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3 years ago

The diagram shows a solid cuboid with

Mathematics

1 answer:

nirvana33 [79]3 years ago

7 0

Answer:

$s = (3 \times 4)2 = 24 \\ s =(3 \times 5)2 = 30 \\ s = (4 \times 5)2 = 40 \\ \\ 24 + 30 + 40 = 94$

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A climber is on a hike.after 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet. What is

aniked [119]

75 ft

Hope that helps, Good luck! (:

8 0

3 years ago

DIscrete Math

Daniel [21]

Answer:

Step-by-step explanation:

As the statement is ‘‘if and only if’’ we need to prove two implications

$f : X \rightarrow Y$ is surjective implies there exists a function $h : Y \rightarrow X$ such that $f\circ h = 1_Y$ .
If there exists a function $h : Y \rightarrow X$ such that $f\circ h = 1_Y$ , then $f : X \rightarrow Y$ is surjective

Let us start by the first implication.

Our hypothesis is that the function $f : X \rightarrow Y$ is surjective. From this we know that for every $y\in Y$ there exist, at least, one $x\in X$ such that $y=f(x)$ .

Now, define the sets $X_y = \{x\in X: y=f(x)\}$ . Notice that the set $X_y$ is the pre-image of the element $y$ . Also, from the fact that $f$ is a function we deduce that $X_{y_1}\cap X_{y_2}=\emptyset$ , and because $f$ the sets $X_y$ are no empty.

From each set $X_y$ choose only one element $x_y$ , and notice that $f(x_y)=y$ .

So, we can define the function $h:Y\rightarrow X$ as $h(y)=x_y$ . It is no difficult to conclude that $f\circ h(y) = f(x_y)=y$ . With this we have that $f\circ h=1_Y$ , and the prove is complete.

Now, let us prove the second implication.

We have that there exists a function $h:Y\rightarrow X$ such that $f\circ h=1_Y$ .

Take an element $y\in Y$ , then $f\circ h(y)=y$ . Now, write $x=h(y)$ and notice that $x\in X$ . Also, with this we have that $f(x)=y$ .

So, for every element $y\in Y$ we have found that an element $x\in X$ (recall that $x=h(y)$ ) such that $y=f(x)$ , which is equivalent to the fact that $f$ is surjective. Therefore, the prove is complete.

3 0

3 years ago

A photographer is planning to enlarge a photograph by a scale factor of 1:5 . The original photograph has an area of 154 square

uranmaximum [27]

Whenever you are given a scale factor, that factor will apply to each dimension and because area is a two dimensional measurement, you multiply the area by 5 twice (so x5 x5). This means the new area would be 154x5^2. The new area of the photograph is 3850 square inches.

6 0

3 years ago

I attached the question in the image below

djyliett [7]

Answer:

45°

Step-by-step explanation:

$tan^{-1}(1)$ = 45°