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2 years ago

10). A boat traveled 27 miles in 2 hours. At

Mathematics

1 answer:

NARA [144]2 years ago

4 0

Answer:

6.75 miles per 0.5 hours.

Step-by-step explanation:

The ratio 27/2 is equal to the ratio of 6.75/0.5. This can be shown by dividing the 2 in the denominator by 4, getting you 0.5, and dividing the numerator, 27, by 4 also, which gets you 6.75. Hope this helps!

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Calculus 3 chapter 16

o-na [289]

Evaluate $\vec F$ at $\vec r$ :

$\vec F(x,y,z) = x\,\vec\imath + y\,\vec\jmath + xy\,\vec k \\\\ \implies \vec F(\vec r(t)) = \vec F(\cos(t), \sin(t), t) = \cos(t)\,\vec\imath + \sin(t)\,\vec\jmath + \sin(t)\cos(t)\,\vec k$

Compute the line element $d\vec r$ :

$d\vec r = \dfrac{d\vec r}{dt} dt = \left(-\sin(t)\,\vec\imath+\cos(t)\,\vec\jmath+\vec k\bigg) \, dt$

Simplifying the integrand, we have

$\vec F\cdot d\vec r = \bigg(-\cos(t)\sin(t) + \sin(t)\cos(t) + \sin(t)\cos(t)\bigg) \, dt \\ ~~~~~~~~= \sin(t)\cos(t) \, dt \\\\ ~~~~~~~~= \dfrac12 \sin(2t) \, dt$

Then the line integral evaluates to

$\displaystyle \int_C \vec F\cdot d\vec r = \int_0^\pi \frac12\sin(2t)\,dt \\\\ ~~~~~~~~ = -\frac14\cos(2t) \bigg|_{t=0}^{t=\pi} \\\\ ~~~~~~~~ = -\frac14(\cos(2\pi)-\cos(0)) = \boxed{0}$

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2 years ago

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Step-by-step explanation:

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3 years ago

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3 years ago

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3 years ago

Hello how are you today. Question 2(×+-5)+×=×+(-6)

andre [41]

Answer:

x = 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Distributive Property

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify

2(x + -5) + x = x + (-6)

Step 2: Solve for x

[Distributive Property] Distribute 2: 2x - 10 + x = x - 6
[Addition] Combine like terms (x): 3x - 10 = x - 6
[Subtraction Property of Equality] Subtract x on both sides: 2x - 10 = -6
[Addition Property of Equality] Add 10 on both sides: 2x = 4
[Division Property of Equality] Divide 2 on both sides: x = 2

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3 years ago

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