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jasenka [17]
3 years ago
15

List the measurement below from smallest to largest .7 cm 18 mm 1 m 3 dm

Mathematics
1 answer:
Ivanshal [37]3 years ago
4 0
In order to list the measurements from smallest to largest, we convert all the measurement to a common unit. In this item, we convert the given to meters, m.

A. The conversion factor to be used here is 1 m = 100 cm
      (7 cm)(1 m / 100 cm) = 0.07 m

B. Conversion factor: 1 m = 1000 mm
     (18 mm) (1 m / 1000 mm) = 0.018 m

C. Let us list this as is, 1 m

D. The conversion factor here is 1 m = 10 dm
    (3 dm)(1 m / 10 dm) = 0.3 m

By the converted values, we are then able to arrange the given measurements.Hence, the arrangement should be 18 mm, 7 cm, 3 dm, and 1 m.
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Find the general solution of x'1 = 3x1 - x2 + et, x'2 = x1.
Ann [662]
Note that if {x_2}'=x_1, then {x_2}''={x_1}', and so we can collapse the system of ODEs into a linear ODE:

{x_2}''=3{x_2}'-x_2+e^t
{x_2}''-3{x_2}'+x_2=e^t

which is a pretty standard linear ODE with constant coefficients. We have characteristic equation

r^2-3r+1=\left(r-\dfrac{3+\sqrt5}2\right)\left(r+\dfrac{3+\sqrt5}2\right)=0

so that the characteristic solution is

{x_2}_C=C_1e^{(3+\sqrt5)/2\,t}+C_2e^{-(3+\sqrt5)/2\,t}

Now let's suppose the particular solution is {x_2}_p=ae^t. Then

{x_2}_p={{x_2}_p}'={{x_2}_p}''=ae^t

and so

ae^t-3ae^t+ae^t=-ae^t=e^t\implies a=-1

Thus the general solution for x_2 is

x_2=C_1e^{(3+\sqrt5)/2\,t}+C_2e^{-(3+\sqrt5)/2\,t}-e^t

and you can find the solution x_1 by simply differentiating x_2.
7 0
3 years ago
What is the solution to the equation -√(15+x)=-3?
marin [14]
So, the negative would be divided out to make it 3, then square both sides to get rid of the square root and get 9, then subtract 15 and you get -6.  <span />
7 0
3 years ago
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Which statement is true?
Vlada [557]
I think a but not sure
7 0
3 years ago
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URGENT!!!!<br> Please add workings out
Artist 52 [7]

Answer: 26.457 cm

Explanation:

First, the height of an equilateral triangle of side length a is:

h = \frac{\sqrt{3} }{2}*a

In this case, the side-length of the triangles is a = 10cm, then the height will be:

h = \frac{\sqrt{3} }{2}*10cm = 8.66cm

Now we can think on a triangle rectangle such that:

Point A and point F are vertexes of the triangle.

The line we want to find, the line from A to F, is the hypotenuse.

One cathetus is a the height of the triangle, that comes down from point A, the length of this cathetus is 8.66cm

The other cathetus is equal to half the side length of the triangles (5cm) plus the segments BD and DF (of 10cm each)

Then the length of this cathetus is 10cm + 10cm + 5cm = 25cm

Now, we can remember the Pythagorean theorem.

If H is the hypotenuse, and A and B are the catheti, then we have:

A^2 + B^2 = H^2

In this case, we know the length of both cathetus, and want to know the length of the hypotenuse, then:

(25cm)^2 + (8.66cm)^2 = H^2

√( (25cm)^2 + (8.66cm)^2) = H = 26.457 cm

Then the line from A to F is 26.457 cm

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Shtirlitz [24]

Answer:

1. 0.85, 8/9, 0.92

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