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3 years ago

Graph the function f(x) = 2 √ X +3

Mathematics

1 answer:

Sophie [7]3 years ago

5 0

Answer:

Find the domain for

√

−

y=x-3+2

so that a list of

values can be picked to find a list of points, which will help graphing the radical.

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[

∞

)

[3,∞)

{

≥

}

{x|x≥3}

To find the radical expression end point, substitute the

value

, which is the least value in the domain, into

(

)

√

−

f(x)=x-3+2

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The radical expression end point is

(

)

(3,2)

(

)

(3,2)

Select few

values from the domain. It would be more useful to select the values so that they are next to the

value of the radical expression end point.

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3.41

xy324353.41

Step-by-step explanation:

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Find the greatest common factor: 9a3bc2 + 12ac4 + 15a2b3c 3abc 15a3b3c4 3ac 9a2b2c2

VARVARA [1.3K]

The greatest common factor is 3abc

8 0

4 years ago

A barrel of tomato sauce has spilled on a tile floor. The sauce flow can be expressed with the function r(t) = 2t, where t repre

IrinaVladis [17]

For the answer to the question above, I'll show my solution for the answer below.
Area A = pi r^2
The rate of change of area = d A/ d t = 2 pi r d r/d t 
r= 2t, d r = 2 d t 
This gives 
d A/ d t = 2 pi 2t 2 d t = 8 pi t dt 
Integrate it 
A= 4 pi t^2. 
After t=5, the area will be 100* 3.14 square= 314 square units.

3 0

3 years ago

Read 2 more answers

Rachel babysits the Michaelson’s kids on Saturdays for 4 hours and is paid $12.50 per hour. On Sundays, she babysits at the Smit

NeTakaya

Answer:

She earns $8.00 more on Sunday

Step-by-step explanation:

Saturday 12.50x4=50.00

Sunday 14.50x4=58.00

5 0

3 years ago

White and black shapes are used in a game Some of the shapes are circles All the other shapes are squares The ratio of white to

PIT_PIT [208]

Answer:

The fraction of all shapes which are square in shape is $\frac{23}{32}$ .

Step-by-step explanation:

Given that , in a game , white and black shapes are used. Some of them are circle in shape and remains are square in shape.

The ratio of white to black shapes are 5:11.

Consider 5x= the number of shapes which are white in color.

11x= The number of shapes which are black in color.

There are (5x+11x)= 16x shapes in the game.

The white circle and white square are in the ratio 3:7.

The number of white square is

$=(\textrm{The number of white shape})\times (\frac{7}{3+7})$

$=(5x)\times (\frac{7}{10})$

$=\frac{7x}{2}$

The black circles and black square are in the ratio 3:8

The number of black square is

$=(\textrm{The number of black shape})\times (\frac{8}{3+8})$

$=(11x)\times (\frac{8}{11})$

=8x

Therefore the total number of shape which are square is

$=\frac{7x}{2}+8x$

$=\frac{7x+16x}{2}$

$=\frac{23x}{2}$

The fraction of all shape are square is

$=\frac{\textrm{shape in square}}{\textrm{Total number shape}}$

$=\frac{\frac{23x}{2}}{16x}$

$=\frac{23}{32}$

5 0

4 years ago

The number of bacteria after t hours is given by N(t)=250 e^0.15t a) Find the initial number of bacteria and the rate of growth

Art [367]

Answer:

a) $N_0=250\; k=0.15$

b) 334,858 bacteria

c) 4.67 hours

d) 2 hours

Step-by-step explanation:

a) Initial number of bacteria is the coefficient, that is, 250. And the growth rate is the coefficient besides “t”: 0.15. It’s rate of growth because of its positive sign; when it’s negative, it’s taken as rate of decay.

Another way to see that is the following:

Initial number of bacteria is N(0), which implies $t=0$ . And $N(0)=N_0$ . The process is:

$N(t)=250 e^{0.15t}\\N(0)=250 e^{0.15(0)}\\ N_0=250e^{0}\\N_0=250\cdot1\\ N_0=250$

b) After 2 days means $t=48$ . So, we just replace and operate:

$N(t)=250 e^{0.15t}\\N(48)=250 e^{0.15(48)}\\ N(48)=250e^{7.2}\\N(48)=334,858\;\text{bacteria}$

c) $N(t_1)=4000; \;t_1=?$

$N(t)=250 e^{0.15t}\\4000=250 e^{0.15t_1}\\ \dfrac{4000}{250}= e^{0.15t_1}\\16= e^{0.15t_1}\\ \ln{16}= \ln{e^{0.15t_1}} \\ \ln{16}=0.15t_1 \\ \dfrac{\ln{16}}{0.15}=t_1=4.67\approx 5\;h$

d) $t_2=?\; (N_0→3N_0 \Longrightarrow 250 → 3\cdot250 =750)$

$N(t)=250 e^{0.15t}\\ 750=250 e^{0.15t_2} \\ \ln{3} =\ln{e^{0.15t_2}}\\ t_2=\dfrac{\ln{3}}{0.15} = 2.99 \approx 3\;h$

6 0

3 years ago