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3 years ago

3.695 to 4 name the place value to which each number was rounded

2 answers:

8 0

3.695 was rounded to the nearest whole number. In order to do this, you look at the digit to the right, which would be the tenths place. Since the number in the tenths place is greater than 5, you rounded up. (:

oksian1 [2.3K]3 years ago

5 0

In this, 3.695 to 4, the tenths was rounded

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A juggler tosses a ball into the air . The balls height, h and time t seconds can be represented by the equation h(t)= -16t^2+40

malfutka [58]

PART A

The given equation is

$h(t) = - 16 {t}^{2} + 40t + 4$

In order to find the maximum height, we write the function in the vertex form.

We factor -16 out of the first two terms to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + 4$

We add and subtract

$- 16(- \frac{5}{4} )^{2}$

to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t) + - 16( - \frac{5}{4})^{2} - -16( - \frac{5}{4})^{2} + 4$

We again factor -16 out of the first two terms to get,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4})^{2} ) - -16( - \frac{5}{4})^{2} + 4$

This implies that,

$h(t) = - 16 ({t}^{2} - \frac{5}{2} t + ( - \frac{5}{4}) ^{2} ) + 16( \frac{25}{16}) + 4$

The quadratic trinomial above is a perfect square.

$h(t) = - 16 ( t- \frac{5}{4}) ^{2} +25+ 4$

This finally simplifies to,

$h(t) = - 16 ( t- \frac{5}{4}) ^{2} +29$

The vertex of this function is

$V( \frac{5}{4} ,29)$

The y-value of the vertex is the maximum value.

Therefore the maximum value is,

$29$

PART B

When the ball hits the ground,

$h(t) = 0$

This implies that,

$- 16 ( t- \frac{5}{4}) ^{2} +29 = 0$

We add -29 to both sides to get,

$- 16 ( t- \frac{5}{4}) ^{2} = - 29$

This implies that,

$( t- \frac{5}{4}) ^{2} = \frac{29}{16}$

$t- \frac{5}{4} = \pm \sqrt{ \frac{29}{16} }$

$t = \frac{5}{4} \pm \frac{ \sqrt{29} }{4}$

$t = \frac{ 5 + \sqrt{29} }{4} = 2.60$

or

$t = \frac{ 5 - \sqrt{29} }{4} = - 0.10$

Since time cannot be negative, we discard the negative value and pick,

$t = 2.60s$

8 0

3 years ago

Can someone please help me answer this?

sammy [17]

Answer:

Not clear enough

Step-by-step explanation:

please resend the question and make it more clear and readable

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4 years ago

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Yuliya22 [10]

Answer:

Step-by-step explanation:

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When possible, the best way to esatblish that an observed association is the result of a cuase and effect relation is by means o

vovangra [49]

Answer:

The answer is a well designed experiment.

Step-by-step explanation:

When possible, the best way to establish that an observed association is the result of a cause and effect relation is by means of - well designed experiment.

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3 years ago

2x^2 -7= 74 please show all work

skad [1K]

$2x^2-7=74\\
2x^2=81\\
x^2=\dfrac{81}{2}\\
x=-\sqrt{\dfrac{81}{2}} \vee x=\sqrt{\dfrac{81}{2}}\\
x=-\dfrac{9}{\sqrt2} \vee x=\dfrac{9}{\sqrt2}}\\
x=-\dfrac{9\sqrt2}{2} \vee x=\dfrac{9\sqrt2}{2}}\\$

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3 years ago