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Ket [755]
3 years ago
11

Help me, Thanks!!

Mathematics
1 answer:
Marrrta [24]3 years ago
5 0

2.) dT/dt = -t^2 + 3t

dT = (-t^2 + 3t)dt

T = -t^3/3 + 3t^2/2 + C

at 4:00 AM

80 = -4^3/3 + 3*4^2/2 + C

C = 80 + 4^3/3 - 3*4^2/2

C = 77.33

T = -t^3/3 + 3t^2/2 + 77.33

at 8:00 AM

T = -8^3/3 + 3*8^2/2 + 77.33

T = 2.67 deg

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I need help finding both volume and surface area
Svetradugi [14.3K]

Answer:

<u>Volume</u>

For the rectangle, h = 3cm, l = 8cm, w = 6cm
V = length x width x height
V = 8cm x 6cm x 3cm
V = 144cm^3

For the semi circle, we need to find the radius. The radius is width/2, so 6cm/2 = 3cm. r = 3cm, \pi = 3.14
V = radius^2 x height x \pi
V = 3cm^2 x 3cm x 3.14
V = 84.8 cm^3/2 (because the cylinder needs to be divided to form a semi-circle)
V= 42.4cm^3 (there are two cylinders though so we will multiply this by 2 in the total volume)

Total volume:
V = 144cm^3 + 42.4cm^3(2)
V = 186.4cm^3

<u>Surface Area</u>

Rectangular prism:
A = 2[w(l) + h(l) + h(w)]
A = 2[6cm(8cm) + 3cm(8cm) + 3cm(6cm)]
A = 180cm^2
But there are two sides that are covered by the semi-circular prisms, so we will have to calculate those sides and remove them.
A = l x w
A = 6cm x 3cm
A = 18cm^2(2) (2 being the two faces)
A = 36cm^2

A = 180cm^2 - 36cm^2
A = 144cm^2 (the area of the rectangle)

Semi-circular prism:
A = 2\pirh + 2\pir^2
Earlier, we found out that the radius of the circle is 3cm, so we will plug that in.
A = 2(3.14)(3cm)(3cm) + 2(3.14)(3cm)^2
A = 113.09cm^2

Total surface area:
A = 144cm^2 + 133.09cm^2
A = 277.09cm^2

Therefore the total volume of the prism is 186.4cm^3 and the total surface area is 277.09cm^2.





6 0
2 years ago
Determine the mean, median, mode, and range for the data set:
s2008m [1.1K]

Answer:

Step-by-step explanation:

Mean (Average): 8

Median (Middle): 8

Mode (Most Common): 8

Range (Biggest - Smallest): 7

6 0
3 years ago
Barbara deposited $300 in the bank. If the bank pays her simple interest at the rate of 4 percent per year, how much money will
grigory [225]

Answer:

309

Step-by-step explanation:

The formula for simple interest is

A = P(1 + rt)

where A is the amount of money in the account

P is the principal invested

r is the interest rate in decimal form

t is the time invested in years

We know

P = 300

r = 4% = .04

t = 9 months = 9 months * 1 year/12 months = .75 year

Substituting into the equation

A = 300(1 + .04*.75)

  =300 (1+.03)

  =300(1.03)

   = 309

4 0
3 years ago
Silvio created a table of the possible outcomes of spinning a spinner divided into 4 equal sections labeled A, B, C, and D and r
fgiga [73]

Answer:

there is a 1/4 chance of getting a on the spinner and there is a 50% percent chance of getting less than 4 on the die.

Step-by-step explanation:

because there are 4 spaces and one answer is shown so yeah

3 0
3 years ago
Given that f(x)=x^2-7x-1, g(x)=2x-3, and h(x)=4x-5 find each function. (f+g)(x)
Alexxandr [17]

Answer:

x^2-7x-1+2x-3

x^2-5x-4

5 0
3 years ago
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