The total amount accrued, principal plus interest, with compound interest on a principal of $1,000.00 at a rate of 3% per year compounded 12 times per year over 0.5 years is $1,015.09.
Compound InterestGiven Data
Principal = $1000Rate = 3%Time = 6 months = 0.5 yearsFirst, convert R as a percent to r as a decimal
r = R/100
r = 3/100
r = 0.03 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt
A = 1,000.00(1 + 0.03/12)^(12)(0.5)
A = 1,000.00(1 + 0.0025)^(6)
A = $1,015.09
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[tex] \sf \large \: find \: \frac{dy}{dx} \: if \: x=a ( \Theta + sin \Theta ) , y= a (1- Cos \Theta ) \: at \: \Theta = \frac{π}{2} \\ \\ \\ \\ \\ [/tex]
Kindly Don't Spàm!
Thanks!!!!
Given :
[tex] \: \: \: [/tex]
[tex] \rm \large \: x = a ( \Theta + Sin \Theta )[/tex][tex] \: \: \: [/tex]
[tex] \rm \large y = a ( 1 - cos \: \Theta )[/tex][tex] \: \: [/tex]
Now , x = a ( θ + sin θ )
[tex] \: \: [/tex]
Diff w.r.t " θ "
[tex] \: \: \: [/tex]
[tex] \rm \large\frac{dx}{dθ } = a \: \frac{d}{dθ} (θ + \sin\theta )[/tex][tex] \: \: [/tex]
[tex] \boxed{ \rm \large\underline{ \frac{dx}{d \theta} = a(1 + \cos \theta ) }}[/tex][tex] \: \: [/tex]
Now y = a ( 1-cosθ)
[tex] \: \: [/tex]
Diff w.r.t " θ " we get .
[tex] \: \: [/tex]
[tex] \rm \large \frac{dy}{d \theta} = a \frac{d}{d \theta} (1 - cos \theta) [/tex][tex] \: \: \: [/tex]
[tex] \boxed{ \rm \large \underline{ \frac{dy}{d \theta} = a \sin \theta}}[/tex][tex] \: \: \: [/tex]
From eqn ( 1 ) & ( 2 )
[tex] \: \: [/tex]
[tex] \rm \large \frac{dy}{dx} = \frac{ \frac{dy}{d \theta} }{\frac{dx}{d \theta}} [/tex][tex] \: \: \: [/tex]
[tex] \: \: \: \rm \large = \frac{ \cancel{a} \: sin \theta}{ \cancel a \: (1 + cos \theta)} [/tex][tex] \: \: [/tex]
[tex] \rm \large \: = \frac{sin \theta}{1 + \cos \theta } [/tex][tex] \: \: \: [/tex]
[tex] \rm \large \: \frac{2 \sin( \frac{\theta }{2} ) cos\frac{\theta }{2} }{2 \: cos ^{2} \frac{\theta }{2}} \: \: ......(sin \: a \: = 2 \: sin \frac{a}{2} \: cos \frac{a}{2} 1 + \: cos \: a \: = 2cos ^{2} \frac{a}{2} )[/tex][tex] \: \: [/tex]
[tex] \rm \large \: \frac{dy}{dx} = \frac{sin \frac{ \theta}{2} }{cos \frac{ \theta}{2} } [/tex][tex] \: \: [/tex]
[tex] \rm \large \: \frac{dy}{dx} = tan \frac{ \theta}{2} [/tex][tex] \: \: [/tex]
[tex] \rm \large \: ( \frac{dy}{dx} ) = tan \frac{ \frac{ \theta}{2} }{2} [/tex][tex] \: \: [/tex]
[tex] \rm \large \: = tan( \frac{ \theta}{4} )[/tex][tex] \: \: [/tex]
[tex] \boxed{ \rm \large \underline{ ( \frac{dy}{dx} ) = \frac{\pi}{2} = 1}}[/tex][tex] \: \: [/tex]
Hope Helps!:)
Solve for b
SOLVE ASAP!!
Answer:
Step-by-step explanation:
<A and <B are alternate interior angles. That means they are in the interior of the parallel lines and they are on opposite sides of the transversal.
When that happens <A = <B
8x + 78 = 2x + 114 Subtract 2x from both sides.
8x - 2x + 78 = 2x - 2x + 114 Combine
6x + 78 = 114 Subtract 78 from both sides
6x + 78 - 78 = 114 - 78
6x = 36 Divide by 6
6x/6 = 36/6
x = 6
I think you are asked for B
<B = 2x + 114
<B = 2*6 + 114
<B = 12 + 114
<B = 126
I went to the store with $20. After buying all my groceries, I spent $15.87. How much money do I have left?
you would have 4.13 left
20-15.87=4.13
Answer:
The answer is $4.13
Step-by-step explanation:
It is easier to do this if we add two zeros at the end of 20 to make it 20.00 so the decimal places line up. Lets take it one place at a time. first is the hundreths, which is 0-7. This is not possible, so we borrow from the tenths, but the tenths is also a zero. The tenths zero has to borrow from the ones zero. Basically, the 2 in 20 becomes 1, and the zeros in the ones and tenths place become nines, and the last zero becomes 10. 10 minus 7 is 3, 9 minus 8 is 1, 9-5 is 4, and 1-1 is 0.
