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3 years ago

If a(x) = 3x + 1 and b (x) = StartRoot x minus 4 EndRoot, what is the domain of (b circle a) (x)?

Mathematics

1 answer:

Stella [2.4K]3 years ago

8 0

Answer:

The domain is [1,∞)

Step-by-step explanation:

The given functions are:

$a(x)=3x+1$

and

$b(x) = \sqrt{x - 4}$

We want to find the domain of

$(b\circ a)= \sqrt{3x + 1 - 4}$

Simplify to get:

$(b\circ a)= \sqrt{3x -3}$

This function is defined when the expression under the radical is greater or equal to zero.

$3x -3 \geqslant 0 \\ x \geqslant 1$

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MIDDLE SCHOOL MATH- 4 QUESTIONS

Contact [7]

Answer:

( I am assuming that these are all fractions)

1. 14 $\frac{4}{7}$

2. 8

3. $\frac{4}{15}$

4. 5 $\frac{8}{11}$

Step-by-step explanation:

1. First you have to convert 15 into a fraction but it must have the same denominator causing the equation to look like 105/7 - 3/7= 102/7. But you cannot just leave the fraction like that it must be simplified 14 $\frac{4}{7}$

2. Three-fifths of an hour is 36 minutes. You would next multiply 5 by 60 which would the hours into minutes 5 x 60 = 300. You would then divide 300 by 36 which would give you 8.3333333333, which I just simplified it to 8

3. In order for you to multiply a fraction you would first multiply the top then the bottom. 12 x 6= 72, 15 x 18= 270. The fraction would look like 72/270 which is simplified to $\frac{4}{15}$ .

4. First I changed the fractions into improper fractions causing the fraction to look like 36/8 x 14/11 (I got these answers by 8 by 4 then adding 4, then for the next fraction I multiplied 11 by 1 then added 3.) 36 x 14= 1224, 11 x 8= 88 the fraction would look like 1,224/88 you would simplify to 5 $\frac{8}{11}$

Hope this helps

Please tell me if I made any mistakes I enjoy learning from them.

6 0

2 years ago

A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require

Aleksandr-060686 [28]

Answer:

$r\approx 1.084\ feet$

$h\approx 1.084\ feet$

$\displaystyle A=11.07\ ft^2$

Step-by-step explanation:

<u>Optimizing With Derivatives </u>

The procedure to optimize a function (find its maximum or minimum) consists in :

Produce a function which depends on only one variable
Compute the first derivative and set it equal to 0
Find the values for the variable, called critical points
Compute the second derivative
Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 $ft^3$ . The volume of a cylinder is given by

$\displaystyle V=\pi r^2h$

Equating it to 4

$\displaystyle \pi r^2h=4$

Let's solve for h

$\displaystyle h=\frac{4}{\pi r^2}$

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

$\displaystyle A=\pi r^2+2\pi rh$

Replacing the formula of h

$\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )$

Simplifying

$\displaystyle A=\pi r^2+\frac{8}{r}$

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

$\displaystyle A'=2\pi r-\frac{8}{r^2}=0$

Rearranging

$\displaystyle 2\pi r=\frac{8}{r^2}$

Solving for r

$\displaystyle r^3=\frac{4}{\pi }$

$\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet$

Computing h

$\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet$

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

$\displaystyle A''=2\pi+\frac{16}{r^3}$

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.

The minimum area is

$\displaystyle A=\pi(1.084)^2+\frac{8}{1.084}$

$\boxed{ A=11.07\ ft^2}$

8 0

2 years ago

Mike argues the following side lengths can make a triangle. Sam says he is incorrect. Who is correct and why? 3m, 5m, 10m

victus00 [196]

Answer:

Sam is correct

Step-by-step explanation:

The third side is the one with greatest length. To make a triangle the other two lengths have to be greater than the greatest one when combined.

Hope this Helps.

5 0

1 year ago

Read 2 more answers

What is the area of this trapezoid?

Sonbull [250]

Find the area of the square first
Area = Length x Width
Area = 12 x 9
Area = 108

Find the area of the right triangles
Area = 1/2(Length x Base)
Area = 1/2(9 x 2)
Area = 1/2(18)
Area = 9
Since there is 2 triangles multiply by 2
9 x 2 = 18

Now add
108 + 18 = 126
126 is your area

8 0

2 years ago

Read 2 more answers

Witch operation should you do first when you simplify 85+ (25 x 5)?

olya-2409 [2.1K]

Answer:

25X5

Step-by-step explanation:

If you follow the PEMDAS rule the first thing you must do is the equation inside the parenthesis.

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

7 0

2 years ago

Read 2 more answers