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katrin [286]
2 years ago
8

(x - 4)(x + 2) in factored form, use the FOIL method to turn it into standard form

Mathematics
1 answer:
Verdich [7]2 years ago
7 0

Answer:

{x}^{2}  - 2x - 8

Step-by-step explanation:

(X - 4)(X+2)

( {x}^{2}  + 2x - 4x - 8) \\ ( {x}^{2}  - 2x - 8)

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EXAMPLE 5 If f(x, y, z) = x sin(yz), (a) find the gradient of f and (b) find the directional derivative of f at (1, 2, 0) in the
solong [7]

Answer:

<h2>a) f =  sin(yz)i + xzcos(yz)j + xycos(yz)k</h2><h2>b) -2</h2>

Step-by-step explanation:

Given f(x, y, z) = x sin(yz), the formula for calculating the gradient of the function is expressed as ∇f(x, y, z) = fx(x, y, z)i+ fy(x, y, z)j+fz(x, y, z)k where;

fx, fy and fz are the differential of the functions with respect to x, y and z respectively.

a) ∇f(x, y, z) = sin(yz)i + xzcos(yz)j + xycos(yz)k

The gradient of f =  sin(yz)i + xzcos(yz)j + xycos(yz)k

b) Directional derivative of f at (1,2,0) in the direction of v = i + 4j − k is expressed as ∇f(1, 2, 0)*v

∇f(1, 2, 0) = sin(2(0))i +1*0cos(2*0)j + 1*2cos(2*0)k

∇f(1, 2, 0) = sin0i +0cos(0)j + 2cos(0)k

∇f(1, 2, 0) = 0i +0j + 2k

Given v = i + 4j − k

∇f(1, 2, 0)*v (note that this is the dot product of the two vectors)

∇f(1, 2, 0)*v =  (0i +0j + 2k)*(i + 4j − k )

Given i.i = j.j = k.k =1 and i.j=j.i=j.k=k.j=i.k = 0

∇f(1, 2, 0)*v = 0(i.i)+4*0(j.j)+2(-1)k.k

∇f(1, 2, 0)*v = 0(1)+0(1)-2(1)

∇f(1, 2, 0)*v =0+0-2

∇f(1, 2, 0)*v= -2

 

Hence, the directional derivative of f at (1, 2, 0) in the direction of v = i + 4j − k is -2

7 0
3 years ago
Suppose the same quantity is measured but with a more precise method giving an average and standard deviation of 15.0 ± 2.5. how
abruzzese [7]

To solve this, we use the z test.

The formula:

z = (x – u) / s

where x is sample value = 20, u is the mean = 15, and s is the standard deviation = 2.5

z = (20 – 15) / 2.5

z = 2

Since we are looking for values greater than 20, this is right tailed test. We use the standard distribution tables to find for P.

P = 0.0228

 

Therefore:

number of students = 100 * 0.0228 = 2.28

 

<span>2 to 3 students will get greater than 20 measurement</span>

7 0
3 years ago
The distance between 1 - 10 1/4
Pani-rosa [81]

The distance between 1 - 10 1/4​

____________________

1 - 10 1/4 = -9 1/4

_________________________

Answer

-9 1/4

9 1/4 (in absolute value)

5 0
1 year ago
Read 2 more answers
rewrite f(x)=x^2+8x-20 in the form that would most easily help you identify the zeros of the function
Snowcat [4.5K]

Answer:

f(x) = (x-2) (x+10)

Step-by-step explanation:

f(x)=x^2+8x-20

Factor the right hand side

What 2 numbers multiply to -20 and add to 8

-2 * 10 = -20

-2 + 10 = 8

f(x) = (x-2) (x+10)

Then we can use the zero product property to help us to find the zero's

8 0
3 years ago
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2/4 = 1/2 1/3 circle the equivalent fraction
Strike441 [17]

Answer:

1/3

Step-by-step explanation:

5 0
3 years ago
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