Hello there!
There are two ways to find the minimum value of this function, but before I show you how, I am going to teach you a little bit about minimum value.
The minimum value on a parabola is the vertex or turning point. This means that the slope of the tangent line is horizontal, having a slope of 0.
The algebraic way to find the minimum or maximum value on a parabola is to use the formula -b/2a. Let's do it...
y=4x^2+4x-35
where a=4, b=4, and c=-35
-b/2a
-4/2(4)
-4/8
-1/2
Now let me show you the other way...
Take the derivative of
y=4x^2+4x-35
y'=8x+4
And set it equal to 0...
8x+4=0
8x=-4
x=-1/2
We got the same answer. Now that we know x=-1/2, plug this into the original equation to find y.
y=4x^2+4x-35
y=4(-1/2)^2+4(-1/2)-35
y=-1-2-35
y=-38
So the minimum point on this parabola is (-1/2,-38)
I really hope th
A circle is a curve sketched out by a point moving in a plane. The circumference of the ring of fire is 6.2831 meters.
<h3>What is a circle?</h3>
A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
The circumference of the ring if the radius is 1 meter is,
Circumference of the ring = 2πr = 2 × π × 1 = 6.2831 meters
Hence, the circumference of the ring of fire is 6.2831 meters.
Learn more about Circle:
brainly.com/question/11833983
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Step-by-step explanation:
21)
Frog C - Frog B
318.5-199.25=119.25 cm
22)
Frog A = 213.33
to the nearest whole number= 213 cm
9514 1404 393
Answer:
(x, y) = (1/2, 5)
Step-by-step explanation:
We observe that the y-terms have coefficients 7 and -14. If we want to eliminate the y-terms, we need to multiply 7 by a factor that makes it be the opposite of -14. That factor will be -(-14)/7 = 2.
After multiplying the first equation by 2, we have ...
- 16x +14y = 78
- 4x -14y = -68
Adding these two equations gives ...
20x = 10
Solving for x, we need to divide by 20:
x = 10/20 = 1/2
Substituting this into the first equation, we get ...
8(1/2) +7y = 39
7y = 35 . . . . . . subtract 4
y = 35/7 = 5 . . . divide by 7
Then the solution is (x, y) = (1/2, 5).
_____
<em>Check</em>
We used the first equation to find y, so we know the x- and y-values satisfy the first equation. We need to check the result using the second equation.
4(1/2) -14(5) = -68
2 -70 = -68 . . . . . . . true; result checks OK
Answer:
y= 7x-73
Step-by-step explanation:
the equation form is y=mx+c where m is the slope and c a constant
m= (25-(-10))/14-9 = 35/5 = 7
so y= 7x+c
replace x and y by 14 and 25 respectively
25 = 7*14+c
c= 25-7*14
c = -73
so y= 7x-73
