Answer:
Step-by-step explanation:
sin 30+tan²(60)+sec²(45)
=1/2+ (√3)^2+(√2)²
=1/2+3+2
=5 1/2
=5.5
Answer:
is your average rate of change,
Step-by-step explanation:
average rate of change is
, by slope formula
simplify this to get 
, which is the definition of the derivative as h goes to 0
since you defined x=a, we can substitute a for x and vice versa to find our derivative.
simplifying
(your average rate of change)
Answer: 280 = x
Step-by-step explanation: Okay you are using this equation! y = kx But you must rearrange it!
When rearranged you get y/x = k
Plug in x and y!
y/x = k
35/140 = k
0.25 = k
Now find the value of x.
You use this formula now, y/k = x
Plug in k from the last problem and y = 70
y/k = x
70/0.25 = x
280 = x
We have to present the number 41 as the sum of two squares of consecutive positive integers.
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
16 + 25 = 41
<h3>Answer: 4 and 5</h3>
Other method:
n, n + 1 - two consecutive positive integers
The equation:
n² + (n + 1)² = 41 <em>use (a + b)² = a² + 2ab + b²</em>
n² + n² + 2(n)(1) + 1² = 41
2n² + 2n + 1 = 41 <em>subtract 41 from both sides</em>
2n² + 2n - 40 = 0 <em>divide both sides by 2</em>
n² + n - 20 = 0
n² + 5n - 4n - 20= 0
n(n + 5) - 4(n + 5) = 0
(n + 5)(n - 4) = 0 ↔ n + 5 = 0 ∨ n - 4 =0
n = -5 < 0 ∨ n = 4 >0
n = 4
n + 1 = 4 + 1 = 5
<h3>Answer: 4 and 5.</h3>
