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puteri [66]
2 years ago
14

Solve 2 log(x) + log(5) = log (80) using the one-to-one property.

Mathematics
1 answer:
vodomira [7]2 years ago
5 0

x=4

Step-by-step explanation:

2log(x)+log(5)=log(80)

log(x^2)+log(5)=log(80)

log(5x^2)=log(80)

5x^2 =80

x^2 =80/5

x^2=16 , taking square root both sides

x=√16

=4

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What is the surface area of this shape?<br> 1 cm<br> 5 cm<br> 4 cm<br> 2 cm<br> 6 cm<br> 3 cm
a_sh-v [17]

Answer:

88 cm²

Step-by-step explanation:

Each square is 1 cm². Count the squares of each face and add them.

Front face (purple): 14 cm²

Back face (hidden): 14 cm²

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Right upper face (orange): 6 cm²

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2 years ago
An aircraft manufacturer wants to determine the best selling price for a new airplane. The company estimates that the initial co
Blizzard [7]

Answer:

(a) C(x)=500+20x-5x^{\frac{3}{4}}+0.01x^2

    p(x)=320-7.7p

    R(x)=(320-7.7p)p=320p-7.7p^2

(b) x=82 \text{planes}

(c) p=\$30.91 M\;\; \text{per plane}

(d) maximum profit =\$ 15.90M

Step-by-step explanation:

Given that,

The company estimates that the initial cost of designing the aeroplane and setting up the factories in which to build it will be 500 million dollars.

The additional cost of manufacturing each plane can be modelled by the function.

m(x)=20x-5x^{\frac{3}{4}}+0.01x^2

(a)  Find the cost, demand (or price), and revenue functions.

   C(x)=500+20x-5x^{\frac{3}{4}}+0.01x^2

   p(x)=320-7.7p

   R(x)=(320-7.7p)p=320p-7.7p^2

(b)  Find the production level that maximizes profit.

    f=R(x)-C(x)

 \Rightarrow f=320p-7.7p^2-(500+20x-5x^{\frac{3}{4}}+0.01x^2)

\Rightarrow df=320dp-15.4pdp-20dx+5(\frac{3}{4} )x^{\frac{-1}{4} }dx-0.02xdx

     x=320-7.7p

     p=\frac{320-x}{7.7}

    \frac{dp}{dx} = \frac{-1}{7.7}

\frac{df}{dx}=\frac{320}{-7.7} -\frac{15.4(320-x) }{7.7(\frac{-1}{7.7} )}-20+5\frac{3}{4} x^{\frac{-1}{4}} -0.02x=0

    \Rightarrow -41.5584+83.1169-0.2597x-20+3.75x^{\frac{-1}{4} }-0.02x=0

   \Rightarrow 21.5585+3.75x^{\frac{-1}{4} }-0.279x=0

   \Rightarrow x=82 \text{planes}

(c)  Find the associated selling price of the aircraft that maximizes profit.

  p=\frac{320-82}{7.7}

\Rightarrow p=\$30.91 M\;\; \text{per plane}

(d)  Find the maximum profit.

Manufacturing cost of one plane is:

m(1)=20-5+0.01

         =\$15.01 M

maximum profit =\$(30.91-15.01)M

                           =\$15.90M

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