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IgorLugansk [536]
4 years ago
8

Find the directional derivative of the function at the given point in the direction of vector v. g(x, y, z) = (x + 2y + 3z)3/2,

(5, 4, 4), v = 4j − k dug(5, 4, 4) =
Mathematics
1 answer:
dedylja [7]4 years ago
8 0
g(x,y,z)=(x+2y+3z)^{3/2}

\implies\nabla g(x,y,z)=\dfrac32\left((x+2y+3z)^{1/2},2(x+2y+3z)^{1/2},3(x+2y+3z)^{1/2}\right)

In the direction of \mathbf v=4\,\mathbf j-\mathbf k=(0,4,-1), with norm \sqrt{17}, we have the directional derivative

D_{\mathbf v}g(5,4,4)=\nabla g(5,4,4)\cdot\dfrac{(0,4,-1)}{\sqrt{17}}=\dfrac1{\sqrt{17}}\left(\dfrac{15}2,15,\dfrac{45}2\right)\cdot(0,4,-1)=\dfrac{75}{2\sqrt{17}}
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The number of books donated to a library is increasing by 25% each month. Initially, there were 80 books donated to the library.
mamaluj [8]

Answer: 745

Step-by-step explanation: if there were initialy 80 books and its increasing by 25% every month, for month 1 we have:

25% = 0,25

increase is 1+0.25

M1 = 80.(1+0.25)¹ = 80.1.25 = 100

M10 = 80 (1+0.25)¹⁰ = 80. 9.313225 = 745.05 (end of the month)

6 0
3 years ago
If i give my sister 17 dollars, then we will have the same amount of money. if instead she gives me 23 dollars, then i'll have t
EleoNora [17]
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6 0
3 years ago
Alexander and Jo live 5 miles apart. They decide to leave their homes at 3 p.M. And travel toward each other. If Alexander bikes
lukranit [14]

Answer:

Step-by-step explanation:

Here is an illustration of the problem:

             ----------------------------->|<------------------

            A                                  t                     J

Alex and Jo start from their separate homes and drive towards one another.  The t indicates the time at which they meet, which is the same time for both.  Filling in a d = rt table:

              d           =        r        x        t

Alex                              14                t

Jo                                   6                t

The formula for motion is d = rt, so that means that Alex's distance is 14t and Jo's distance is 6t.

             

                      14t                               6t

   ---------------------------------->|<------------------

   A                                       t                      J

The distance between them is 5 miles, so that means that Alex's distance plus Jo's distance equals 5 miles.  In equation form:

14t + 6t = 5 and

20t = 5 so

t = .25 hours or 15 minutes.

If they leave their homes at 3 and they meet 15 minutes later, then they meet at 3:15.

3 0
3 years ago
5/2 (7x-15)+x&gt;13/2-3/2
Evgen [1.6K]

5(7x - 15) + 2x ≥ 13x - 3    <em>multiplied both sides by 2 to clear the denominator</em>

35x - 75 + 2x ≥ 13 x - 3     <em>distributed 5 into 7x-15</em>

37x - 75  ≥ 13x - 3             <em>added like terms (35x and 2x)</em>

24x - 75 ≥ -3                     <em>subtracted 13x from both sides</em>

24x ≥ 72                           <em>added 75 to both sides</em>

x ≥ 3                                  <em>divided both sides by 24</em>

Answer: x ≥ 3        Notation: [3, ∞)


8 0
3 years ago
Someone help me I promise I will give u a brainliest only if it is correct
PtichkaEL [24]
Perimeter is adding up all of the sides
the top and bottom are 3 and the left and right 10

so top (3)+ bottom (3)+ left (10)+ right(10)

3+3+10+10= 26

So your answer is c 26units
3 0
3 years ago
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