Answer:
it -1
Step-by-step explanation:
Answer:
Step-by-step explanation:
Equation of a line is given as:
y = mx + b
Where
m is the slope
and
b is the y-intercept (y-axis cutting point)
Since we know slope is -4, we can write:
y= mx + b
y = -4x+ b
Given the point (-2,7) , we can say:
x = -2
and
y = 7
Plugging these 2 values, we can solve for b:
y = -4x + b
7 = -4(-2) + b
7 = 8 + b
b = 7 - 8
b = -1
Now, we have the equation:
The function, as presented here, is ambiguous in terms of what's being deivded by what. For the sake of example, I will assume that you meant
3x+5a
<span> f(x)= ------------
</span> x^2-a^2
You are saying that the derivative of this function is 0 when x=12. Let's differentiate f(x) with respect to x and then let x = 12:
(x^2-a^2)(3) -(3x+5a)(2x)
f '(x) = ------------------------------------- = 0 when x = 12
[x^2-a^2]^2
(144-a^2)(3) - (36+5a)(24)
------------------------------------ = 0
[ ]^2
Simplifying,
(144-a^2) - 8(36+5a) = 0
144 - a^2 - 288 - 40a = 0
This can be rewritten as a quadratic in standard form:
-a^2 - 40a - 144 = 0, or a^2 + 40a + 144 = 0.
Solve for a by completing the square:
a^2 + 40a + 20^2 - 20^2 + 144 = 0
(a+20)^2 = 400 - 144 = 156
Then a+20 = sqrt[6(26)] = sqrt[6(2)(13)] = 4(3)(13)= 2sqrt(39)
Finally, a = -20 plus or minus 2sqrt(39)
You must check both answers by subst. into the original equation. Only if the result(s) is(are) true is your solution (value of a) correct.
You can make 4rectangular prisms with 16 cubes
