All categories

2 years ago

A diagonal of a parallelogram is 20 inches long and makes angles of 17° and 49° with the sides. How long is the longest side?

1 answer:

3 0

Angles of the parallelogram which is given in the problem are:α = 49° + 17 °= 66°

β = 180° - 66° = 114°

x - length of the longest side of the parallelogram;

Use the Sine Law:x / sin 49° = 20/ sin 17°

x / 0.7547 = 20 / 0.2924

0.2924 x = 15.094

x = 15.094 : .2924

x = 51.62 is the longest side of the parallelogram.

You might be interested in

A tank contains 240 liters of fluid in which 20 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pu

Novosadov [1.4K]

Answer:

$A(t)=240-220e^{-\frac{t}{40}}$

Step-by-step explanation:

A tank contains 240 liters of fluid in which 20 grams of salt is dissolved.

Volume of the tank = 240 liters
Initial Amount of Salt in the tank, A(0)=20 grams

Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 6 L/min

$R_{in}=$ (concentration of salt in inflow)(input rate of fluid)

$R_{in}=(1\frac{gram}{liter})( 6\frac{Liter}{min})=6\frac{gram}{min}$

$R_{out}=$ (concentration of salt in outflow)(output rate of fluid)

$R_{out}=(\frac{A(t)}{240})( 6\frac{Liter}{min})\\R_{out}=\frac{A}{40}$

Rate of change of the amount of salt in the tank:

$\dfrac{dA}{dt}=R_{in}-R_{out}$

$\dfrac{dA}{dt}=6-\dfrac{A}{40}$

We then solve the resulting differential equation by separation of variables.

$\dfrac{dA}{dt}+\dfrac{A}{40}=6\\$The integrating factor: e^{\int \frac{1}{40}dt} =e^{\frac{t}{40}}\\$Multiplying by the integrating factor all through\\\dfrac{dA}{dt}e^{\frac{t}{40}}+\dfrac{A}{40}e^{\frac{t}{40}}=6e^{\frac{t}{40}}\\(Ae^{\frac{t}{40}})'=6e^{\frac{t}{40}}$

Taking the integral of both sides

$\int(Ae^{\frac{t}{40}})'=\int 6e^{\frac{t}{40}} dt\\Ae^{\frac{t}{40}}=6*40e^{\frac{t}{40}}+C, $(C a constant of integration)\\Ae^{\frac{t}{40}}=240e^{\frac{t}{40}}+C\\$Divide all through by e^{\frac{t}{40}}\\A(t)=240+Ce^{-\frac{t}{40}}$

Recall that when t=0, A(t)=20 (our initial condition)

$20=240+Ce^{-\frac{0}{40}}\\20-240=C\\C=-220\\$Therefore, the number A(t) of grams of salt in the tank at time t\\A(t)=240-220e^{-\frac{t}{40}}$

3 0

2 years ago

How would you find the value of x is x equals five, in the equation...5x+29=45?

gavmur [86]

5x+29 = 45
5x = 16 (subtract 29 from both sides)
x = 16/5.

That is the answer, I don't know where you got the value of 5 but it doesn't make sense. To prove it, let's try put it into the equation:

5x5 + 29 =45
25 + 29 = 45
Wrong! 25 + 29 = 54.

4 0

2 years ago

The answer to this question HELP ME PLS

Papessa [141]

The answer is a because 552.50 x .12 is 66.30. 66.30 minus 552.50 is 486.50 and that divided by 7 is 69.45

8 0

3 years ago

Find the sum: -11 + (-8)

Kipish [7]

Answer:

-19

Step-by-step explanation:

-11+(-8)

-11-8

-19

hole this is correct

3 0

1 year ago

for a March past competition on sports day the house captain of one house cut 25 pieces of ribbon each 1/2 metre in length.what

zzz [600]

Answer:

not lenguague spanish

Step-by-step explanation:

that bad

7 0

2 years ago