The tangent of the angle is
... tan(α) = ay/ax = -8.6/6.1
Then the angle (measured CCW from +x) is
... α = arctan(-86/61) ≈ 305°
This question is difficult to give a definite answer to because it's an approximation, but I estimate the solutions to be around x = 2.6 and x = -2.6.
When they ask for solutions of the graphed function they are asking for an approximation of where the graph intercepts the x-axis, and we can see it kind of intercepts in the middle of 2 and 3, except slightly closer to 3, which is why I estimated 2.6.
The graph also appears to be symmetrical, which means the solutions will be the same except one would be negative and one would be positive, which means the second solution would be -2.6.
I hope this helps! Let me know if you have any questions :)
Answer:
5/6
Step-by-step explanation:
<em>Dividing fractions:</em>
<em>Step 1: Rewrite the first fraction as it is.</em>
<em>Step 2: Replace the division sign with a multiplication sign.</em>
<em>Step 3: Flip the second fraction.</em>
<em>Step 4: Multiply the fractions and reduce the product if necessary.</em>
Let's use the rule of dividing fractions on your problem.
Step 1: Rewrite the first fraction as it is.
Step 2: Replace the division sign with a multiplication sign.
Step 3: Flip the second fraction.
Step 4: Multiply the fractions and reduce the product if necessary.
To multiply fractions, multiply the numerators together, and multiply the denominators together.
We notice that the greatest common factor of 20 and 24 is 4, so we divide both the numerator and denominator by 4 to reduce the fraction.
Answer:
no
Step-by-step explanation:
Let f represent the fraction of C-14 remaining as a function of the time t in years. Since the half-life of C-14 is about 5570 years, we have ...
f = (1/2)^(t/5570)
Taking the log and solving for t, we get ...
log(f) = (t/5570)log(1/2)
5570·log(f)/log(1/2) = t
Filling in the given value for f, the value of t we get is ...
5570·log(0.65)/log(0.5) = t ≈ 3462
It appears the estimate of 4000 years is a bit high.
