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3 years ago

Evaluate the expression. 1.2 + 0.8 ÷ 4 – 3(0.7 – 0.81) plz hurry

Mathematics

1 answer:

bekas [8.4K]3 years ago

7 0

Answer:

1.73

Step-by-step explanation:

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A ball is thrown into the air. The path it takes is modeled by the equation: -3t+24t = h, where t is the time in seconds and h i

astra-53 [7]

Given:

The given equation is:

$-3t^2+24t=h$

Where, t is the time in seconds and h is the height of the ball above the ground, measured in feet.

To find:

The inequality to model when the height of the ball is at least 36 feet above the ground. Then find time taken by ball to reach at or above 36 feet.

Solution:

We have,

$-3t^2+24t=h$

The height of the ball is at least 36 feet above the ground. It means $h\geq 36$ .

$-3t^2+24t\geq 36$

$-3t^2+24t-36\geq 0$

$-3(t^2-8t+12)\geq 0$

Splitting the middle term, we get

$-3(t^2-6t-2t+12)\geq 0$

$-3(t(t-6)-2(t-6))\geq 0$

$-3(t-2)(t-6)\geq 0$

The critical points are:

$-3(t-2)(t-6)=0$

$t=2,6$

These two points divide the number line in 3 intervals $(-\infty,2),(2,6),(6,\infty)$ .

Intervals Check point $-3(t-2)(t-6)\geq 0$ Result

$(-\infty,2)$ 0 $(-)(-)(-)=(-)$ False

$(2,6)$ 4 $(-)(+)(-)=+>0$ True

$(6,\infty)$ 8 $(-)(+)(+)=(-)$ False

The inequality is true for (2,6) and the sign of inequality is $\geq$ . So, the ball is above 36 feet between 2 to 6 seconds.

$6-2=4$

Therefore, the required inequality is $-3t^2+24t\geq 36$ and the ball is 36 feet above for 4 seconds.

3 0

3 years ago

If f(x)=x^4+6, g(x)=x-2 and h(x)= sqrt (x), then f(g(h(x)))=

patriot [66]

Answer:

x^2 + 4x * (3 - sqrt(x)) - 2(5 + sqrt(x))

Step-by-step explanation:

Firstly let us split this up, we need to first work out what g(h(x)) is:

h(x) = Sqrt(x) so g(h(x)) = g(sqrt(x)) = sqrt(x) - 2

Now to work out f(g(h(x))) = f(sqrt(x) - 2) = (sqrt(x) - 2)^4 + 6

= (sqrt(x) - 2) * (sqrt(x) - 2) * (sqrt(x) - 2) * (sqrt(x) - 2) - 6

= (x - 2 * sqrt(x) + 4) * (x - 2 * sqrt(x) + 4) - 6

= x^2 - 2x * sqrt(x) + 4x - 2x * sqrt(x) + 4x - 8 * sqrt(x) + 4x - 8 * sqrt(x) + 16 - 6

= x^2 - 4x * sqrt(x) + 12x - 16 * sqrt(x) + 10

= x^2 + 4x * (3 - sqrt(x)) - 2(5 + sqrt(x))

3 0

3 years ago

What is the area of a triangle with a base of 7 mm and a height of 10 mm

galina1969 [7]

Answer:

A≈3.5×10-5m²

Step-by-step explanation:

5 0

3 years ago

In an exponential function like the one shown below, what does the a term and the b term

Ivenika [448]

The duma a term is the x interest

5 0

3 years ago

The dimensions of this rectangle of half by seven show how you can divide the rectangle below to calculate the area

mariarad [96]

Is that the whole thing?

8 0

3 years ago