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3 years ago

What number represents thr same amount as 3 hundreds + 4 tens + 16 ones

Mathematics

2 answers:

Anna007 [38]3 years ago

5 0

356 because:

300
+. 40
16
_______
3 5 6

PilotLPTM [1.2K]3 years ago

3 0

Answer:

356

Step-by-step explanation:

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Norma-Jean [14]

Answer:

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Step-by-step explanation:

6 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

Diana ,and Jennifer and Christina are making class for the craft fair Diana has made three tenths of her Jennifer has made Two f

Sladkaya [172]

A- Christina
B-Diana

4 0

3 years ago

3 Prove that cos130°+cos 110+ cos10=0

Evgesh-ka [11]

We know, cos A + cos B = 2cos(C+D)/2 × cos(C - D)/2

So,

cos 130 + cos 110 + cos 10

cos 130 + 2cos (110+10)/2 × cos( 110-10)/2

cos 130 + 2cos 60 × cos 50

cos ( 180 - 50 ) + 2cos60 cos 50

We know, cos ( 180 - A ) = -cos A

2cos 60 cos 50 - cos 50

Also, cos 60 = 0.5

2×0.5 cos 50 - cos50

cos 50 - cos 50

0 = RHS.

Hence proved

5 0

3 years ago

A model of a human heart is 14 ft tall. If the scale used is 1 ft: 1/4 inch, how tall is the actual heart?

Simora [160]

The actual height of the heart is 3.5 inches

14 * .25 = 3.5 inches

I hope this helps :)

6 0

3 years ago