All categories

4 years ago

The Pythagorean Theorem

2 answers:

8 0

The Pythagorean theorem states that for any right angle triangle with legs of length a, b and the hypotenuse of length c, the sum of the squares of the legs equals the a square of hypotenuse. It is represented by the equation.

a^2 + b^2 = c^2

Example:-

3^2 + 4^2 = 5^2

9 + 16 = 25

25 = 25

PilotLPTM [1.2K]4 years ago

5 0

Answer:

a²+b²=c²

Step-by-step explanation:

a= side of right triangle

b= side of right triangle

c= hypotenuse

You might be interested in

Suppose that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved. Another br

Lina20 [59]

Answer:

The differential equation for the amount of salt A(t) in the tank at a time t > 0 is $\frac{dA}{dt}=12 - \frac{2A(t)}{500+t}$ .

Step-by-step explanation:

We are given that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min.

The concentration of the solution entering is 4 lb/gal.

Firstly, as we know that the rate of change in the amount of salt with respect to time is given by;

$\frac{dA}{dt}= \text{R}_i_n - \text{R}_o_u_t$

where, $\text{R}_i_n$ = concentration of salt in the inflow $\times$ input rate of brine solution

and $\text{R}_o_u_t$ = concentration of salt in the outflow $\times$ outflow rate of brine solution

So, $\text{R}_i_n$ = 4 lb/gal $\times$ 3 gal/min = 12 lb/gal

Now, the rate of accumulation = Rate of input of solution - Rate of output of solution

= 3 gal/min - 2 gal/min

= 1 gal/min.

It is stated that a large mixing tank initially holds 500 gallons of water, so after t minutes it will hold (500 + t) gallons in the tank.

So, $\text{R}_o_u_t$ = concentration of salt in the outflow $\times$ outflow rate of brine solution

= $\frac{A(t)}{500+t} \text{ lb/gal } \times 2 \text{ gal/min}$ = $\frac{2A(t)}{500+t} \text{ lb/min }$

Now, the differential equation for the amount of salt A(t) in the tank at a time t > 0 is given by;

= $\frac{dA}{dt}=12\text{ lb/min } - \frac{2A(t)}{500+t} \text{ lb/min }$

or $\frac{dA}{dt}=12 - \frac{2A(t)}{500+t}$ .

4 0

3 years ago

Julio's father is 4 times as old as Julio. The sum of their ages is no less than 55.

seropon [69]

Call (F) the age of the father and (J) the age of Julio

The F & J are related in this way: F=4J

Now you have a restriction in the form of inequality: The sum of both ages has to be greater or equal than 55.

Algebraically that is: F + J ≥ 55

You can substitute F with 4J to find the solution for J:

4J + J ≥ 55

5J ≥ 55

Now divide both sides by 5

5J/5 ≥ 55/5

J ≥ 11

That Imposes a lower boundary for the value of J of 11, meaning that the youngest age of Julio can be 11

8 0

3 years ago

Write a phythagoras triplet whose one is no. 17

hjlf

So the Pythagorean triplet is 8,15and 17

3 0

3 years ago

Read 2 more answers

Solve: 7/9 = x/3<br> 0.33<br> 2.33<br> 23.3<br> 33

Novosadov [1.4K]

Step-by-step explanation:

$\frac{7}{9} = \frac{x}{3} \\ \\ x = \frac{7 \times 3}{9} \\ \\ x = \frac{7}{3} \\ \\ \huge \red{ \boxed{x = 2. 33}}$