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3 years ago

Please help this is confusing.

Mathematics

1 answer:

Makovka662 [10]3 years ago

7 0

Answer:

The mashi e drilled down 45 feet. So -45

Step-by-step explanation:

72 = 24h

X = 15h

24x = 1080

x = 45

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Sin(0)= cos(6) what is the value of 0?

Licemer1 [7]

We need to find Ο for : sin(Ο)= cos(6)

We know that:

cos θ =sin (90 - θ), so if we call θ = 6 then O will be:

O = 90 - θ

O = 90 - 6

8 0

3 years ago

Solve the initial value problem where y′′+4y′−21 y=0, y(1)=1, y′(1)=0 . Use t as the independent variable.

igor_vitrenko [27]

Answer:

$y = \frac{7}{10} e^{3(t - 1)} + \frac{3}{10}e^{-7(t - 1)}$

Step-by-step explanation:

y′′ + 4y′ − 21y = 0

The auxiliary equation is given by

m² + 4m - 21 = 0

We solve this using the quadratic formula. So

$m = \frac{-4 +/- \sqrt{4^{2} - 4 X 1 X (-21))} }{2 X 1}\\ = \frac{-4 +/- \sqrt{16 + 84} }{2}\\= \frac{-4 +/- \sqrt{100} }{2}\\= \frac{-4 +/- 10 }{2}\\= -2 +/- 5\\= -2 + 5 or -2 -5\\= 3 or -7$

So, the solution of the equation is

$y = Ae^{m_{1} t} + Be^{m_{2} t}$

where m₁ = 3 and m₂ = -7.

So,

$y = Ae^{3t} + Be^{-7t}$

Also,

$y' = 3Ae^{3t} - 7e^{-7t}$

Since y(1) = 1 and y'(1) = 0, we substitute them into the equations above. So,

$y(1) = Ae^{3X1} + Be^{-7X1}\\1 = Ae^{3} + Be^{-7}\\Ae^{3} + Be^{-7} = 1 (1)$

$y'(1) = 3Ae^{3X1} - 7Be^{-7X1}\\0 = 3Ae^{3} - 7Be^{-7}\\3Ae^{3} - 7Be^{-7} = 0 \\3Ae^{3} = 7Be^{-7}\\A = \frac{7}{3} Be^{-10}$

Substituting A into (1) above, we have

$\frac{7}{3}B e^{-10}e^{3} + Be^{-7} = 1 \\\frac{7}{3}B e^{-7} + Be^{-7} = 1\\\frac{10}{3}B e^{-7} = 1\\B = \frac{3}{10} e^{7}$

Substituting B into A, we have

$A = \frac{7}{3} \frac{3}{10} e^{7}e^{-10}\\A = \frac{7}{10} e^{-3}$

Substituting A and B into y, we have

$y = Ae^{3t} + Be^{-7t}\\y = \frac{7}{10} e^{-3}e^{3t} + \frac{3}{10} e^{7}e^{-7t}\\y = \frac{7}{10} e^{3(t - 1)} + \frac{3}{10}e^{-7(t - 1)}$

So the solution to the differential equation is

$y = \frac{7}{10} e^{3(t - 1)} + \frac{3}{10}e^{-7(t - 1)}$

6 0

4 years ago

Find the vertex and the x-inter of the function given below. y = x^2 + 2x + 6

DIA [1.3K]

Answer: Vertex = (-1, 5) x-intercepts = No real solutions

Step-by-step explanation:

Vertex = -2/2= -1

-1^2 + 2(-1) +6

1 -2 +6

-1 +6

Discrminats= 2^2 -4(1)(6)

4 -4(1)(6)

4-24

= -20 (It's a negative so there's no real solutions, meaning there's no xintercepts/R0XS)

7 0

3 years ago

Mathswatch Unit 13-Relative Frequencey

bekas [8.4K]

Answer:

Relative Frequency

relative frequency, divide the frequency by the total number of data values.

8 0

3 years ago

12 cm<br> 8 cm<br> 10.5 cm<br> Find the volume

topjm [15]

The Volume is 1008

<u>Multiply</u>

12*8*10.5=1008

Hope This Helps!

8 0

3 years ago