In this problem, y = c1ex + c2e−x is a two-parameter family of solutions of the second-order de y'' − y = 0. find a solution of the second-order ivp consisting of this differential equation and the given initial conditions. y(0) = 1, y'(0)= 8

The total distance Gabriella flew that day with distances measuring 8.05 meters, 17.71 meters, 14.38 meters, and 19.35 meters is,

⇒ 51.44 meters

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that,

On Saturday she performed in four shows.

Shot from a cannon, her distances measured 8.05 meters, 17.71 meters, 14.38 meters, and 19.35 meters.

Now, To find the total distance Gabriella flew that day with distances measuring 8.05 meters, 17.71 meters, 14.38 meters, and 19.35 meters we can add all the distances,

⇒ 8.05 m + 17.71 m + 14.38 m + 19.35 m

⇒ 51.44 meters

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Answer:

5

Step-by-step explanation:

The estimation of 9.9 squared multiplied by 1.79 is 180.

To estimate the value of 9.9 squared multiplied by 1.79, use rounded numbers to simplify the calculation.

First, round 9.9 to 10 and calculate 10 squared, which is 100.

Next, we round 1.79 to 1.8.

Now, we can perform the multiplication:

100 x 1.8 = 180

Therefore, an estimation is 180.

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The value of 9.9 Squared x 1.79 is 175.59

Let's  calculate

[tex]9.9^{2}[/tex]×1.79 let's break it down step by step:

[tex]9.9^{2}[/tex] means 9.9 [tex]\times[/tex] 9.9 multiplied by itself:

9.9×9.9, which equals 98.01

Now, multiply

98.01 × 1.79 = 175.5879

Rounded to a reasonable precision, the value is approximately

175.59

The process involves squaring

9.9 first and then multiplying the result by

[tex]1.79.9.9^{2}[/tex] gives us 98.01 and then that result is multiplied by

1.79 to obtain 175.59.

The explanation illustrates the order of operations: performing the exponentiation before the multiplication. This follows the basic principles of arithmetic, ensuring each step is carried out accurately to arrive at the final result.

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divide 3/4 by 1/16

3/4 / 1/16 =

3/4 * 16/1 =

48/4 = 12

he can write 12

Answer:

V shape.

Vertex at (4,0)

Intersect with y axis at (0,4)

Step-by-step explanation:

In order to solve this you just ahve to search fo the graph that grows like a V because when you deal with functions that have absolute values you can have negative and positive values for the independent variable but not for the dependent, in this case x is the independent so x will have negative and positive values while Y will only grow in the postives, now the vertex of the function is found where Y=0 so to calculate that you equal the function to 0

y=|x-4|

0=|x-4|

x=4

So the vertex will be at (4,0) and the intersect with the y axis will be located where x=0, so you evaluate the function for 0:

y=|x-4|

y=|o-4|

y=|-4|

y=4

So the intersect with the y axis will be at (0,4).

Final answer:

Amy needs to cover 23 feet through 7 full cycles of climbing and slipping, followed by a final climb of 5 feet without slipping. It takes her 15.17 minutes for the cycles and an additional 2 minutes for the final climb, summing up to a total of 17.17 minutes to reach the top.

Explanation:

Amy is learning how to rock climb and faces a challenge of climbing a 26 ft wall by moving up 5 ft in 2 minutes, then slipping back 2 ft in 10 seconds. To calculate the total time it will take her to reach the top, we can start by finding the net distance she covers in each cycle of climbing and slipping.

During each cycle, Amy climbs 5 ft but then slips back 2 ft, making her net gain per cycle 3 ft (5 ft up - 2 ft back). To reach the top of the 26 ft wall, she doesn't slip back after the final climb, so the last part of the climb she only needs to cover the distance that takes her to 26 ft without slipping back.

Let's consider the entire climb except the final push to the top:

Total distance to cover without the last climb: 26 ft - 3 ft = 23 ft.

Number of full cycles to cover 23 ft: 23 ft / 3 ft per cycle = 7.67 cycles. Since she can't do a partial cycle, we round down to 7 full cycles, covering 21 ft (7 cycles * 3 ft/cycle).

Remaining distance after 7 cycles: 26 ft - 21 ft = 5 ft, which she covers in her last climb.

