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White raven [17]
3 years ago
15

What layer in the atmosphere has the greatest depth and how deep is it?

Mathematics
1 answer:
Levart [38]3 years ago
8 0
Trophosphere; and how thick it is varies on what part of the Earth
You might be interested in
Find the directional derivative of f(x,y,z)=z3−x2yf(x,y,z)=z3−x2y at the point (−5,5,2)(−5,5,2) in the direction of the vector v
olga_2 [115]

We are given

f=z^3 -x^2y

Firstly, we can find gradient

so, we will find partial derivatives

f_x=0 -2xy

f_x=-2xy

f_y=0 -x^2

f_y=-x^2

f_z=3z^2

now, we can plug point (-5,5,2)

f_x=-2*-5*5=50

f_y=-(-5)^2=-25

f_z=3(2)^2=12

so, gradient will be

gradf=(50,-25,12)

now, we are given that

it is in direction of v=⟨−3,2,−4⟩

so, we will find it's unit vector

|v|=\sqrt{(-3)^2+(2)^2+(-4)^2}

|v|=\sqrt{29}

now, we can find unit vector

v'=(\frac{-3}{\sqrt{29} } , \frac{2}{\sqrt{29} } , \frac{-4}{\sqrt{29} })

now, we can find dot product to find direction of the vector

dir=(gradf) \cdot (v')

now, we can plug values

dir=(50,-25,12) \cdot (\frac{-3}{\sqrt{29} } , \frac{2}{\sqrt{29} } , \frac{-4}{\sqrt{29} })

dir=(-\frac{150}{\sqrt{29} } - \frac{50}{\sqrt{29} } - \frac{48}{\sqrt{29} })

dir=-\frac{248\sqrt{29}}{29}.............Answer



7 0
3 years ago
Read 2 more answers
Ten times the square of a non-zero number is equal to fifty times the number. what is the number?
lys-0071 [83]
10x^2 = 50x.....subtract 50x from both sides
10x^2 - 50x = 0...factor
10x(x - 5) = 0

10x = 0
x = 0 <== this one is eliminated because x cannot be zero

x - 5 = 0
x = 5 <== ur answer
4 0
3 years ago
If f(x) = 3x2 – 4 and g(x) = 2x - 6, what is g(f(2))?
saveliy_v [14]

Answer:

10

Step-by-step explanation:

find out f(2)

f(2)= (3×2×2) - 4= 8

then g(8) = 16 - 6= 10

4 0
3 years ago
If cos -105º = -0.26 and csc -105º = -1.03, then cos 105º = and csc 105º = .
andreyandreev [35.5K]

Answer:

cos (105°) = - 2.6

csc (105°) = 1.03

Step-by-step explanation:

Given that cos (-105°) = - 0.26 {The negative sign is due to the angle - 105° lies in the third quadrant where cos value is negative}

Again, given that csc (- 105°) = - 1.03 {{The negative sign is due to the angle - 105° lies in the third quadrant where csc value is negative}

Now, cos (105°) = - 2.6, because 105° lies in the second quadrant and here cos value is negative.

And csc (105°) = 1.03, because 105° lies in the second quadrant and here csc value is positive. (Answer)

3 0
3 years ago
A box of apples weights 1,058 pounds. If one apples weights 46 pounds, how many apples are there in the box?
Arte-miy333 [17]
There will be23 apples in the bow
5 0
3 years ago
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