Find the quadratic polynomial ax^2+bx+c which best fits the function f(x)=8^x at x=0, in the sense that g(0)=f(0), and f'(0)=g'(0), and f''(0)=g''(0).
g(x)=?

The first thing we are going to do for this case is define variables.

We have then:

w: width

l: length

The perimeter is given by:

[tex] 2w + 2l = 520
[/tex]

The area is given by:

[tex] A = w * l
[/tex]

The area as a function of a variable is:

[tex] A (w) = w * (260-w)
[/tex]

Rewriting we have:

[tex] A (w) = -w ^ 2 + 260w
[/tex]

To obtain the maximum area, we derive:

[tex] A '(w) = -2w + 260
[/tex]

We equal zero and clear the value of w:

[tex] -2w + 260 = 0

2w = 260
[/tex]

[tex] w = \frac{260}{2}

w = 130
[/tex]

Then, the length is given by:

[tex] l = 260 - w

l = 260 - 130

l = 130
[/tex]

Finally, the maximum area obtained is:

[tex] A = w * l

A = 130 * 130

A = 16900
[/tex]

Answer:

A retangle that maximizes the enclosed area has a length of 130 yards and a width of 130 yards.

The maxium area is 16900 square yards

The range of the function h(x) = -8x is all real numbers, as there are no restrictions on the output the function can produce. This is typical of a linear function.

The range of a function refers to the possible outputs it can produce. In the case of the function h(x) = -8x, it is a linear function, and there are no restrictions on the values that x can take, meaning x can be any real number between -∞ and +∞. The output, h(x), therefore, can be any real number, also between -∞ and +∞, given that it will be the result of -8 multiplied by x. Therefore, the range of the function h(x) = -8x is all real numbers from -∞ to +∞.

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Answer:

[tex]x=\frac{3}{16}[/tex]

Step-by-step explanation:

Given : Exponential function [tex]9^{8x}=27[/tex]

We have to solve the given exponential equation.

Consider the given exponential function [tex]9^{8x}=27[/tex]

[tex]\mathrm{Convert\:}9^{8x}\mathrm{\:to\:base\:}3[/tex]

[tex]9^{8x}=\left(3^2\right)^{8x}[/tex]

Function becomes,

[tex]\left(3^2\right)^{8x}=27[/tex]

Convert 27 to base 3, we have,

[tex]\left(3^2\right)^{8x}=3^3[/tex]

Apply exponent rule, [tex]\left(a^b\right)^c=a^{bc}[/tex]

We have, [tex]3^{2\cdot \:8x}=3^3[/tex]

[tex]\mathrm{If\:}a^{f\left(x\right)}=a^{g\left(x\right)}\mathrm{,\:then\:}f\left(x\right)=g\left(x\right)[/tex]

We have,

[tex]2\cdot \:8x=3[/tex]

Simplify, we have,

[tex]16x=3[/tex]

Thus, [tex]x=\frac{3}{16}[/tex]

Answer:

False.

Step-by-step explanation:

Given,

Chord AB Is 3 inches from the center and chord CD is 5 inches from the center of the same circle,

Since, the distance of a chord is inversely proportional to the length of the chord,

That is, the chord that has the smallest distance from the center is largest.

3 < 5

⇒ The distance of chord AB from center < The distance of Chord CD from center

By the above statement,

⇒ The length of chord AB > The length of chord CD.

Hence, the given statement is FALSE.

The cost of 1.1 kilograms of hamburger meat at $5.00 per kilogram is $5.50

Multiply the weight of the meat (1.1 kg) by the price per kilogram ($5.00):

1.1 kg x $5.00/kg = $5.50.

Therefore, it cost Isabella $5.50 to buy 1.1 kilograms of top-quality hamburger meat.

The annual loss of income due to missing one work day every two weeks at $9.29 per hour, working 8 hours per missed day, is $1,932.32.

To calculate the amount of pay being lost each year due to missing one work day every two weeks, we need to consider the weekly work schedule and hourly wage.

The annual loss of income due to missing one day of work every two weeks at an hourly wage of $9.29 is $1,932.32.

Quadratic functions are functions that has a degree of 2. The factored form of the function is (2x-10)(x+8)

Quadratic functions are functions that has a degree of 2. Given the function below;

2x^2 + 6x - 80

Factorize

2x^2+16x - 10x - 80

Group

(2x^2+16x)-(10x+80)

Factor out the GCF

2x(x + 8)-10(x+8)

(2x-10)(x+8)

Hence the factored form of the function is (2x-10)(x+8)

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Answer: The number of air conditioners sold per day in a city and the daily temperature

Step-by-step explanation:

We know that if there is a causal relationship between two variables then one variable is responsible for causing the other variable.

there is no causal relationship between the variables since both are independent variables.

there is no causal relationship between the variables since both are independent variables.

there is no causal relationship between the variables since both are independent variables.

there can be causal relationship between the variables since by increasing  or decreasing temperature the the number of air conditioners sold per day in a city can be increased or decreased respectively.

there is no causal relationship between the variables since both are independent variables.

The sequence alternates between letters and squares of integers. The letters seem to follow a particular positional increment pattern, and the numbers are squares of consecutive positive integers. The missing elements in the sequence are R and 36.

The given sequence is: A, 4, D, H, 16, M, 25, _, _. This sequence appears to have two separate patterns interleaved. One pattern is a sequence of letters and the other is a sequence of numbers. For the letters part, A (1st letter), D (4th letter), H (8th letter), M (13th letter), so the next letters might follow an increasing pattern with the position of the letters in the alphabet. For the numbers, we have 4, 16, 25 which are squares of 2, 4, and 5 respectively. To solve for the next elements in the pattern, we would have to decipher the rule that connects the letters with their positions and the next squares of numbers.

The numbers are squares of consecutive positive integers: 2², 4², 5². The next number is 6² which is 36. Following the pattern in letters, after M (the 13th letter), the next letter should be the letter that is five positions ahead because the interval between the previous letters increased by 3 each time (D is 3 letters after A, H is 4 letters after D, M is 5 letters after H), so the next letter should be R (the 18th letter, which is 5 letters after M).

Therefore, the sequence should continue with R, 36.

To solve the inequality -5r + 6 ≤ -5(r+2), the answer is that this inequality has no solution.

Solve the Inequality:

-5r + 6 ≤ -5(r+2)

Distribute the -5 on the right side: -5r + 6 ≤ -5r - 10

Combine like terms: 6 ≤ -10

Since 6 is not less than or equal to -10, the inequality has no solution.

Answer:

14 questions.

Step-by-step explanation:

We have been given that your teacher tells you to do questions 28 through 41 in your math book for homework. We are asked to find he total number of questions.

Since we need to solve questions 28 through 41, this means we have to solve question number 28 and 41 as well.

We know that 28-37 would be 10 questions and 38-41 would be 4 questions.

[tex]\text{Total questions}=10+4[/tex]

[tex]\text{Total questions}=14[/tex]

Therefore, you need to solve 14 questions to complete the homework.

To write an improper fraction as a mixed number, divide the denominator into the numerator.

Image is provided.

Therefore, the improper fraction 11/9 can be written as the mixed number 1 and 2/9.

Answer:

Always double check first but I am pretty sure that it is 6