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3 years ago

Why is it important to rename 4 1/4 if you subtract 3/4 from it

1 answer:

4 0

Because 3 2/4 would be the answer when you subtract it and most teachers and/or tests want you to simplify the answer which would be 1/2 because you would divide the numerator and denominator by 2.

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You deposit $6500 into an account paying 8% annual interest compounded monthly. How much money will be in the account after 7 ye

guajiro [1.7K]

Hi! Your answer is 11358.24 dollars. I hope that helps!

3 0

3 years ago

Read 2 more answers

mary has 39 square feet of patio bricks. each square brick has sides 1 foot long. what is the greatest perimeter of a rectangle

bearhunter [10]

-- The smallest perimeter you can make with a certain area
is a circle.

-- The NEXT smallest perimeter with the same area is a square.

 With 1-ft by 1-ft square bricks, the shortest perimeter she could
make would be by using her bricks to make it as square as possible.
Without cutting bricks into pieces, the best she could do would be

 (13 bricks) x (3 bricks) .

= (13-ft) x (3-ft)

 Perimeter = (2 x length) + (2 x width)

 = (2 x 13-ft) + (2 x 3-ft)

 = (26-ft) + (6-ft) = 32 feet <== shortest perimeter.

-- Then, the more UNSQUARE you make it, the more perimeter
it takes to enclose the same area. That means Mary has to make
a rectangle as long and skinny as she can.

The longest perimeter she can make (without cutting bricks into
pieces) is (39 bricks) x (1 brick) .

 = (39-ft) x (1-ft) .

Perimeter = (2 x length) + (2 x width)

 = (2 x 39-ft) + (2 x 1-ft)

 = (78-ft) + (2-ft) = 80 feet .

What she'll have then is a brick path, 39 feet long and 1 foot wide,
and when you walk on it, you'll need to try hard to avoid falling off
because it's only 1 foot wide.

7 0

4 years ago

Rewrite the fraction as a decimal -19/50

Wittaler [7]

To get the decimal you have to divide the numerator by the denominator. -19÷-50=-0.38 -19/50=-0.38

6 0

3 years ago

Scatter plots and Line of Best Fit

m_a_m_a [10]

The answer will be 60+ because 48 minutes is a long time and if youstudy for a long time you memorize more

6 0

4 years ago

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