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3 years ago

Answer to part A and B for Question 5?

Mathematics

1 answer:

e-lub [12.9K]3 years ago

3 0

(a) Since true bearings are measured clockwise from 0° from the north line, the south line is 180°.
S48°W is 48° from the South line to the West line and goes clockwise so the true bearing is
180° + 48° = 228°

Reverse the procedure for (b). 335° is 25° away from the north line (360° - 335° = 25°) so it's N25°W

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On a bicycle, Caitlyn rides for 4 hours and is 46 miles from her house. After riding for 7 hours, she is 79 miles away. What is

KiRa [710]

Answer:

Caitlyn's average is roughly 11.4.

Step-by-step explanation:

You get this by dividing 46 by 4, which gets you 11.5.

You then divide 79 by 7, that equals 11.3, rounded.

The number in-between the two numbers is 11.4.

Hope this helps!

Pls mark brainliest! ;)

8 0

3 years ago

(1,-7) with a slope of -5 as an equation

Liono4ka [1.6K]

Answer:

y=-5x-2

Step-by-step explanation:

y=mx+b

where m is the slope

y=-5x+b

to solve for b, which is the y intercept, plug in (1,-7)

-7=-5(1)+b

-7=-5+b

-2=b

y=-5x-2

7 0

3 years ago

Find equations of the tangent plane and the normal line to the given surface at the specified point. x + y + z = 8exyz, (0, 0, 8

Dima020 [189]

Let $f(x,y,z)=x+y+z-8e^{xyz}$ . The tangent plane to the surface at (0, 0, 8) is

$\nabla f(0,0,8)\cdot(x,y,z-8)=0$

The gradient is

$\nabla f(x,y,z)=\left(1-8yze^{xyz},1-8xze^{xyz},1-8xye^{xyz}\right)$

so the tangent plane's equation is

$(1,1,1)\cdot(x,y,z-8)=0\implies x+y+(z-8)=0\implies x+y+z=8$

The normal vector to the plane at (0, 0, 8) is the same as the gradient of the surface at this point, (1, 1, 1). We can get all points along the line containing this vector by scaling the vector by $t$ , then ensure it passes through (0, 0, 8) by translating the line so that it does. Then the line has parametric equation

$(1,1,1)t+(0,0,8)=(t,t,t+8)$

or $x(t)=t$ , $y(t)=t$ , and $z(t)=t+8$ .

(See the attached plot; the given surface is orange, (0, 0, 8) is the black point, the tangent plane is blue, and the red line is the normal at this point)