Answer:
f(x)=-18x^2
Step-by-step explanation:
Given:
1+Integral(f(t)/t^6, t=a..x)=6x^-3
Let's get rid of integral by differentiating both sides.
Using fundamental of calculus and power rule(integration):
0+f(x)/x^6=-18x^-4
Additive Identity property applied:
f(x)/x^6=-18x^-4
Multiply both sides by x^6:
f(x)=-18x^-4×x^6
Power rule (exponents) applied"
f(x)=-18x^2
Check:
1+Integral(-18t^2/t^6, t=a..x)=6x^-3
1+Integral(-18t^-4, t=a..x)=6x^-3
1+(-18t^-3/-3, t=a..x)=6x^-3
1+(6t^-3, t=a..x)=6x^-3
That looks great since those powers are the same on both side after integration.
Plug in limits:
1+(6x^-3-6a^-3)=6x^-3
We need 1-6a^-3=0 so that the equation holds true for all x.
Subtract 1 on both sides:
-6a^-3=-1
Divide both sides by-6:
a^-3=1/6
Raise both sides to -1/3 power:
a=(1/6)^(-1/3)
Negative exponent just refers to reciprocal of our base:
a=6^(1/3)
Answer:
A = 53 degree
90-37 = 53 degree
As the triangle is a right angle triangle we see complimentary to the other angles and as all angles in a triangle equal 180, we see the other two which compliment this.
Step-by-step explanation:
Missing data:
Viewer's Age Group Excellent Good Average Poor Marginal Total
16–25 52 42 12 7 113
26–35 33 50 5 9 97
36–45 58 12 28 34 132
46–55 25 17 22 12 76
56 + 12 5 3 8 28
Marginal Total 180 126 70 70 446
A rating of good or excellent indicates the audience liked the movie, while a rating of poor indicates the audience disliked the movie.
<h3>How to determine the rating of the film from the 46–55 age group?</h3>
A movie producer accomplished a survey behind a preview screening of her latest movie to estimate how the film would be accepted by viewers from various age groups. The table displays the numbers of viewers in various age groups who ranked the film excellent, good, average, and poor.
25/446 = 0.05605
0.05605 
100% = 5.605%
Out of the entire respondents, the percentage of respondents from the 46–55 age group who ranked the film excellent exists at 5.605%.
To learn more about data refer to:
brainly.com/question/4219149
#SPJ4
Answer:
Step-by-step explanation:
y=mx+b
y= -2x + 3
hope this helped :)
Answer:
Step-by-step explanation:
Hope this helps!
