Answer:
See below
Step-by-step explanation:
Here we need to prove that ,
Imagine a right angled triangle with one of its acute angle as 
.
- The side opposite to this angle will be perpendicular .
- Also we know that ,
And by Pythagoras theorem ,
Where the symbols have their usual meaning.
Now , taking LHS ,
- Substituting the respective values,
Since LHS = RHS ,
Hence Proved !
I hope this helps.
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Answer:
The base is decreasing at 2 cm/min.
Step-by-step explanation:
The area (A) of a triangle is given by:
(1)
Where:
b: is the base
h: is the altitude = 10 cm
If we take the derivative of equation (1) as a function of time we have:
We can find the base by solving equation (1) for b:
Now, having that dh/dt = 1 cm/min, dA/dt = 2 cm²/min we can find db/dt:
Therefore, the base is decreasing at 2 cm/min.
I hope it helps you!
Answer: $48
Step-by-step explanation:
From the question, we are told that in Michigan, the sales tax rate is 6% and that an item costs $50.88 including tax.
Let the cost of the item before tax be x. This means that x plus 6% of x equals to $50.88. This can be mathematically expressed as:
x + (6% of x) = $50.88
x + (6/100 × x) = $50.88
x + (0.06 × x) = $50.88
x + 0.06x = $50.88
1.06x = $50.88
When then divide by the coefficient of x
1.06x/1.06 = #50.88/1.06
x = $48
The price before the tax is $48
