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stepladder [879]

3 years ago

14

Ricardo deposits $30 and it increases by 15% each month how much money will he have in 6 months and what is the linear equation

to represent

1 answer:

aniked [119]3 years ago

3 0

Answer: 207$ I think..

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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

(MATH PROBLEM) v + w at v = 2, w = 5 <br> pls helpp me <br> uwu

raketka [301]

Answer:

7

Step-by-step explanation:

hope this helps:))))))

3 0

2 years ago

Read 2 more answers

5m-8=2m+2 <br><br> what does m equal

vesna_86 [32]

Answer:

m = 10/3

<em>(as a decimal: m = 3.333...)</em>

<em />

Step-by-step explanation:

5m - 8 = 2m + 2

5m - 8 = 2m + 2

- 2m - 2m <em>(make all "m" on one side to isolate variable)</em>

3m - 8 = 2

+ 8 + 8 <em>(get m entirely on 1 side)</em>

3m = 10

÷3 ÷3 <em>(divide by 3 to get 1m)</em>

m = 10/3

<em>(as a decimal: m = 3.333...)</em>

<em />

<em />

hope this helps!! have a lovely day :)

5 0

2 years ago

Please help & show me how you got it! <br>6-7

Nadya [2.5K]

Number 6 the y intercept is 50 because that’s the point where it crosses the y axis and 7 I believe it would be D= 200

4 0

4 years ago

If |x| = 2 does X = 2 or x = -2? What is the solution to x = -2?

Effectus [21]

Both solutions are x<span> = 2 and x = -2 are correct

because
</span>when x = 2 , |2| = 2
and
<span>when x = -2, |-2| = 2

hope it helps</span>

7 0

3 years ago