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Artyom0805 [142]
3 years ago
15

I need the answer ASAP

Mathematics
1 answer:
jekas [21]3 years ago
7 0

Answer:

b

Step-by-step explanation:

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The function h = -16t2 + 1700 gives an object’s height h, in feet, at t seconds.
katen-ka-za [31]
What do you want me to solve for?
3 0
3 years ago
What is y if x is 12 for this slope intercept form equation y=-1/3x-2
natta225 [31]

Answer:

-6

Step-by-step explanation:

y=-1/3(12)-2

=(-1/3x12/1)-2

=-4-2

y=-6

8 0
2 years ago
Read 2 more answers
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
Solve the system of equations for x and y.<br> y = x + 5<br> y = 2x + 2
DIA [1.3K]
Answer (x,y) (3, -2)

Explanation:
using the
substitution method
y
=
x
−
5
→
(
1
)
y
=
−
2
x
+
4
→
(
2
)
since both equations are expressed in terms of x we

can equate them
⇒
x
−
5
=
−
2
x
+
4
add 2x to both sides
2
x
+
x
−
5
=
−
2
x
+
2
x
+
4
⇒
3
x
−
5
=
4
add 5 from both sides
3
x
+
5
−
5
=
4
+
5
⇒
3
x
=
9
divide both sides by 3
3
x
3
=
9
3
⇒
x
=
3
substitute this value in
(
1
)
y
=
3
−
5
=
−
2
As a check
substitute these values into
(
2
)
right
=
−
6
+
4
=
−
2
=
left
⇒
point of intersection
=
(
3
,
−
2
)
3 0
2 years ago
Iris is building a model of the Washington Monument. Her model measures 15 in. tall and is 1.5 in. wide at the base. The actual
barxatty [35]
The answer will be 550 ft
3 0
3 years ago
Read 2 more answers
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