Answer:
3x^4 + 7x^3 - 5x^2 + 8x - 13
Step-by-step explanation:
(3x^4 + 7x^3 - 9) - (5x^2 - 8x + 4) =
The negative sign to the left of the second set of parentheses changes every sign inside the parentheses.
The first set of parentheses is unnecessary, so we just drop it.
= 3x^4 + 7x^3 - 9 - 5x^2 + 8x - 4
Now we combine like terms.
= 3x^4 + 7x^3 - 5x^2 + 8x - 13
The sequence 1, 3, 6, 10, 15, etc find dy/dx...
dy/dx=2,3,4,5 this is not a constant so find d2y/dx2
d2y/dx2=1,1,1, this is a constant, specifically a constant acceleration, which is a property of a quadratic function of the form ax^2+bx+c and if we use three points of the sequence we can solve for all of the variables...
9a+3b+c=6
4a+2b+c=3
a+b+c=1 getting differences
5a+b=3
3a+b=2 and again
2a=1, so a=1/2, making 3a+b=2 become:
1.5+b=2, so b=1/2, making a+b+c=1 become
1/2+1/2+c=1 so c=0 so our function is:
a(n)=(n^2+n)/2
which can be expressed, if you factor the numerator as:
a(n)=n(n-1)/2
now, the + is growth, and - is decay
well, let's see hmm "something" is increasing at a rate of say hmm 25%, r = 25% or 25/100 or 0.25
now, if we plug that in the equation, the amount is increasing the rate is positive, so we get A = P(1+0.25)ᵗ or A = P(1.25)ᵗ
now, notice, the value in the parentheses, is "greater than 1", because the 0.25 got added
now, let's say something decreases by 25%, so we use a negative rate, thus A = P(1 - 0.25)ᵗ or A = P(0.75)ᵗ
notice again, the value inside the parentheses, is "less than 1"
anyhow, that's the tell-tale part of an exponential function
Answer:
23.7 miles or 24 miles rounded
Step-by-step explanation:
To do this, you only need to know the conversion of inch to mile. In this case, 1 inch equals 1.58x10^-5 miles, so:
1.5x10^6 inches * 1.58x10^-5 miles/inch = 23.7 miles
Now, as you want it to the nearest hundredth, the answer is simply 24 miles
Answer:
Circumcenter = (4,0)
Circumcircle = √5
Step-by-step explanation:
The circumcentre is the point of intersection of the perpendicular bisectors of a triangle. The vertices of the triangle are equidistant to the circumcentre.
Let us assume the coordinate of the circumcentre is at O(x, y). Therefore the distance between the cirmcumcenter and the vertices are:
AO = BO, therefore
√(x² + y²-4x-2y+5) = √(x² + y² - 10x - 4y + 29)
x² + y²-4x-2y+5 = x² + y² - 10x - 4y + 29
6x + 2y = 24 (1)
BO = CO
√(x² + y² - 10x - 4y + 29) = √(x² + y² - 9x - 8y + 25)
x² + y² - 10x - 4y + 29 = x² + y² - 9x - 8y + 25
-x + 4y = -4 (2)
Multiply equation 2 by 6 and add to equation 1:
26y = 0
y=0
Put y = 0 in -x + 4y = -4
-x + 4(0) = -4
x = 4
The cicumcenter is at (4, 0)
The radius of the circumcircle = AO = BO = CO. Therefore: