MATHEMATICS HIGH SCHOOL

Find the perimeter of a rectangle whose width is 5 cm and diagonal is 13 cm. (Please show the steps and answer it really fast!!)

Answers

Answer 1

Answer:

Answer:

....se attachment

Perimeter =2(length+width)

we calculate the length

ADC right triangle in D

AC = diagonal: 13cm

AD = width: 5cm

pythagoras to calculate DC

DC²=AC²-AD²

DC²= 13²-5²

DC=√144 = 12cm

we calculate the perimeter:

P=2(12+5)=2*17=34cm

Step-by-step explanation:

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Y varies directly with x, and y=16
in. when x=8 in.

Answers

Answer:

y= 2x

Step-by-step explanation:

To figure out what the equation would be you would set up an equation..

16 = 8z

Then you find z

16/8 = 8z/8

2 = z

Now you can set up a variable expression although it isn't necessary

y = zx

Now you plug in the value of z to complete the equation

y= 2x

I hope this is what you wanted!!!

A cup of coffee at 181 degrees is poured into a mug and left in a room at 66 degrees. After 6 minutes, the coffee is 139 degrees. Assume that the differential equation describing Newton's Law of Cooling is (in this case) dT/dt=k(T-66).1) What is the temperature of the coffee after 16 minutes?
2) After how many minutes will the coffee be 100 degrees?

Answers

The temperature of the coffee after 16 minutes is 134 degrees and after 1.3 minutes the coffee be 100 degrees.

What is Differential equation?

A differential equation is an equation that contains one or more functions with its derivatives.

A cup of coffee at 181 degrees is poured into a mug and left in a room at 66 degrees.

After 6 minutes, the coffee is 139 degrees.

Assume that the differential equation describing Newton's Law of Cooling is (in this case) dT/dt=k(T-66).

T=∫k(t-66)dt

=k(t²/2-66)+c

When t=0 and T=181

181=k(0-66)+c

181=-66k+c

when t=6, T=139

139=k(6²/2-66)+c

139=-48k+c

-42=-18k

Divide both sides by 18

k=7/3

139=-48×7/3+c

c=139+112=251

T=7/3(t-66)+251

The temperature of the coffee after 16 minutes

T=7/3(16-66)+251

T=7/3(-50)+251

T=134 degrees

After how many minutes will the coffee be 100 degrees

100=7/3(t-66)+251

100=7/3t-7/3(66)+251

100=7/3t-154+251

100=7/3t+97

100-97=7/3t

3=7/3t

9/7=t

1.3=t

Hence, the temperature of the coffee after 16 minutes is 134 degrees and after 1.3 minutes the coffee be 100 degrees.

To learn more on Differentiation click:

brainly.com/question/24898810

#SPJ5

Answer:

Step-by-step explanation:

$(dT)/(dt) =k(t-66)\nT=\int\ {k(t-66)} \, dt=K((t^2)/(2) -66)+c\nwhen t=0,T=181\n181=K(0-66)+c\n181=-66k+c\nwhen t=6,T=139\n139=k((6^2)/(2) -66)+c\n139=-48k+c\n181-139=-66k+48k\n-42=-18k\n7=3k\nk=(7)/(3) \n139=-48*(7)/(3) +c\nc=139+112=251\nT=(7)/(3) (t-66)+251\nnow complete the question$

What is the difference between the product of 19 and 3.6 and the sum of 2.87 and 3.5

Answers

19 × 3.6 =68.4
and 2.87 + 3.5 =6.37
Therefore,68.4-6.37=62.03

product of 19 and 3.6 = 19 X 3.6 = 68.4
sum of 2.87 and 3.5 = 2.87 + 3.5 = 6.37
Difference = 68.4 - 6.37 = 62.03

The diagonals of parallelogram QRST and intersect at point U. If RS = 10, ST = 12, and RU = 9.5, find the length of

Answers

I am assuming that parallelogram QRST is rectangle.
RS is the width and ST is the length.
RT is the diagonal. RU is half of the diagonal and TU is the other half of the diagonal.

Length = 12 ; Width = 10

to find the diagonal:
d = √(L²+W²
d = √ 12² + 100²
d = √ 144 + 100
d = √244
d = 15.62

RU + TU = 15.62
TU = 15.62 - 9.5
TU = 6.12

20. There are 15 members of the show choir. In how many ways can you arrange 4 members in the front row when order does not matter?

Answers

The first chair can be any one of the 15.
   For each of those ...
The second chair can be any one of the remaining 14.
      For each of those ...
The third chair can be any one of the remaining 13.
   For each of those ...
The fourth chair can be any one of the remaining 12.

Number of ways to fill the 4 chairs = (15 x 14 x 13 x 12) = 32,760 .

But ...

Each set of 4 people can be seated in (4 x 3 x 2 x 1) = 24 orders.
So each group of 4 people is represented 24 times among the 32,760.

If the order doesn't matter, you're really asking how many different
groups of 4 people can occupy the front row.

That's (32,760) / (24) = 1,365 sets of 4 members, in any order.

Say that the front four people's names are John, Kathy, Mia, and Alex, in that order. You can arrange them as follows.

John, Kathy, Alex, Mia
John, Alex, Kathy, Mia
John, Alex, Mia, Kathy
John, Mia, Alex, Kathy
John, Mia, Kathy, Alex
Alex, John, Kathy, Mia
Alex, John, Mia, Kathy
There are many more, but my guess would be 16 combinations. Test for yourself if you don't think thats right!

A savings account earns simple interest at a rate of 6% per year. Last year the account earned $10.86 in interest. What was the balance in the account at the beginning of last year?