Hope this helps!
what will be the answer to 20 x 20
Answer:
400
Step-by-step explanation:
you can do 2x2 and you get 4 then add the zeros
solve ps brainliest!
Answer:
W = 17
Step-by-step explanation:
Hi! Ok so the equation is: 24=2w-10
24=2w-10 First add =10 to each side
10+24= 2w +10 -10 the tens on the right cancel.
34=2w then divide each side by negative two
(34/2)=(2/2)w can be simplified to 17=w
The area of a rectangle is 48 square inches. The length is 98 inches. Write an equation that can be used to find the width of the square.
Answer:
48 = 98x (where x is the width)
Step-by-step explanation:
Area of a rectangle = length × width
Let x = width
Given:
area = 48 in²length = 98 in⇒ 48 = 98x
Answer:
x=0.4897599184
Step-by-step explanation:
→Solution,
Area(A)=48 in²
Lenght(l)=98in
Breadth(b)=?
Let the breadth be x.
As we have,
Area of rectangle=l×b
48 in²=98 in × x
48 in²/98 in = x
x=0.4897599184
which experssion is equivalent to 5(4x+3)-2x
Answer:
18x + 15
Step-by-step explanation:
First, deal with the first part of the question:
5(4x+3)
We multiply the outside of the brackets with the inside. So, we do
5 x 4x = 20x
and 5 x 3 = 15
then put them together:
20x+15
Now, the second part:
- 2x
We cannot simplify this further so we put the two parts together:
20x + 15 - 2x
Collect like terms (20x - 2x) =
18x + 15
I hope this helped. If you have any further questions, do ask.
- profparis
Type your answer into the box. Butter and flour are mixed in the ratio 2:3. Chris has 640 grams of butter and 880 grams of flour. How much more flour does he need?
Answer:
80 grams
Step-by-step explanation:
since butter & flour are in the ratio 2:3
2/5 = 640
then 3/5 = flour(?)
eliminate 5 since it is common so that
2= 640
3= x
cross multiply
x= 3 /2× 640
= 960
640 grams of butter needs to mix with 960grams of flour so that they can be in the ratio of 2:3
960-880 = 80
hence 80 more grams of flour are needed.
I need the answer please
Answer: sqrt(182)
Step-by-step explanation:
Line c has a slope of -9/2. line d is parallel to like c. what is the slope of line d?
Step-by-step explanation:
parallel lines have equal slopes
therefore,
line d will have slope -9/2
MARK ME AS BRAINLIST3.
The height of a triangle is 4 inches shorter
than its base. The area of the triangle is 198
square inches. Find the dimensions of the
triangle
(system of equation) only 2 please thanks
Answer:
Base is equal to 22
Hight is equal to 18
Step-by-step explanation:
Because 22 × 18 ÷ 2 is equal to 198
Formula
Hight × base ÷ 2
find the 10th term of the geometric sequence whose common ratio is 2/3 and whose first term is 3.
Answer:
[tex]\frac{512}{6561}[/tex]
Step-by-step explanation:
1) if according to the condition a₁=3 and r=2/3, then a₁₀ can be calculated as:
a₁₀=a₁*r⁹;
2) according to the rule above:
a₁₀=3*(2/3)⁹=512*3/(6561*3)=512/6561.
Darin planted 24 packets of seeds in his garden. He planted a combination of bean seeds and corn seeds. If Darin planted 8 packets of bean seeds, which set of steps can be used to find n, the number of packets of corn seeds Darin planted?
The number of packets of corn seeds Darin planted is 16 packets.
How to write and solve equationTotal packets of seeds = 24Packets of bean seeds = 8Packets of corn seeds = nThe equation:
Total Packets = Bean seeds + corn seeds
24 = 8 + n
subtract 8 from both sides24 - 8 = n
16 = n
Therefore, the number of packets of corn seeds Darin planted is 16 packets.
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I need help
Imagine that you designed a firework. When the firework first explodes, it splits into eight sparkles. Each of those sparkles then explodes and splits into eight new sparkles.
How many sparkles would the second explosion produce? Explain how you determined your answer.
Answer:
8 x 8 = 64
Step-by-step explanation:
Just including the second explosion, each of the 8 sparks bursts into 8, that means 8 sparks were produced 8 times, or 8x8
Answer:
1 sparkle Burst it produces 8 sparkles so you say 8×8×8×8×8×8×8×8
Write a numerical expression to represent the phrase.
5 more than the product of 12 and 8
Answer:
(12x8) + 5
Step-by-step explanation:
The product of 12 and 8 would be multiplication, so you can represent that as. (12x8) or 12x8.
Hello!
