A school newspaper took a survey of 100 students. The results of the survey showed that 43 students are

victus00 [196]

This a pretty typical right triangle trig problem; the first step is to figure out what we have and what we want in relation to an acute angle in the problem.

Here we have a right triangle, G=90°, and we're given angle F=23°. So we have to name everything in relation to F.

31 = FG is <em>adjacent </em>to F.

x = GE is <em>opposite </em>to F.

OK, we have an opposite and adjacent; that tells us we need to use the tangent of F. Let's write it:

tan 23° = tan F = opp/adj = x/31

Solving,

x = 31 tan 23°

I hate the calculator part. I used to love that part.

x = 31 tan 23° ≈ 13.16 feet

Answer: 4) x ≈ 13.2 ft

8 0

2 years ago

If a price decreases by 20% I can calculate 20% of the price and subtract it from the original price or I can calculate it in on

Irina-Kira [14]

Answer:

both statements are fine

Step-by-step explanation:

To find the price of a product after decreasing it, they can be done in the two ways that the statement tells us,

First, calculate that% that was decreased and then subtract it from the original price or simply multiply that original price by the percentage in which the new price would remain.

For example:

let "x" be the original price

in the first case it would be:

0.2 * x and then subtract from x, i.e .:

x - 0.2 * x

in the second case it is:

1 - 0.2 = 0.8

that is, the new price would be 0.8 * x

6 0

2 years ago

In the air, it had an average speed of 16 1616 m/s m/sstart text, m, slash, s, end text. In the water, it had an average speed o

Diano4ka-milaya [45]

Answer:

t_a = 7 s

t_w = 5 s

Step-by-step explanation:

Given:

- The average speed in air v_a = 16 m/s

- The average speed in water v_w = 3 m/s

- The total distance D = 127 m

- The total time T = 12 s

Find:

How long did the stone fall in air and how long did it fall in the water?

Solution:

- Lets time taken by stone to drop through air as t_a = t_a.

- The time taken in water would be t_w = (12 - t_a)

- The total distance covered can be calculated as:

D = v_a*t_a+ v_w*(12 - t_a)

127 = 16*t_a + 3*(12 - t_a)

Simplify and solve for t:

91 = 16*t_a - 3t_a

13*t_a = 91

t_a = 7 s

t_w = 5 s

8 0

3 years ago

A street light is at the top of a 25 ft pole. A 4 ft tall girl walks along a straight path away from the pole with a speed of 6

Burka [1]

Answer:

Tip of the shadow of the girl is moving with a rate of 7.14 feet per sec.

Step-by-step explanation:

Given : In the figure attached, Length of girl EC = 4 ft

Length of street light AB = 25 ft

Girl is moving away from the light with a speed = 6 ft per sec.

To Find : Rate ( $\frac{dw}{dt}$ ) of the tip (D) of the girl's shadow (BD) moving away from th

light.

Solution : Let the distance of the girl from the street light is = x feet

Length of the shadow CD is = y feet

Therefore, $\frac{dx}{dt}=6$ feet per sec. [Given]

In the figure attached, ΔAFE and ΔADE are similar.

By the property of similar triangles,

$\frac{x}{21}=\frac{x+y}{25}$

25x = 21(x + y)

25x = 21x + 21y

25x - 21x = 21y

4x = 21y

y = $\frac{4x}{21}$

Now we take the derivative on both the sides,

$\frac{dy}{dt}=\frac{4}{21}\times \frac{dx}{dt}$

= $\frac{4}{21}\times 6$

= $\frac{8}{7}$

≈ 1.14 ft per sec.

Since w = x + y

Therefore, $\frac{dw}{dt}= \frac{dx}{dt}+\frac{dy}{dt}$

$\frac{dw}{dt}=6+1.14$

= 7.14 ft per sec.

Therefore, tip of the shadow of the girl is moving with a rate of 7.14 feet per sec.

3 0

3 years ago

Michael wants to rent a boat and spend less than $53 the boat cost six dollars per Michael wants to rent a boat and spend less t

ASHA 777 [7]

Hi hope I helped, ok so first 6×7=42 and its less than 53 so ur answer is 42

5 0

3 years ago