Answer:
Correct integral, third graph
Step-by-step explanation:
Assuming that your answer was 'tan³(θ)/3 + C,' you have the right integral. We would have to solve for the integral using u-substitution. Let's start.
Given : ∫ tan²(θ)sec²(θ)dθ
Applying u-substitution : u = tan(θ),
=> ∫ u²du
Apply the power rule ' ∫ xᵃdx = x^(a+1)/a+1 ' : u^(2+1)/ 2+1
Substitute back u = tan(θ) : tan^2+1(θ)/2+1
Simplify : 1/3tan³(θ)
Hence the integral ' ∫ tan²(θ)sec²(θ)dθ ' = ' 1/3tan³(θ). ' Your solution was rewritten in a different format, but it was the same answer. Now let's move on to the graphing portion. The attachment represents F(θ). f(θ) is an upward facing parabola, so your graph will be the third one.
Solve for K by simplifying both sides of the equation, then isolate the variable.
K = 193
Answer:
C
Step-by-step explanation:
We want a line of best fit, which means we want to create a line that the data points will lie closest to.
One thing we can do is find the slope between the bottom-leftmost point and the top-rightmost point. This is because if we were to draw a line connecting these two, it will cut through the data quite well.
Those two points are (9, 15) and (16, 18), so the slope is change in y divided by the change in x:
(18 - 15) ÷ (16 - 9) = 3 ÷ 7 ≈ 0.4
Eliminate A and B.
Now we need to determine the y-intercept. This needs no calculations; simply look at the graph: there's no way a line cutting through the y-intercept point of (0, 18) will perfectly match the data points; instead it must be a y-intercept lower than 18. So, eliminate D.
The answer is C.
Answer:
The first number is <u>18</u> and the second number is <u>27</u>.
Step-by-step explanation:
Given:
A first number is nine less than a second.
The sum of the numbers is 45.
Now, to find the numbers.
Let the second number be 
And the first number be 
The sum of the both numbers is 45.
According to question:
⇒ 
⇒ 
<em>Adding both sides by 9 we get:</em>
⇒ 
<em>Dividing both sides by 2 we get:</em>
⇒ 
<u><em>The second number = 27</em></u>.
Now, to get the first number we put the value of 
:
Therefore, the first number is 18 and the second number is 27.
Answer:
BC=11
Step-by-step explanation:
we need to find BC
and we know that
AB= x+2
AC=13
BC=2x+11
A, B and C are collinear
that means that
AB+BC=AC
x+2+2x+11=13
3x+13=13
3x=0
x=0
so BC=2(0)+11
BC=11
