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3 years ago

Which is the better buy? a 12-pack of Pepsi for $3.50 or a 6 pack for $1.80

Mathematics

2 answers:

pashok25 [27]3 years ago

6 0

Answer:

I wanna say it's the 12 pack because your getting 6 more for only $1.70 extra.

xxMikexx [17]3 years ago

4 0

Answer:

1.80

Step-by-step explanation:

it very useful to understand very well

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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

3 years ago

Please help me simplify 9x-3(2+4x)=

denis23 [38]

solution

1) Expand
9x−6−12x

2) Gather like terms
(9x−12x)−6

3) Simplify
−3x−6

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4 years ago

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3241004551 [841]

Answer:

Step-by-step explanation:

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3 years ago

The sum of the reciprocals of two consecutive integers is 9/20. Determine the consecutive integers algebraically.

DochEvi [55]

The answer is 2 1/5.

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Zaheer, a boy of height 1.5m was watching the entire programme. Initially he observed the top of theflagpoleat an angle of eleva

torisob [31]

Answer:

$h = 15.163\ meters$

Step-by-step explanation:

(Assuming the correct angles are 30° and 45°)

We can use the tangent relation of the angle of elevation to find two equations, then we can use these equations to find the height of the pole.

Let's call the initial distance of the boy to the pole 'x'.

Then, with an angle of elevation of 30°, the opposite side to this angle is the height of the pole (let's call this 'h') minus the height of the boy, and the adjacent side to the angle is the distance x:

$tan(30) = (h - 1.5) / x$

Then, with an angle of elevation of 45°, the opposite side to this angle is still the height of the pole minus the height of the boy, and the adjacent side to the angle is the distance x minus 10:

$tan(45) = (h - 1.5) / (x - 10)$