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olga_2 [115]
3 years ago
6

Match the expressions given in words with their values when m=6.

Mathematics
1 answer:
Gemiola [76]3 years ago
4 0

Answer:

Value of expression 1 = 3

Value of expression 2 = 42

Value of expression 3 = 15

Value of expression 4 = 2

Step-by-step explanation:

Expression 1 : the sum of m and 3 divided by the  difference of m minus 3

Expression 1: \frac{m+3}{m-3}

Substitute m = 6

So, value of expression 1=\frac{6+3}{6-3}=3

Expression 2 : the sum of 3 times m and 4 times m

Expression 2: 3m+4m

Substitute m = 6

So, value of expression 2=3m+4m=3(6)+4(6)=42

Expression 3 : the difference of the product of 3 and m  minus the quotient of m divided by 2

Expression 3:3m-\frac{m}{2}

Substitute m = 6

So, value of expression 2= 3m-\frac{m}{2}=3(6)-\frac{6}{2}=15

Expression 4 :the quotient of 6 divided by the  difference of m minus 3

Expression 4:\frac{6}{m-3}

Substitute m = 6

So, value of expression 4=\frac{6}{m-3}=\frac{6}{6-3}=2

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Find dy/dx by implicit differentiation.
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dy/dx by implicit differentiation is cos(πx)/sin(πy)

<h3>How to find dy/dx by implicit differentiation?</h3>

Since we have the equation

(sin(πx) + cos(πy)⁸ = 17, to find dy/dx, we differentiate implicitly.

So, [(sin(πx) + cos(πy)⁸ = 17]

d[(sin(πx) + cos(πy)⁸]/dx = d17/dx

d[(sin(πx) + cos(πy)⁸]/dx = 0

Let sin(πx) + cos(πy) = u

So, du⁸/dx = 0

du⁸/du × du/dx = 0

Since,

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= dsin(πx)/dx + (dcos(πy)/dy × dy/dx)

= πcos(πx) - πsin(πy) × dy/dx

So, du⁸/dx = 0

du⁸/du × du/dx = 0

8u⁷ × [ πcos(πx) - πsin(πy) × dy/dx] = 0

8[(sin(πx) + cos(πy)]⁷ ×  (πcos(πx) - πsin(πy) × dy/dx) = 0

Since 8[(sin(πx) + cos(πy)]⁷ ≠ 0

(πcos(πx) - πsin(πy) × dy/dx) = 0

πcos(πx) = πsin(πy) × dy/dx

dy/dx = πcos(πx)/πsin(πy)

dy/dx = cos(πx)/sin(πy)

So, dy/dx by implicit differentiation is cos(πx)/sin(πy)

Learn more about implicit differentiation here:

brainly.com/question/25081524

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