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3 years ago

Explain why angle is considered a defined term in geometry.

Mathematics

1 answer:

77julia77 [94]3 years ago

5 0

Answer:

An angle is considered a defined term in geometry because defined terms are terms that have a formal definition and can be defined using other geometrical terms.

Angle: Two rays that share the same endpoint, however, the rays take off in different directions. The area in the middle of the two rays is the angle measure.

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A manufacturing plant earned $80 per man-hour of labor when it opened. Each year, the plant earns an additional 5% per man-hour.

baherus [9]

A function that gives the amount that the plant earns per man-hour t years after it opens is $\mathrm{A}(\mathrm{t})=80 \times 1.05^{\mathrm{t}}$

<h3><u>Solution:</u></h3>

Given that

A manufacturing plant earned $80 per man-hour of labor when it opened.

Each year, the plant earns an additional 5% per man-hour.

Need to write a function that gives the amount A(t) that the plant earns per man-hour t years after it opens.

Amount earned by plant when it is opened = $80 per man-hour

As it is given that each year, the plants earns an additional of 5% per man hour

So Amount earned by plant after one year = $80 + 5% of $80 = 80 ( 1 + 0.05) = (80 x 1.05)

Amount earned by plant after two years is given as:

$=(80 \times 1.05)+5 \% \text { of }(80 \times 1.05)=(80 \times 1.05)(1.05)=80 \times 1.052$

Similarly Amount earned by plant after three years $=80 \times 1.05^{t}$

$\begin{array}{l}{\Rightarrow \text { Amount earned by plant after } t \text { years }=80 \times 1.05^{t}} \\\\ {\Rightarrow \text { Required function } \mathrm{A}(t)=80 \times 1.05^{t}}\end{array}$

Hence a function that gives the amount that the plant earns per man-hour t years after it opens is $\mathrm{A}(t)=80 \times 1.05^{t}$

5 0

3 years ago

Be granted 10 points plus brainliest

BartSMP [9]

Answer:

8 square feet

Step-by-step explanation:

5 0

2 years ago

Water is leaking out of an inverted conical tank at a rate of 6800 cubic centimeters per min at the same time that water is bein

Bad White [126]

Answer:

The rate at which water is being pumped into the tank is 13,913.27 cubic centimetre per minute

Step-by-step explanation:

Given that, the height of the conical tank is 13 meters and diameter is 3 meters.

Radius = $\frac32$ meters

$\therefore \frac{radius }{height}=\frac {\frac{3}{2}}{13}$

$\Rightarrow \frac{radius }{height}=\frac {3}{26}$

$\Rightarrow radius=\frac {3}{26}\times height$ ......(1)

The volume of the cone is $V=\frac13 \pi r^2 h$

Now putting $r=\frac{3}{26} h$

$V=\frac13 \pi (\frac3{26}h)^2 h$

$\Rightarrow V=\frac{3}{676} \pi h^3$

Differentiating with respect to t

$\frac{dV}{dt}=\frac{3}{676}\pi .3h^2 \frac{dh}{dt}$

$\Rightarrow \frac{dV}{dt}=\frac{9}{676}\pi h^2 \frac{dh}{dt}$

Given that, the water level is rising at a rate of 17 cm per minute when the height 1 meter= 100 cm .i.e $\frac{dh}{dt}=17$ cm/min

Putting $\frac{dh}{dt}=17$

$\frac{dV}{dt}=\frac{9}{676}\pi h^2 \times 17$

$\frac{dV}{dt}|_{h=100}=\frac{9}{676}\pi (100)^2 \times 17$

≈7,113 cubic centimetre per minute

The volume of water increases 7,113 cubic centimetre per minute while 6,800 cubic centimetre per minute is leaking out.

It means the required rate at which water is being pumped into the tank is

=(7,113+6,800)cubic centimetre per minute

=13,913 cubic centimetre per minute

4 0

3 years ago

Need help quick Picture provided

goldfiish [28.3K]

Answer:

I think 22.5

Step-by-step explanation:

okay so we know that lines bc and pf equal eachother

18/8 = 2.25 this is the scale factor

10 times 2.25 is. 22.5

I think it would be 22.5

8 0

3 years ago

Given that f(x) = x^2 - 6x + 8 and g(x) = x – 2, find (f.g)(x) and express

Vaselesa [24]

Answer:

(F.g(x))=x^2-10x+24

Step-by-step explanation:

when when we have a composition function, like f of g of x, we put the second function g of x in place of every x in f of x,

so f(x)=x^2-6x+8

and we will put x-2 which is g(x) in the place of every x

so f(g(x))=(x-2)^2-6(x-2)+8

so we ca n simplify that into f(g(x))=x^2-4x+4-6x+12+8

which simplifies to f(g(x))=x^2-10x+24

5 0

2 years ago