Prove that if AC=DF and AB=DE then BC=EF

Hello from MrBillDoesMath!

Answer:

3,8

Discussion:

Let "n" and "p" be the two positive integers. Then

n = p - 5   (*)

and

np = 24  (**)

Substituting  (*) in (**) gives

np = 24                            =>    as  p = n+5

n(n+5) = 24                      =>

n^2 + 5n - 24 = 0             =>   factor polynomial (n+8)(n-3)

So n = 3 or -8 but as n is positive, n = 3 Then p  = n + 5 = 8

Check:

Is n (3) 5 less than p (8). Yes

Does np = 3 *8 24. Yes

Thank you,

MrB

Answer:  The required solution for p is

Step-by-step explanation:  We are given to solve the following equation for the unknown variable p :

To solve the given equation for p, we must find the value of p in terms of D.

From equation (i), we have

Thus, the required solution for p is

Answer:

To compute the length of the curve f(x)=47(4−x2) over the interval 0≤x≤2, we need to use the formula for the arc length of a function:

L=∫ab1+(f′(x))2dx

where a and b are the endpoints of the interval. First, we need to find the derivative of f(x), which we can do by using the chain rule and the power rule:

f′(x)=4dxd7(4−x2)

f′(x)=427(4−x2)1dxd(7(4−x2))

f′(x)=427(4−x2)1(−14x)

f′(x)=−7(4−x2)28x

Next, we need to plug in f′(x) into the formula and simplify:

L=∫021+(−7(4−x2)28x)2dx

L=∫021+7(4−x2)784x2dx

L=∫027(4−x2)7(4−x2)+784x2dx

L=∫024−x228−21x2dx

Now, we need to evaluate the integral, which we can do by using a trigonometric substitution. Let x=2sinu, then dx=2cosudu and u=arcsin(x/2). The limits of integration change as follows:

x=0⟹u=0

x=2⟹u=2π

The integral becomes:

L=∫02π4−(2sinu)228−21(2sinu)2(2cosu)du

L=∫02π4−4sin2u28−84sin2u(2cosu)du

L=∫02π1−sin2u7−21sin2u(2cosu)du

L=∫02πcos2u7−21sin2u(2cosu)du

L=∫02π27−21sin2udu

Using a trigonometric identity, we can write:

L=∫02π4127−1221cos(2u)du

Using another trigonometric substitution, let v=2u, then dv=2du and u=v/2. The limits of integration change as follows:

u=0⟹v=0

u=2π⟹v=π

The integral becomes:

L=∫0π4127−1221cosv(21)dv

L=6∫0π 

Answer:

$42.60

Step-by-step explanation:

change 6.5% to. 065 and multiply it by 40. $2.60 is your sales tax. then add 2.60 to $40 which equals $42.60