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Eduardwww [97]
4 years ago
12

What greater 1,500 mL oe 1.5 L

Mathematics
1 answer:
qwelly [4]4 years ago
7 0

They are equal hope this answer helped. next time do your homework

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For the function​ below, find a formula for the upper sum obtained by dividing the interval [a comma b ][a,b] into n equal subin
Vlad [161]

Answer:

See below

Step-by-step explanation:

We start by dividing the interval [0,4] into n sub-intervals of length 4/n

[0,\displaystyle\frac{4}{n}],[\displaystyle\frac{4}{n},\displaystyle\frac{2*4}{n}],[\displaystyle\frac{2*4}{n},\displaystyle\frac{3*4}{n}],...,[\displaystyle\frac{(n-1)*4}{n},4]

Since f is increasing in the interval [0,4], the upper sum is obtained by evaluating f at the right end of each sub-interval multiplied by 4/n.

Geometrically, these are the areas of the rectangles whose height is f evaluated at the right end of the interval and base 4/n (see picture)

\displaystyle\frac{4}{n}f(\displaystyle\frac{1*4}{n})+\displaystyle\frac{4}{n}f(\displaystyle\frac{2*4}{n})+...+\displaystyle\frac{4}{n}f(\displaystyle\frac{n*4}{n})=\\\\=\displaystyle\frac{4}{n}((\displaystyle\frac{1*4}{n})^2+3+(\displaystyle\frac{2*4}{n})^2+3+...+(\displaystyle\frac{n*4}{n})^2+3)=\\\\\displaystyle\frac{4}{n}((1^2+2^2+...+n^2)\displaystyle\frac{4^2}{n^2}+3n)=\\\\\displaystyle\frac{4^3}{n^3}(1^2+2^2+...+n^2)+12

but  

1^2+2^2+...+n^2=\displaystyle\frac{n(n+1)(2n+1)}{6}

so the upper sum equals

\displaystyle\frac{4^3}{n^3}(1^2+2^2+...+n^2)+12=\displaystyle\frac{4^3}{n^3}\displaystyle\frac{n(n+1)(2n+1)}{6}+12=\\\\\displaystyle\frac{4^3}{6}(2+\displaystyle\frac{3}{n}+\displaystyle\frac{1}{n^2})+12

When n\rightarrow \infty both \displaystyle\frac{3}{n} and \displaystyle\frac{1}{n^2} tend to zero and the upper sum tends to

\displaystyle\frac{4^3}{3}+12=\displaystyle\frac{100}{3}

8 0
4 years ago
I need help asap!!!!!
Sladkaya [172]

The surface area of the trash can = 25.12 ft²

Solution:

The given image is splitted into two shapes.

One is Cylinder and the other is hemisphere.

Radius of the cylinder = 2 ÷ 2 = 1 ft

Height of the cylinder = 4 – 1 = 3 ft

Curved surface area of the cylinder = 2\pi rh

                                                            =2\times 3.14 \times 1 \times 3

                                                            = 18.84 ft²

Curved surface area of the cylinder = 18.84 ft²

Curved surface area of the hemisphere = 2 \pi r^2

                                                                  = 2\times 3.14 \times 1^2

                                                                  = 6.28  ft²

Curved surface area of the hemisphere = 6.28  ft²

Surface area of the trash = CSA of cylinder + CSA of hemisphere

                                           = 18.84 ft² + 6.28 ft²

                                           = 25.12 ft²

The surface area of the trash can = 25.12 ft²

6 0
4 years ago
A baseball team won 75% of its games. If the team played 48 games, how many games did it win?
Troyanec [42]
The team won 36 games. 0.75 multiplied by 48.
4 0
3 years ago
Read 2 more answers
At another theater, workers have to cut a new trap door. The door can be no more than 137 square feet in area, with whole-number
otez555 [7]

Answer:

Step-by-step explanation:

Given:

trap door = 130 square feet.

1st item: 6ft 5in wide & 8ft 9in long

⇒ (6ft * 12 in) + 5 in & (8ft *12 in) + 9 in

⇒ 77inches by 105 inches

⇒ 8,085 square inches

2nd item: 13ft 4in wide & 7ft 8in long

⇒ (13ft * 12in)+ 4 in & (7ft *12in) + 8 in

⇒ 160 inches by 92 inches

⇒ 14,720 square inches

3rd item: 5ft 6in wide & 12ft 4in long

⇒ (5 ft * 12in) + 6 in & (12ft * 12in) + 4in

⇒ 66 inches by 148 inches

⇒ 9,768 square inches

130 square feet convert to square inches.

130 sq. ft * 144 sq.in/sq.ft = 18,720 sq. in

18,720 sq. in / 160 inches = 117 inches

Length = 160 inches ; Width = 117 inches

Perimeter = 2(160 + 117)

P = 2(277)

P = 554 inches

4 0
3 years ago
Debra has 2/3 of a pound of loose green tea leaves. If she wants to keep one-half of the tea at home and the other half at work,
Elena L [17]

Answer:

1/3

Step-by-step explanation: she keeps 1/3 at home and takes the other 1/3 to work

5 0
4 years ago
Read 2 more answers
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