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KiRa [710]
3 years ago
6

Cayden has several screws on a scale, and the scale reads 80.955\,\text{g}80.955g. Cayden adds 11 more screw, and the scale read

s 84.81\,\text{g}84.81g. What is the mass of the last screw Cayden adds?
Mathematics
2 answers:
kolezko [41]3 years ago
8 0

Answer:

moo

Step-by-step explanation:

moo

cupoosta [38]3 years ago
5 0

Answer:

3.855 gm.

Step-by-step explanation:

We have been given that Cayden has several screws on a scale and the scale reads 80.955 g. Cayden added 1 more screw, the scale reads 84.81 g.

To find the mass of last screw we will subtract mass of screws before adding the last screw from mass of all the screws after adding last screw.

\text{Mass of the last screw}=\text{Mass of screws with the last screw-Mass of screws without last screw}

\text{Mass of the last screw}=\text{84.81 g-80.955 g}

\text{Mass of the last screw}=\text{3.855 g}    

Therefore, the mass of the last screw is 3.855 gm.        

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Find e^cos(2+3i) as a complex number expressed in Cartesian form.
ozzi

Answer:

The complex number e^{\cos(2+31)} = \exp(\cos(2+3i)) has Cartesian form

\exp\left(\cosh 3\cos 2\right)\cos(\sinh 3\sin 2)-i\exp\left(\cosh 3\cos 2\right)\sin(\sinh 3\sin 2).

Step-by-step explanation:

First, we need to recall the definition of \cos z when z is a complex number:

\cos z = \cos(x+iy) = \frac{e^{iz}+e^{-iz}}{2}.

Then,

\cos(2+3i) = \frac{e^{i(2+31)} + e^{-i(2+31)}}{2} = \frac{e^{2i-3}+e^{-2i+3}}{2}. (I)

Now, recall the definition of the complex exponential:

e^{z}=e^{x+iy} = e^x(\cos y +i\sin y).

So,

e^{2i-3} = e^{-3}(\cos 2+i\sin 2)

e^{-2i+3} = e^{3}(\cos 2-i\sin 2) (we use that \sin(-y)=-\sin y).

Thus,

e^{2i-3}+e^{-2i+3} = e^{-3}\cos 2+ie^{-3}\sin 2 + e^{3}\cos 2-ie^{3}\sin 2)

Now we group conveniently in the above expression:

e^{2i-3}+e^{-2i+3} = (e^{-3}+e^{3})\cos 2 + i(e^{-3}-e^{3})\sin 2.

Now, substituting this equality in (I) we get

\cos(2+3i) = \frac{e^{-3}+e^{3}}{2}\cos 2 -i\frac{e^{3}-e^{-3}}{2}\sin 2 = \cosh 3\cos 2-i\sinh 3\sin 2.

Thus,

\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2-i\sinh 3\sin 2\right)

\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2\right)\left[ \cos(\sinh 3\sin 2)-i\sin(\sinh 3\sin 2)\right].

5 0
3 years ago
Solve for p.<br> –<br> 19p–2p+16p+12=<br> –<br> 18<br> p=
fomenos

Answer:

6

<em>BRAINLIEST, PLEASE!</em>

Step-by-step explanation:

-19p - 2p + 16p + 12 = -18

-5p + 12 = -18

-5p = -30

p = 6

7 0
3 years ago
Read 2 more answers
what is the vertical change shown on the graph? give the answer as a decimal rounded to the nearest tenth, if necessary
Savatey [412]

Answer:

where is the graph ?

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8 0
3 years ago
1. Which of the following is the best description of the process shown in the image above?
Gnoma [55]
The answer would be B
3 0
3 years ago
What is porpotinal to 1/5
Irina-Kira [14]

An equation of the form y=ax+b, where y and x are variables, and a and b are constants, is called a linear equation.

The reason it is called linear is because the graph of the equation is a line.

The line passes through the origin only if b=0, as in our problem.

Any line (except vertical lines) represents a proportional relationship in that the change in y is proportional with the change in x. It is not a condition that the line passes through the origin.

In our specific case, y=(1/5)x, means that the change in y is always 1/5 of the change in x. That is, if x changes by 5 units, y changes by 1. If x changes by 10 units, y changes by 2, and so on.

So, the constant of proportionality is 1:5, or 0.2.

7 0
2 years ago
Read 2 more answers
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