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rosijanka [135]
3 years ago
6

One half of a number is 14 more than 2 times the number.

Mathematics
1 answer:
frozen [14]3 years ago
7 0

1/2 * n = 2n + 14

Multiply everything by 2 to get rid of the fraction

n = 4n + 28

n - 4n = 28

-3n = 28

n = -9.333333

n = -28/3

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On Monday, there was no snow on the ground in Buffalo, New York. On Tuesday, three inches of snow fell.On Wensday a half an inch
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Read 2 more answers
Find the ordered pairs for x and y intercepts of the equation 3x - 2y =18
My name is Ann [436]
                  
                                                           3x - 2y = 18
Wherever the line crosses the
x-axis, y=0.                                         3x        = 18
                                                             x        =  6
The x-intercept is                                    (6, 0)  .


                                                           3x - 2y = 18
Wherever the line crosses the
y-axis,  x=0.                                            - 2y = 18
                                                                   y = -9
The y-intercept is                                        (0, -9)  .

8 0
3 years ago
Read 2 more answers
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
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