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3 years ago

1. Consider this dilation in this question for A and B

Mathematics

1 answer:

Readme [11.4K]3 years ago

3 0

Answer:

a) enlargement

b) scale factor is 2

Step-by-step explanation:

As we can see, we went from the block to the red figure

a) Since the red figure is bigger, then what we have is an enlargement of the original figure

b) As we can see, the coordinates of the red is two times the value of the coordinates of the black

So, we can conclude that what we have as a scale factor is 2

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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).

5 0

3 years ago

A school is organizing a cookout where hotdogs will be served. The hotdogs come in small packs and large packs. Each small pack

Bas_tet [7]

6 x 18
7 x 8
6 x 18 = 108
7 x 8 = 56
108 + 56 = 164

6 0

3 years ago

A right rectangular prism has these dimensions: Length − Fraction 1 and 1 over 4 units Width − Fraction 5 over 8 unit Height − F

Sav [38]

Volume of rectangular prism = 1 1/3 x 5/6 x 2/3 = 4/3 x 5/6 x 2/3 = 20/27

Volume of cube = 1/6 x 1/6 x 1/6 = 1/216

Number of cubes that will pack the rectangular prism = 20/27 / 1/216 = 160

5 0

3 years ago

Read 2 more answers

A figure is broken into a rectangle and a triangle. The triangle has a base of 8 inches and a height of 6 inches. The rectangle

DerKrebs [107]

Answer:

triangle area = 24

rectangle areea = 32

figure area = 56

Step-by-step explanation:

5 0

3 years ago