Step-by-step explanation:
The position of the mouse at time t is 4 + 12t.
The position of the cat at time t is 17t.
When the positions are equal:
4 + 12t = 17t
4 = 5t
t = 0.8
It takes 0.8 seconds.
Answer:
144 ft^2
Step-by-step explanation:
property of 45-45-90 triangle: side lengths are 12rt2
12rt2*12rt2/2=144
3/4 feet
You can set this up as an equation and solve

There are 5 eggs which remained. In a fraction, the eggs which are not cracked is expressed as 5/12. Converting it to decimals, the answer is 0.4166667. Since the answer only requires 2 decimal places, the number has to be rounded off to the hundredths place. Since 6 is more than 5, the value of the hundredths place is added by 1. Hence the final answer is 0.42.
The given equation, x.cosec²x = cot x - d/dx x.cot x, is proved using the product rule of differentials.
In the question, we are asked to show that x.cosec²x = cot x - d/dx x.cot x.
To prove, we go by the right-hand side of the equation:
cot x - d/dx x.cot x.
We solve the differential d/dx using the product rule, according to which, d/dx uv = u. d/dx(v) + v. d/dx(u), where u and v are functions of x.
cot x - {x. d/dx(cot x) + cot x. d/dx(x)}
= cot x - {x. (-cosec²x) + cot x} {Since, d/dx(cot x) = -cosec²x, and d/dx(x) = 1}
= cot x + x. cosec²x - cot x
= x. cosec²x
= The left-hand side of the equation.
Thus, the given equation, x.cosec²x = cot x - d/dx x.cot x, is proved using the product rule of differentials.
Learn more about differentials at
brainly.com/question/14830750
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