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3 years ago

Find the inverse of the linear function y=1/2x+3.

Mathematics

2 answers:

Anni [7]3 years ago

7 0

Answer:

2(x-3) = y

Step-by-step explanation:

y = 1/2 x +3

To find the inverse, exchange x and y and then solve for y

Exchange x and y

x = 1/2y +3

Then solve for 3

Subtract 3 from each side

x-3 = 1/2 y -3+3

x-3 = 1/2 y

Multiply each side by 2

2 (x-3) = 1/2 *2 y

2(x-3) = y

This is the inverse

Natasha_Volkova [10]3 years ago

6 0

Interchange the variables:

x = 1/2y + 3

Solve for y:

Subtract 3 from each side:

x-3 = 1/2y

Multiply both sides by 2:

2x-6 = y

Rewrite the equation with y on the left side:

y = 2x-6

Replace y with f^-1(x):

f^-1(x) = 2x-6

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OlgaM077 [116]

The answer should be the third one

6 0

3 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 $=\$(30.91-15.01)M$

$=\$15.90M$

3 0

3 years ago

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Valentin [98]

Remark

At first glance, one would think this problem isn't possible. But if you use the magnifying glass, you see that it is.

Solve

25 carrots puts you somewhere to the left of the shaded area, so C and D are both wrong.

That leaves you with A or B. You need 30 carrots (or just very slightly less) at least to solve this problem. The way to distinguish between A and B is to look at the line that goes from lower right to upper left. When you magnify this graph, you see that at 30 carrots the line or boundary goes through 20 cucumbers. 21 is just very slightly above that and 25 is far above the other line. 21 cucumbers is the only possible right answer for the number of cucumbers. 25 is too high. B is wrong. The answer is A.

4 0

3 years ago

I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS CORRECTLY PLEASE HELP!!!

professor190 [17]

52 kilometers in 4 hours = 52 x 4 = 208 km in 4 hours

Total of 5 hours = 208 km + 62 km = 270 km

Average speed = 270 km / 5 hours = 54 km per hour

Answer

54 km per hour

5 0

3 years ago

Is 4/6 bigger than 5/8

nikitadnepr [17]

4/6=66.67%
5/8=62.5%
Therfore 4/6 is bigger than 5/8

7 0

4 years ago

Read 2 more answers