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2 years ago

5) A farmer raises turkeys and pigs. There are 15 animals all together. The farmer

Mathematics

1 answer:

nika2105 [10]2 years ago

6 0

Answer:

2 pigs, 13 turkeys

Step-by-step explanation:

34=2t+4p (equation for legs)

t+p=15 (equation for total # of animals) --> t=15-p

substitution:

34=2(15-p)+4p

p=2

plug back in to other equation

t=15-(2)

t= 13

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Please hurry<br> What function is represented in the table?

Natalija [7]

Answer:

B. 3(2^x)

Step-by-step explanation:

3(2^x) is the only function that yielded the given outputs when the inputs were plugged in.

3 0

2 years ago

15 pts. Prove that the function f from R to (0, oo) is bijective if - f(x)=x2 if r- Hint: each piece of the function helps to "c

solniwko [45]

Answer with explanation:

Given the function f from R to $(0,\infty)$

f: $R\rightarrow(0,\infty)$

$-f(x)=x^2$

To prove that the function is objective from R to $(0,\infty)$

Proof:

$f:(0,\infty )\rightarrow(0,\infty)$

When we prove the function is bijective then we proves that function is one-one and onto.

First we prove that function is one-one

Let $f(x_1)=f(x_2)$

$(x_1)^2=(x_2)^2$

Cancel power on both side then we get

$x_1=x_2$

Hence, the function is one-one on domain [tex[(0,\infty)[/tex].

Now , we prove that function is onto function.

Let - f(x)=y

Then we get $y=x^2$

$x=\sqrt y$

The value of y is taken from $(0,\infty)$

Therefore, we can find pre image for every value of y.

Hence, the function is onto function on domain $(0,\infty)$

Therefore, the given $f:R\rightarrow(0.\infty)$ is bijective function on $(0,\infty)$ not on whole domain R .

Hence, proved.

3 0

3 years ago

Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by

11111nata11111 [884]

Answer:

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is 8.217 cubic inches.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the open rectangular box ?

Solution :

Let the height be 'x'.

The length of the box is '11-2x'.

The breadth of the box is '7-2x'.

The volume of the box is $V=l\times b\times h$

$V=(11-2x)\times (7-2x)\times x$

$V=4x^3-36x^2+77x$

Derivate w.r.t x,

$V'(x)=4(3x^2)-2(36x)+77$

$V'(x)=12x^2-72x+77$

The critical point when V'(x)=0

$12x^2-72x+77=0$

Solve by quadratic formula,

$x=\frac{18+\sqrt{93}}{6},\frac{18-\sqrt{93}}{6}$

$x=4.607,1.392$

Derivate again w.r.t x,

$V''(x)=24x-72$

Now, $V''(4.607)=24(4.607)-72=38.568>0$ (+ve)

$V''(1.392)=24(1.392)-72=-38.592$ (-ve)

So, there is maximum at x=1.392.

The length of the box is $l=11-2x$

$l=11-2(1.392)=8.216$

The breadth of the box is $b=7-2x$

$b=7-2(1.392)=4.216$

The height of the box is h=1.392.

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is $V=l\times b\times h$

$V=8.216\times 4.216\times 1.392$

$V=48.217\ in.^3$

The volume of the box is 8.217 cubic inches.

5 0

3 years ago

Is 1,250 More than or less than 1.25

sweet [91]

1,250 is more then 1.25 because it’s a greater number

5 0

2 years ago

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How many ways can you arrange 8 objects?

Sergio [31]

Answer:

40,320

Step-by-step explanation:

The first object in the arrangement can be chosen 8 ways. The second, 7 ways (after the first one is chosen). And so on down to the last object, which will be the only remaining one. Altogether, the number of ways you can arrange the objects is ...

8·7·6·5·4·3·2·1 = 8! = 40,320

7 0

3 years ago

Read 2 more answers