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emmasim [6.3K]
4 years ago
7

How do you these two questions?

Mathematics
1 answer:
loris [4]4 years ago
8 0

Answer:

dy/dx = e⁻²ᵗ (1 − t)

d²y/dx² = -e⁻³ᵗ (3 − 2t)

(1.5, ∞)

Step-by-step explanation:

x = eᵗ

y = te⁻ᵗ

dx/dt = eᵗ

dy/dt = -te⁻ᵗ + e⁻ᵗ

dy/dt = e⁻ᵗ (1 − t)

dy/dx = (dy/dt) / (dx/dt)

dy/dx = e⁻ᵗ (1 − t) / eᵗ

dy/dx = e⁻²ᵗ (1 − t)

d²y/dx² = d(dy/dx)/dt / (dx/dt)

d²y/dx² = (-e⁻²ᵗ − 2(1 − t) e⁻²ᵗ) / eᵗ

d²y/dx² = -e⁻²ᵗ (1 + 2(1 − t)) / eᵗ

d²y/dx² = -e⁻³ᵗ (3 − 2t)

The function is concave up when the second derivative is positive.  -e⁻³ᵗ is always negative, so the second derivative is positive when 3 − 2t is negative.

3 − 2t < 0

3 < 2t

t > 3/2

Or, in interval notation, (1.5, ∞).

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1/4, 0.25

Step-by-step explanation:

6 0
3 years ago
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harkovskaia [24]
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pleeeeeeeeeeeease hellllllllp meeeeeee the circle has a center of 0.its raduis is 3 cm,and the central angle A measures 100.what
Vsevolod [243]

Answer:

2.5 pi

Step-by-step explanation:

Comment

If you were trying to get the area of a whole circle, you would use

Area = pi r^2

You have to modify the formula to show that just part of the circle has an area that you are interested in.

The new formula is

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Givens

r = 30 cm

theta = 100

Solution

Area = (100 / 360) * pi * r^2       Substitute the givens into this formula

Area = (5 / 18) * pi * 3^2              Expand

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7 0
2 years ago
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Answer:

D. <b ≅ <g

Step-by-step explanation:

Given that lines p and q are parallel to each other, therefore the following can be concluded:

✔️<f ≅ <h, this is because they are both Vertical angles.

✔️<d and <h are supplematry, this is because they are same side consecutive interior angles. Consecutive angles are supplematry.

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