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3 years ago

I WILL MARK BRAINIEST

Mathematics

1 answer:

balu736 [363]3 years ago

8 0

Answer:

C is the correct one.

Step-by-step explanation:

You can find answer by RHS rule of congruency.

RHS stands for Right angle, Hypotenuse, and Side

Answered by,

Z.Khan,

India

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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

One of the ancient stone pyramids in Egypt has a square base that measures 140 m on each side. The height is 96 m. What is the v

miv72 [106K]

Volume of a pyramid = $\frac{1}{3}*base*height$

Given base is = 140 m

Given height is = 96 m

Volume = $\frac{1}{3}\times140\times96=4480$

Hence, volume of pyramid is 4480 m³

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The scale of the map is messing the actual distance from library to the west quill is 72 miles and it is 6 inches on the map wha

Sonbull [250]

Answer:

A) 12 miles per inch

B) 36 miles from west quail, 48 from liberty

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3 years ago

When you calculate the number of permutations of n distinct objects taken r at a time, what are you counting?.

expeople1 [14]

Answer:

The number of ordered arrangements of n objects taken r at a time.

Step-by-step explanation:

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2 years ago

A professor wanted to find a linear model that relates the number of hours a student plays video games each week, h, to the cumu

Paladinen [302]

Answer:

question seems incomplete but with the limited information one can deduce that the professor was trying to investigate how students CGPA is affected by the length of period spent on video games.

Step-by-step exp

independent variables are constants. they do not change or depend on any other variable.

dependent variables, they do depend on other variables, we call them resulting variables..

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3 years ago