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3 years ago

Will a geometric figure and its rotated image always,sometimes,or never have to same perimeter?

Mathematics

1 answer:

mash [69]3 years ago

7 0

They will have the same Perimeter, unless you shrink or grow the image then nothing with change

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ryan took 15 minutes to type his 450 - word report. At this rate, how many words could be type in 20 minutes ?

gogolik [260]

Answer:

600

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Astronomers treat the number of stars in a given volume of space as a Poisson random variable. The density in the Milky Way Gala

umka21 [38]

Answer:

a) 0.264

b) 48 cubit light-years

Step-by-step explanation:

For calculating a) What is the probability of 3 or more stars in 16 cubic light years?

λ= 1 star/16 cubic light-years

t= measure t in units of 16 cubic light years.

E(Y) = λ t = (1/16)(16) = 1 star

P(X>=2) = 1 - P(X<2)

= 1 - [e^-1 + (e^-1)(1)/1!]

= 0.264

P(X≥1) = 1 - P(X=0)

= 1 - e^-μ

0.95 = 1 - e^-μ

e^-μ = 1 - 0.95

e^-μ = 0.05

ln(e^-μ) = ln(0.05)

-μ = -3

μ = 3

Therefore 3 x 16 = 48 cubic light years of space

4 0

4 years ago

Let II be the tangent plane to the graph of f(x, y) = 8 – 2x^2 – 3y^2 at the point (1, 2,-6). Let S, x² + y^2 + z = 4 be another

stealth61 [152]

Let $F(x,y,z)=f(x,y)-z$ . The tangent plane to $f(x,y)$ at (1, 2, -6) has equation

$\nabla F(1,2,-6)\cdot(x-1,y-2,z+6)=0$

We have

$\nabla F(x,y,z)=(-4x,-6y,-1)\implies\nabla F(1,2,-6)=(-4,-12,-1)$

Then the tangent plane has equation

$(-4,-12,-1)\cdot(x-1,y-2,z+6)=0\implies -4(x-1)-12(y-2)-(z+6)=0\implies 4x+12y+z=22$

Let $g(x,y)=4-x^2-y^2$ , and $G(x,y,z)=g(x,y)-z$ . The tangent plane to $S$ at a point $(a,b,c)$ is

$\nabla G(a,b,c)\cdot(x-a,y-b,z-c)=0$

We have

$\nabla G(x,y,z)=(-2x,-2y,-1)\implies \nabla G(a,b,c)=(-2a,-2b,-1)$

so that this plane has equation

$(-2a,-2b,-1)\cdot(x-a,y-b,z-c)=0\implies2ax+2by+z=2a^2+2b^2+c$

In order for this plane to be parallel to the previous plane, we need to have

$\begin{cases}2a=4\\2b=12\end{cases}\implies a=2,b=6\implies g(a,b)=c=-36$

so the point we're looking for is (2, 6, -36).

6 0

3 years ago

Which expression is equivalent to

rodikova [14]

Step-by-step explanation:

$\log_{12}\left(\dfrac{\frac{1}{2}}{8w}\right)=\log_{12}\left(\dfrac{1}{16w}\right)\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\=\log_{12}(16w)^{-1}\qquad\text{use}\ \log_ab^n=n\log_ab\\\\=-1\log_{12}(16w)\qquad\text{use}\ \log_a(bc)=\log_ab+\log_ac\\\\=-\left(\log_{12}16+\log_{12}w\right)=-\log_{12}2^4-\log_{12}w\qquad\text{use}\ \log_ab^n=n\log_ab\\\\=-4\log_{12}2-\log_{12}w$

8 0

4 years ago

-75 - 82 plus 83 plus 54

anzhelika [568]

Answer:

Hey!

Your answer is -20!

Step-by-step explanation:

(-75) - 82 gives us = -157

(-157) + 83 gives us = -74

(-74) + 54 gives us = -20

I HOPE THIS HELPED!

8 0

3 years ago