Find the maximum and the minimum value of the following objective​ function, and the value of x and y at which they occur. The function F=2x+16y subject to 5x+3y≤37, 3x+5y≤35, x≥0, y≥0
The maximum value of the objective function is ___ when x=___ and y=___

Answer:

√154/π

Step-by-step explanation:

thể tích nón = thể tích hình chóp

1/3πr².h=1/3S.h

πr²=154(rút gọn h và 1/3)

=> r=√154/π

The radius of the cone is 7 cm if the cone and a pyramid have equal heights and volumes.

It is defined as a three-dimensional shape in which the base is a circular shape and the diameter of the circle decreases as we move from the circular base to the vertex.

[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]

We have:

A cone and a pyramid have equal heights and volumes.

154 = πr²

π = 22/7

r = 7 cm

Thus, the radius of the cone is 7 cm if the cone and a pyramid have equal heights and volumes.

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Answer:

100000

Step-by-step explanation:

9514 1404 393

Answer:

  A: -1, 3/5

  B: (-1/5, -3 1/5)

  2: plot the given points and draw a curve through them.

Step-by-step explanation:

The x-intercepts are most easily found from a graph of the function. I like the Desmos graphing calculator for this purpose. The x-intercepts are -1 and 3/5.

You can also find the x-intercepts by factoring the function.

  f(x) = 5x^2 +5x -3x -3 = 5x(x +1) -3(x +1) = (5x -3)(x +1)

The x-intercepts are the values of x that make the factors zero:

  5x -3 = 0   ⇒   x = 3/5

  x +1 = 0   ⇒   x = -1

__

The vertex is on the axis of symmetry, which is the vertical line at the value of x halfway between the zeros. (-1 +3/5)/2 = (-2/5)/2 = -1/5

The value of f(x) there is ...

  f(-1/5) = (5(-1/5) +2)(-1/5) -3 = (-1 +2)(-1/5) -3 = -1/5 -3 = -3 1/5

The vertex is (-1/5, -3 1/5).

__

The easiest step to take to graph the function is to type it into a graphing calculator (see attached).

If you're graphing this by hand, the three points given in parts A and B will be on the graph. The leading coefficient in the function is 3, so the x^2 parent function is vertically stretched by a factor of 3. This can make it a little more difficult to find points that lie on the graph.

Recognizing that the vertex form equation is ...

  f(x) = 3(x +1/5) -3 1/5

I might choose x-values that are -1/5 ± 1/2 to get y-values that are -3 1/5 + 3/4. And, x = -1/5 ± 1 ⇒ y = -3 1/5 +3.

[tex] - | 4 | < x < - |1| [/tex]

dunno if that's the desired form tough, but it states the same definition

The given inequality rewritten using absolute value sign​ as |-4|<x<|-1|.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is -4<x<-1.

An absolute value inequality is an expression with absolute functions as well as inequality signs.

Here, using absolute value sign​ we get

|-4|<x<|-1|

Therefore, the given inequality rewritten using absolute value sign​ as |-4|<x<|-1|.

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36 is a whole number.

Answer:

The number 3.6 is a rational number.

All numbers that can be represented as fractions made of two integers (whole numbers) are considered to be

Answer:

659604 students

Step-by-step explanation:

86047-31080=54967 more students per game

54967 students per game x 12 games = 659,604 students

4,6,8,10 are in A.P

[tex]\\ \rm\Rrightarrow a_n=a+(n-1)d[/tex]

[tex]\\ \rm\Rrightarrow a_20=4+(20-1)2[/tex]

[tex]\\ \rm\Rrightarrow a_20=4+19(2)[/tex]

[tex]\\ \rm\Rrightarrow a_20=4+38[/tex]

[tex]\\ \rm\Rrightarrow a_20=42[/tex]

I believe that the answers in order are: Rational, Irrational, Irrational, Irrational. I think these answers are correct, but if not, please let me know. Thanks.

Answer:

I think 0.5 and 0/100 are rational

the others are irrational

Answer:

[tex]f(x) = (x + 2)(x - 2)(x - 6)[/tex]

[tex]f(x) = ({x}^{2} + 4)(x - 6)[/tex]

[tex]f(x) = {x}^{3} - 6 {x}^{2} + 4x - 24[/tex]

Step-by-step explanation:

Multiply factors.

Answer:

y=5x+3

Step-by-step explanation:

The equation of line is y=5x+3 since the y intercept is 3

9514 1404 393

Answer:

  (8, 22)

Step-by-step explanation:

For endpoints A and B, and midpoint M, the relationship of interest is ...

  B = 2M -A

  B = 2(3, 10) -(-2, -2) = (6+2, 20+2)

  B = (8, 22)

The other end point is (8, 22).

Step-by-step explanation:

It takes 20 Hours to get to Los Angeles

Now it takes 12 hours....

Therefore we subtract 20 from 12

which becomes

20 - 12= 8.

So it's 8 hours shorter

Asnwer: C

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

Answer:

Step-by-step explanation:

Answer:

(b) 0.30 atm

Step-by-step explanation:

Given data

Initial pressure= 1.2atm

Initial volume= 1.0L

Final volume= 4.0L

Final pressure= ???

