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3 years ago

Is the area of a key on a calculator 6.5 mm^2 , 65 mm^2 or 0.65 cm^2?

Mathematics

1 answer:

Lubov Fominskaja [6]3 years ago

3 0

Answer:

65 $mm^2$ or 0.65 $cm^2$ which are exactly the same area

Step-by-step explanation:

Notice that 65 $mm^2$ is exactly the same as 0.65 $cm^2$ .

The most likely answer is 65 $mm^2$ , since 8 mm by 8 mm is a reasonable size for a square shaped key of a hand-held calculator to fit a human finger.

The answer 6.5 $mm^2$ is an area too small (about a square 3 mm by 3 mm which is to small for a human finger. It would be more appropriate for a pen or point of some type.

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Look at these numbers. 0.3,

timama [110]

0.3.......the 3 is in the tenths place
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0.13.....the 3 is in the hundredths place

0.3 is ur answer

8 0

3 years ago

Read 2 more answers

Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant below the line y=5 and betw

vfiekz [6]

First, complete the square in the equation for the second circle to determine its center and radius:

x ² - 10x + y ² = 0

x ² - 10x + 25 + y ² = 25

(x - 5)² + y ² = 5²

So the second circle is centered at (5, 0) with radius 5, while the first circle is centered at the origin with radius √100 = 10.

Now convert each equation into polar coordinates, using

x = r cos(θ)

y = r sin(θ)

Then

x ² + y ² = 100 → r ² = 100 → r = 10

x ² - 10x + y ² = 0 → r ² - 10 r cos(θ) = 0 → r = 10 cos(θ)

y = 5 → r sin(θ) = 5 → r = 5 csc(θ)

See the attached graphic for a plot of the circles and line as well as the bounded region between them. The second circle is tangent to the larger one at the point (10, 0), and is also tangent to y = 5 at the point (0, 5).

Split up the region at 3 angles θ₁, θ₂, and θ₃, which denote the angles θ at which the curves intersect. They are

θ₁ = 0 … … … by solving 10 = 10 cos(θ)

θ₂ = π/6 … … by solving 10 = 5 csc(θ)

θ₃ = 5π/6 … the second solution to 10 = 5 csc(θ)

Then the area of the region is given by a sum of integrals:

$\displaystyle \frac12\left(\left\{\int_0^{\frac\pi6}+\int_{\frac{5\pi}6}^{2\pi}\right\}\left(10^2-(10\cos(\theta))^2\right)\,\mathrm d\theta+\int_{\frac\pi6}^{\frac{5\pi}6}\left((5\csc(\theta))^2-(10\cos(\theta))^2\right)\,\mathrm d\theta\right)$

$=\displaystyle 50\left\{\int_0^{\frac\pi6}+\int_{\frac{5\pi}6}^{2\pi}\right\} \sin^2(\theta)\,\mathrm d\theta+\frac12\int_{\frac\pi6}^{\frac{5\pi}6}\left(25\csc^2(\theta) - 100\cos^2(\theta)\right)\,\mathrm d\theta$

To compute the integrals, use the following identities:

sin²(θ) = (1 - cos(2θ)) / 2

cos²(θ) = (1 + cos(2θ)) / 2

and recall that

d(cot(θ))/dθ = -csc²(θ)

You should end up with an area of

$=\displaystyle25\left(\left\{\int_0^{\frac\pi6}+\int_{\frac{5\pi}6}^{2\pi}\right\}(1-\cos(2\theta))\,\mathrm d\theta-\int_{\frac\pi6}^{\frac{5\pi}6}(1+\cos(2\theta))\,\mathrm d\theta\right)+\frac{25}2\int_{\frac\pi6}^{\frac{5\pi}6}\csc^2(\theta)\,\mathrm d\theta$

$=\boxed{25\sqrt3+\dfrac{125\pi}3}$

We can verify this geometrically:

• the area of the larger circle is 100π

• the area of the smaller circle is 25π

• the area of the circular segment, i.e. the part of the larger circle that is bounded below by the line y = 5, has area 100π/3 - 25√3

Hence the area of the region of interest is

100π - 25π - (100π/3 - 25√3) = 125π/3 + 25√3

as expected.

3 0

3 years ago

What is the distance between (-6, 2) and (8, 10) on a coordinate grid?

lawyer [7]

Answer:

The answer is 2(the square root of 65 )

Step-by-step explanation:

Plug ( -6, 2) and (8, 10) into the distance formula and solve.

Distance = the square root of ((x2 - x1)^2 + (y2 - y1)^2))

Distance = the square root of ((8 - -6)^2 + (10 - 2)^2))

Distance = the square root of (14^2 + 8^2)

Distance = the square root of (196 + 64)

Distance = the square root of 260 which can be simplified to 2(the square root of 64)

5 0

3 years ago

Suppose that in the country of Workanda, the population is 330 million, and 170 million people are working (have a job). If 70 m

zubka84 [21]

Answer:

30%

Step-by-step explanation:

The unemployment rate is 30%

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2 years ago

Which point of intersection is the solution to the system that of equations y= 2/5x-1/2 and y=-1/3x+2/3

harina [27]

Answer:

Are there no options for this question

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3 years ago