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2 years ago

What is the maximum value of this function? f(x)=−16x²+32x+20

Mathematics

1 answer:

cestrela7 [59]2 years ago

6 0

Answer: The maximum value is 35.94

Step-by-step explanation:

We have the function:

f(x) = -16*x^2 + 34*x + 20

This is a quadratic equation, and the first thing we can see is that the leading coefficient is smaller than zero, which means that the "arms" of the graph will go downwards, which means that the maximum of our function will be at the vertex.

First, we know that the vertex of a quadratic function is when f'(x) = 0.

f'(x) = 2*(-16*x) + 34 = 0.

x = -34/(-2*16) = 34/32 = 17/16.

Now we evaluate our function in the point x = 17/16.

f(17/16) = -16*(17/16)^2 + 32*(17/16) + 20 = 35.94

The maximum value is 35.94

You might be interested in

Identify two numbers less than 20 with the most factors

Anastaziya [24]

<u>Answer</u>

18 and 12

<u>Explanation</u>

Factor is a number or algebraic expression that divides another number or expression evenly that is with no remainder.

Odd number have few factors so the can't be the answer.

WE are going to try the even numbers.

18 ⇒ 18, 9, 6, 3, 2, 1

16 ⇒ 16, 8, 4, 2, 1

12 ⇒ 12, 6, 4, 3, 2, 1

10 ⇒ 10, 5, 2, 1

Other number less than 10 has factors less than 5.

It can be seen from above that 18 and 12 have the most factors.

3 0

2 years ago

Read 2 more answers

What is the recursive rule for an=4n−1? a1=4;an=an−1−1 a1=3;an=an−1+4 a1=−1;an=an−1+4 a1=3;an=an−1−1

navik [9.2K]

Plug in n = 1 into the nth term formula
a(n) = 4n-1
a(1) = 4*1-1
a(1) = 3
So the first term is 3

The second term will be 7 because we add on 4 each time, as indicated by the slope of 4. This is also known as the common difference.

So the nth term is found by adding 4 to the (n-1)st term, in other words,
a(n) = a(n-1)+4

----------------------------------------------------------------------------

In summary, the answer is
a1=3; an=an-1+4
which is choice B

4 0

2 years ago

Read 2 more answers

If m∠DEF = 117°, find the value of x

ollegr [7]

Answer:

x = 7

Step-by-step explanation:

Given:

∠DEF = 117°

∠DEG = (12x + 1)°

∠GEF = (5x - 3)°

Find:

value of x

Computation:

∠DEF = ∠DEG + ∠GEF

117° = (12x + 1)° + (5x - 3)°

117° = 17 x - 2

x = 7

4 0

2 years ago

Jose is blocking off several rooms in a hotel for guests coming to his wedding. The hotel can reserve small rooms that can hold

emmasim [6.3K]

Answer:

No. of large rooms = 7

No. of small rooms = 14

Set of equations

4x + 3y = 70

y = 2x

Variable definitions

No. of large rooms is x

No. of small rooms is y

Step-by-step explanation:

capacity of large rooms = 4 people

let the no. of large rooms be x

thus, total no of people which can be accommodated in x rooms = 4*x = 4x

capacity of small rooms = 3 people

let the no. of small rooms be y

thus, total no of people which can be accommodated in y rooms = 3*y = 3y

total no. of people which can be accommodated in x large room and y small room will be = 4x + 3y

It is given that total small room and large room can accommodate 70 guests

thus,

4x + 3y = 70 _________equation 1

_________________

It is also given that Jose reserved twice as many small rooms as large rooms,

so, if no. of large rooms is x and no. of small rooms is y

then

y = 2x _________equation 2

substituting value of y in equation 1 we have

4x + 3(2x) = 70

=>4x + 6x = 70

=> 10x = 70

=> x = 70/10 = 7

No. of large rooms = 7

No. of small rooms = y= 2x = 2*7 = 14

Set of equations

4x + 3y = 70

y = 2x

Variable definitions

No. of large rooms is x

No. of small rooms is y

8 0

2 years ago

in 2 h, kelly laid new floor tile over 1/5 of the room. when she was joined by annette, the rest of the work was completed in 3h

jeyben [28]

Answer: Annette will take 6 hours to do the entire job alone.

Step-by-step explanation:

Given: Time taken by Kelly to do $\dfrac{1}{5}$ of job = 2 hours

i.e. Time for complete job done alone by Kelly = $5\times2=10\ hours$

Rest of work = $1-\dfrac{1}{5}=\dfrac{4}{5}$ of the job

$\dfrac{4}{5}$ of the complete job done by both Kelly and Annette in 3 hours

Time would be taken by then to do entire job together = $3\times\dfrac{5}{4}=3.75\ hours$

Let t be the time taken by Annette to do job alone.

Then, as per situation

$\dfrac{1}{3.75}=\dfrac{1}{10}+\dfrac{1}{t}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{1}{3.75}-\dfrac{1}{10}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{4}{15}-\dfrac{1}{10}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{1}{6}\\\\\Rightarrow\ t=6$

hence, Annette will take 6 hours to do the entire job alone.

7 0

2 years ago