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3 years ago

Choose the graph of y = -4 cot x.

Mathematics

1 answer:

noname [10]3 years ago

7 0

Suppose y= cot x is our parent function then remember general rules of transformation.

1) y= -f(x), reflects the graph of f(x) across x-axis.

2) y= cf(x), stretches the graph of f vertically by factor of c , for c >1.

Now, apply these rules to y= -4 cot(x)

the -ve sign reflects the graph of cot(x) across x-axis and the number 4 will stretch it vertically by 4 units.

The graph of both parent function (y=cot x ) and transformed function (y= -4 cot(x)) are attached below.

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An object is thrown straight up from the top of a 100-foot platform at a velocity of 48 feet per second. The height h(t) of the

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Answer:

The maximum height is 136 ft

The time it takes to achieve this height is 1.5 s.

Explanation:

1. Function for the height (given):

$h(t)=-16t^2+48t+100$

2. Type of function

That is a quadatic function, whose graph is a parabola that opens downward.

The maximum of the function, i.e. the maximum height, is the vertex of the parabola.

The vertex of a parabola with the genral equation $y=ax^2+bx+c$ is at the x-coordinate

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3. Time to achieve the maximum height

Substitute b with 48 and a with - 16:

$t=-48/(2(-16))=48/32=3/2=1.5$

Then, time when the object achieves the maximum height it 1.5s

4. Maximum height:

Replace t with 1.5 in the equation, to find the maximum height, h(1.5)

$h(1.5)=-16(1.5)^2+48(1.5)+100=136$

Then, the maximum height is 136 ft

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3
x
+
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x
+
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y
>
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y
y
.
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y
>
−
3
x
2
+
12
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>
-
3
x
2
+
12
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−
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2
-
3
2
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y
y
is greater than
−
3
x
2
+
12
-
3
x
2
+
12
.
y
>
−
3
x
2
+
12
y
>
-
3
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2
+
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