \times 4x - 5y \times 3z \\ = 20xy - 15yz[/tex]
hope this helps...
Good luck on your assignment...
Answer:
D is the answer.
Step-by-step explanation:
Using distribution you can simplify this.
5y(4x - 3z) =
20xy - 15yz
Which line segment could be mid segment of abc? 21 points!!!!
Answer:
DF
Step-by-step explanation:
the mid segment is a line that connects the midpoints.
Answer:
DF or option 3
Step-by-step explanation:
DF, since it connects midpoints of sides AB and CB and is parallel to one side: AC
Thus the answer is DF or option 3
Help me out with this question look at the picture
Answer:
B.
Step-by-step explanation:
The dots are completely random.
What the answer to these 3x-2a+5x+4a 6x-2x+8y-2y
Answer:
the first one is 8x-2a
second is 4x+6y
You should combine like factors- factors with the same variable and get your answer.
Answer:
3x-2a+5x+4a
8x + 2a
6x-2x+8y-2y
4x + 6y
explanation:
These are about combining "like terms" so you put the x-terms together by adding or subtracting the "coefficients," the numbers attached to the variables. Combine only terms that have the same letters when adding or subtracting.
Solve the equation, 2x + 1 = 3, for x. Which of the following properties of equality did you apply? Question 8 options: A) Subtraction and multiplication B) Addition and division C) Addition and multiplication D) Subtraction and division
Answer:
2x+1=3
2x=3-1
(Subtraction)
x=1
(Division)
(subtract and divide)
Help plz
Find the volume of the rectangular prism.
length = 5 1/4 inches
Width = 2 1/2 inches
Height = 2 inches
Answer:
Step-by-step explanation:
length = 5 1/4 = 21/4 inches
Width = 2 1/2 = 5/2 inches
Height = 2 inches
Volume of rectangular prism = length * width * height
[tex]= \frac{21}{4}*\frac{5}{2}*2\\\\= \frac{21}{4}*5\\\\=\frac{105}{4}[/tex]
= 26.25 cubic inches
Answer:
26 1/4 i think
Step-by-step explanation:
5 1/4 times 2 1/2 times 2 is 26 2/8 but then you simplify it and you get 26 1/4
Jerold takes out a 60-month loan for $21,500. At a 1% interest rate, what is his monthly payment?
use Amortization formula:
a) $295
b) $315
c) $321
d) $368
Answer:
D
Step-by-step explanation:
In 2005 a house was purchased for $280,000 and
in 2013 it was sold at $334,000. Assuming that
the value of the house increased at a constant
annual rate what will be the price of the house in
the year 2018?
Given that in 2005 a house was purchases for 280,000 and was later sold in 2013 for 334,000, determine the increase value of the house and what the price of the house will be in 2018.
First, we subtract the two values of the house on both dates.
334,000 - 280,000 = 54,000
Then, divide the difference by the amount of years from 2005 to 2013.
54,000/8 = 6,750
Since, it says the value increases at a constant rate, this indicates that it is a linear function.
So, the linear function would start at 280,000 as the y-intercept and the slope is 6,750.
Linear Function: y = 6750x + 280,000
Lastly, to find the price of the house in 2018, we just need to plug in 13 for x since x represents the years.
y = 6750x + 280,000
Plug in 13 for x.
y = 6750(13) + 280,000
y = 87750 + 280,000
y = 367,750
Thus, the value of the house in 2018 is $367,750.
HELP ME PLEASSEE!!! ASAP!!!!!!!
Mindy, a local artist, sells a piece of art at the pizza shop for $15, and the shop takes 15 percent commission. Instead of receiving money, Mindy would like a $12 pizza, including 5 percent sales tax. Is this a fair trade? Explain how to find the solution. Please answer quickly!! I have seen many other answers to this question, however, I don't see anybody who answered the sales tax. What does the sales tax mean??? Do you add it to the $12 pizza???
ASAP PLEASE!!!
Your cousin Vinny wants to borrow $23750. He’s willing to pay you back over 8 years with simple interest. Your alternative is to invest in the $23750 into an account paying 7.75% compounded monthly. A) How much interest would you earn in your investment if you deposit $23750 into an investment account for 8 years? Round to nearest cent. B) What annual interest rate to you charge Vinny in order to make the same amount of interest on his loan as your investment account? Round to nearest hundredth of a percent.
