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nirvana33 [79]
3 years ago
5

webassign If a snowball melts so that its surface area decreases at a rate of 6 cm2/min, find the rate at which the diameter dec

reases when the diameter is 10 cm.
Mathematics
1 answer:
drek231 [11]3 years ago
3 0

Answer:

The answer is \frac{3}{10\pi }  cm/min

Step-by-step explanation:

Assuming the snowball is a perfect sphere, then if A denotes the surface area and D the diameter then:

A=4\pi r^{2} = 4\pi (\frac{D}{2} )^{2} =\pi  D^{2}

Differentiating wrt r we have:

\frac{dA}{dD} =2\pi D

We are told that \frac{dA}{dt}= -6 and we want to find \frac{dD}{dt}

By the chain rule we have:

\frac{dA}{dD}=\frac{dA}{dt}.\frac{dt}{dD}=\frac{\frac{dA}{dt} }{\frac{dD}{dt} }

∴2\pi D=-\frac{6}{\frac{dD}{dt} }

∴\frac{dD}{dt}=-\frac{6}{2\pi D}

When D=10 then

\frac{dD}{dt} =-\frac{6}{10*2\pi } =-\frac{3}{10\pi }

The sign (-) shows that the D is decreasing.

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The length of a new rectangular playing field is 3 yards longer than double the width. If the perimeter of the rectangular playi
Romashka-Z-Leto [24]

Answer:

121 x 59 (Dimensions)

Step-by-step explanation:

6x + 6 = 360

Take away 6 from both sides

6x = 354

Divide both sides by 6

x = 59

The length is 2x + 3 because it says 3 more than double the width (lenght is x). You have 2 widths and 2 lengths. The two widths are both x (2x). The two lengths are both 2x + 3 (4x + 6). 2x + 4x + 6 = 6x + 6.

Now input 59 for x

2(59) + 3 = 121

x = 59

Check Your Answer

121 is just one length and 59 is just one width, so you have to multiply both sides by 2 because you have 2 widths and 2 lengths.

121 x 2 = 242

59 x 2 = 118

242 + 118 = 360

8 0
3 years ago
Mrs.Manning is making cookies for the bake sale. She jas 3/4 cup of flour and needs 1/3 cup of flour for her chocolate chip cook
Sedbober [7]

Answer:

<em>The fraction of the flour Mrs. Mannng will use for her chocolate chip cookies is 4/9</em>

Step-by-step explanation:

<u>Fraction of Portion</u>

Suppose we have a number n and another number m such as m>n. The portion or fraction of size n of m is given by the quotient n/m.

For example, 3 pieces of cake out of a total of 6 make them a fraction of 3/6 = 1/2 of the whole cake, i.e. half of the total available.

Mrs. Manning needs 1/3 cup of flour to make cookies for the bake sale. She actually has 3/4 cups of flour. Calculate the fraction of needed against the available flour:

\displaystyle \frac{\frac{1}{3}}{\frac{3}{4}}

The division can be easier performed by multiplying by the reciprocal of the denominator:

\displaystyle \frac{1}{3}\cdot \frac{4}{3}=\frac{1*4}{3*3}

\displaystyle =\frac{4}{9}

The fraction of the flour Mrs. Mannng will use for her chocolate chip cookies is 4/9

3 0
3 years ago
Circle P has a circumference of approximately 75 inches.
photoshop1234 [79]

Answer:

12in is you answer

Step-by-step explanation:

The formula to find circumference is C=2\pi r

so to rearrange to solve for radius that will be r=\frac{C}{2\pi }

=\frac{75}{2\pi }

=11.94in

5 0
3 years ago
The price of a CD on sale is 0.65c, where c is the original price of the CD. What does that mean?
Nuetrik [128]
Hey there!

If the price of a CD on sale is 0.65c, then 0.35 was taken off of the original price. You can find this if you subtract 0.65 from 1, or 65% from 100%. 

Your answer would not be your second option or your fourth option, since the price you're paying is 0.65 of the original price and you are getting 0.35 of the price off. Also, your third option wouldn't be correct either, since 0.35 isn't being added on top of the total price. 

Your answer is your first option. 

Hope this helped you out! :-)
6 0
4 years ago
How many numbers are equal to the sum of two odd, one-digit numbers?
Dennis_Churaev [7]

Answer:

Seven numbers.

Step-by-step explanation:

Finding the numbers, which are equal to the sum of two odd number and it has to be single digit number.

Lets look into numbers which are odd and single digit.

1 = 1+3, 1+5, 1+7, 1+9

∴ Sum of the number is 4,6,8\ and\ 10

3 = 3+5, 3+7, 3+9

∴ Sum of above number is 8,10\ and\ 12

5 = 5+7, 5+9

∴ Sum of above number is 12\ and\ 14

7= 7+9

∴ Sum of above number is 16

Now, accumlating numbers which are fullfiling the criteria, however, making sure no number should get repeated.

∴ Numbers are: 4,6,8,10,12,14\ and\ 16

Hence, there are total 7 numbers, which  are equal to the sum of two odd, one-digit numbers.

4 0
4 years ago
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