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2 years ago

Multiplication property: if angle j equals 30 then 2m angle j equals

Mathematics

1 answer:

EastWind [94]2 years ago

6 0

If m∡J=30, then 2(m∡J) = 2(30) = 60

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A cone-shaped paper drinking cup is to be made to hold 27 cm of water. Find the height h and radius r of the cup that will use t

andreyandreev [35.5K]

Answer:

r = 2.632 cm
h = 3.722 cm

Step-by-step explanation:

The formula for the volume of a cone of radius r and height h is ...

V = (1/3)πr²h

Then r² can be found in terms of h and V as ...

r² = 3V/(πh)

The lateral surface area of the cone is ...

A = (1/2)(2πr)√(r² +h²) = πr√(r² +h²)

The square of the area is ...

T = A² = π²r²(r² +h²)

Substituting for r² using the expression above, we have ...

T = π²(3V/(πh))((3V/(πh) +h²) = 9V²/h² +3πVh

We want to find the minimum, which we can do by setting the derivative to zero.

dT/dh = -18V²/h³ +3πV

This will be zero when ...

3πV = 18V²/h³

h³ = 6V/π . . . . . multiply by h³/(3πV)

For V = 27 cm³, the value of h that minimizes paper area is ...

h = 3∛(6/π) ≈ 3.7221029

The corresponding value of r is ...

r = √(3V/(πh)) = 9/√(π·h) ≈ 2.6319242

The optimal radius is 2.632 cm; the optimal height is 3.722 cm.

_____

The second derivative test applied to T finds that T is always concave upward, so the value we found is a minimum.

Interestingly, the ratio of h to r is √2.

8 0

2 years ago

A motorboat heads upstream a distance of 24 miles on a river whose current is running at 3 miles per hour. The trip up and back

Kryger [21]

To get speed you do Distance/Time.

6 0

2 years ago

Read 2 more answers

Latoya's annual salary is $26,000. A total of $7352.24 will be deducted for taxes and health insurance. She will receive her pay

Anna71 [15]

Step-by-step explanation:

Lets translate this word problem into math.

"Latoya's annual salary is $26,000" = We start with the number 26,000

"A total of $7352.24 will be deducted for taxes and health insurance" = It's the number we started with "deducted" (minus) 7352.24

"She will receive her paycheck monthly in 12 equal installments" = Our number will be divided by 12

"How much will she get paid with each paycheck?" = "Find answer pls thx"

To put it all together...

$\frac{26,000-7,352.24}{12}$

Now all we have to do is solve!

$\frac{26,000-7,352.24}{12}$

Subtract.

$\frac{18,647.76}{12}$

Divide.

$1,553.98$

Answer:

Latoya will get paid $1,553.98 with each paycheck.

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2 years ago

Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 16 yr to 20 yr

Ugo [173]

4/5

just take 16/20 and divde both be 4

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2 years ago

Calvin has 13 coins , all of which are quarters and nickels. The coins are worth $2.45. How many of each coin does Calvin have ?

zalisa [80]

Answer:

Step-by-step explanation:

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2 years ago