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Wewaii [24]
3 years ago
13

The profit on a teddy bear can be found by using the function P(x) = - 2x2 + 35x - 99 where x is the price of the bear.Calculate

the price that maximizes profit.
Mathematics
1 answer:
Ipatiy [6.2K]3 years ago
8 0

Answer:

x=8.75

Step-by-step explanation:

The price x that maximizes profit is the maximum value of the function, and the maximum value of the function is located at a point where the first derivative of the function is equal to zero. The first derivative is:

P(x) = - 2x^2+35x-99\\P'(x)=-2(2)x^{(2-1)}+35(1)-0\\P'(x)=-4x+35

Using P'(x)=0:

0=-4x+35\\4x=35\\x=35/4\\x=8.75

The minimum value of the function is also at a point where the first derivative of the function is equal to zero. To differentiate if x=8. is a minimum or a maximum obtain the second derivative and evaluate it at x=8.75 if the value P''(x)>0 x is minimum and if P''(x)<0 x is a maximum.

P'(x)=-4x+35\\P''(x)=-4(1)\\P''(x)=-4

Evaluating at x=8.75:

P''(8.75)=-4

Therefore, x=8.75 is the maximum value of the function and it is the price that maximizes profit.

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F(x)=x^4+3, g(x)=x-7 and h(x)=square root of x then f(g(h(x))=
SpyIntel [72]

Answer:

<em>x² - 28x√x + 294x - 1372√x + 2404 </em>

Step-by-step explanation:

f(x) = x^{4} + 3

g(x) = x - 7

h(x) = √x

f(g(h(x))) - ?

g(h(x)) = √x - 7

f(g(h(x))) = (\sqrt{x} -7) ^{4} + 3 = ( √x - 7 )² × ( √x - 7 )² + 3 =

= (x - 14√x + 49)(x - 14√x + 49) + 3 =

= x² - 14x√x + 49x - 14x√x + 196x - 686√x + 49x - 686√x + 2401 + 3 =

=  <em>x² - 28x√x + 294x - 1372√x + 2404</em>

8 0
3 years ago
Which line has a slope of 5/8 and goes through the point (8, 2)
lapo4ka [179]
The slope m and a point (x_{0},\;y_{0}) that the line goes through, give us a equation for the line:

y-y_{0}=m\cdot (x-x_{0})\\\\ y-2=\dfrac{5}{8}\cdot (x-8)\\\\\\ y-2=\dfrac{5}{8}\,x-\dfrac{5}{8}\cdot 8\\\\\\ y-2=\dfrac{5}{8}\,x-5\\\\\\ y=\dfrac{5}{8}\,x-5+2\\\\\\ \boxed{\begin{array}{c} y=\dfrac{5}{8}\,x-3 \end{array}}

6 0
3 years ago
What does n equal in 2(n+5)=-2
KonstantinChe [14]
1. 2n + 2*5 =2
2. 2n + 10 = 2
3. 2n = 2 -10
4. 2n= -8
5. n = -8/2
6. n = -4
6 0
3 years ago
Which equation represents a linear function rule for the following set of ordered pairs?
d1i1m1o1n [39]

The equation that represents the linear function for the set of ordered pairs is: A. y = -3x + 2.

<h3>What is the Equation of a Linear Function?</h3>

Equation of a linear function, where m is the slope and b is the y-intercept, is expressed as y = mx + b.

Find the slope (m):

Slope (m) = change in y/change in x = (-7 -(-4)) / (3 - 2)

Slope (m) = -3/1 = -3

Find b by substituting m = -3 and (1, -1) = (x, y) into y = mx + b:

-1 = -3(1) + b

-1 = -3 + b

-1 + 3 = b

2 = b

b = 2

Substitute m = -3 and b = 2 into y = mx + b

y = -3(x) + 2

y = -3x + 2

Therefore, the equation that represents the linear function for the set of ordered pairs is: A. y = -3x + 2.

Learn more about equation of linear function on:

brainly.com/question/15602982

3 0
3 years ago
Write 19/50 as a decimal and round to the hundredths place
-Dominant- [34]

Answer:

0.38

Step-by-step explanation:

Divide 19 by 50.

4 0
3 years ago
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