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erastovalidia [21]
2 years ago
13

A car travels at a speed of s miles per hour. It covers 126 miles in 3 hours.

Mathematics
1 answer:
makvit [3.9K]2 years ago
8 0

Answer:

s=42

Step-by-step explanation: 126 divided by 3 = 42

42mph

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(b) For those values of k, verify that every member of the family of functions y = A sin(kt) + B cos(kt) is also a solution. y =
frutty [35]

Answer:

Check attachment for complete question

Step-by-step explanation:

Given that,

y=Coskt

We are looking for value of k, that satisfies 4y''=-25y

Let find y' and y''

y=Coskt

y'=-kSinkt

y''=-k²Coskt

Then, applying this 4y'"=-25y

4(-k²Coskt)=-25Coskt

-4k²Coskt=-25Coskt

Divide through by Coskt and we assume Coskt is not equal to zero

-4k²=-25

k²=-25/-4

k²=25/4

Then, k=√(25/4)

k= ± 5/2

b. Let assume we want to use this

y=ASinkt+BCoskt

Since k= ± 5/2

y=A•Sin(±5/2t)+ B •Cos(±5/2t)

y'=±5/2ACos(±5/2t)-±5/2BSin(±5/2t)

y''=-25/4ASin(±5/2t)-25/4BCos(±5/2t

Then, inserting this to our equation given to check if it a solution to y=ASinkt+BCoskt

4y''=-25y

For 4y''

4(-25/4ASin(±5/2t)-25/4BCos(±5/2t))

-25A•Sin(±5/2t)-25B•Cos(±5/2t).

Then,

-25y

-25(A•Sin(±5/2t)+ B •Cos(±5/2t))

-25A•Sin(±5/2t) - 25B •Cos(±5/2t)

Then, we notice that, 4y'' is equal to -25y, then we can say that y=Coskt is a solution to y=ASinkt+BCoskt

4 0
3 years ago
Find the distance between the points (1,8) and (9, 2).
grin007 [14]

Answer:

distance = \sqrt{(x_{1} -x_{2})^2+(y_{1} -y_{2})^2  }\\\\

             =\sqrt{(9-1)^2+(2-8)^2  }\\\\=\sqrt{8^2 + 6^2}\\\\=\sqrt{64 +36 }\\\\=\sqrt{100} = 10units

6 0
3 years ago
Sam has 15 identical rectangular windows in his home. The length of each window is twice the width, and the area of each window
marshall27 [118]
The answe would be 300 because, the perimeter of the windows is 12, then you have to multiply 25 to 12 then bam you get 300, yay!

5 0
3 years ago
What is the sum of an infinite geometric series if the first term is 81 and the common ratio is 2⁄3?
Marrrta [24]

C

the sum to infinity of a geometric series  = \frac{a}{1-r}

where a is the first term and r the common ratio

= \frac{81}{\frac{1}{3} } = 81 × 3 = 243



4 0
3 years ago
Round 1,819 to the nearest 100
Naddika [18.5K]

Answer:

1,800

Step-by-step explanation:

1,819

----^

1 is less than five so you round down even if you round the 19 to 20 it would still be needed to round down because it is less than 50.

Hope this helps, have a good day! :)

(Brainliest would be appreciated?)

6 0
3 years ago
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