Answer:
x= 2
x= -3
Step-by-step explanation:
<u>Solving as normal quadratic equation:</u>
- 2x^2+2x=12
- x^2 +x = 6
- x^2 + x - 6= 0
- x = (-1 ± √(1+4*1*6)/2
- x = ( - 1 ± √25)/2
- x = (-1 ± 5)/2
- x= 2
- x= -3
<u>Roots are</u> 2 and -3
30X15=450. 450:100= 4,50. 30+4,50= 34,50
Answer:
Step-by-step explanation:
If 
, and 
then 
can be calculated via:
Answer:
- <u>1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, and 6T.</u>
Explanation:
The quetion is:
- <em>list all the outcomes in the same format </em>
<h2 /><h2>Solution</h2>
Understand the format:
- first character is the number that appears on the top face of the dice: it can be 1, 2, 3, 4, 5, or 6.
- second charater is one of two letters that represent the flip of the coin: H for heads or T for tails.
Then, the list of the combinations that represent all the possible outcomes is:
- 1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, and 6T.
They are 12 possible outcomes: 6 × 2 = 12: 6 from the 6 possible outmoes of the dice, and 2 for the two possible outcomes of the coin.
How fast the volume of the sphere is changing when the surface area is 10 square centimeters is it is increasing at a rate of 30 cm³/s.
To solve the question, we need to know the volume of a sphere
<h3>
Volume of a sphere</h3>
The volume of a sphere V = 4πr³/3 where r = radius of sphere.
<h3>How fast the volume of the sphere is changing</h3>
To find the how fast the volume of the sphere is changing, we find rate of change of volume of the sphere. Thus, we differentiate its volume with respect to time.
So, dV/dt = d(4πr³/3)/dt
= d(4πr³/3)/dr × dr/dt
= 4πr²dr/dt where
- dr/dt = rate of change of radius of sphere and
- 4πr² = surface area of sphere
Given that
- dr/dt = + 3 cm/s (positive since it is increasing) and
- 4πr² = surface area of sphere = 10 cm²,
Substituting the values of the variables into the equation, we have
dV/dt = 4πr²dr/dt
dV/dt = 10 cm² × 3 cm/s
dV/dt = 30 cm³/s
So, how fast the volume of the sphere is changing when the surface area is 10 square centimeters is it is increasing at a rate of 30 cm³/s.
Learn more about how fast volume of sphere is changing here:
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