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2 years ago

Find the circumference of a circle with a radius of 18.5m, give answers in pie

Mathematics

1 answer:

Simora [160]2 years ago

5 0

Answer:

C = pi * 37m

Step-by-step explanation:

Diameter = 2(18.5m) = 37m

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Amy is pulling a wagon with a force of 30 pounds up a hill at an angle of 25°. Give the force exerted on the wagon as a vector a

Fofino [41]

Answer:

Vector (ordered pair - rectangular form)

$\vec F = (27.189,12.679)\,[lbf]$

Vector (ordered pair - polar form)

$\vec F = (30\,lbf, 25^{\circ})$

Sum of vectorial components (linear combination)

$\vec F = 27.189\cdot \hat{i} + 12.679\cdot \hat{j}\,[N]$

Step-by-step explanation:

From statement we know that force exerted on the wagon has a magnitude of 30 pounds-force and an angle of 25° above the horizontal, which corresponds to the +x semiaxis, whereas the vertical is represented by the +y semiaxis.

The force ( $\vec F$ ), in pounds-force, can be modelled in two forms:

Vector (ordered pair - rectangular form)

$\vec F = \left(\|\vec F\|\cdot \cos \theta, \|\vec F\|\cdot \sin \theta\right)$ (1)

Vector (ordered pair - polar form)

$\vec F = \left(\|\vec F\|, \theta\right)$

Sum of vectorial components (linear combination)

$\vec {F} = \left(\|\vec F\|\cdot \cos \theta\right)\cdot \hat{i} + \left(\|\vec F\|\cdot \sin \theta \right)\cdot \hat{j}$ (2)

Where:

$\|\vec F\|$ - Norm of the vector force, in newtons.

$\theta$ - Direction of the vector force with regard to the horizontal, in sexagesimal degrees.

$\hat{i}$ , $\hat{j}$ - Orthogonal axes, no unit.

If we know that $\|\vec F\| = 30\,lbf$ and $\theta = 25^{\circ}$ , then the force exerted on the wagon is:

Vector (ordered pair - rectangular form)

$\vec F= \left(30\cdot \cos 25^{\circ}, 30\cdot \sin 25^{\circ}\right)\,[lbf]$

$\vec F = (27.189,12.679)\,[lbf]$

Vector (ordered pair - polar form)

$\vec F = (30\,lbf, 25^{\circ})$

Sum of vectorial components (linear combination)

$\vec F = (30\cdot \cos 25^{\circ})\cdot \hat{i} + (30\cdot \sin 25^{\circ})\cdot \hat{j}\,[N]$

$\vec F = 27.189\cdot \hat{i} + 12.679\cdot \hat{j}\,[N]$

8 0

2 years ago

How many ways can six friends be arranged around a circular dinner table?

Mice21 [21]

A question such as this one is a little tricky since the people seated are not in a straight line.

For a circular table seating question, (n-1)! formula is used. Without restrictions 5! people can be seated.

You might be wondering why it is not 6!, this is because the first person will the the 6 person so you are accounting for the same person twice.

Hope I helped :)

6 0

2 years ago

PLEASE HELP

vova2212 [387]

5 x 5/2 = 25/2

answer
25/2 units

8 0

2 years ago

Read 2 more answers

Krutika was thinking of a number. Krutika adds 4 to it, then doubles it and gets an answer of 83.9. What was the original number

mr Goodwill [35]

Answer:37.95

Step-by-step explanation: