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Gelneren [198K]
2 years ago
5

What is the function written in vertex firm​

Mathematics
1 answer:
barxatty [35]2 years ago
6 0

Answer:

Step-by-step explanation:

The vertex form of a quadratic function is f(x) = a(x – h)2 + k, where a, h, and k are constants. of the parabola is at (h, k).

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Six identical squares are cut from the corners and edges of an 80 cm by 50 cm cardboard rectangle. the remaining piece is folded
Anna11 [10]
Check the picture.

let the length of a side of each of the squares removed be x.

The box formed will have dimensions: 80-2x, 50-2x, x(the height)

So the volume can be expressed as a function of x as follows:

f(x)=(80-2x)(50-2x)x=[4000-160x-100x+4 x^{2} ]x=(4 x^{2}-260x+4000)x

so f(x)=4 x^{3}-260x^{2}+4000x

the solutions of f'(x)=0 gives the inflection points, so the candidates for maxima points,

f'(x)=12x^{2}-520 x +4000=0

solving the quadratic equation, either by a calculator, graphing software, or by other algebraic methods as the discriminant formula, we find the solutions

x=10 and x=33.333

plug in f(x) these values to see which greater:

f(10)=(80-20)(50-20)10=60*30*10=18000 cm cubed

f(33.333)=(80-66.666)(50-66.666)33.333= which is negative because (50-66.666)<0



Answer: 18000 cm cubed

5 0
3 years ago
Read 2 more answers
If the 102,619 residents of a city are divided into 57 equal groups, then some residents don't fit into a group.
valentinak56 [21]

Answer:

1,800, 19

Step-by-step explanation:

102,619÷57=1800 (nearest one)

102,619-1800×57=19

3 0
2 years ago
Create an inequality for the situation below.<br><br> Please help!!
OlgaM077 [116]

1 gallon of milk costs 0.50 more than 5 times a gallon of water.

From that information milk is 5x +0.50 the cost of water.


The cost of milk is $3.75, so now we have:

3.75 = 5x + 0.50


Subtract 0.50 from each side:

3.25 = 5x

Divide both sides by 5:

X = 3.25 / 5

x = 0.65

The cost of water = $0.65

8 0
3 years ago
The difference of twice a number and 3 is -21
never [62]

Answer:

The answer to the promblem is -7

4 0
3 years ago
The route used by a certain motorist in commuting to workcontains two intersections with traffic signals. The probabilitythat he
zavuch27 [327]

Answer:

a) 0.2

b) 0.2

c) 0.5

Step-by-step explanation:

Let S be the event "the car stops at the signal.

In the attached figure you can see a tree describing all possible scenarios.

For the first question the red path describes stopping at the first light but not stopping at the second. We can determine the probability of this path happening by multiplying the probabilities on the branches of the tree, thus

P(a)=0.4\times0.5=0.2

For the second one the blue path describes the situation

P(b)=0.4\times 0.5=0.2

For the las situation the sum of the two green path will give us the answer

P(c)=0.6\times 0.5 + 0.4\times 0.5=0.3+0.2=0.5

7 0
3 years ago
Read 2 more answers
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