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andreyandreev [35.5K]
3 years ago
10

Help me please and thank you!

Mathematics
1 answer:
lorasvet [3.4K]3 years ago
6 0

Answer:

-4/3

Step-by-step explanation:

-2 - 1 is -3

6-2 is 4

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Answer:

1st one

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Consider the differential equationy′′+3y′−10y=0.(a) Find the general solution to this differential equation.(b) Now solve the in
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Answer:

Y= 2e^(5t)

Step-by-step explanation:

Taking Laplace of the given differential equation:

s^2+3s-10=0

s^2+5s-2s-10=0

s(s+5)-2(s+5) =0

(s-2) (s+5) =0

s=2, s=-5

Hence, the general solution will be:

Y=Ae^(-2t)+ Be^(5t)………………………………(D)

Put t = 0 in equation (D)

Y (0) =A+B

2 =A+B……………………………………… (i)

Now take derivative of (D) with respect to "t", we get:

Y=-2Ae^(-2t)+5Be^(5t)   ....................... (E)

Put t = 0 in equation (E) we get:

Y’ (0) = -2A+5B

10  = -2A+5B ……………………………………(ii)

2(i) + (ii) =>

2A+2B=4 .....................(iii)

-2A+5B=10 .................(iv)

Solving (iii) and (iv)

7B=14

B=2

Now put B=2 in (i)

A=2-2

A=0

By putting the values of A and B in equation (D)

Y= 2e^(5t)

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A giraffe runs at a rate of 32 miles per hour. Which equation models the situation? h = time spent running, in hours d = distanc
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What is the area of parallelogram rstu? 21 square units 24 square units 28 square units 32 square units
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The area of the considered parallelogram RTSU is given by: Option A: 21 sq. units

<h3>How to find the area of a parallelogram?</h3>

Area of a parallelogram  = (its height × its base) sq. units.

<h3>What is the distance between two points ( p,q) and (x,y)?</h3>

The shortest distance(length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units

For this case, the missing diagram is attached below.

If we take the base as ST then as ST is parallel to y axis, the line perpendicular to ST would be parallel to x axis. The heigth of a parallogram  is the perpendicular distance between its base and top.

The base is ST and top is RU, the line segment US is perpendicular to both RU and US and its length,therefore, will serve as height as its length=perpendicular distance between the base and the top of the parallelogram.

Thus, we get:

Area of RTSU = Length of ST × Length of US

The coordinates of endpoints of ST are (4,-1), (4,-4)

Thus, the length of ST = distance between S and T = \sqrt{(4-4)^2 + (-1 - (-4))^2 }= 3

The coordinates of endpoints of US are (-3,-1), (4,-1)

Thus, the length of US = distance between U and S = \sqrt{(-3-4)^2 + (-1 - (-1))^2 }= 7

Thus, Area of RTSU = Length of ST × Length of US = 3 × 7 = 21 sq. units.

Thus, the area of the considered parallelogram RTSU is given by: Option A: 21 sq. units

Learn more about distance between two points here:

brainly.com/question/16410393

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