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4 years ago

3. Use the diagram to answer the following questions.

Mathematics

1 answer:

Nuetrik [128]4 years ago

4 0

Answer:

See explanation

Step-by-step explanation:

A. There are 8 points: A, B, C, D, E, F, G and H

B. There are 9 lines in the figure: AB, BC, AC, DE, DF, EF, BE, AD and CF

C. There are 5 planes in the figure: ABC, DEF, ABED, ACFD and BEFC

D. Three points are collinear if they lie on the same line. Collinear points are D,G and F or C,H and F

E. Coplanar points are those which lie in the same plane. Coplanar points are B, E, F and C or A, C, F and D or A, B, E and D or other combinations of four points lying in the same plane

I. Planes ABC and ABE intersect by a line AB

G. Planes BCH and DEF intersect by a line EF

H. Lines AD and DF intersect at a point D

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3 years ago

a. If cosθ=−45 where θ is in quadrant 3, find sin2θ. b. If cosθ=2√2 where θ is in quadrant 1, find cos2θ. c. If sinθ=817 where θ

sesenic [268]

Answer:

Part A) $sin(2\theta)=\frac{24}{25}$

Part B) $cos(2\theta)=0$

Part C) $tan(2\theta)=-\frac{240}{161}$

Step-by-step explanation:

Part A) we have $cos(\theta)=-\frac{4}{5}$

θ is in quadrant 3 ----> the sine is negative

Find $sin(2\theta)$

we know that

$sin(2\theta)=2sin(\theta)cos(\theta)$

Remember that

$cos^{2} (\theta)+sin^{2} (\theta)=1$

substitute

$(-\frac{4}{5})^{2}+sin^{2} (\theta)=1$

$(\frac{16}{25})+sin^{2} (\theta)=1$

$sin^{2} (\theta)=1-\frac{16}{25}$

$sin^{2} (\theta)=\frac{9}{25}$

$sin(\theta)=-\frac{3}{5}$ ---> remember that the sine is negative (3 quadrant)

Find $sin(2\theta)$

we have

$cos(\theta)=-\frac{4}{5}$

$sin(\theta)=-\frac{3}{5}$

$sin(2\theta)=2sin(\theta)cos(\theta)$

substitute

$sin(2\theta)=2(-\frac{3}{5})(-\frac{4}{5})$

$sin(2\theta)=\frac{24}{25}$

Part B) we have $cos(\theta)=\frac{\sqrt{2}}{2}$

θ is in quadrant 1

Find $cos(2\theta)$

we know that

$cos(2\theta)=2cos^{2} (\theta)-1$

substitute

$cos(2\theta)=2(\frac{\sqrt{2}}{2} )^{2}-1$

$cos(2\theta)=0$

Part C) we have $sin(\theta)=\frac{8}{17}$

θ is in quadrant 2 ----> the cosine is negative

Find $tan(2\theta)$

we know that

$tan(2\theta)=\frac{2tan(\theta)}{1-tan^{2} (\theta)}$

Remember that

$cos^{2} (\theta)+sin^{2} (\theta)=1$

substitute

$cos^{2} (\theta)+(\frac{8}{17})^{2}=1$

$cos^{2} (\theta)=1-\frac{64}{289}$

$cos^{2} (\theta)=\frac{225}{289}$

$cos(\theta)=-\frac{15}{17}$

Find $tan(\theta)$

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

substitute

$tan(\theta)=\frac{(8/17)}{(-15/17)}$

$tan(\theta)=-\frac{8}{15}$

Find $tan(2\theta)$

$tan(2\theta)=\frac{2tan(\theta)}{1-tan^{2} (\theta)}$

substitute

$tan(2\theta)=\frac{2(-\frac{8}{15})}{1-(-\frac{8}{15})^{2}}$

$tan(2\theta)=\frac{(-\frac{16}{15})}{1-(\frac{64}{225})}$

$tan(2\theta)=\frac{(-\frac{16}{15})}{1-\frac{64}{225}}$

$tan(2\theta)=\frac{(-\frac{16}{15})}{\frac{161}{225}}$

$tan(2\theta)=-\frac{240}{161}$

3 0

3 years ago

Devin is collecting signatures for a petition to open a new park in her town. She needs to collect at least 1,000 signatures bef

steposvetlana [31]

Answer:

The correct opion is;

7 ≤ p

Step-by-step explanation:

The number of signatures Devin needs to collect = 1,000 signatures

The numer of signatures Devin has already = 380 signatures

The number ofsignatures each petition page can hold = 80 signatures

Therefore;

The number of extra signatures required = 1,000 - 380 = 680 signatures

The number of petition pages required = 1,000 petitions /(80 signatures/page) = 12.5 pages

The number of pages already filled = 380 petitions /(80 signatures/page) = 4.75 pages

The number of pages remaining, p = 12.5 - 4.75 = 7.75 pages

Therefore, 7 ≤ p.

8 0

4 years ago

Read 2 more answers