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3 years ago

Danielle wants to paint a ceramic planter. The total price is the cost of the

Mathematics

1 answer:

zysi [14]3 years ago

7 0

Answer:

4 hours

Step-by-step explanation:

Danielle spent 4 hours painting. You can get this answer by subtracting how much money she spent on the pot from the total bill. This gets you 24. Then you divide this by 6, the amount of money if costs to paint an hour, which gets you 4.

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A wire b units long is cut into two pieces. One piece is bent into an equilateral triangle and the other is bent into a circle.

mezya [45]

1. Divide wire b in parts x and b-x.

2. Bend the b-x piece to form a triangle with side (b-x)/3

There are many ways to find the area of the equilateral triangle. One is by the formula A= $\frac{1}{2}sin60^{o}side*side= \frac{1}{2} \frac{ \sqrt{3} }{2} (\frac{b-x}{3}) ^{2}= \frac{ \sqrt{3} }{36}(b-x)^{2}$
A= $\frac{ \sqrt{3} }{36}(b-x)^{2}=\frac{ \sqrt{3} }{36}( b^{2}-2bx+ x^{2} )=\frac{ \sqrt{3} }{36}b^{2}-\frac{ \sqrt{3} }{18}bx+ \frac{ \sqrt{3} }{36}x^{2}$

Another way is apply the formula A=1/2*base*altitude,
where the altitude can be found by applying the pythagorean theorem on the triangle with hypothenuse (b-x)/3 and side (b-x)/6

3. Let x be the circumference of the circle.

$2 \pi r=x$

so $r= \frac{x}{2 \pi }$

Area of circle = $\pi r^{2}= \pi ( \frac{x}{2 \pi } )^{2} = \frac{ \pi }{ 4 \pi ^{2} }* x^{2} = \frac{1}{4 \pi } x^{2}$

4. Let f(x)= $\frac{ \sqrt{3} }{36}b^{2}-\frac{ \sqrt{3} }{18}bx+ \frac{ \sqrt{3} }{36}x^{2}+\frac{1}{4 \pi } x^{2}$

be the function of the sum of the areas of the triangle and circle.

5. f(x) is a minimum means f'(x)=0

f'(x)= $\frac{ -\sqrt{3} }{18}b+ \frac{ \sqrt{3} }{18}x+\frac{1}{2 \pi } x$ =0

$\frac{ -\sqrt{3} }{18}b+ \frac{ \sqrt{3} }{18}x+\frac{1}{2 \pi } x=0$

$(\frac{ \sqrt{3} }{18}+\frac{1}{2 \pi }) x=\frac{ \sqrt{3} }{18}b$

$x= \frac{\frac{ \sqrt{3} }{18}b}{(\frac{ \sqrt{3} }{18}+\frac{1}{2 \pi }) }$

6. So one part is $\frac{\frac{ \sqrt{3} }{18}b}{(\frac{ \sqrt{3} }{18}+\frac{1}{2 \pi }) }$ and the other part is b- $\frac{\frac{ \sqrt{3} }{18}b}{(\frac{ \sqrt{3} }{18}+\frac{1}{2 \pi }) }$

4 0

3 years ago

Read 2 more answers

What is the volume of a pyramid 4 cm,4 cm by 12 cm

Alenkinab [10]

Answer:

The volume of pyramid with dimensions 4cm , 4cm by 12cm is $\bold{64 \mathrm{cm}^{3}}$

Solution:

Volume of a pyramid can be found out by using the below formula,

$\bold{v = \frac{1}{3} l w h}$

where,

v is the volume of pyramid

l is the length of pyramid

w is the width of pyramid

h is the height of pyramid

from question, given that l = 4 ; w = 4; h = 12

hence the volume of pyramid for the given dimensions is

$v = \frac{1}{3} \times 4 \times 4 \times 12$

$= 4 \times 4 \times 4$

$= 64 \mathrm{cm}^{3}$

So the volume of pyramid is $\bold{64 \mathrm{cm}^{3}}$

3 0

3 years ago

Which model shows 25%?

Stels [109]

Answer:

The first one shows 25%

In the 1st modal, a whole is divided into 4 and 1 of the 4 is selected or highlighted

And as the whole rectangle is 100% and being divided into four its becomes 100/4% and when we solve we get 100/4=25

And thus its the first modal that shows 25%

In the second case its divide into 3 boxes so.. 100/3% and when we solve we get 33.3333333.......and this is not what we want

THEREFORE, THE CORRECT ANSWER IS 1ST MODAL

8 0

2 years ago

Q # 20 please help to solve

spin [16.1K]

If submarine is at the surface (the initial position) and then dives 375 ft, the coordinate of submarine becomes -375 ft relatively to the initial position. When the submarine dives another 175 ft down, the coordinate of submarine becomes -375-175=-550 ft relatively to the initial position.

Answer: Correct choice is A.

8 0

3 years ago

Box and whisker plots please help!

kotykmax [81]

The correct answer is D. 100%
Each tick counts as 8 so the beginning of the plot would be at 28 which is only 2 from 30 and everything else is on the plot is greater than 30 so the answer would have to be D since 75% would be too little coverage of the plot

5 0

2 years ago