Using algebra...
n and n+2 are the integers
n*(n+2)=288
n^2+2n=288
n^2+2n-288=0
288=2*2*2*2*2*3*3=(2*2*2*2)*(2*3*3)=16*18 and 18-16=2
factor
(n+18)(n-16)=0
n+18=0
n=-18
n+2=-16
this is one solution
n-16=0
n=16
n+2=18

this is another solution
as you can see, it's just a matter of factoring
288

using arithmetic...
√288=16.97≈17

16 and 18 are the integers (as well as -16 and -18)

3 0

3 years ago

"Verify the identity of (sinx cosx)^2/sinx cosx = 2 + secx cscx"

nata0808 [166]

(sinx + cosx)^2/((sinx)(cosx)) = 2 + (secx)(cscx)
(sinx + cosx)^2/((sinx)(cosx)) = 2 + 1/(sinxcosx); subtract 1/sinxcosx both sides 
(sinx + cosx)^2/((sinx)(cosx)) - 1/(sinxcosx)= 2; multiply through by sinxcosx 
(sinx + cosx)^2 -1 = 2(sinxcosx) 
sin^2 + 2sinxcosx + cos^2 - 1 = 2(sinxcosx); since sin^x + cos^2x = 1 
1 + 2sinxcosx -1 = 2sinxcosx 
2sinxcosx = 2sinxcosx

5 0

4 years ago

Read 2 more answers

Hey can anyone tell me how to do slope

netineya [11]

The main thing is rise/run. y=mx+b that is the formula for slope

7 0

3 years ago

Read 2 more answers

If the square of a number is added to 8 times the number, the result is 100.

klasskru [66]

$\huge \boxed{\mathbb{QUESTION} \downarrow}$

If the square of a number is added to 8 times the number, the result is 100. Find x.

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

Let's take the number as 'x'.

Square of x = x²
8 times x = 8x

We are given that, 8x + x² = 100

Now, let's solve for x.

__________________

$8 x + x ^ { 2 } = 100$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x²+bx=c.

$x^{2}+8x=100$

Divide 8, the coefficient of the x term, by 2 to get 4. Then add the square of 4 to both sides of the equation. This step makes the left-hand side of the equation a perfect square.

$x^{2}+8x+4^{2}=100+4^{2}$