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3 years ago

14. A company rents bicycles for a fee of $10 plus

Mathematics

2 answers:

densk [106]3 years ago

7 0

Answer:

y equals 4x + 10

Step-by-step explanation:

because you get how much per something is plus the initial fee

oksian1 [2.3K]3 years ago

6 0

Totally cost = 4h + 10

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Aviation:

kolezko [41]

Change in altitude:

42,000 - 18,000 = 24,000 feet

Rate of change = 24,000 feet / 12 minutes = 2,000 feet per minute

Because the plane was going down, the rate of change would be negative.

The rate would be -2,000 feet per minute.

8 0

2 years ago

Identify the conic whose equation is given.

irina1246 [14]

Answer:

Hyperbola

Step-by-step explanation:

The polar equation of a conic section with directrix ± d has the standard form:

r=ed/(1 ± ecosθ)

where e = the eccentricity.

The eccentricity determines the type of conic section:

e = 0 ⇒ circle

0 < e < 1 ⇒ ellipse

e = 1 ⇒ parabola

e > 1 ⇒ hyperbola

Step 1. Convert the equation to standard form

r = 4/(2 – 4 cosθ)

Divide numerator and denominator by 2

r = 2/(1 - 2cosθ)

Step 2. Identify the conic

e = 2, so the conic is a hyperbola.

The polar plot of the function (below) confirms that the conic is a hyperbola.

5 0

3 years ago

At 6:00 PM, a flagpole that is 35 feet tall casts a shadow that is 50 feet long. At the same time, how long will a person's shad

sertanlavr [38]

Answer:

The length of the person’s shadow is 5.7ft

Explanation:

Length of the flagpole =a= 35ft

Length of the shadow of the flagpole= b=50ft

Length of the person=c= 4ft

Suppose the length of the person’s shadow is=d

According to the rules of trigonometry

$\frac{\text { Length of the flagpole }}{\text { Length of the shadow of the flagpole }}=\frac{\text { Length of the person }}{\text { Length of the person's shadow }}$

$\frac{a}{b}=\frac{c}{d}$

$\frac{35}{50}=\frac{4}{d}$

35d=200

d= $\frac{200}{35}$

d=5.7ft

Hence, The length of the person’s shadow is 5.7ft.

3 0

3 years ago

Which value is equivalent to (7x5x2/7x3)^2 x (5^0/2^-3)^3 x2^-9?

koban [17]

Answer:

100/9

Step-by-step explanation:

(7*5*2/7*3)² * (5^0/2^-3)³ * 2^-9

Solution:

We know that any number with power 0 = 1

(7*5*2/7*3)² * (1/2^-3)³ * 2^-9

Now cancel out 2 by 2

= (7*5*2/7*3)² * (1/1^-3)³ * 1^-9

=(70/21)² * (1)³/(1^-3)³ * 1^-9

=(10/3)^2 * 1/1^-1 * 1/1^9

=100/9 *1 *1

=100/9....

7 0

3 years ago

Next door to me lives a man with his son. They both work in the same factory. I watch them going to work through my window. The

kirza4 [7]

9514 1404 393

Answer:

k = 5

Step-by-step explanation:

Suppose the distance to the factory is 1 unit. Then the speed the father walks is ...

speed = distance/time = 1 / 30 . . . . units per minute

When the father leaves 10 minutes earlier than the son, his position t minutes after the son starts walking is ...

d = 1/30(t +10)

Similarly, when the father starts 5 minutes earlier than the son, his position t minutes after the son starts walking is ...

d = (1/30)(t +5)

We want that to be the same as the distance the son covers t minutes after he starts walking. The son's progress is ...

d = 1/20t

To find the value of k such that the distance covered is the same 2k minutes after the son starts, we will use t=2k and d=d, so ...

(1/30)(2k +5) = (1/20)(2k)

4k +10 = 6k . . . . . multiply by 60

10 = 2k . . . . . . . . . subtract 4k

5 = k . . . . . . . . . . . divide by 2

The attached graph shows the different scenarios, where the blue line is the son's progress. When the father starts 5 minutes earlier, the son meets him half-way to the factory after 10 minutes, so k = 10/2 = 5.

5 0

2 years ago