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Morgarella [4.7K]

3 years ago

9

Find the measures of the angles of a triangle of the measure of one angle is three times the measure of a second angle and the t

hird angle measures five times the second angle decreased by 90

1 answer:

Vinil7 [7]3 years ago

5 0

Answer:

hii

x=30

Step-by-step explanation:

x+3x+5x-90=180

9x=270

x=30

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How to answer this? A farmer had 455 ducks and chickens. He sold 2/5 of the ducks and bought another 104 chickens. As a result,

julia-pushkina [17]

Answer:

(a) 25

(b) $4816

Step-by-step explanation:

Let's say the starting amount of ducks is d, and the starting amount of chickens is c. Since there are only ducks and chickens, we can say that d + c= 455.

Next, the farmer sells 2/5 of the ducks, so we subtract 2/5 of the ducks so that the ending duck amount is d - (2/5)d = (3/5) d

After that, the farmer buys another 104 chickens, so we add 104 chickens to the current amount of chickens to get the ending chicken number as 104+c

Given the ending duck and chicken count, we can say that the ending farm animal count (we can represent this as a) is (3/5)d + 104 + c = a

The number of ducks is 2/3 the total number of animals at the end, so (3/5)d = (2/3)a

Let's list our equations out so it is easier to solve:

d+c = 455

(3/5)d + 104 + c = a

(3/5)d = (2/3)a

We have three equations and need to solve for three variables. One common variable in all three equations is d, so it might help if we put everything in terms of d.

Starting with d+c=455, if we subtract d from both sides, we get c=455-d. We can substitute this in the second equation to get

(3/5)d + 104 + 455 - d = a

-(2/5)d + 559 = a

(3/5)d = (2/3)a

Next, we can substitute for a. If we multiply both sides by 3 and then divide by 2 in (3/5)d = (2/3)a , we get

(9/10)d = a

Substitute that in to the second equation to get

-(2/5)d + 559 = (9/10) d

-(4/10)d + 559 = (9/10) d

add (4/10)d to both sides to isolate the variable and its coefficient

(13/10)d = 559

multiply both sides by (10/13) to isolate the coefficient

d = 430

Therefore, the starting number of ducks is 430 and the starting amount of chickens is 455-430 = 25

For (b), 2/5ths of the ducks are sold, so this is (430) * (2/5) = 172. Each duck is sold for 28 dollars, so this is 172*28=$4816 as the total price

7 0

2 years ago

Find the function y1 of t which is the solution of 121y′′+110y′−24y=0 with initial conditions y1(0)=1,y′1(0)=0. y1= Note: y1 is

strojnjashka [21]

Answer:

Step-by-step explanation:

The original equation is $121y''+110y'-24y=0$ . We propose that the solution of this equations is of the form $y = Ae^{rt}$ . Then, by replacing the derivatives we get the following

$121r^2Ae^{rt}+110rAe^{rt}-24Ae^{rt}=0= Ae^{rt}(121r^2+110r-24)$

Since we want a non trival solution, it must happen that A is different from zero. Also, the exponential function is always positive, then it must happen that

$121r^2+110r-24=0$

Recall that the roots of a polynomial of the form $ax^2+bx+c$ are given by the formula

$x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}$

In our case a = 121, b = 110 and c = -24. Using the formula we get the solutions

$r_1 = -\frac{12}{11}$

$r_2 = \frac{2}{11}$

So, in this case, the general solution is $y = c_1 e^{\frac{-12t}{11}} + c_2 e^{\frac{2t}{11}}$

a) In the first case, we are given that y(0) = 1 and y'(0) = 0. By differentiating the general solution and replacing t by 0 we get the equations

$c_1 + c_2 = 1$

$c_1\frac{-12}{11} + c_2\frac{2}{11} = 0$ (or equivalently $c_2 = 6c_1$

By replacing the second equation in the first one, we get $7c_1 = 1$ which implies that $c_1 = \frac{1}{7}, c_2 = \frac{6}{7}$ .

So $y_1 = \frac{1}{7}e^{\frac{-12t}{11}} + \frac{6}{7}e^{\frac{2t}{11}}$

b) By using y(0) =0 and y'(0)=1 we get the equations

$c_1+c_2 =0$

$c_1\frac{-12}{11} + c_2\frac{2}{11} = 1$ (or equivalently $-12c_1+2c_2 = 11$

By solving this system, the solution is $c_1 = \frac{-11}{14}, c_2 = \frac{11}{14}$

Then $y_2 = \frac{-11}{14}e^{\frac{-12t}{11}} + \frac{11}{14} e^{\frac{2t}{11}}$

c)

The Wronskian of the solutions is calculated as the determinant of the following matrix

$\left| \begin{matrix}y_1 & y_2 \\ y_1' & y_2'\end{matrix}\right|= W(t) = y_1\cdot y_2'-y_1'y_2$

By plugging the values of $y_1$ and

We can check this by using Abel's theorem. Given a second degree differential equation of the form y''+p(x)y'+q(x)y the wronskian is given by

$e^{\int -p(x) dx}$

In this case, by dividing the equation by 121 we get that p(x) = 10/11. So the wronskian is

$e^{\int -\frac{10}{11} dx} = e^{\frac{-10x}{11}}$

Note that this function is always positive, and thus, never zero. So $y_1, y_2$ is a fundamental set of solutions.

8 0

3 years ago

A man is listening to his radio at the top of a mountain where the altitude is 4500 feet

AURORKA [14]

But what say it again wit what is this

7 0

2 years ago

PLEASE HELP!! If f (x) = 4x^-2 + 1/4x^2 + 4, then f’(2) =

Elena-2011 [213]

<h3>Answer: D) 0</h3>

Work Shown:

f(x) = 4x^(-2) + (1/4)x^2 + 4

f ' (x) = 4*(-2)x^(-3) + (1/4)*2x .... power rule

f ' (x) = -8x^(-3) + (1/2)x

f ' (2) = -8(2)^(-3) + (1/2)*(2)

f ' (2) = 0

4 0

3 years ago

Geometry help! Find part B

hram777 [196]

Answer: It looks like Part B is about 4 times that of part A.

Step-by-step explanation: I think the answer would be 12.

A would be 3. B would be 12.

I'm terribly sorry if it is wrong.

3 0

3 years ago

Read 2 more answers