First of all, "the product" of 2 numbers means you multiply these 2 numbers.
Then, "5 more" means we add 5.
This is how the phrase "5 more than the product of 12 and 8" is written as a numerical expression:
(12×8)+5
[In case you need to simplify it]
96+5
101
Hope everything is clear.
Let me know if you have any questions!
Always remember: Knowledge is power!
)Sammy is trying to determine how many triangles she can create out of a square grid that has a side of 10 inches. Use the image below to determine the area of the triangle and how many she can cut out.
Answer:
types of waves in physics
Mr. Gates has $52 in his bank account. What will his account balance be after a purchase of $33 and then a deposit of $29?
Answer:
the answer is 48
Step-by-step explanation:
(05.05)
Describe the y-intercept and end behavior of the following graph:
Answer:
Y-Intercept: (0,-8), End behavior: Asymptote
Step-by-step explanation:
The y-intercept is where the line crosses the y axis, which would be (0, -8). The end behavior looks like an asymptote, but I'm not sure of how you would answer this.
HELP!!!! I can’t figure this out
Answer:
A
Step-by-step explanation:
Tina's teacher wrote 7/8 on the whiteboard. What percentage is equivalent to the fraction that Tina's teacher wrote on the whiteboard?
I think it's like 0.88, but I believe that's it rounded up.
A food truck did a daily survey of customers to find their food preferences. The data is partially entered in the frequency table. Complete the table to analyze the data and answer the questions:
Likes hamburgers Does not like hamburgers Total
Likes burritos 38 77
Does not like burritos 95 128
Total 134 71
Part A: What percentage of the survey respondents do not like both hamburgers and burritos? (2 points)
Part B: What is the marginal relative frequency of all customers that like hamburgers? (3 points)
Part C: Use the conditional relative frequencies to determine which data point has strongest association of its two factors. Use complete sentences to explain your answer. (5 points)
Answer:
A:
18.5%
B:
124 / 205
C:
75 / 113. 66.4% Strongest
49 / 92. 53.2% Middle
38 / 81 46.9% Weakest
75 / 113 is the strongest because it has the highest percentage fore the conditional relative frequencies. The others are weaker because they have as high of a percentage.
Step-by-step explanation:
The answers are shown below:
What is Conditional relative frequency?A conditional relative frequency compares a frequency count to the marginal total that represents the condition of interest.
a) Out of 205 people, 38 like neither, hence:
Percentage= 38/ 205 *100= 18.54%
b) Out of the 205 participants, 205 - 81 = 124 like hamburgers, hence:
= 124 / 205
=0.6049
c)The table is, dis considering the totals:
49 - 43
75 - 38
Due to the higher total, the data that has the strongest association of its two factors is liking hamburgers and not liking burritos.
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help? can you figure this out?
Answer:
C. Is the answer
Step-by-step explanation:
Hope it helps
Write the ratio 2 : 5 in the form of 1 : n ?
Answer:
1:2.5
Step-by-step explanation:
just divide each side by 2
What is the five-number summary of this data set? {852, 687, 515, 986, 907, 784, 967, 685, 965} Drag the numbers into the boxes to correctly complete the five-number summary.
Answer:
Minimum: 515
Q1: 686
Q2: 852
Q3: 966
Maximum: 986
Step-by-step explanation:
Please answer 26. Thank you.
A=2(wl+hl+hw)
Plug in the variables in the formula.
Help me pleaseeeeeee
Answer:
926% and I'm pretty sure the other one is 0.7
Step-by-step explanation: For a you have to remove the decimal. for b you have to remove the %
Ramona went to a theme park during spring break she was there for 7 hours and rode 21 rides at what rate did I Ramona ride rides in rides per hour
Answer:
57393487
Step-by-step explanation:
un kilo por hora espero que te ayude
Answer:
3 rides/hour
Step-by-step explanation:
Not sure what ^^ guy was saying... And I don't understand why?
The correct answer is number of rides / hours.
21 / 7 = 3
Help find tqs I’ll give brainlist
Answer:
91 degrees
Step-by-step explanation:
Angle RT = 46 degrees
Angle RU = 180 degrees
Angle RS = 89 degrees
So 46 + 89 = 135
180 - 135 = 45
So Angle UT = 45 degrees
Which means that Angle QR = 45 degrees also because they are vertical from each other
So you add 45 + 46 = 91
Angle TQS = 91 degrees
Evaluate the function (f-g)(x) for x=6
Answer: I think its 8
Step-by-step explanation:
For a ride on a rental scooter, Felipe paid a $2 fee to start the scooter plus 12 cents per minute of the ride. The total bill for Felipes ride was $22.28. For how many minutes did Felipe ride the scooter?
Answer:
169 minutes
Step-by-step explanation:
First, deduct the fee:
22.28 - 2 = 20.28
Change the dollars into cents:
20.28 x 100 = 2028
Then divide the amount by 12 cents:
2028 / 12 = 169.
He rode it for 169 minutes or 2 hours and 49 minutes