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Bezzdna [24]
1 year ago
15

Really need help with 11 and 12 just started learning this today and I don't quite understand it would really appreciate it

Mathematics
1 answer:
sineoko [7]1 year ago
4 0

11.

Given:

y=x^2

Differentiate with respect to x, we get

\frac{dy}{dx}=2x

The given point is (3,9)

Substitute x=3 in the derivative, we get

\frac{dy}{dx}=2\times\times3=6

Hence the slope is 3.

12.

Given:

y=x^2+4

Differentiate with respect to x, we get

\frac{dy}{dx}=2x+0

The given point is (0,4)

Substitute x=0 in the derivative, we get

\frac{dy}{dx}=2(0)+0=0

Hence the slope is 0.

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Write f(x)=8x^2-4x+11 in vertex form
Vlad [161]

Answer:

f(x)=8(x-\frac{1}{4})^{2}+\frac{21}{2}

or

f(x)=8(x-0.25)^{2}+10.5

Step-by-step explanation:

we have

f(x)=8x^{2}-4x+11

This is a vertical parabola open upward (because the leading coefficient is positive)

The vertex is a minimum

Convert to vertex form

Factor the leading coefficient

f(x)=8(x^{2}-\frac{1}{2}x)+11

Complete the square. Remember to balance the equation by adding the same constants to each side.

f(x)=8(x^{2}-\frac{1}{2}x+\frac{1}{16})+11-\frac{1}{2}

f(x)=8(x^{2}-\frac{1}{2}x+\frac{1}{16})+\frac{21}{2}

Rewrite as perfect squares

f(x)=8(x-\frac{1}{4})^{2}+\frac{21}{2} ----> equation in vertex form

or

f(x)=8(x-0.25)^{2}+10.5

The vertex is the point  (0.25,10.5)

3 0
3 years ago
A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. no fencing is needed along the bar
jeyben [28]

Hi,

Let assume a the west side,

b the length of the north wall (i suppose the answer is smaller then the barn.

Cost of the fence= a*6+a*12+b*12=3000 $.

So 3a+2b=500==>b=(500-3a)/2

Area =a*b=a(500-3a)/2= 250a-3/2a²

Derivate the area ==> 250-3a=0

==> a=250/3 and b=(500-3*250/3)/2=125

Width=125 (feet)

Length=250/3=83.333 (feet)

3 0
3 years ago
The graph of the equation x + 3y = 6 intersects at the y axis at the point whose coordinates are
svp [43]

Answer:

4. (6,0)

Step-by-step explanation:

Plug the points into the equation.

6+3(0)=6

6+0=6

6=6

5 0
3 years ago
Please help solve 16+x=12
melamori03 [73]

Answer:

x=-4

Step-by-step explanation:

1. subtract 16 from both sides which leaves you left with

x=-4

3 0
3 years ago
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Henry and 28 classmates go to the roller skating rink . Each van can hold 11 students . If all of the vans are full except one h
Rudik [331]
You divide 29:11= 2 7/11
so you have 2 full vans and one with 7 students.
so the answer is 7
8 0
3 years ago
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