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3 years ago

Two semicircles are attached to the sides of a rectangle as shown.

Mathematics

2 answers:

Tatiana [17]3 years ago

7 0

Ok so this answer is 194 try an do it you will get this answer

iragen [17]3 years ago

5 0

Answer:

$194\ ft^{2}$

Step-by-step explanation:

we know that

The area of the figure is equal to the area of the rectangle plus the area of one circle (Remember that the area of two semicircles is equal to the area of one circle)

step 1

Find the area of rectangle

The area of rectangle is equal to

$A=bh$

we have

$b=8\ ft$

$h=18\ ft$

substitute

$A=8*18=144\ ft^{2}$

step 2

Find the area of one circle

The area of the circle is equal to

$A=\pi r^{2}$

we have

$r=8/2=4\ ft$

$\pi=3.14$

substitute

$A=(3.14)(4^{2})=50.24\ ft^{2}$

step 3

Find the area of the figure

$144\ ft^{2}+50.24\ ft^{2}=194.24\ ft^{2}$

Round to the nearest whole number

$194.24\ ft^{2}=194\ ft^{2}$

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Mr green makes some compost he mixes soil, manure and leaf mould in the ratio 3:1:2 mr greenmakes 72 literes of the compost. How

love history [14]

Answer:

$36\ liters\ of\ soil$

Step-by-step explanation:

we know that

The ratio of soil, manure and leaf mould is $3:1:2$

That means

For every 6 liters of the compost, he use 3 liters of soil

so by proportion

Find how many liters of soil does he use for 72 liters of compost

$\frac{3}{6}=\frac{x}{72}\\ \\x=3*72/6\\ \\x=36\ liters\ of\ soil$

8 0

3 years ago

Let f(x) = 1/x^2 (a) Use the definition of the derivatve to find f'(x). (b) Find the equation of the tangent line at x=2

Verdich [7]

Answer:

(a) $f'(x)=-\frac{2}{x^3}$

(b) $y=-0.25x+0.75$

Step-by-step explanation:

The given function is

$f(x)=\frac{1}{x^2}$ .... (1)

According to the first principle of the derivative,

$f'(x)=lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}$

$f'(x)=lim_{h\rightarrow 0}\frac{\frac{1}{(x+h)^2}-\frac{1}{x^2}}{h}$

$f'(x)=lim_{h\rightarrow 0}\frac{\frac{x^2-(x+h)^2}{x^2(x+h)^2}}{h}$

$f'(x)=lim_{h\rightarrow 0}\frac{x^2-x^2-2xh-h^2}{hx^2(x+h)^2}$

$f'(x)=lim_{h\rightarrow 0}\frac{-2xh-h^2}{hx^2(x+h)^2}$

$f'(x)=lim_{h\rightarrow 0}\frac{-h(2x+h)}{hx^2(x+h)^2}$

Cancel out common factors.

$f'(x)=lim_{h\rightarrow 0}\frac{-(2x+h)}{x^2(x+h)^2}$

By applying limit, we get

$f'(x)=\frac{-(2x+0)}{x^2(x+0)^2}$

$f'(x)=\frac{-2x)}{x^4}$

$f'(x)=\frac{-2)}{x^3}$ .... (2)

Therefore $f'(x)=-\frac{2}{x^3}$ .

(b)

Put x=2, to find the y-coordinate of point of tangency.

$f(x)=\frac{1}{2^2}=\frac{1}{4}=0.25$

The coordinates of point of tangency are (2,0.25).

The slope of tangent at x=2 is

$m=(\frac{dy}{dx})_{x=2}=f'(x)_{x=2}$

Substitute x=2 in equation 2.

$f'(2)=\frac{-2}{(2)^3}=\frac{-2}{8}=\frac{-1}{4}=-0.25$

The slope of the tangent line at x=2 is -0.25.

The slope of tangent is -0.25 and the tangent passes through the point (2,0.25).

Using point slope form the equation of tangent is

$y-y_1=m(x-x_1)$

$y-0.25=-0.25(x-2)$

$y-0.25=-0.25x+0.5$

$y=-0.25x+0.5+0.25$

$y=-0.25x+0.75$

Therefore the equation of the tangent line at x=2 is y=-0.25x+0.75.

5 0

3 years ago

Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2 and the profit

blondinia [14]

Answer:

Step-by-step explanation: For part 1, it makes sense that the form is y = m + c. So, it is a simply rearrangement of the equation to start with, in order to make the subject. This is the graph in slope-intercept form. From here it is easy to see that gradient = and the y-intercept = 490. The easiest way to draw a straight-line graph, such as this one, is to plot the y-intercept, in this case (0, 490), then plot another point either side of it at a fair distance (for example substitute = -5 and = 5 to procure two more sets of co-ordinates). These can be joined up with a straight line to form a section of the graph, which would otherwise extend infinitely either side - use the specified range in the question for x-values, and do not exceed it (clearly here the limit of -values is 0 ≤ x ≤ 735, since neither x nor y can be negative within the context of the question - the upper limit was found by substituting = 0). In easy terms, the graph of this function represents how the value of the function varies as the value of x varies. Looking back at the question context, this graph specifically represents how many wraps could have been sold at each number of sandwich sales, in order to maintain the same profit of $1470. When the profit is higher, the gradient is not changed (this is defined by the relationship between the $2 and $3 prices, not the overall profit) - instead the -intercept is higher, therefore we have gleaned that the new y-intercept is 531. Clearly I cannot see the third straight line. However the method for finding the equation of a straight line graph is fairly simple:

1. Select two points on the line and write down their coordinates

2. The gradient of the line =

3. Find the change in (Δ

4. Find the change in (Δ

5. Divide the result of stage 3 by the result of stage 4

6. This is your gradient

7. Take one of your sets of coordinates, and arrange them in the form , where your is the gradient you just calculated

8. There is only one variable left, which is (the y-intercept). Simply solve for this

9. Now generalise the equation, in the form , by inputting your gradient and y-intercept whilst leaving the coordinates as and

For example if the two points were (1, 9) and (4, 6):

Δ = 6 - 9 = -3

Δ = 4 - 1 = 3

= = -1

I choose the point (4, 6)

6 = (-1 * 4) + c

6 = c - 4

c = 10

Therefore, generally,

Within the context of the question, I imagine the prices of the two lunch specials will be the same in the third month and hence the gradient will still be - this means steps 1-6 can be omitted. Furthermore if the axes are clearly labelled, you may even be able to just read off the y-intercept and hence dispose with steps 1-8!

4 0

3 years ago

For a treasure hunt game, 300 balls are hidden. Of the balls that ate hidden, 40% of them are yellow and the rest are white. Sal

Mamont248 [21]

300*.4=120
300-120=180

there are 120 yellow balls and 180 white balls.

120*.2=24
180*.8=144

sallys team found 168 balls

4 0

2 years ago

Read 2 more answers

There are 182 seats in a theater. The seats are evenly divided into 13 rows. How many seats are in each rows?

erica [24]

182÷13

Answer: