Explanation

To solve the equation sqrt(x + 3) = 2,

we need to isolate x by getting rid of the square root.

Given equation:

sqrt(x + 3) = 2

Square both sides to eliminate the square root:

(x + 3) = 2^2

x + 3 = 4

Subtract 3 from both sides to solve for x:

x = 4 - 3

x = 1

Explanation

We use the product rule since it's the product of two functions:

$$f(x) = x^3 cdot ln(x)$$

Let:

• $u = x^3 Rightarrow u' = 3x^2$

• $v = ln(x) Rightarrow v' = frac{1}{x}$

Apply the product rule:

f′(x)=u′v+uv′=3x^2⋅ln(x)+x^3⋅1/x​
f′(x)=3^x2ln(x)+x^2

Explanation

Given the information that the sum of two numbers is 35 and one number is 8 more than the other, we can set up a system of equations to solve for the numbers.

Let's denote the two numbers as  and , where:

 = one of the numbers

 = the other number

Given:

1. The sum of the two numbers is 35: 

x + y = 35

2. One number is 8 more than the other: 

x = y + 8

Substitute the value of  from the second equation into the first equation:

y + y + 8 = 35

2y + 8 = 35 

2y + 8 = 35 

2y = 27 

y = 13.5

Now, substitute the value of y back into:

x = y +8 

x = 13.5 + 8 

x = 21.5

Explanation

Explanation

Let the son's age be x.

Then the father's age is 5x.

In 15 years, the son's age will be x+15

the father's age will be 5x+15.

According to the problem, in 15 years the father will be twice as old as his son:

                                              5x+15 = 2(x+15)

                                                      3x = 15

                                                           x = 5

Therefore, the son is currently 5 years old. 

The father's current age is 5 times that, which is 25 years old.

SH19-8-2023

Explanation

 1 + 2 + 3 + ... + n = 15  

This is an arithmetic series. Use the formula:

n(n + 1)/2 = 15  

→ Multiply both sides by 2:  

n(n + 1) = 30  

Try n = 5:  

5(6) = 30 

So, n = 5

Now calculate:  

1³ + 2³ + 3³ + ... + n³  

Use formula:  

[n(n + 1)/2]² = [5×6/2]² = (15)² = 225

Explanation

Explanation

To find the value of x  in the equation ( 3x + 7 = 22 ), we need to isolate ( x ).

Here are the steps:

1. Subtract 7 from both sides of the equation to get rid of the constant term on the left side:

[ 3x + 7 - 7 = 22 - 7 ]

[ 3x = 15 ]

2. Divide both sides by 3 to solve for ( x ):

[ frac{3x}{3} = frac{15}{3} ]

[ x = 5]

So, the value of  ( x ) is ( 5).

Explanation

A = 5ab; make b the subject of the formula.

A = 5ab

A/5a = b (required formula)

ND2-03-2023

Explanation