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3 years ago

a particle moves along the x-axis so that anytime t comma measured in seconds it's position is given by...

Mathematics

1 answer:

Natali5045456 [20]3 years ago

7 0

Given the position function s(t), you can get the acceleration function by differentiating s twice:

velocity = s'(t) = -5 sin(t ) + 3 cos(3t )

acceleration = s''(t) = -5 cos(t ) - 9 sin(3t )

Then when t = π, the particle's acceleration is

s''(π) = -5 cos(π) - 9 sin(3π)

… = -5 • (-1) - 9 • 0 = 5

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A culture started with 5,000 bacteria. After 2 hours, it grew to 6,500 bacteria. Predict how many bacteria will be present after

lesya [120]

This can be expressed as exponential growth of the form:

f=ir^t, f=final amount, i=initial amount, r=common ratio (rate), t=time

In this case we are given the point (2, 6500) and i=5000 so we can solve for the rate...

6500=5000r^2 divide both sides by 5000

1.3=r^2 take the square root of both sides and note that we know r>0

r=1.3^(1/2) so our equation becomes:

f=5000(1.3)^(1/2)^t and knowing that (a^b)^c=a^(b*c) we can say:

f=5000(1.3)^(t/2) so for t=18

f=5000(1.3)^9

f≈53022 (to nearest whole bacteria)

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3 years ago

If x^2+y^2=1, what is the largest possible value of |x|+|y|?

Marianna [84]

If x² + y² = 1, then y = ±√(1 - x²).

Let f(x) = |x| + |±√(1 - x²)| = |x| + √(1 - x²).

If x < 0, we have |x| = -x ; otherwise, if x ≥ 0, then |x| = x.

• Case 1: suppose x < 0. Then

f(x) = -x + √(1 - x²)

f'(x) = -1 - x/√(1 - x²) = 0 → x = -1/√2 → y = ±1/√2

• Case 2: suppose x ≥ 0. Then

f(x) = x + √(1 - x²)

f'(x) = 1 - x/√(1 - x²) = 0 → x = 1/√2 → y = ±1/√2

In either case, |x| = |y| = 1/√2, so the maximum value of their sum is 2/√2 = √2.

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3 years ago

Hitman42 [59]

Answer:

Assignment: 01.07 Laboratory TechniquesAssignment: 01.07 Laboratory Techniques

Step-by-step explanation:

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2 years ago

A recipe that makes eight Jamberma muffins calls for 1 1/2 teaspoons of baking powder how much baking powder is needed to make t

dimulka [17.4K]

8/ (1 1/2) = 36/x....8 muffins to 1 1/2 tsp = 36 ( 3 doz) muffins to x tsp
this is a proportion, so we cross multiply
(8)(x) = (1 1/2)(36)
8x = 3/2 * 36
8x = 108/2
8x = 54
x = 54/8
x = 6 3/4 <=== 6 3/4 tsps are needed to make 3 doz muffins

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3 years ago

Read 2 more answers

What is equivalent to 1 / 12

inysia [295]

The answer could be something of the sort like 2/24, because 1/12 can't be simplified, you would just keep multiplying both numbers until you get another fraction equal to 1/12

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3 years ago

Read 2 more answers

a particle moves along the x-axis so that anytime t comma measured in seconds it's position is given by...​

a particle moves along the x-axis so that anytime t comma measured in seconds it's position is given by...