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3 months ago

Find the length of the curve. r(t) = 3 i + t2 j + t3 k, 0 ≤ t ≤ 1

1 answer:

3 0

The length of the curve denoted as $C$ can be derived from the provided line integral

$\displaystyle\int_C\mathrm dS=\int_{t=0}^{t=1}\|\mathbf r'(t)\|\,\mathrm dt=\int_{t=0}^{t=1}t\sqrt{9t^2+4}\,\mathrm dt=\frac{13\sqrt{13}-8}{27}$

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Students have organized

tester [12383]

Answer:

Part A. At least 6 hours

Part B. In less than 2.5 hours, Elijah will fall behind Mercedes

Part C. In over 2.5 hours, Elijah will lead Aubrey

Step-by-step explanation:

D = distance

v = speed

t = time

Formula connecting D, v, and t:

$D=v\cdot t$

Part A.

Steve's speed: $v=3.5\ mph$

Distance: a minimum of 21 miles

Time: unknown, so

$3.5\cdot t\ge 21\\ \\35t\ge 210\ [\text{Multiplied by 10}]\\ \\t\ge \dfrac{210}{35}\\ \\t\ge \dfrac{30}{5}\\ \\t\ge 6$

It would require Steve a minimum of 6 hours to traverse at least 21 miles on Day 1.

Part B.

Mercedes's speed: $v_M=2.4\ mph$

Elijah's speed: $v_E=3.2\ mph$

Elijah's Distance walked: $D_E$ miles

Mercedes's Distance walked: $D_M$ miles

Time: x hours

Mercedes is 2 miles ahead, therefore

$D_E=3.2x\\ \\D_M=2.4x+2$

Elijah will trail behind until

$D_E$

In 2.5 hours, Elijah will close the gap on Mercedes, and in less than 2.5 hours, Elijah will trail behind her.

Part C.

Aubrey's speed: $v_M=3\ mph$

Elijah's speed: $v_E=3.2\ mph$

Elijah's Distance walked: $D_E$ miles

Aubrey's Distance walked: $D_A$ miles

Time: x hours

At the beginning of Day 3, Elijah starts from Mile 42, while Aubrey begins at Mile 42.5.

$D_E=42+3.2x\\ \\D_A=42.5+3x$

Elijah will be ahead of Aubrey when

$D_E>D_A\\ \\42+3.2x> 42.5+3x\\ \\3.2x-3x>42.5-42\\ \\0.2x>0.5\\ \\2x>5\ [\text{Multiplied by 10}]\\ \\x>\dfrac{5}{2}\\ \\x>2.5\ hours$

In 2.5 hours, Elijah will surpass Aubrey, and after more than 2.5 hours, Elijah will outpace Aubrey.

4 0

3 months ago

You have 80 pieces of fabric to make a wall hanging. Each piece of fabric is a square with a side length of 5 inches. You use as

tester [12383]

The area would amount to 25

and we could create 3 squares. This would leave 75

5 inches remaining.

8 0

2 months ago

Read 2 more answers

Anand needs to hire a plumber. He's considering a plumber that charges an initial fee of $ 65 $65dollar sign, 65 along with an h

AnnZ [12381]

Answer:

Step-by-step explanation:

Initial Charge = $ 65

Hourly Rate = $ 28

Hours Worked = H

Cost for H hours = 28 * H = 28H

Inequality:

65 + 28H ≤ 250

7 0

3 months ago

Read 2 more answers