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3 years ago

What units will you use to measure an Indian ocean

Mathematics

1 answer:

Anastaziya [24]3 years ago

8 0

Answer:

Kilometers most likely for any other measurement would be to small to do so otherwise.

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Could someone help me rnnn?

GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola: $y=3x^2-4$

Step-by-step explanation:

Given:

y-intercept of parabola: -4
parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola: $y=a(x-h)^2+k$

(where (h, k) is the vertex and $a$ is some constant)

Substitute point (0, -4) into the equation:

$\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}$

Substitute point (-2, 8) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}$

Substitute point (1, -1) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}$

Equate to find h:

$\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}$

Substitute found value of h into one of the equations to find a:

$\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}$

Substitute found values of h and a to find k:

$\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}$

Therefore, the equation of the parabola in vertex form is:

$\implies y=3(x-0)^2-4=3x^2-4$

So the vertex of the parabola is (0, -4)

5 0

2 years ago

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Hans leaned a 17 ft ladder against his house. He placed the base of the ladder 8 ft from his house, and the top of the ladder re

Fynjy0 [20]

Answer:

Step-by-step explanation:

so 17 squared minus 8 squared is 225. the square root of 225 is 15

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3 years ago

Find the vertices of the following functions.<br> Y=4(x-2)(x-3)<br><br> Y=-4(x+2)^2 -5

Natalija [7]

1) 5/2 , -1
2) -2,-5

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3 years ago

What is the gradient of the graph shown?

JulijaS [17]

Answer:

Step-by-step explanation:

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2 years ago

A tiger can eat food that weighs up to 15% of its body weight. If a tiger can eat 75 pounds of food, how much does the tiger wei

Oksanka [162]

He body weight is 5 74 dived by 15 = 5

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3 years ago

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