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3 years ago

!!!!!!!!!!!!help me

Mathematics

1 answer:

steposvetlana [31]3 years ago

5 0

Answer:

Step-by-step explanation:

i'll do a few of them

1) one inch plus a half inch plus an eighth inch plus a sixteenth inch

1 + 1/2 + 1/8 + 1/16 read the tick marks

1 + 8/16 + 2/16 + 1/16 find a common denominators

1 and 11/16 add the sixteenth numerator

4) 6 inch plus an eighth inch plus a sixteenth inch

6 + 1/8 + 1/16 read the tick marks

6 + 2/16 + 1/16 find a common denominators

6 and 3/16 add the sixteenth numerator

5) nine inch plus a quarter inch plus an eighth inch

9 + 1/4 + 1/8 read the tick marks

9 + 2/8 + 1/8 find a common denominators

9 and 3/8 add the sixteenth numerator

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A surveyor leaves her base camp and drives 42km on a bearing of 032degree she then drives 28km on a bearing of 154degree,how far

ValentinkaMS [17]

Answer:

The surveyor is 36.076 kilometers far from her camp and her bearing is 16.840° (standard form).

Step-by-step explanation:

The final position of the surveyor is represented by the following vectorial sum:

$\vec r = \vec r_{1} + \vec r_{2} + \vec r_{3}$ (1)

And this formula is expanded by definition of vectors in rectangular and polar form:

$(x,y) = r_{1}\cdot (\cos \theta_{1}, \sin \theta_{1}) + r_{2}\cdot (\cos \theta_{2}, \sin \theta_{2})$ (1b)

Where:

$x, y$ - Resulting coordinates of the final position of the surveyor with respect to origin, in kilometers.

$r_{1}, r_{2}$ - Length of each vector, in kilometers.

$\theta_{1}, \theta_{2}$ - Bearing of each vector in standard position, in sexagesimal degrees.

If we know that $r_{1} = 42\,km$ , $r_{2} = 28\,km$ , $\theta_{1} = 32^{\circ}$ and $\theta_{2} = 154^{\circ}$ , then the resulting coordinates of the final position of the surveyor is:

$(x,y) = (42\,km)\cdot (\cos 32^{\circ}, \sin 32^{\circ}) + (28\,km)\cdot (\cos 154^{\circ}, \sin 154^{\circ})$

$(x,y) = (35.618, 22.257) + (-25.166, 12.274)\,[km]$

$(x,y) = (10.452, 34.531)\,[km]$

According to this, the resulting vector is locating in the first quadrant. The bearing of the vector is determined by the following definition:

$\theta = \tan^{-1} \frac{10.452\,km}{34.531\,km}$

$\theta \approx 16.840^{\circ}$

And the distance from the camp is calculated by the Pythagorean Theorem:

$r = \sqrt{(10.452\,km)^{2}+(34.531\,km)^{2}}$

$r = 36.078\,km$

The surveyor is 36.076 kilometers far from her camp and her bearing is 16.840° (standard form).

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3 years ago

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olga_2 [115]

Step-by-step explanation:

Let original price be x

Price after 40% discount is $201

Therefore

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x = 201 ÷ (40/100)

x = 502.5

Therefore, the original price is $502.5

Hope it helps :)

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