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2 years ago

Choose a point on the terminal side of theta theta= 5pi/4

Mathematics

1 answer:

adell [148]2 years ago

3 0

Answer:

Step-by-step explanation:

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Two boats depart from a port located at (–8, 1) in a coordinate system measured in kilometers and travel in a positive x-directi

miss Akunina [59]

Answer:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

Step-by-step explanation:

1st boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=1\\ \\b=-2a$

Equation:

$y=ax^2 -2ax+c$

The y-coordinate of the vertex:

$y_v=a\cdot 1^2-2a\cdot 1+c\Rightarrow a-2a+c=10\\ \\c-a=10$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-2a\cdot (-8)+c\\ \\80a+c=1$

Solve:

$c=10+a\\ \\80a+10+a=1\\ \\81a=-9\\ \\a=-\dfrac{1}{9}\\ \\b=-2a=\dfrac{2}{9}\\ \\c=10-\dfrac{1}{9}=\dfrac{89}{9}$

Parabola equation:

$y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}$

2nd boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=0\\ \\b=0$

Equation:

$y=ax^2+c$

The y-coordinate of the vertex:

$y_v=a\cdot 0^2+c\Rightarrow c=-7$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-7\\ \\64a-7=1$

Solve:

$a=-\dfrac{1}{8}\\ \\b=0\\ \\c=-7$

Parabola equation:

$y=\dfrac{1}{8}x^2 -7$

System of two equations:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

7 0

3 years ago

Read 2 more answers

Use distributive property to remove the parentheses -5(-2v+3y-1)

RoseWind [281]

Answer:

10v+-15y+5

Step-by-step explanation:

With distributive property, you multiply the number outside the parentheses to the numbers inside the parentheses separately then add them together and combine like terms.

4 0

2 years ago

Yoko is going for a walk. She takes 5 hours to walk 12.5 miles. What is her speed?

Dennis_Churaev [7]

Answer:

2.5mph (miles per hour)

Step-by-step explanation:

Simple, 12.5/5 = 2.5 mph (miles per hour)

8 0

2 years ago

The vet says Ray's puppy will grow to be at most 28 inches tall. Ray's puppy is currently 1 foot tall. How much more will the pu

Nat2105 [25]

28=12+x

28 represents how tall he will get, 12 represents how tall he is in inches, and x is how much he still has left to grow! Hope it helps!

4 0

2 years ago

What is the sum of first 6 terms

zvonat [6]

Answer:

182

Step-by-step explanation:

Sum = a(r^n -1) ÷ r - 1

1(-3^6 - 1) ÷ -3 -1

= 182

r = t2 ÷ t1 * since they stated that it is geometric

7 0

1 year ago