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3 years ago

If f(x) is defined as follows,

Mathematics

1 answer:

Phantasy [73]3 years ago

5 0

Answer: The required values are

f(-2) = 120, f(0) = 64 and f(1) = 84.

Step-by-step explanation: We are given the following function f(x) :

$f(x)=16x^2+4x+64~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We are to find the values of the following :

$(a)~f(-2),\\\\(b)~f(0),\\\\(c)~f(1).$

To find the values of the function at the given points, we need to substitute the corresponding values of x in equation (i).

Substituting x = -2 in equation (i), we get

$f(-2)=16\times(-2)^2+4\times(-2)+64=64-8+64=120.$

Substituting x = 0 in equation (i), we get

$f(0)=16\times0^2+4\times0+64=0+0+64=64.$

Substituting x = 1 in equation (i), we get

$f(1)=16\times1^2+4\times1+64=16+4+64=84.$

Thus, the required values are

f(-2) = 120, f(0) = 64 and f(1) = 84.

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Assume that the total revenue received from the sale of x items is given by, R(x)equals34 ln (4 x plus 5 ), while the total c

katen-ka-za [31]

Answer:

63 units

Step-by-step explanation:

The profit function P(x) is given by the revenue function minus the cost function:

$P(x) = R(x) - C(x)\\P(x) = 34ln(x+5)-\frac{x}{2}$

The number of units sold 'x' for which the derivate of the profit function is zero, is the number of units that maximizes profit:

$P(x) = 34ln(x+5)-\frac{x}{2}\\P'(x) =0= \frac{34}{x+5}-\frac{1}{2}\\x+5=68\\x=63\ units$

The number of units that should be manufactured so that profit is maximum is 63 units.

5 0

3 years ago

Cheryl has a 14-foot pole that she wants to cut into 4 equal pieces to help support her tomato plants.

Vikki [24]

B 3.5 divide 14 and 4 to get 3.5.

7 0

3 years ago

Read 2 more answers

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Vikki [24]

Answer:

1020.5

Step-by-step explanation:

3.14×(5)^2×13= 1020.5 cubic units

4 0

2 years ago

4 3/5 + 5 1/2 Help me please and thank you

Studentka2010 [4]

Answer:

Step-by-step explanation:

4 3/5 + 5 1/2= (10 1/10)

Step 1: Find the common multiple between the numbers, and simplify-

4 3/5=4 6/10 5 1/2= 5 5/10

Step 2: Convert to improper fractions-

4 6/10 as an improper fraction is 46/10 and 5 5/10 as an improper fraction is 55/10 (Formula for mixed numbers to improper fractions is denominator multiplied by whole number plus numerator)

Step 3: Add numerator of improper fractions, then add back denominator-

46+55=10 1 numerator:101 denominator:10 101/10

Step 4: Convert into mixed number-

101/10= 10 1/10

ANSWER: 10 1/10

5 0

3 years ago

Read 2 more answers

A number has the property that its square is equal to 84 more than five times the number. Enter all numbers that have this prope

Liono4ka [1.6K]

Answer:

The numbers for which the given property hold true are 12 and -7

Step-by-step explanation:

Let the number be $x$ .

As per the given statement:

Square of the number ( $x^{2}$ ) is 84 more than five times of the number ( $5x+84$ ).

Writing in the equation form:

$x^{2} =5x+84$

To find:

All the numbers for which above equation holds true.

Solution:

$x^{2} =5x+84$

Let us solve the above equation by rearranging the terms and then let us find the roots of the equation.

It is a quadratic equation(i.e. maximum power of $x$ is 2) so it will have 2 solutions i.e. 2 values of $x$ for which the above equation will hold true.

$x^{2} -5x-84=0$

Let us factorize the equation.

$\Rightarrow x^{2} -12x+7x-84=0\\\Rightarrow x(x -12)+7(x-12)=0\\\Rightarrow (x+7)(x-12)=0\\\Rightarrow \bold{x=12, -7 }$

So, the numbers for which the given property hold true are 12 and -7.

8 0

3 years ago

If​ f(x) is defined as​ follows,

If f(x) is defined as follows,