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BlackZzzverrR [31]

3 years ago

7

You’re looking at the apple pie nutrition label above. Find the number of calories in 1 g. Use the calories in a serving in the

grams in a serving to figure this out. Show your work and answer with a sentence in correct units round to the nearest 10th of a gram

1 answer:

Serggg [28]3 years ago

8 0

Answer i think 588

Step-by-step explanation:

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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 57,909,000 in scientific notation?

LenaWriter [7]

Hello,

Shall we begin?

<span>57,909,000
</span>
= 5.7909 * 10 ^7

Answers: 5.7909 * 10 ^7

5 0

3 years ago

a tree 20 feet tall with a circumference of 3 ft has a vine wound around 7 times. How long is the vine?

FinnZ [79.3K]

If the tree is 20 feet tall with circumference 3 feet then the length of vince is around 21 feet.

Given the height of tree is 20 feet and the circumference of tree is 3 feet.

We have to find the length of vine.

Circumference is the perimeter of a circular object. Because the trunk of a tree is in shape of circle so the perimeter of the trunk is 2πr.

We have been given the circumference of tree be 3 feet.

Circumference=2πr

Because vine is 7 times the circumference so the length of vine being:

Length of vine=7*3

=21 feet.

Hence if the tree is 20 feet tall with circumference 3 feet then the vince is around 21 feet long.

Learn more about circumference at brainly.com/question/20489969

#SPJ1

4 0

2 years ago

Read 2 more answers

Solve each equation. Check your solution.<br> 9= 4a + 13<br> Oa. -16<br> Ob. -1<br> c. 1<br> Od 5

Paha777 [63]

Answer:

b. -1

Step-by-step explanation:

9=4a+13

-13 -13

--------------

-4=4a

4a/-4

a=-1

4 0

3 years ago

Consider the glven solids with the dimensions shown. Which solids are similar?

never [62]

Answer:

A) only figure 1 and figure 2

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers