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Alexeev081 [22]
3 years ago
10

Income Vincent earns $15 per hour during the week and $18 per hour for overtime

Mathematics
1 answer:
Sedaia [141]3 years ago
3 0

Step-by-step explanation:

1) let's say X will be next to our 15 dollars and y next to 18 dollars

so

15x + 18y = 252

it also tells us that the weekdays is 3 times as many hours as y. In other words:

x = 3y

2) As the question asks for the number of weekend hours, let's solve for y.

Here, it's easier to just substitute x in the original equation. If you put 3y as a replacement of x, the equation becomes:

(15*3y) + 18y = 252

expand to: 

45y + 18y = 252

add on 

63y = 252

divide both by 13

y=4

Therefore Vincent works 4 hours on the weekend so during the weeks he works 20 hours

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Step-by-step explanation:

24÷3=8

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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
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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.

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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]

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Answer:

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Step-by-step explanation:

(5a×a)+(5a×4)+(2×a)+(2×4)

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Answer:

Step-by-step explanation:

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