Answer:
Our two intersection points are:
Step-by-step explanation:
We want to find where the two graphs given by the equations:
Intersect.
When they intersect, their <em>x-</em> and <em>y-</em>values are equivalent. So, we can solve one equation for <em>y</em> and substitute it into the other and solve for <em>x</em>.
Since the linear equation is easier to solve, solve it for <em>y: </em>
<em />
<em />
<em />
Substitute this into the first equation:
Simplify:
Square. We can use the perfect square trinomial pattern:
Multiply both sides by 16:
Combine like terms:
Isolate the equation:
We can use the quadratic formula:
In this case, <em>a</em> = 25, <em>b</em> = -22, and <em>c</em> = -159. Substitute:
Evaluate:
Hence, our two solutions are:
We have our two <em>x-</em>coordinates.
To find the <em>y-</em>coordinates, we can simply substitute it into the linear equation and evaluate. Thus:
And:
Thus, our two intersection points are:
25% = 25% : 100% = 0,25 ← the end
60% = 60% : 100% = 0,6 ← the end
72,1% = 72,1% : 100% = 0,721 ← the end
7% = 7% : 100% = 0,07 ← the end
9,5% = 9,5% : 100% = 0,095 ← the end
66% = 66% : 100% = 0,66
The Riemann sum with n = 6, taking the sample points to be midpoints is - 12.0625
<h3>What is Riemann sum?</h3>
Formula for midpoints is given as;
M = ∑0^n-1f((xk + xk + 1)/2) × Δx;
From the information given, we have the following parameters
Let' s find the parameters
Δx = (3 - 0)/6 = 0.5
xk = x0 + kΔx = 0.5k
xk+1 = x0 + (k +1)Δx
Substitute the values
= 0 + 0.5(k +1) = 0.5k - 0.5;(xk + xk+1)/2
We then have;
= (0.5k + 0.5k + 05.)/2
= 0.5k + 0.25.
Now f(x) = 2x^2 - 7
Let's find f((xk + xk+1)/2)
Substitute the value of (xk + xk+1)/2)
= f(0.5k+ 0.25)
= 2(0.5k + 0.25)2 - 7
Put values into formula for midpoint
M = ∑05[(0.5k + 0.25)2 - 7] × 0.5.
To evaluate this sum, use command SUM(SEQ) from List menu.
M = - 12.0625
A Riemann sum represents an approximation of a region's area from addition of the areas of multiple simplified slices of the region.
Thus, the Riemann sum with n = 6, taking the sample points to be midpoints is - 12.0625
Learn more about Riemann sum here:
brainly.com/question/84388
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Answer:
Step-by-step explanation:
1) √2 + 2√2 = ( 1 + 2 ) √2 = 3*√2 = 3√2
4) √8 + √2 = √2*2*2 + √2 = 2√2 + √2 = ( 2 +1 ) √2 = 3√2
7) 2√5 - √5 = (2 - 1)√5 = 1 √5
10 3√5 - 2√5 = (3 - 2) √5 = 1√5
