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3 years ago

What are all the angle measures for right triangle ABC?

Mathematics

1 answer:

Alenkasestr [34]3 years ago

3 0

Answer:

$\alpha = 60°,\:\beta = 30°, \: 90°$

Step-by-step explanation:

$Arccos( \frac{ \sqrt{3} }{2} ) = \beta \\ Arccos( \cos \: 30 \degree ) = \beta \\30 \degree = \beta \\ \therefore \: \alpha = 60 \degree \\ remaining \: angle = 90 \degree \\$

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Which method(s) can be used to solve a system of equations? Select all that apply. distributing graphing substitution formulas a

katovenus [111]

Distributing, formulas, and addition

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3 years ago

Find the solution of the differential equation dy/dt = ky, k a constant, that satisfies the given conditions. y(0) = 50, y(5) =

irga5000 [103]

Answer: The required solution is $y=50e^{0.1386t}.$

Step-by-step explanation:

We are given to solve the following differential equation :

$\dfrac{dy}{dt}=ky~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

where k is a constant and the equation satisfies the conditions y(0) = 50, y(5) = 100.

From equation (i), we have

$\dfrac{dy}{y}=kdt.$

Integrating both sides, we get

$\int\dfrac{dy}{y}=\int kdt\\\\\Rightarrow \log y=kt+c~~~~~~[\textup{c is a constant of integration}]\\\\\Rightarrow y=e^{kt+c}\\\\\Rightarrow y=ae^{kt}~~~~[\textup{where }a=e^c\textup{ is another constant}]$

Also, the conditions are

$y(0)=50\\\\\Rightarrow ae^0=50\\\\\Rightarrow a=50$

and

$y(5)=100\\\\\Rightarrow 50e^{5k}=100\\\\\Rightarrow e^{5k}=2\\\\\Rightarrow 5k=\log_e2\\\\\Rightarrow 5k=0.6931\\\\\Rightarrow k=0.1386.$

Thus, the required solution is $y=50e^{0.1386t}.$

8 0

3 years ago

Read 2 more answers

Is this right?? please help!

Ganezh [65]

Answer:

6 < x < 8

Step-by-step explanation:

The compound inequality in this instance represent the "and" condition, not the "or" condition.* We might solve it like this.

-47 > 1 -8x > -63 . . . . given

Multiply by -1:

47 < -1 +8x < 63

Add 1:

48 < 8x < 64

Divide by 8:

6 < x < 8

______

* You can tell this is the case by looking at the ends of the given statement:

-47 > -63 . . . . a true statement, so the solution set will be an intersection, not a union.

4 0

3 years ago

Juana compró una camioneta 4x4 a S/ 42 000; además, sabe que la camioneta se depreciará (bajará su precio) en forma lineal duran

prohojiy [21]

Answer:

Una relación lineal es de la forma:

y = a*x + b.

donde a es la pendiente y b es la ordenada al origen.

en este caso, y es el precio de la camioneta, x es el numero de años que pasaron, a es la razon de depreciación de la camioneta y b es el precio inicial de la camioneta, b = $42,000.

Sabemos que después de 5 años, el precio de la camioneta es 21,000, entonces podemos resolver:

$21,000 = a*5 + $42,000

a*5 = $21,000 - $42,000 = -$21,000

a = -$21,000/5 = -$4,200

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3 years ago

What is the equation for the hyperbola shown?

amid [387]

Answer:

D. y²/5² - x²/8² = 1

Step-by-step explanation:

A and B are both incorrectly oriented, and D is the only hyperbola that contains the points (0,5) and (0,-5).

Verification (0,5) and (0,-5) are in the hyperbola:

First replace x and y with corresponding x and y values (We will start with x=0 and y=5)

$\frac{5^{2}}{5^{2}}-\frac{0^{2}}{8^{2}}=1$

Then simplify.

$\frac{25}{25}-\frac{0}{16}=1$

$1-0=1$

$1=1$

If the result is an equation (where both sides are equal to each other) then the original x and y values inputted are valid. The same is true with x and y inputs x=0 and y=-5, or any other point along the hyperbola.

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3 years ago

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