A boy who weighs 66 Ib on earth 10.92 Ib on the moon.

A bus has velocity 20 m/s towards east and another bus has velocity 15 m/s in west direction. If they start to move from a point

Mashutka [201]

Answer:

The first bus has covered 2,400 m and the second bus has covered 1,800 m. They are separated by 4,200 m

Step-by-step explanation:

Constant Velocity Motion

A bun has a velocity of 20 m/s towards the east. It means it travels 20 meters each second in that direction. Assuming the east direction is positive, the distance traveled by this bus can be calculated as follows:

X1=20*t

Where t is the time in seconds.

Similarly, the distance traveled by the second bus towards the west is:

X2=-15*t

Note the negative sign because the direction points at the negative reference.

After 2 minutes = 120 seconds have passed, the distance of each bus is

X1= 20*120=2,400 m

X2=-15*120 = 1,800 m

They are separated by 2,400-(-1,800) = 4,200 m

The first bus has covered 2,400 m and the second bus has covered 1,800 m. They are separated by 4,200 m

6 0

3 years ago

The length of a rectangle is increasing at a rate of 4 meters per day and the width is increasing at a rate of 1 meter per day.

puteri [66]

Answer:

$\displaystyle \frac{dA}{dt} = 102 \ m^2/day$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Geometry

Area of a Rectangle: A = lw

l is length
w is width

Calculus

Derivatives

Derivative Notation

Implicit Differentiation

Differentiation with respect to time

Derivative Rule [Product Rule]: $\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Step-by-step explanation:

Step 1: Define

$\displaystyle l = 10 \ meters$

$\displaystyle \frac{dl}{dt} = 4 \ m/day$

$\displaystyle w = 23 \ meters$

$\displaystyle \frac{dw}{dt} = 1 \ m/day$

Step 2: Differentiate

[Area of Rectangle] Product Rule: $\displaystyle \frac{dA}{dt} = l\frac{dw}{dt} + w\frac{dl}{dt}$

Step 3: Solve

[Rate] Substitute in variables [Derivative]: $\displaystyle \frac{dA}{dt} = (10 \ m)(1 \ m/day) + (23 \ m)(4 \ m/day)$
[Rate] Multiply: $\displaystyle \frac{dA}{dt} = 10 \ m^2/day + 92 \ m^2/day$
[Rate] Add: $\displaystyle \frac{dA}{dt} = 102 \ m^2/day$

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Implicit Differentiation

Book: College Calculus 10e

8 0

3 years ago

3. Two quantities, x and y, are in a

frez [133]

Answer:

y = x + 1.8

Step-by-step explanation:

6 0

3 years ago

Apply the distributive property to factor out the greatest common factor. 44h-33=

Flauer [41]

Answer:

11(4h-3)

Step-by-step explanation:

The greatest known common factor of 44h and 33 is 11. So using the distributive property, I got 11(4h-3)

8 0

3 years ago

A sixth grade math student made this conjecture: every prime number can be expressed as the product of two prime numbers. Do you

iren [92.7K]

Answer:

No, I do not agree with the conjecture because 1 is not a prime number.

Step-by-step explanation:

A prime number is one that can be divided by 1 and itself only. Thus it can be expressed in 2 factors only, 1 and the number itself.

Examples are; 2, 3, 5, 13, 19 , 23 etc.

So, 2 = 1 x 2

3 = 1 x 3

23 = 1 x 23

Prime numbers must be expressed as the product of 1 and the number.

The conjecture that every prime number can be expressed as the product of two prime numbers is false. Because 1 is not a prime number, since it has no 2 factors.

5 0

3 years ago