Answer:
Below in bold
Step-by-step explanation:
∫ dx / (x^2√(9-x^2))
Substitute x = 3sinu and dx = 3cosu du
then the √(9-x^2) = √( 9 - 9sin^2u) = 3 cos u and u = arcsin(x/3)
= 3 ∫(csc^2 u du )/ 27
= 1/9 ∫(csc^2 u du
= -1/9 cot u
= -√9-x^2) / 9x.
Answer:
y - 7 = -2(x - 4)
Step-by-step explanation:
We are asked to write the equation of a line in point slope form
Step 1 : find slope
We are given the slope to be -2
Slope m = -2
Step 2: substitute m into point slope form
y - y_1 = m( x - x_1)
y - y_1 = -2 ( x - x _1)
Step 3: substitute the point into the equation
y - y_1 = -2( x - x _1)
( 4 , 7)
x_1 = 4
y_1 = 7
y - 7 = -2( x - 4)
We don't need to open the bracket because we are asked to write the equation in a point slope form
<span>The
<u>correct answers</u> are:
Malcolm's maximum speed is 200 km/hr and Robbie's is 320 km/hr.
Explanation<span>:
Let R be Robbie's maximum speed and M be Malcolm's maximum speed. If Malcolm's speed is doubled (2M), it is 80 more than Robbie's (R+80); this gives us the equation
2M = R + 80.
We can isolate M by dividing both sides by 2:
2M/2 = R/2 + 80/2
M=R/2+40.
We know that their average is 260 km/hr. The average is found by adding the two maximum speeds together and dividing by 2:
(M+R)/2=260.
We will substitute our value for M from above:
</span></span>
<span><span>
To solve this, we can multiply both sides by 2:
</span></span>
<span><span>
We can combine like terms, but to do that, we must write R as a fraction over 2. Since it is 1R, this is 2R/2:
</span></span>
<span><span>
Subtract 40 from both sides:
</span></span>
<span><span>
Now we will multiply both sides by 2:
</span></span>
<span><span>
Divide both sides by 3:
</span></span>
<span><span>
Plugging this into our first equation for M, we have:
M = R/2+40
M = 320/2+40
M = 160+40
M=200.</span></span>
The answer is the 3rd one because it cancels out all.