How do i solve these problems:
1. 2(-5y^3)^2+(-3y^3)^3
2. Lemon juice is 10^2 times as acidic as tomato juice. Tomato juice is 10^3 times as acidic as egg whites. How many times as acidic is lemon juice as egg whites? Write as a monomial.
3. The seismic waves of a magnitude 6 earthquake are 10^2 times as great as a magnitude 4 earthquake. The seismic waves of a magnitude 4 earthquake are 10 times as great as a magnitude 3 earthquake. How many times as great are the seismic waves of a magnitude 6 earthquake as those of a magnitude 3 earthquake? Write a monomial.
These problems are all very similar and you have not tried them so I will do the third and you try the others
call magnitude 3 = q for quake
then mag 4 = 10^1 q
then mag 6 = 10^2 *10^1 q = 10^3 q = 1000 times the mag 3
M6 = 10^3 M3
in general by the way
Msub(n+1) = 10 Msub(n)
In number 2
10^2*10^3 = 10^(2+3) = 10^5
to multiply, add exponents of same quantity
to raise to power, multiply exponents
remember:
x^2* x^3 = x^(2+3) = x^5
BUT
(x^2)^3 = x^(2*3) = x^6
1. To solve this problem, follow the order of operations (PEMDAS):
First, simplify the expressions inside parentheses:
2(-5y^3)^2 = 2(25y^6) = 50y^6
(-3y^3)^3 = (-3)^3(y^3)^3 = -27y^9
Next, substitute the simplified expressions back into the original equation:
2(-5y^3)^2 + (-3y^3)^3 = 50y^6 + (-27y^9)
2. To find the number of times lemon juice is as acidic as egg whites, we need to multiply the acidity ratios.
Lemon juice is 10^2 times as acidic as tomato juice.
Tomato juice is 10^3 times as acidic as egg whites.
Multiply the two ratios together:
10^2 * 10^3 = 10^(2+3) = 10^5
So, lemon juice is 10^5 times as acidic as egg whites.
3. To find the number of times the seismic waves of a magnitude 6 earthquake are as great as those of a magnitude 3 earthquake, we need to multiply the amplitude ratios.
The seismic waves of a magnitude 6 earthquake are 10^2 times as great as a magnitude 4 earthquake.
The seismic waves of a magnitude 4 earthquake are 10 times as great as a magnitude 3 earthquake.
Multiply the two ratios together:
10^2 * 10 = 10^(2+1) = 10^3
So, the seismic waves of a magnitude 6 earthquake are 10^3 times as great as those of a magnitude 3 earthquake.
1. To solve the expression 2(-5y^3)^2+(-3y^3)^3, we follow the order of operations (PEMDAS).
Step 1: Simplify the exponents within each parentheses.
- For the first term, (-5y^3)^2, we raise -5y^3 to the power of 2, which gives us (25y^6).
- For the second term, (-3y^3)^3, we raise -3y^3 to the power of 3, which gives us (-27y^9).
Now our expression becomes 2(25y^6) + (-27y^9).
Step 2: Apply the multiplication to each term.
Multiply 2 by 25 to get 50. The expression becomes 50y^6 + (-27y^9).
2. To determine how many times more acidic lemon juice is compared to egg whites, we'll follow the given information.
Lemon juice is 10^2 times as acidic as tomato juice.
Tomato juice is 10^3 times as acidic as egg whites.
To find the relationship between lemon juice and egg whites, we combine the two statements using multiplication:
Lemon juice = (10^2) * (10^3) * egg whites
= 10^(2+3) * egg whites
= 10^5 * egg whites
Therefore, lemon juice is 10^5 times as acidic as egg whites.
3. Similar to the previous problem, we'll use the given information to find the relationship between the seismic waves of a magnitude 6 earthquake and a magnitude 3 earthquake.
The seismic waves of a magnitude 6 earthquake are 10^2 times as great as a magnitude 4 earthquake.
The seismic waves of a magnitude 4 earthquake are 10 times as great as a magnitude 3 earthquake.
Combining the two statements using multiplication:
Magnitude 6 earthquake = (10^2) * (10) * magnitude 3 earthquake
= 10^(2+1) * magnitude 3 earthquake
= 10^3 * magnitude 3 earthquake
Therefore, the seismic waves of a magnitude 6 earthquake are 10^3 times as great as those of a magnitude 3 earthquake.