3 years ago

01.01

Mathematics

1 answer:

Sholpan [36]3 years ago

8 0

A plane is an undefined term, because it does not have a formal definition.

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Find the length of the arc of the circular helix with vector equation r(t) = 2 cos t i + 2 sin t j + tk from the point (2, 0, 0)

USPshnik [31]

$\vec r(t)=2\cos t\,\vec\imath+2\sin t\,\vec\jmath+t\,\vec k$

$\implies\vec r'(t)=-2\sin t\,\vec\imath+2\cos t\,\vec\jmath+\vec k$

$\implies\|\vec r'(t)\|=\sqrt{(-2\sin t)^2+(2\cos t)^2+1^2}=\sqrt5$

Then the length of the arc is

$\displaystyle\int_0^{2\pi}\|\vec r'(t)\|\,\mathrm dt=\sqrt5\int_0^{2\pi}\mathrm dt=2\sqrt5\,\pi$

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3 years ago

Find the GCF<br> 50x^4, -10x^5, 2x^6

shtirl [24]

Answer:

2 x^4

Step-by-step explanation:

Recall that the GCF is the greatest of the product of factors that are common to all these three expressions

then for the pure numerical part, the factor common to 50, -10 , and 2 is "2"

and for the variable part x^4 is the largest common to all three expressions.

Therefore the GCF is: 2 x^4

7 0

2 years ago

Read 2 more answers

(05.04 MC) At a school carnival, the diameter of the mat of a trampoline is 16 feet and the diameter of its metal frame is 18 fe

xenn [34]

Answer:

Step-by-step explanation:

You're looking for the circumference here, which is the distance around the outside of a circle. The formula is

C = πd or C = 2πr

Since we are given the diameter, we will use that one:

C = (3.14)(18) so

C = 56.5 feet

3 0

3 years ago

What is the slope of the line? 7x+2y=57x+2y=5

skad [1K]

Answer:

Step-by-step explanation:

6 0

3 years ago

Help! Will give crown to the most helping

kolbaska11 [484]

The first one seems more reasonable

8 0

2 years ago