Explanation

A concave lens causes light rays to diverge or spread apart after passing through it.

That's why it’s also called a diverging lens.

Explanation

The chemical formula of quick lime (commonly referred to as lime) is Calcium Oxide (CaO).

It is used in construction, steelmaking, and as a chemical reagent.

Explanation

Let's denote the width as w.

Given the length is 3 times the width:

Length = 3w

Area = Length × Width

243 = 3w × w

243 = 3w^2

Dividing both sides by 3:

w^2 = 81

w = 9

Length = 3w = 3 × 9 = 27

Perimeter = 2(Length + Width)

= 2(27 + 9)

= 2 × 36

= 72

Explanation

The speed of light traveling through a vacuum is exactly 299,792,458 meters (983,571,056 feet) per second. That's about 186,282 miles per second.

A universal constant is known in equations as "c," or light speed.

The speed of light in air is 2.9 × 10⁸ m/s.

Explanation

Step 1: Substitute the values of a and b into the inequality

2 - a + 2 < b - 1

2 - 5 + 2 < 7 - 1

Step 2: Simplify both sides of the inequality

-1 < 6

Step 3: Determine the truth value of the inequality

Since -1 is less than 6, the inequality is true.

Explanation

Let's calculate the work done by both taps in 5 minutes:

Tap 1 fills the tank in 20 minutes, so in 1 minute it fills 1/20 of the tank. In 5 minutes, it fills 5/20 = 1/4 of the tank.

Tap 2 fills the tank in 25 minutes, so in 1 minute it fills 1/25 of the tank. In 5 minutes, it fills 5/25 = 1/5 of the tank.

Combined work in 5 minutes = 1/4 + 1/5 = (5 + 4)/20 = 9/20

Work left = 1 - 9/20 = 11/20

Now, Tap 1 fills 1/20 of the tank in 1 minute. To fill 11/20 of the tank, it will take:

(11/20) / (1/20) = 11 minutes

Explanation

Let's analyze the final positions:

Car A: 20 km East + 30 km North = (20, 30)

Car B: 20 km West = (-20, 0)

Distance between Car A and Car B:

= √((20 - (-20))² + (30 - 0)²)

= √((40)² + (30)²)

= √(1600 + 900)

= √2500

= 50 km

Explanation

In the number 62.53, the digit 2 is in the tens place.

The number can be read as: 60 (tens) + 2 (ones) + 0.5 + 0.03

So, place value of 2 = 2 × 10 = 20

Explanation

To find the largest number that divides 237, 132, and 62 leaving the same remainder, we need to find the differences between the numbers:

237 - 132 = 105

237 - 62 = 175

132 - 62 = 70

Now, let's find the greatest common divisor (GCD) of 105, 175, and 70:

GCD(105, 175) = 35

GCD(35, 70) = 35

The largest number that divides the given numbers leaving the same remainder is 35.

Explanation

In the number 458.21:

The 8 is in the tens place (second digit from the right before the decimal).

Place values from left to right:

4 = hundreds, 5 = ones, 8 = tens

So, 8 represents 80, which is 8 tens.