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lyudmila [28]
3 years ago
9

A banner in the shape of an isosceles triangle is hung over the side of a building. The banner has a base of 30ft (at the roof),

a height of 20ft, and weighs 50lb. Write down an integral for the work required to lift the banner entirely onto the roof of the building.
Mathematics
1 answer:
Rashid [163]3 years ago
7 0

Answer:

W = 9600000 joules

Step-by-step explanation:

From the given information:

The area of the banner = 1/2 × 30 × 20 = 300 ft²

The mass of the banner = 300 × 50 = 15000 pounds

Now; the integral for the required work is:

W = \int^h_o F \ ds

here;

h = height of the building

F = mg = 15000g

g = 32 ft/s²

Therefore;

W = \int ^h_o 15000g \ ds

W = \int ^{20}_0 \ 15000 (32)(20)

W = 9600000 joules

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A tech company bought a number of computers for its employees: 66 costing \$1600$1600 each, 44 costing \$1200$1200 each, and yy
daser333 [38]

Answer:

5

Step-by-step explanation:

A tech company bought a number of computers for its employees: 6 costing $1600 each, 4 costing $1200 each, and y costing $900 each, where y is a positive odd integer. what is the greatest possible value of y

Solution:

The median of a group of numbers is the middle number when the group of numbers have been arranged either in ascending of descending other. The median of an even group of numbers is the average of the two most middle most numbers while the median of an odd group of numbers is the middle number.

Since there are 6 computers costing $1600, 4 computers costing $1200 each and y computers costing $900 each. Since y is odd, hence y + 6 + 4 would be odd and the median would be the middle number.

Given that the median price = $1200, this means that the middle of the group of numbers is $1200

900, 900, ..., 1200, 1200, 1200, 1200, 1600, 1600, 1600, 1600, 1600, 1600

Since y is odd, for the median price to be $1200, y has to be 3 or 5.

If y = 3:

900, 900, 900, 1200, 1200, 1200, 1200, 1600, 1600, 1600, 1600, 1600, 1600

median = $1200

If y = 5:

900, 900, 900, 900, 900, 1200, 1200, 1200, 1200, 1600, 1600, 1600, 1600, 1600, 1600

Median = $1200

Therefore the greatest possible value of y is 5

5 0
3 years ago
Find the volume of a right circular cone that has a height of 16.8 in and a base with a
alexgriva [62]

Answer:

Volume of right circular cone is 388.43 in³

Step-by-step explanation:

Height of circular cone = 16.8 in

Radius of circular cone = 4.7 in

We need to find Volume of right circular cone

The formula used for calculating volume of a right circular cone is: Volume=\pi r^2\frac{h}{3}

Putting values and finding volume

Volume=\pi r^2\frac{h}{3}\\Volume=3.14\times (4.7)^2 \times \frac{16.8}{3}\\Volume=3.14\times 22.09 \times 5.6\\Volume= 388.43 \:in^3

So, Volume of right circular cone is 388.43 in³

5 0
2 years ago
The following data show the weight, in ounces, of 10 different bags of candy:
LuckyWell [14K]
B) is correct; on average, each bag of candy has a weight that is 2.6 oz different than the mean weight of 5 oz.

To find the mean absolute deviation, we first find the mean.  Find the sum of the data points and divide by the number of data points (without the outlier, 21, in it):
(10+3+7+3+4+6+10+1+2+4)/10 = 50/10 = 5

Now we find the difference between each data point and the mean, take its absolute value, and find their sum:
|10-5|+|3-5|+|7-5|+|3-5|+|4-5|+|6-5|+|10-5|+|1-5|+|2-5|+|4-5| =
5+2+2+2+1+1+5+4+3+1 = 26

We now divide this by the number of data points:
26/10 = 2.6

This is a measure of how much each bag of candy varies from the mean.
4 0
3 years ago
Read 2 more answers
Factor 3x^2 - 14x + 8​
atroni [7]

Answer: (3x- 2)(x-4)

Factor by grouping.

6 0
3 years ago
Read 2 more answers
Timothy put $300 in a bank that pays 7% interest rate, if he leaves his interest from the first year in the bank, how much money
andriy [413]

Answer: he would have $343.47 after 2 years.

Step-by-step explanation:

if he leaves his interest from the first year in the bank, we would assume that his interest was compounded. We would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = $300

r = 7% = 7/100 = 0.07

n = 1 because it was compounded once in a year.

t = 2 years

Therefore,.

A = 300(1 + 0.07/1)^1 × 2

A = 300(1.07)^2

A = $343.47

7 0
3 years ago
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