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2 years ago

In the following shape, two semicircles

Mathematics

1 answer:

Andrei [34K]2 years ago

8 0

Answer:

The length around the figure in terms of r is 2r ( $\pi$ + 4).

Step-by-step explanation:

The perimeter of an object is the total length of the boundary of the object.

The figure consists two similar semicircle and a rectangle.

Adding the two semicircles, a complete circle is formed. The circumference of a circle = 2 $\pi$ r.

The rectangle has a length which is twice its height.

i.e l = 2h

But,

r = $\frac{h}{2}$ (the diameters of the semicircles equal the height of the rectangle)

⇒ h = 2r

Thus, one side length of rectangle = 2 × 2r (l = 2 × h)

= 4r

The length around the figure in terms of r is:

= 2 $\pi$ r + 4r + 4r

= 2 $\pi$ r + 8r

= 2r ( $\pi$ + 4)

The length around the figure in terms of r is 2r ( $\pi$ + 4).

You might be interested in

How do you use a number line to solve 235+123

Novosadov [1.4K]

Number line refers to a mathematical process of solving the equation with the use of lines.
=> 235 + 123
Starting from 0 you count 1 up to 235. Then starting from 235 you additionally count another 123.
Then from zero start counting the total number to the line you stopped when adding 123 to 235.

This simply equals to
=> 235 + 123
=> 358.
Pls. see attached image for illustration of number line.Answer here

6 0

2 years ago

The speed, s, of the current in a certain whirlpool is modeled by s=300/d, where d is the distance from the center of the whirlp

Ivan

Answer:

The answer is C. As you move closer to the center of the whirlpool, the speed of the current approaches infinity.

This means the closer you get, the faster you go, and the further the distance is the slower the speed. Hope this helps!

(Btw I got this right on the test)

6 0

2 years ago

Read 2 more answers

Which statements describe a residual plot for a line of best fit that is a good model for a scatterplot? Check all that apply. T

lidiya [134]

Answer:

The points are randomly scattered with no clear pattern

The number of points is equal to those in the scatterplot.

Step-by-step explanation:

The points in the residual plot of the line of best fit that is a good model for a scatterplot are randomly scattered with no clear pattern (like a line or a curve).

The number of points in the residual plot is always equal to those in the scatterplot.

It doesn't matter if there are about the same number of points above the x-axis as below it, in the residual plot.

The y-coordinates of the points are not the same as the points in the scatterplot.

8 0

2 years ago

Read 2 more answers

Foggy Optics, Inc., makes laboratory microscopes. Setting up each production run costs $2500. Insurance costs, based on the aver

Ray Of Light [21]

Answer: 4

Step-by-step explanation:

Let N be the total number of runs.

The microscopes per year will be equal to the total number of runs * microscopes per run

total number of microscopes = total number of runs * microscopes per run

now we have each run to cost 2500, therefore:

run costs = 2500 * total runs = 2500*N

we also have insurance and storage costs (note the average thats why we divide by 2):

storage costs = 20* microscopes per run /2 = 20*N/2

insurance costs = 15 * microscopes per run = 15*N

the costs are:

costs = run costs + storage + insurance

now the comany sells 1600 microscopes a year, so in order to figure out the number of microscopes per run we divide 1600 by the total number of runs N and replace in the costs

costs = 2500N + 40000/N => C(N) = 2500N + 40000/N

now derivate the function with respect to N and equal to 0:

$\frac{d}{dN}(2500N + 40000/N) = 2500(1-16/N^2) \\\\ 2500(1-16/N^2) = 0\\$

this gives you two solutions, N = -4 which is not eligible (you cant make negative microscopes lol) and N = 4 which is the answer

have a nice day

4 0

2 years ago

Trapezoid STUV with vertices S(-3,6),T(0,7),U(1,4),and V(-5,2): (x,y)>(x+7,y-9)

hjlf

Answer:

See below

Step-by-step explanation:

Given points:

S(-3,6),T(0,7),U(1,4),and V(-5,2)

Translation rule:

(x,y) → (x+7,y-9)

New coordinates by applying the rule:

S'(4, -3), T'(7, -2), U'(8, -5), V'(2, -7)

See attached for the graph

The blue trapezoid is STUV and the red one is S'T'U'V'

7 0

2 years ago