Check the picture below.
Estimate how many times larger 4 x 10^15 is than 8 x 10^9 in the form of a single digit times an integer power of 10.
1 answer:
Problem A
When you use the term larger, you mean that (if the power is positive) the bigger number is in the numerator. 4*10^15 > 8 * 10^9 So 8 * 10^9 is in the denominator
Solution
Note:The tricky part is recognizing what to do with the 0.5 * 10^6. You can always break apart a power into it's parts. Since 6 = 5 + 1, the power can be broken down into 10^1*10^5. The 10^1 is used to get the 0.5 to a number that is a single digit.
Problem 2
I'm just going to give you the answer to this. Please use Problem A as a guide.
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Answer:
Step-by-step explanation:
Solve Using the Quadratic Formula
4x^2 + 8x − 5 = 0
Use the quadratic formula to find the solutions.
−b ± √b^2 − 4 (ac)
-------------------------
2a
Substitute the values a = 4, b = 8, and c = −5 into the quadratic formula and solve for x.
−8 ± √82 − 4 ⋅ (4 ⋅ −5)
-------------------------
2 ⋅ 4
Simplify the numerator.
Raise 8 to the p ower of 2.
−8 ± √64 − 4 ⋅ 4 ⋅ −5
x= ---------------------------
2 ⋅ 4
Multiply −4 by 4.
−8 ± √64 − 16 ⋅ −5
x = -------------------------
2 ⋅ 4
Multiply −16 by −5.
−8 ± √64 + 80
x = -------------------
2 ⋅ 4
Add 64 and 80.
−8 ± √144
x = --------------
2 ⋅ 4
Rewrite 144 as 12^2.
−8 ± √122
x = ------------
2 ⋅ 4
Pull terms out from under the radical, assuming positive real numbers.
multiply 2 by 4
−8 ± 12
x= ------------
8
simplify
−2 ± 3
x= ---------
2
The final answer is the combination of both solutions.
x= 1/2, -5/2
Hope this helped!