4. A sphere with a diameter of 16 mm has the same surface area as the total surface area of a right cylinder with the base diameter equal to the sphere diameter.How high is the cylinder?
O A. 8 mm
OB. 14 mm
O C. 16 mm
O D. 18 mm

Answers

Answer 1

Answer:

Answer: The answer is A, 8 mm.

Step-by-step explanation:

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Alder cut 3 pieces of fabric from a roll. Each piece of fabric she cut is 11/2 yd. long. she has 2 yards of fabric left on the roll. How much fabric was on the roll before she cut it

Answers

1 piece = 11/2 yards long
3 pieces = 11/2 x 3 = 33/2 yard long

She still has 2 yards left,
so the roll has 33/2 + 2 = 37/2 = 18 1/2 yards.

Answer: 18 1/2 yards

Answer:

Step-by-step explanation:

3 One-fourth yd pieces of fabric from a StartFraction 6 Over 8 EndFraction yd piece of fabric.

Sketch the region R defined by 1 ≤ x ≤ 2 and 0 ≤ y ≤ 1/x^3 .a. Find (exactly) the number a such that the line x = a divides R into two parts of equal area.
b. Then find (to 3 decimal places) the number b such that the line y = b divides R into two parts of equal area.

Answers

For part (a), you're looking to find $a$ such that

$\displaystyle\int_1^a(\mathrm dx)/(x^3)=\int_a^2(\mathrm dx)/(x^3)$

You have

$\displaystyle\int_1^a(\mathrm dx)/(x^3)=-\frac1{2x^2}\bigg|_(x=1)^(x=a)=-\frac12\left(\frac1{a^2}-1\right)$

and

$\displaystyle\int_a^2(\mathrm dx)/(x^3)=-\frac1{2x^2}\bigg|_(x=a)^(x=2)=-\frac12\left(\frac14-\frac1{a^2}\right)$

Setting these equal, you get

$\displaystyle-\frac12\left(\frac1{a^2}-1\right)=-\frac12\left(\frac14-\frac1{a^2}\right)\implies a=2√(\frac25)$

For part (b), you have

$y=\frac1{x^3}\implies x=\frac1{\sqrt[3]y}$

and you want to find $b$ such that

$\displaystyle\int_0^(1/8)\mathrm dy+\int_(1/8)^b(\mathrm dy)/(\sqrt[3]y)=\int_b^1(\mathrm dy)/(\sqrt[3]y)$

You have

$\displaystyle\int_0^(1/8)\mathrm dy+\int_(1/8)^b(\mathrm dy)/(y^(1/3))=\frac18+\frac32y^(2/3)\bigg|_(y=1/8)^(y=b)=-frac14+\frac32b^(2/3)$

and

$\displaystyle\int_b^1(\mathrm dy)/(y^(1/3))=\frac32y^(2/3)\bigg|_(y=b)^(y=1)=\frac32-\frac32b^(2/3)$

Setting them equal gives

$-\frac14+\frac32b^(2/3)=\frac32-\frac32b^(2/3)\implies b=\frac7{24}√(\frac73)\approx0.446$

Find the distance between the points.
(1, 6, 3), (-5, 3, 7)

Answers

Answer:

Step-by-step explanation:

HELPPPPPP ASAPPPPPPPPP!!!!!!!!!!

Answers

1877m/min
Just multiple the Miles by the meters, then divide by 60

A manufacturer uses 34 yard of fabric in each skirt.How many yards of fabric will the manufacturer use in 4 skirts? in 7 skirts? in 9 skirts?

Answers

Answer:

She would use 136 yards in 4 skirts, 238 yards in 7 skirts, and 306 yards in 9 skirts. Hope this helps

Step-by-step explanation:

Which method can be used to find the area of the composite shape? 2 semicircles on each side of a rectangle. Decompose the figure into one semicircle and one rectangle and add the areas. Decompose the figure into one semicircle and one rectangle and subtract the areas. Decompose the figure into two semicircles and one rectangle and subtract the areas. Decompose the figure into two semicircles and one rectangle and add the areas.

Answers

Answer:

Decompose the figure into two semicircles and one rectangle and add the areas.

Step-by-step explanation:

A composite shape is a given shape that comprises more than a plane figure. The total area is determined by addition of separate areas of figures making up the composite figure.

When two semicircles are included on the two sides of a rectangle, a composite figure is formed. To determine its area, calculate the individual areas of each semicircle and rectangle, then add the values.

Therefore, decompose the figure into two semicircles and one rectangle and add the areas is the accurate answer.

Answer:

The Answer is (D)

Step-by-step explanation:

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