-7+2 Chises: 6 5 -5 9

At 3:00 AM, the temperature was 44 degrees. By 7:00 AM, the temperature had risen to 60 degrees. What was the average change in

White raven [17]

60-44=16
16/4hrs= 4deg per hour

4 0

2 years ago

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

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3. A dish contains 100 candies. Juan removes candies from the dish each day and no

iVinArrow [24]

Answer:

11

Step-by-step explanation:

If i am correct n= the days so with the days adding up day 10 juan would have 55 of the 100 candies, day 11 he would have 66. The statement said at least 64, so it would have to be 64 or the closet amount to 64 but it cannot be lower than 64. So there for 66 is the closest to the given amount, and in order for juan to get 64 he would need to take candies out for 11 days.

7 0

2 years ago

Which statement is true about Angle B P D? Line A B intersect line C D at point P. It is adjacent to Angle A P C. It is compleme

mel-nik [20]

Answer:

It is congruent to Angle A P C

Step-by-step explanation:

we know that

Vertical angles are the angles opposite each other when two lines cross. They are always congruent.

In this problem we have that

$m\angle APC=m\angle BPC$ -----> by vertical angles

see the attached figure to better understand the problem

therefore

It is congruent to Angle A P C

7 0

3 years ago

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amber owns a skateboard shop. amber wants to buy one thousand eight hundred forty six skateboard wheels. skateboard wheels sell

Sonbull [250]

Amber spends $5,307.25 and she can make 461 skateboards.
Divide 1846 by 2 and you get 923, you then multiply that by $5.75 and get $5,307.25.
Then, you'll divide 1,845 by 4 and get 461.5. (she can only make 461 full skateboards.)

8 0

3 years ago