Ask question

Ask question

All categories

3 years ago

10

A vertical flagpole, AB,has a height of 42m. The points B, C and D lie on level ground, and BCD is a straight line Point C is 24

m from the base of the flagpole. The angle of elevation of the top of the flagpole from point D is 48 degrees
How far apart are points C and D?

2 answers:

Genrish500 [490]3 years ago

7 0

Answer: 13.8

Step-by-step explanation:

42/tan(48˚)=37.81696986

37.81696986-24=13.81696986

=13.8

Misha Larkins [42]3 years ago

6 0

Answer:

Points C and D are 13.82 meters apart.

Step-by-step explanation:

Given : Flag AB, with point B , C ,D lying on ground.

BD = 24 m . AB = 42 m

To find; CD

Solution:

In triangle ABD, with angle of elevation from D to top of flag pole is 48 degrees.

$\tan \theta =\frac{perpendicular}{base}$

$\tan 48^o=\frac{AB}{BD}$

$1.1106=\frac{42 m}{BD}$

$BD=\frac{42 m}{1.1106}=37.82 m$

From the figure:

BD = BC + CD

37.82 m = 24 m + CD

CD = 37.82 m - 24 m = 13.82 m

Points C and D are 13.82 meters apart.

You might be interested in

For f(x) = 2x+1 and g(x) = x2 - 7, find (f+ g)(x).

____ [38]

Answer:

the answer is A. it good answer

5 0

3 years ago

Brittany and Ashley can paint a room in 7 hours if they work together. If Ashley were to work by himself, it would take him 2 ho

stich3 [128]

Answer:

Step-by-step explanation:

Brittany paints the room in x hours, completing 1/x of the room per hour.

Ashley paints the room in x+2 hours, completing 1/(x+2) of the room per hour.

Working together, they complete 1/x + 1/(x+2) = ⅐ of the room per hour.

7(x+2) + 7x = x(x+2)

14x + 15 = x^2 + 2x

x^2 - 12x - 15 = 0

x = [12 ±√(12²+60)]/2= 6±√51

6-√51 is an extraneous solution.

x = 6+√51 ≈ 13.14

Brittany paints the room in 12.14 hours

3 0

3 years ago

10 points for answering!<br> What is the answer to 13, 14, and 15?

ki77a [65]

Step-by-step explanation:

<h2>13. </h2>

$\implies\sf{ {x}^{2} = 144 } \\ \\ \implies\sf{ x = \pm \sqrt{144} } \\ \\ \implies\sf{ x = \pm 12 }$

<h2>14.</h2>

$\implies\sf{ {x}^{2} = \dfrac{25}{289} } \\ \\ \implies\sf{ x = \pm \sqrt{ \frac{25}{289} } } \\ \\ \implies\sf{ x = \pm \frac{5}{17} }$

<h2>15.</h2>

$\implies\sf{ {x}^{3} = 216 } \\ \\ \implies\sf{ x = \sqrt[3]{216} } \\ \\ \implies\sf{ x = 6 }$

4 0

3 years ago

A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 7 vinegar, and the second brand con

SOVA2 [1]

Answer:

78 ml of 7% vinegar and 312 ml of 12% vinegar.

Step-by-step explanation:

Let x represent ml of 7% vinegar brand and y represent ml of 12% vinegar brand.

We have been given that chef wants to make 390 milliliters of the dressing. We can represent this information in an equation as:

$x+y=390...(1)$

$y=390-x...(1)$

We are also told that 1st brand 7% vinegar, so amount of vinegar in x ml would be $0.07x$ .

The second brand contains 12 vinegar, so amount of vinegar in y ml would be $0.12y$ .

We are also told that the chef wants to make 390 milliliters of a dressing that is 11% vinegar. We can represent this information in an equation as:

$0.07x+0.12y=390(0.11)...(2)$

Upon substituting equation (1) in equation (2), we will get:

$0.07x+0.12(390-x)=390(0.11)$

$0.07x+46.8-0.12x=42.9$

$-0.05x+46.8=42.9$

$-0.05x+46.8-46.8=42.9-46.8$

$-0.05x=-3.9$

$\frac{-0.05x}{-0.05}=\frac{-3.9}{-0.05}$

$x=78$

Therefore, the chef should use 78 ml of the brand that contains 7% vinegar.

Upon substituting $x=78$ in equation (1), we will get:

$y=390-78$

$y=312$

Therefore, the chef should use 312 ml of the brand that contains 12% vinegar.

4 0

3 years ago

Kasie has a square rug that has an area measuring 72.25 ft determine how long the rug is

solmaris [256]

Answer:

the rug is 8.5 feet

Step-by-step explanation:

7 0

3 years ago