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3 years ago

The G.CD of the number is 17 and the L.C.M is 140,If one of the number is 20, Find the other number

Mathematics

1 answer:

Alik [6]3 years ago

6 0

Answer:

HCF Of two nos. is 17

Let another no. be x

we know that HCF ×LCM = Product of two numbers

17×140=20×(x)

20x=2380

x =2380/20

x=119

The other no. is 119

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2 years ago

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avanturin [10]

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Step-by-step explanation:

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3 years ago

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

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3 years ago

Help my math please<br> Due date is in 3 hours

Bumek [7]

Answer:

see explanation

Step-by-step explanation:

(a)

To change a mixed number to an improper fraction

Multiply the whole number by the denominator of the fraction and add the numerator. This value is the numerator of the improper fraction while the denominator remains unchanged, that is

(2 × 13) + 12 = 26 + 12 = 38 ← numerator

2 $\frac{12}{13}$ = $\frac{38}{13}$