Find the area of the trapezoidal cross-section of the irrigation canal shown below. Your answer will be in terms of h, w, and θ.

garri49 [273]

Answer:

It's not specific enough, I'll come back to you!

6 0

2 years ago

A rectangular prism has a length that is 3 inches shorter than the height and a width that is 5 inches longer than the height. F

LUCKY_DIMON [66]

An equation for the volume of the prism as a function of the height is Volume = h³ + 2h² - 15h.

We are given a rectangular prism.
A rectangular prism is no different than a cuboid.
Let the height of the rectangular prism be "h".
The length of the rectangular prism is "h-3".
The width of the rectangular prism is "h+5".
The volume of the rectangular prism is the same as that of the cuboid.
The volume of the rectangular prism is the product of its length, its width, and its height.
The volume of the rectangular prism is (h - 3)*(h + 5)*h.
An equation for the volume of the prism as a function of the height is :
Volume = (h - 3)*(h + 5)*h
Volume = (h² + 2h - 15)*h
Volume = h³ + 2h² - 15h

To learn more about prism, visit :

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5 0

10 months ago

Consider the function f ( x ) = − 2 x 3 + 27 x 2 − 108 x + 9 . For this function there are three important open intervals: ( − [

Darya [45]

Answer:

A=3 and B=6

Step-by-step explanation:

Increasing and Decreasing Intervals of Functions

Given f(x) as a real function and f'(x) its first derivative.

If f'(a)>0 the function is increasing in x=a

If f'(a)<0 the function is decreasing in x=a

If f'(a)=0 the function has a critical point in x=a

As we can see, the critical points may define open intervals where the function has different behaviors.

We have

$f ( x ) = - 2 x^3 + 27 x^2 - 108 x + 9$

Computing the first derivative:

$f' ( x ) = - 6 x^3 + 54 x - 108$

We find the critical points equating f'(x) to zero

$- 6 x^3 + 54 x - 108=0$

Simplifying by -6

$x^2 -9 x +18=0$

We get the critical points

$x=3,\ x=6$

They define the following intervals

$(-\infty,3),\ (3,6),\ (6,+\infty)$

Thus A=3 and B=6

3 0

2 years ago

35% is 7 out of what number?

o-na [289]

Answer:

The number is 20.

Step-by-step explanation:

In this question, it is said that 35% of a number is equal to 7, then what is that number?

So, let the number be x.

Now, according to the question :

$\begin{gathered} \begin{array}{l} \quad{\dashrightarrow{\sf{35 \% \: of \: x = 7}}}\\\\\quad{\dashrightarrow{\sf{\dfrac{35}{100} \: of \: x = 7}}}\\\\\quad{\dashrightarrow{\sf{\dfrac{35}{100} \times x = 7}}}\\\\\quad{\dashrightarrow{\sf{\dfrac{35 \times x}{100} = 7}}}\\\\\quad{\dashrightarrow{\sf{\dfrac{35x}{100} = 7}}}\\\\\quad{\dashrightarrow{\sf{x = 7 \times \dfrac{100}{35}}}}\\\\\quad{\dashrightarrow{\sf{x =\dfrac{700}{35}}}}\\\\ \quad{\dashrightarrow{\sf{x = \cancel{\dfrac{700}{35}}}}}\\\\ \quad{\dashrightarrow{\sf{x =20}}}\\\\ \quad{\star{\underline{\boxed{\tt{\red{x =20}}}}}} \end{array}\end{gathered}$