Answer:
a) I (interest) = $ 20,311.62
b) ≈ 8.03%
A = $ 44,061.62
A = P + I where
P (principal) = $ 23,750.00
I (interest) = $ 20,311.62
A = $ 44,061.62
____________________________________
A = $ 43,959.59
A = P + I where
P (principal) = $ 23,750.00
I (interest) = $ 20,209.59
Step-by-step explanation:
An orange juice can has a diameter of 4 inches and a height of 7 inches. The curved surface of the can is painted orange. How much paint is needed? Round your answer to the nearest tenth.
Answer: 88 in2
Step-by-step explanation:
The side of the can, which when "unrolled" is a rectangle, with width = height of the cylinder (7 in); and length = Circumference = 2π radius
Surface area of the curved surface of the can = 2π (diameter/2) x height
Replacing with the values given:
S = 2π (4/2) x 7 = 2π (2) x 7 = 88 in2
Feel free to ask for more if needed or if you did not understand something.
HELP ASAP!!!!
If the point (x, V3/2)
is on the unit circle, what is X?
Answer:
its 1/2
Step-by-step explanation:
please correct me if im wrong
Which equation best matches the graph shown below
Which equation has only one solution?
Answer:
last option x would =.5
Step-by-step explanation:
Answer:
Step-by-step explanation:
gay
HELP ASAP PLEASE I WILL GIVE YOU THE POINTS !!
What is the area of this polygon?
Enter your answer in the box.
Answer:
51 units2
Step-by-step explanation:
42 + 9 = 51 units2
A taxi charges a flat rate of $3.00 plus $1.50 per mile. If Xander has $45.00, what inequality represents m, the distances in miles he can travel in the taxi?
Answer:
1 1/5
Step-by-step explanation:
48/40 = 1 8/40
1 8/40 Simplify to 1 1/5
Hope this helps!
Answer:
D. m≤28
Step-by-step explanation:
Just trust me my friendings
Linda is building steps for her porch. What is the volume of the steps?
144,000 cm3
288,000 cm3
324,000 cm3
540,000 cm3
Answer:
Step-by-step explanation:
upper block:
length (l) = 120 cm
Width (w) = 30 cm
Height (h) = 60 cm
Volume of upper block = l * w * h
= 120 * 30 *60
= 216,000 cm³
Lower Block
l = 120 cm
w = 30 cm
h = 30 cm
Volume of lower block = 120 * 30 * 30
= 108,000 cm³
Volume of steps = 216,000 + 108,000 = 324,000 cm³
In a statistics class, 10 scores were randomly selected with the following results (mean = 71.5): 74, 73, 77, 77, 71, 68, 65, 77, 67, 66. What is the range?
Answer:
Range: 12
Step-by-step explanation:
65, 66, 67, 68, 71, 73, 74, 77, 77, 77
Formula:
Range: highest value - lowest value = final answer
Range: 77 - 65 = 12
I need help on this.
y = 4r - 9
Complete the missing value in the solution to the equation.
(3, )
Answer:
3
Step-by-step explanation:
Equation given = y=4r-9
substitute r=3
y=4*3-9
y=12-9
y=3
(3,3)
A bike that you really want is on sale of 15% off... If it is normally $83.99, how much would it now that it is on sale?
Answer
$71.4Step-by-step explanation:
[tex]83.99 \times \frac{15}{100} \\ = 12.59[/tex]
Now let's find the new price of the bike.
[tex]83.99 - 12.59 \\ = 71.4 \\ [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
What is the range of y = sin θ ? A. [–1, 1] B. [0, ∞) C. all real numbers D. 2π
Answer:
A. [–1, 1]
Step-by-step explanation:
The range is the values that the output can take
The values that sin can take go from -1 to 1 inclusive
help please asapviv now
Answer:
[tex]46 {in}^{2} [/tex]
First answer is correct.
step by step explanation is attached to the answer.
hope this helps
brainliest appreciated
good luck! have a nice day!
