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2 years ago

A model airplane is built on the scale of 0.5 inch for every 11 feet. The length of the

Mathematics

1 answer:

Tema [17]2 years ago

6 0

Answer:

$9.59$ ft

Step-by-step explanation:

$\frac{211}{11}$

$= 19.181818\\multiply\\by\\0.5\\= 9.59$

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Given the second order homogeneous constant coefficient equation y′′−4y′−12y=0 1) the characteristic polynomial ar2+br+c is r^2-

Vitek1552 [10]

Answer:

The initial value problem $y(x) = 4 e^{-2x} -3 e^{6 x}$

Step-by-step explanation:

<u>Step1:</u>-

a) Given second order homogenous constant co-efficient equation

$y^{ll} - 4y^{l}-12y=0$

Given equation in the operator form is $(D^{2} -4D-12)y=0$

<u>Step 2</u>:-

b) Let f(D) = $(D^{2} -4D-12)y$

Then the auxiliary equation is $(m^{2} -4m-12)=0$

Find the factors of the auxiliary equation is

$m^{2} -6m+2m-12=0$

m(m-6) + 2(m-6) =0

m+2 =0 and m-6=0

m=-2 and m=6

The roots are real and different

The general solution $y = c_{1} e^{-m_{1} x} + c_{2} e^{m_{2} x}$

the roots are $m_{1} = -2 and m_{2} = 6$

The general solution of given differential equation is

$y = c_{1} e^{-2x} + c_{2} e^{6 x}$

<u>Step 3</u>:-

C) Given initial conditions are y(0) =1 and y1 (0) =-26

The general solution of given differential equation is

$y(x) = c_{1} e^{-2x} + c_{2} e^{6 x}$ .....(1)

substitute x =0 and y(0) =1

$y(0) = c_{1} e^{0} + c_{2} e^{0}$

$1 = c_{1} + c_{2}$ .........(2)

Differentiating equation (1) with respective to 'x'

$y^l(x) = -2c_{1} e^{-2x} + 6c_{2} e^{6 x}$

substitute x= o and y1 (0) =-26

$-26 = -2c_{1} e^{0} + 6c_{2} e^{0}$

$-2c_{1} + 6c_{2} = -26$ .............(3)

solving (2) and (3) by using substitution method

$substitute c_{2} =1- c_{1}$ in equation (3)

$-2c_{1} + 6(1-c_{1}) = -26$

on simplification , we get

$-2c_{1} + 6(1)-6c_{1}) = -26$

$-8c_{1} = -32$

dividing by'8' we get $c_{1} =4$

substitute $c_{1} =4$ in equation $1 = c_{1} + c_{2}$

so $c_{2} = 1-4 = -3$

now substitute $c_{1} =4 and c_{2} =-3$ in general solution

$y(x) = c_{1} e^{-2x} + c_{2} e^{6 x}$

$y(x) = 4 e^{-2x} -3 e^{6 x}$

now the initial value problem

$y(x) = 4 e^{-2x} -3 e^{6 x}$

7 0

3 years ago

In isosceles triangle RST below, what is the value of y?

pantera1 [17]

I think Angle T is 38 degrees is the answer

My explanation: Although I did use the words (I think) so that doesn’t mean you’re going to get it correct but I think it’s correct

6 0

3 years ago

Read 2 more answers

If (x + y)^2 = 105 and x^2 + y^2 = 65, what is the value of xy?

lesya692 [45]

$\boxed { \boxed {(a + b)^2 = a^2 + 2ab + b^2}}$

$(x + y) ^2 = 105$

$x^2 + 2xy + y^2 = 105$

$x^2 + y^2 + 2xy = 105$

$\text{Given that } x^2 + y^2 = 65,$

$65 + 2xy = 105$

$2xy = 105 - 65$

$2xy = 40$

$xy = 20$

$\boxed { \boxed {\text{Answer: xy = 20}}}$

8 0

3 years ago

Henry takes out a $650 discounted loan with a simple interest rate of 12% for a period of 7 months. What is the effective intere

Andru [333]

The effective rate of interest will be 9.10 %.

<h3>What is compound interest?</h3>

Compound interest is applicable when there will be a change in principle amount after the given time period.

Let's say you have given 100 for two years with a 10% rate of interest annually than for the second-year principle amount will become 110 instant of 100.

Given for simple interest

Principle amount = $650

Rate of interest = 12%

Time period = 7 months.

Interest= PRT/100

Interest= 650× 12 × 7/100 = 546

So final amount = 650 + 546 = $1196

By compound interest

1196 = 650 $[1 + R/100]^{7}$

R = 9.10%

Hence the effective rate of interest will be 9.10%.

For more information about compound interest,

brainly.com/question/26457073

#SPJ1

6 0

2 years ago

I don't get how to do #10 someone help plez

ExtremeBDS [4]

I can help but the picture does not load, for some reason it takes me to a page that says enter code. I have no idea what it is but i did not mess with it...
you might want to re-post a new picture just to be safe because that code thing might be something of yours thats personal

3 0

3 years ago