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3 years ago

Find the number that makes the ratio equivalent to 7:8. :24

Mathematics

1 answer:

Alika [10]3 years ago

3 0

Answer:

21:24

Step-by-step explanation:

7:8 is your ratio

so if _:24 is equivalent, you have to figure out what 24 is divisible by to equal 8

8×3=24

so now we have to multiply 7 by 3

7×3=21

so your answer is 21:24 = 7:8

hope this helps :)

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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)

4 0

3 years ago

Simplify the expression. (x^3)^-5

Blizzard [7]

X^-15. This is the answer

3 0

4 years ago

What is the measure of X ?

viktelen [127]

Answer:

Step-by-step explanation:

Since 88 and the angle inside the triangle right next to it are a linear pair, their measure must add up to 180 degrees. Therefore, that angle's measure must be 180-88=92 degrees. Since all of the interior angles of a triangle must add up to 180 degrees as well, 50+92+x=180, meaning that x=180-92-50=38 degrees. Hope this helps!

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4 years ago

Read 2 more answers

What is the value of k?

ELEN [110]

Answer:

10°

Step-by-step explanation:

According remote interior angles, 4k + 5 + 6k + 10 = 115.

10k + 15 = 115

10k = 100

k = 10