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Ad libitum [116K]

2 years ago

6

For the real-valued functions f(x)=2x+3 and g(x)=√x-5, find the composition fog and specify its domain using interval notation.

1 answer:

Burka [1]2 years ago

7 0

Find fog

fog(x)
f(g(x))
f(√x-5)
2√(x-5)+3

For real range the domain

x-5≥0
x≥5

Domain is [5,oo)

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Forces of 9 lbs and 13 lbs act at a 38º angle to each other. Find the magnitude of the resultant force and the angle that the re

fiasKO [112]

Answer: $R=20.84\ lb\quad 22.57^{\circ},15.43^{\circ}$

Step-by-step explanation:

Given

Two forces of 9 and 13 lbs acts $38^{\circ}$ angle to each other

The resultant of the two forces is given by

$\Rightarrow R=\sqrt{a^2+b^2+2ab\cos \theta}$

Insert the values

$\Rightarrow R=\sqrt{9^2+13^2+2(9)(13)\cos 38^{\circ}}\\\Rightarrow R=\sqrt{81+169+184.394}\\\Rightarrow R=\sqrt{434.394}\\\Rightarrow R=20.84\ lb$

Resultant makes an angle of

$\Rightarrow \alpha=\tan^{-1}\left( \dfrac{b\sin \theta}{a+b\cos \theta}\right)\\\\\text{Considering 9 lb force along the x-axis}\\\\\Rightarrow \alpha =\tan^{-1}\left( \dfrac{13\sin 38^{\circ}}{9+13\cos 38^{\circ}}\right)\\\\\Rightarrow \alpha =\tan^{-1}(\dfrac{8}{19.244})\\\\\Rightarrow \alpha=22.57^{\circ}$

So, the resultant makes an angle of $22.57^{\circ}$ with 9 lb force

Angle made with 13 lb force is $38^{\circ}-22.57^{\circ}=15.43^{\circ}$

7 0

3 years ago

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Jason and Martin want to share 3 cookies equally. How much cookie will Jason and Martin each receive? Write an equation and expr

Verdich [7]

Answer: each will get 3/2

Step-by-step explanation:

They will each get a whole cookie with one left over that they can break in half.

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3 years ago

If the diameter of the circle is 6 cm, find its circumference. [Use 3.14 for π.] A) 18.84 cm B) 25.12 cm C) 37.68 cm D) 50.24 cm

agasfer [191]

Circumference = π * d

π=3.14
diameter = 6

3.14 * 6 = 18.84.
The answer is A.

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Solve for A<br> Exact (no rounding, no calculator needed)<br><br> 0 = A^2 + 13A + 36

marysya [2.9K]

Answer:

-4 or -9

Step-by-step explanation:

-a^2-13a-36=0

(-a-4)(a+9)=0

-a-4=0

a+9=0

a= -4, -9

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3 years ago

If 3 out of 10 mammalian cell cultures exposed to ultraviolet (UV) radiation developed chromosomal abnormalities while 9 out of

Zina [86]

Answer:

a) Observational Study

b) Risk in observational study

RR = 9/10/3/10 = 3.0

c) Relative risk when exposed to a common NSAID is 3 out of 10 people

Step-by-step explanation:

A) This is observational study

b) The parameter determined here is the risk in observational study

RR = 9/10/3/10 = 3.0

c) Relative risk of mammalian cell to develop chromosomal abnormalities when exposed to a common NSAID is 3 out of 10 people

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3 years ago