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3 years ago

Find the area of the shape shown below.

Mathematics

1 answer:

oee [108]3 years ago

7 0

Answer:

=6 units squared

Step-by-step explanation:

area=1/2h(a+b)

=1/2×2(4+2)

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The function A(b) relates the area of a trapezoid with a given height of 12 and

Flura [38]

Answer:

$B(a)=\frac{a}{6}-9$

Step-by-step explanation:

see the attached figure , to better understand the problem

we have

$A(b)=12(\frac{b+9}{2})$

where

A(b) ---> is the trapezoid's area

b ---> is the other base value

Solve the equation for b

That means ----> isolate the variable b

Divide 12 by 2 right side

$A=6(b+9)$

Divide by 6 both sides

$\frac{A}{6}=b+9$

subtract 9 both sides

$\frac{A}{6}-9=b$

Rewrite

$b=\frac{A}{6}-9$

Convert to function notation

$B(a)=\frac{a}{6}-9$

5 0

2 years ago

Please help me with this question, and show working out.

Andre45 [30]

<h3>Answer: 2072.4 square cm</h3>

===============================================================

Explanation:

If you used scissors to cut a vertical slice down the lampshade, then it can be unrolled to form a rectangle.

The horizontal portion of this rectangle is the distance around the circle, which is the perimeter of the circle, or the circumference. That's C = 2pi*r. Check out the diagram below to see what I mean.

The diagram shows that the diameter is 20 cm, so the radius is half that at 20/2 = 10 cm.

The circumference is C = 2*pi*r = 2*pi*10 = 20pi cm exactly

The height of the rectangle is the height of the cylinder, which is h = 30 as shown in the diagram.

The area of the rectangle is length*height = (20pi)*(30) = 600pi square cm exactly.

If we were to use something like pi = 3.14, then its approximate area is 600*pi = 600*3.14 = 1884 square cm

Let's bump this up by 10%. To do so, we'll multiply by 1.10

1.10*1884 = 2072.4

4 0

2 years ago

A household aquarium tank in the shape of a rectangular prism has a base length of 242424 inches (\text{in})(in)(, start text, i

mars1129 [50]

Answer:

The absolute change in the height of the water is 9.5 inches

Step-by-step explanation:

Given

$l =24in$ --- length

$w = 15in$ --- width

$h =12in$ --- height

$V_1 = 900in^3$ --- the volume removed

Required

The absolute change in the height of the water

First, calculate the base area (b):

$b = l * w$

$b =24in * 15in$

$b =360in^2$

The height of the water that was removed is:

<em /> $H = \frac{V_1}{b}$ <em> i.e. the volume of the water removed divided by the base area</em>

$H = \frac{900in^3}{360in^2}$

$H = \frac{900in}{360}$

$H = 2.5in$

The absolute change in height is:

$\triangle H = |h - H|$

$\triangle H = |12in - 2.5in|$

$\triangle H = |9.5in|$

$\triangle H = 9.5in$

8 0

2 years ago

Analyzing a Graph In Exercise, analyze and sketch the graph of the function. Lable any relative extrema, points of inflection, a

Anit [1.1K]

Answer:

Analyzed and Sketched.

Step-by-step explanation:

We are given $y=\frac{\ln\left(5x)}{x^2}$

To sketch the graph we need to find 2 components.

1) First derivative of y with respect to x to determine the interval where function increases and decreases.

2) Second derivative of y with respect to x to determine the interval where function is concave up and concave down.

$y'=\frac{1-2\ln\left(5x)}{x^3}=0$

$x = \sqrt e/5$ is absolute maximum

$y''=\frac{6\ln\left(5x)-5}{x^4}=0$

$x=e^{5/6}/5$ is the point concavity changes from down to up.

Here, x = 0 is vertical asymptote and y = 0 is horizontal asymptote.

The graph is given in the attachment.

4 0

3 years ago

The fourth grade wants to observe Martin Luther king day. They can show a video about his life or have a guest speaker. They can

nalin [4]

The anwser is 6 possible combinations.

8 0

3 years ago