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3 years ago

What is 22 + 5d = -8(7d-4)

Mathematics

2 answers:

ratelena [41]3 years ago

4 0

22+5d=-8x7d=56d+ -8x-4=32

22+5d=-56d+32

22+32=54 and -56d+5d=-51d

The answer would be 51d+54

pickupchik [31]3 years ago

3 0

Remark

The steps are the same usually. Remove the brackets and collect like terms on each side of the equal sign.

Solution

22+5d = -8(7d - 4) Remove the brackets.

22+5d = -56d + 32 Notice the sign change on 32. 2 minus quantities = a plus when multiplied. Add 56d to both sides.

22 + 5d + 56d = - 56d + 56d + 32

22 + 61d = 32 Subtract 22 from both sides.

61d = 32 - 22

61d = 10 Divide by 51

d = 10/61

d = 0.1639 Answer

Check

LHS

22 + 5*0.1639 = 22.8197

RHS

-8(7*0.1639 - 4)

-8(1.1473 - 4)

-8(-2.8527)

22.8216

The difference is a rounding error.

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4 years ago

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Anarel [89]

we know that

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$a \times (b+c)=a \times b + a \times c$

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so, this is TRUE

option-B:

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option-C:

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4 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)