Let us apply the gas formula to find the Final pressure

P1V1= P2V2

Substitute

1.2*1= x*4

Divide both sides by 4

1.2/4= x

x= 0.3atm

Hence the final pressure is 0.3 atm

Answer:

Answer A

Step-by-step explanation:

[tex]\displaystyle \lim_{n \to -\infty} (3x^3+28)=-\infty\\\\minimum\ of \ f(x)=6\\\\Answer\ A[/tex]

Step-by-step explanation:

f(1) = 3×1 - 1 = 2

f(4) = 3×4 - 1 = 12-1 = 11

so, the functional value changes 11-2=9 units on an x interval of 4-1=3 units length.

the average change rate is the total change across the x interval relative to the interval length.

that is

9/3 = 3

which is the slope (= the factor of x) in the line equation.

for a line its change rate for any point is the same constant. and that is therefore automatically also the average change rate across an interval of x values.

if the change rate would be different for different parts of the function, it would not be a straight line.

Answer:

3

Step-by-step explanation:

The average rate of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Here [ a, b ] = [ 1, 4 ] , then

f(b) = f(4) = 3(4) - 1 = 12 - 1 = 11

f(a) = f(1) = 3(1) - 1 = 3 - 1 = 2

average rate of change = [tex]\frac{11-2}{4-1}[/tex] = [tex]\frac{9}{3}[/tex] = 3

Answer:

1) 35 gallons by the first car 2) 40 gallons by the second car

Step-by-step explanation:

Suppose the first car used x gallons, when the second car used the rest- 75-x

If the first car's efficiency is 35 miles per galon, its milleage is 35*x, the second car's milleage is 15*(75-x). And the summary milleage is equal to 1825.

35x+15(75-x)=1825

35x+1125-15x= 1825

20x=700

x=35- gallons consumed by the first car,

75-35=40- gallons consumed by the second one

Answer:

Hello,

Answer 303028

Step-by-step explanation:

Multiplication in base 9

[tex]\begin{array}{cccccc}9^5&9^4&9^3&9^2&9^1&9^0\\--&--&--&--&--&--\\&&&7&2&5\\&&&3&6&7\\--&--&--&--&--&--\\&&5&5&8&8\\&4&7&6&3&\\2&3&7&6&&\\--&--&--&--&--&--\\3&0&3&0&2&8\end{array}[/tex]

Solution :

Here the probability that exactly 28 out of 304 students will not graduate on time. That is

P (x = 28)

By using the normal approximation of binomial probability,

[tex]$P(x=a) = P(a-1/2 \leq x \leq a+1/2)$[/tex]

∴ [tex]$P(x=28) = P(28-1/2 \leq x \leq 28+1/2)$[/tex]

                   [tex]$=P(27.5 \leq x \leq 28.5)$[/tex]

That is the area between 27.5 and 28.5

Therefore, the correct option is (e). Area between 27.5 and 28.5

Answer:

y=-2x+10

Step-by-step explanation

Hope this helped

Answer:

x = 9

this is a ratio problem. You can see that 12/6 = 2, so you can also take 18/2 to get 9.

Answer:

the answer is 6

Step-by-step explanation:

Because 6 and x are corresponding angle so that means no matter what ( if u want the answer to how long the line is or what degree the angle is ) the answer is always going to be the same as the one above ( which is 6 )

Hop this helpssss

Answer:

This the right order:

4^2+2^2 = 20

5^2= 25

6^2-6 = 30

howdy!!

yr answer is the third graph!

Answer:

Step-by-step explanation:

g(x) has the smallest minimum value. All three functions share the same domain and the y-intercept is also the same for all three thus options (C),(D), and (E) is correct.

A graph is a diametrical representation of any function between the dependent and independent variables.

For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.

As per the given table,

The minimum value among all functions is -204 which is for g(x).

The domain is the set of x since all function defines the same x thus they have the same domain.

At y-intercept x = 0

Since at x = 0 all function is 3 thus all three will have the same y-intercept.

Hence "The smallest minimal value is for g(x). The y-intercept for all three functions is the same, and all three functions have the same domain".

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Answer:

4.

Step-by-step explanation:

Change of base formula is

logb x = loga x / loga b

So logx 25 = log5 25 /log5 x

Now log5 25 = log5 5^2 = 2, so:

logx 25 = 2 / log5 x

So log5 x^2 * logx 25

= log5 x^2 * 2 /log5 x

= 2 log5 x * 2 / log5 x

= 4.

Answer:

34

Step-by-step explanation:

n = 5

f(5) = 6(5)+4

f(5)=34

The fifth term of the sequence is equal to 34.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expression is f(n) = 6n + 4. The value of the fifth term will be calculated as,

n = 5

f(5) = 6(5)+4

f(5)=34

Therefore, the fifth term of the sequence is equal to 34.

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Answer:

sin = opp/hyp

cos = adj/hyp

tan = opp/adj

Answer:

Step-by-step explanation:

ABCD is a square.

side = 24 cm

Area of square = side  * side = 24 * 24 = 576 cm²

Semicircle:

d = 24 cm

r = 24/2 = 12 cm

Area of semi circle =πr²

                               = 3.14 * 12 * 12

                               = 452.16 cm²

Area of shaded region = area of square - area of semicircle  + area of semicircle

  = 576  - 452.16 + 452.16

  = 576 cm²

Perimeter:

Circumference of semicircle = 2πr

               = 2 * 3.14 * 12

               = 75.36

Perimeter = 2* circumference of semicircle + 24 + 24

                = 2 * 75.36 + 24 + 24

                = 150.72 + 24 + 24

                 = 198.72 cm