Answer: t = - 5 ∈ 
= ( -∞ , -4 )
Step-by-step explanation:
The standard form of O.D.E is written as :
+ 
Equation given :
+ 
= 
, 
The first thing to do is to write the O.D.E in standard form , that is we will divide through by 
, so we have
With this , we can see that 
and 
are both continuous in the same domain. Therefore , the intervals are :
= ( -∞ , -4 )
= ( - 4 , 4 )
= ( 4 , -∞ )
recall that y(−5) = 1 , then t = -5
This means that :
t = - 5 ∈ = ( -∞ , -4 )
<h2><u>EQUATIONS</u></h2>
We'll solve this equation:
<h3>5x + 17 = 4(3x - 1)</h3>
First, let's apply the distributive property:
5x + 17 = 4(3x - 1)
5x + 17 = 12x - 4
Now, add 4 to both sides of the equation:
5x + 17 = 12x - 4
5x + 17 + 4 = 12x - 4 + 4
5x + 21 = 12x
Substract 5x from both sides:
5x + 21 = 12x
5x - 5x + 21 = 12x - 5x
21 = 12x - 5x
21 = 7x
Now, divide both sides by 7
21 ÷ 7 = 7x ÷ 7
<h3> 3 = x</h3>
Therefore, x = 3.
<h3>B. The equation has one solution.</h3>
The pot can hold 5.23 quarts
Step-by-step explanation:
- Step 1: Find the volume of the right cylinder shaped pot.
Diameter of the pot = 8 in
⇒ Radius = 4 in
Height = 6 in
⇒ Volume of the pot = πr²h = 3.14 × 4² × 6
= 301.44 in³
- Step 2: Convert inches to quarts.
1 in³ = 0.017316 liquid quarts
⇒ 301.44 in³ = 301.44 × 0.017316 = 5.23 quarts
Money is a medium of exchange
Seven more than 3 times a number is equal to 49 can be put into an equation form, which would be 7 + 3x = 49. With this equation we can work it out, first we will subtract 7 from both sides of the equation to cancel out the 7. 49 - 7 = 42. Now we have 3x = 42. To isolate x and give us the answer we will divide by 3 on both sides, since 3 is being multiplied by x. This will give us our answer, which is 14.
