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3 years ago

What is 1 3/4 divided by 2/5

Mathematics

1 answer:

sveta [45]3 years ago

6 0

Answer:

35/8

Step-by-step explanation:

1 3/4 = 1 + 3/4 = 4/4 + 3/4 = 7/4.

So 1 3/4 ÷ 2/5 = 7/4 × 5/2 = 35/8.

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A norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. Find the dimensions of a norman

Yanka [14]

Answer:

$W\approx 8.72$ and $L\approx 15.57$ .

Step-by-step explanation:

Please find the attachment.

We have been given that a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. The total perimeter is 38 feet.

The perimeter of the window will be equal to three sides of rectangle plus half the perimeter of circle. We can represent our given information in an equation as:

$2L+W+\frac{1}{2}(2\pi r)=38$

We can see that diameter of semicircle is W. We know that diameter is twice the radius, so we will get:

$2L+W+\frac{1}{2}(2r\pi)=38$

$2L+W+\frac{\pi}{2}W=38$

Let us find area of window equation as:

$\text{Area}=W\cdot L+\frac{1}{2}(\pi r^2)$

$\text{Area}=W\cdot L+\frac{1}{2}(\pi (\frac{W}{2})^2)$

$\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W}{2})^2)$

$\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W^2}{4})$

$\text{Area}=W\cdot L+\frac{\pi}{8}W^2$

Now, we will solve for L is terms W from perimeter equation as:

$L=38-(W+\frac{\pi }{2}W)$

Substitute this value in area equation:

$A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2$

Since we need the area of window to maximize, so we need to optimize area equation.

$A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2$

$A=38W-W^2-\frac{\pi }{2}W^2+\frac{\pi}{8}W^2$

Let us find derivative of area equation as:

$A'=38-2W-\frac{2\pi }{2}W+\frac{2\pi}{8}W$

$A'=38-2W-\pi W+\frac{\pi}{4}W$

$A'=38-2W-\frac{4\pi W}{4}+\frac{\pi}{4}W$

$A'=38-2W-\frac{3\pi W}{4}$

To find maxima, we will equate first derivative equal to 0 as:

$38-2W-\frac{3\pi W}{4}=0$

$-2W-\frac{3\pi W}{4}=-38$

$\frac{-8W-3\pi W}{4}=-38$

$\frac{-8W-3\pi W}{4}*4=-38*4$

$-8W-3\pi W=-152$

$8W+3\pi W=152$

$W(8+3\pi)=152$

$W=\frac{152}{8+3\pi}$

$W=8.723210$

$W\approx 8.72$

Upon substituting $W=8.723210$ in equation $L=38-(W+\frac{\pi }{2}W)$ , we will get:

$L=38-(8.723210+\frac{\pi }{2}8.723210)$

$L=38-(8.723210+\frac{8.723210\pi }{2})$

$L=38-(8.723210+\frac{27.40477245}{2})$

$L=38-(8.723210+13.70238622)$

$L=38-(22.42559622)$

$L=15.57440378$

$L\approx 15.57$

Therefore, the dimensions of the window that will maximize the area would be $W\approx 8.72$ and $L\approx 15.57$ .

8 0

3 years ago

Ryker wants a new car. The dealership offers him a loan at 9% annual interest for 6 years. If Ryker wants to do some calculation

Contact [7]

The monthly interest rate is 0.75%

Step-by-step explanation:

The rate of interest= 9%

Total time = 6years

Interest rate per month = 9/12

= 0.75%

Monthly payment =cost of the car + 0.75% of cost of car

Interest per month is 0.75%

3 0

3 years ago

If m = -2 and p=3, then (4p-m)/mp is

ddd [48]

Answer:

-2 1/3

Step-by-step explanation:

((4 * 3) - (-2) /(-2*3)

(12 + 2 ) / (-2 * 3)

14 / -6

-2 1/3

7 0

2 years ago

What's the fraction root of 9 over 49?

irakobra [83]

√9/49

First you figure out the square root of 9 which is 3 since 3 x 3 equals 9. Then you find the square root of 49 which is 7 since 7 x 7 equals 49. Therefore, the answer is 3/7

5 0

3 years ago

Find the number of sides of a regular polygon in which the measure of an interior angle is three times the measure of an exterio

Serhud [2]

The sum of the interior angles of any polygon is given by (n-2)180°, where n is the number of sides.

Also sum of all the exterior angles of any polygon is 360°

Given (n-2)180° = 3(360°)

=> n-2 = 6

=> n = 8.

Hence the number of sides of a polygon is 8

6 0

2 years ago

What is 1 3/4 divided by 2/5​

What is 1 3/4 divided by 2/5