You are playing a video game. For each diamond you collect, you earn 80 points. You also earn 100 bonus points by completing the

Response:

The loop's length is roughly 49.58 km.

Step-by-step details:

Given:

Duration to cycle the loop = 2 hours and 30 minutes

It is known that;

60 minutes = 1 hour

30 minutes = 0.5 hour

therefore, 2 hours and 30 minutes =

∴ Time to cycle the loop = 2.5 hours

Let 's' denote the cycling speed.

Denote the total loop distance as 'd'

From our understanding;

Distance equals speed times time.

Representing this as an equation we have;

Given:

If her speed increased by 1 km/hr, the time taken around the loop would decrease by 7 minutes.

As a result, we can say;

Speed =

The time then will be shortened by 7 minutes.

7 minutes = 0.12 hours

Consequently, time = 2.5 - 0.12 = 2.38

Again, Distance is calculated as speed times time.

This can be expressed with equations;

The distances are equivalent in both scenarios, thus we will determine speed by equating the equations.

So, Speed = 19.83 km/hr

Loop length (d) =

Therefore, the loop length is approximately 49.58 km.

Answer:

6.75g

Step-by-step explanation:

The initial step is to convert all values to grams using rules of three, followed by summation.

In a rule of three calculation, the first step is identifying the measures and how they interrelate; whether their connection is direct or inverse.

In direct relationships, as one measure increases, so does the other.

In inverse relationships, as one measure increases, the other decreases.

Problems involving unit conversion, like this, illustrate a direct relationship between measures.

First step: convert 0.0025kg to grams

One kilogram equals 1000 grams, so:

1kg - 1000g

0.0025kg - xg

x = 1000*0.0025 = 2.5g

Thus, 0.0025kg is equal to 2.5g

Second step: handle 1750 mg

One gram consists of 1000mg, so:

1g - 1000mg

xg - 1750mg

1000x = 1750

x = 1.75g

Therefore, 1750 mg converts to 1.75g

2.25g is fine

Third step: convert 825,000 μg to grams

One gram consists of 1,000,000 micrograms, so:

1g - 1,000,000 μg

xg - 825,000 μg

1,000,000x = 825,000

x = 0.25g

So, 825,000 μg equals 0.25g

Final step: sum all values

0.25g + 2.25g + 1.75g + 2.50g = 6.75g

Answer:

Step-by-step explanation:

Step 1:-

We have c1(t) = e^ t i + (sin(t))j + t³k

and c2(t) = e^−t i + (cos(t))j − 6t³k.

By adding c1(t) and c2(t):

c1(t)+c2(t) = e^ t i + (sin(t))j + t³k + e^−t i + (cos(t))j − 6t³k

Now, employing the derivative formula:

Next, differentiate with respect to 't'

By factoring out i, j, and k terms, we arrive at:

Answer:

120*2.75*60/5280

= 3.75

Step-by-step explanation:

Considering James takes 120 steps in a minute, with 60 minutes in an hour and a mile consisting of 5,280 feet, we can establish his walking pace. By multiplying his steps per minute by the distance of each step (120 * 2.75), we determine the distance he covers in one minute. This value is then multiplied by 60 to account for the total hour. Finally, the total distance is divided by the feet in a mile (5,280), which results in a speed of 3.75 miles per hour. Thus, the calculation becomes 120*2.75*60/5280