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3 years ago

If z is a positive integer, does 4+3(2z-5) represent a number that is greater than, less than, or equal to 2(3z-4)?

1 answer:

5 0

Let us plug in 1 for z. Now we can solve both expressions. 4+3(2x1-5) and 2(3x1-4) and we get that the first expression is equal to -5, and the second expression is equal to -2. So the expression 4+3(2z-5) represents a number that is less than 2(3z-4).

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Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 6z) k C is the line segment from (2, 0, −2) to (5, 4, 2) (a) Find a fun

WITCHER [35]

Answer:

Required solution (a) $f(x,y,z)=xyz+3z^2+C$ (b) 40.

Step-by-step explanation:

Given,

$F(x,y,z)=yz \uvec i +xz\uvec j+(xy+6z)\uvex k$

(a) Let,

$F(x,y,z)=yz \uvec i +xz\uvec j+(xy+6z)\uvex k=f_x \uvec{i} +f_y \uvex{j}+f_z\uvec{k}$

Then,

$f_x=yz,f_y=xz,f_z=xy+6z$

Integrating $f_x$ we get,

$f(x,y,z)=xyz+g(y,z)$

Differentiate this with respect to y we get,

$f_y=xz+g'(y,z)$

compairinfg with $f_y=xz$ of the given function we get,

$g'(y,z)=0\implies g(y,z)=0+h(z)\implies g(y,z)=h(z)$

Then,

$f(x,y,z)=xyz+h(z)$

Again differentiate with respect to z we get,

$f_z=xy+h'(z)=xy+6z$

on compairing we get,

$h'(z)=6z\implies h(z)=3z^2+C$ (By integrating h'(z)) where C is integration constant. Hence,

$f(x,y,z)=xyz+3z^2+C$

(b) Next, to find the itegration,

$\int_C \vec{F}.dr=\int_C \nabla f. d\vec{r}=f(5,4,2)-f(2,0,-2)=(52+C)-(12+C)=40$

3 0

3 years ago

Multiply the sum of -13/8 and 5/12 by their difference.

REY [17]

Answer:

1421/576

Step-by-step explanation:

Sum = - 13/8 + 5/12 = - 39/24 + 10/24 = - 29/24

Difference = - 13/8 - 5/12 = - 39/24 - 10/24 = - 49/24

Sum * Difference = (-29/24)*(-49/24) = 1421/576

6 0

2 years ago

From a set of 27 marbles, 4 white, 12 black, and 11 green, we choose one at random. What are the odds in favor of choosing a

garik1379 [7]

Answer:

4/27 chance of getting a white marble.

Step-by-step explanation:

There are 4 white marbles but there are 27 marbles in total. If you wanted a percentage, then divide 4 by 27 and place the decimal two places to the right once you founded your answer.

(sorry if it's a bad explanation)

6 0

3 years ago

Figure A is a scale image of Figure B.<br> whas the value of x?

spayn [35]

X = 30 because the ratio of 27/45 = .6 so 18/.6 is 30

6 0

2 years ago

Read 2 more answers

Can someone help me with a series of questions?

lora16 [44]

Answer: