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3 years ago

What is length of segment QR? (Show all work)

Mathematics

1 answer:

matrenka [14]3 years ago

5 0

Answer:

$x=15\ units$

Step-by-step explanation:

we know that

The Midpoint Theorem states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of the third side

In this problem

Applying the Midpoint theorem we have that

$x=\frac{30}{2}=15\ units$

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X³+y³+z³= A. 42? B. 45?

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It’s worth 22 points Help please !!!???

4vir4ik [10]

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3 years ago

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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

20 points! ;)

kaheart [24]

So,

The skateboard cost $67.
The protective helmet cost $25.

To find the percent that the price of the skateboard was out of the total amount, add 67 and 25 and divide 67 by the result.

Step 1:
67 + 25 = 92

Step 2:
67/92 = 0.728 or 72.8%.

The correct option is B.

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4 years ago

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