Each cycle takes 2 minutes and 10 seconds (2 minutes for climbing up 5 feet and 10 seconds for slipping back 2 feet). Since 10 seconds is 1/6 of a minute, each cycle takes 2 + (1/6) = 2.167 minutes. For 7 cycles, the time is 7 cycles * 2.167 minutes/cycle = 15.17 minutes. The final climb of 5 ft takes an additional 2 minutes, resulting in a total time of 17.17 minutes to reach the top.

The amount of money the person will have is [tex]\fbox{\begin\\\ \bf \$454,800\\\end{minispace}}[/tex].

Further explanation:

In the question it is given that the amount of money invested per month is [tex]\$100[/tex].

So, the total amount of money invested in [tex]1[/tex] year or [tex]12[/tex] months is calculated as follows:

[tex]\fbox{\begin\\\ 100\times 12=1200\\\end{minispace}}[/tex]

This implies that the total amount of money invested in [tex]1[/tex] year is [tex]\$1200[/tex].

Amount of money invested grows at a rate of [tex]7\%[/tex] per year.

A person started investing the money at an age of [tex]21[/tex] years and decided to withdraw the money at the age of [tex]70[/tex] years.

So, the total time for which the money was invested is calculated as follows:

[tex]\fbox{\begin\\\ 70-21=49\\\end{minispace}}[/tex]

The formula to obtain the future value of the invested money is as follows:

[tex]\fbox{\begin\\\ FV=PV\left[\dfrac{(1+r)^{t}-1}{r}\right]\\\end{minispace}}[/tex]

Substitute [tex]1200[/tex] for [tex]PV[/tex], [tex]0.07[/tex] for [tex]r[/tex] and [tex]49[/tex] for [tex]t[/tex] in the above equation.

[tex]\begin{aligned}FV&=1200\left[\dfrac{(1+0.07)^{49}-1}{0.07}\right]\\&=1200\left[\dfrac{(1.07)^{49}-1}{0.07}\right]\\&=1200\left[\dfrac{26.53}{0.07}\right]\\&=1200\times379\\&=454800\end{aligned}[/tex]

Therefore, the future value of the invested money is [tex]\$454,800[/tex].

Thus, the amount of money the person will have is [tex]\fbox{\begin\\\ \bf \$454,800\\\end{minispace}}[/tex].

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Answer details:

Grade: College

Subject: Mathematics

Topic: Time value of money

Keywords: Future value, present value, interest, time period, investment, money, 7 percent, $100, amount, invested money, formula.

If Olivia wants to prevent interest capitalization, she must pay the accrued interest each month. That amount is

... I = Prt = $13,100×0.076×(1/12) = $82.97

Over 4 years (48 months), these payments total $82.97×48 = $3982.56.

_____

If no payments are made, the loan balance grows by the multiplier (1 +r/12) each month. Then the amount of interest that will be capitalized at the end of 48 months is ...

... $13,100×((1 +0.076/12)^48 -1) = $4637.01

The difference in these amounts is ...

... $4637.01 -3982.56 = $654.45 . . . . . matches selection a.

Answer:

A

Step-by-step explanation:

654.45

A total of 90 people were interviewed in the survey, which was determined by setting up a proportion based on the information that 7 out of 10 people prefer coffee and the remaining prefer tea, with 27 people preferring tea.

To solve the problem, we need to determine the total number of people surveyed based on the information given about their preferences for coffee and tea in the morning.

According to the survey, 7 out of 10 people prefer coffee. The rest, which is 3 out of 10, prefer tea. We are told that 27 people prefer tea. To find the total number of people surveyed, we set up a proportion where 3 people out of 10 is equivalent to 27 people out of the total number of people interviewed:

So, a total of 90 people were interviewed.

6 divided by 1/3 equals 6 times 3

6*3 = 18

The lengths of the 1515th board could range from 32.51 feet to 33.49 feet, considering the maximum measurement error of plus or minus one third inch per cut.

To find the possible lengths of the 1515th board, we need to consider the maximum error in each board measurement. Each time a board is cut, there is a maximum error of plus or minus one third inch. So, the 1515th board could be as short as 33 feet minus 1515 multiplied by one third inch, and as long as 33 feet plus 1515 multiplied by one third inch. Simplifying this, the 1515th board could be as short as 32.51 feet and as long as 33.49 feet.

Answer:

4 out of eleven

Step-by-step explanation: