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3 years ago

Find the zeros of y= x2 - 6x - 4 by completing the square.

Mathematics

1 answer:

Murljashka [212]3 years ago

6 0

Answer:

x = 3 - √13, 3 + √13.

-0.61, 6.61 to the nearest hundredth.

Step-by-step explanation:

x^2 - 6x - 4 = 0

(x - 3)^2 - 9 - 4 = 0

(x - 3)^2 = 13

x - 3 = +/-√13

x = 3 - √13, 3 + √13.

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The height (feet) of an object moving vertically is given by s= (-16t^2)+(208t)+(156), where t is in seconds.

OverLord2011 [107]

Answer:

The object's velocity at t = 7 is -16 ft/s

The maximum height is 832 ft and it occurs when $t=\frac{13}{2}$

Step-by-step explanation:

From the information given, the equation of motion of the object is

$s(t)= -16t^2+208t+156$

For any equation of motion s(t), the instantaneous velocity at time t is given by

$v(t)=\frac{ds}{dt}$

(a) To find the object's velocity at t = 7, you must:

$v(t)=\frac{d}{dt}(-16t^2+208t+156)\\\\v(t)=-\frac{d}{dt}\left(16t^2\right)+\frac{d}{dt}\left(208t\right)+\frac{d}{dt}\left(156\right)\\\\v(t)=-32t+208+0\\\\v(t)=-32t+208$

Next, we evaluate when t = 7

$v(7)=-32(7)+208=-224+208\\\\v(7)=-16$

The object's velocity at t = 7 is -16 ft/s

(b) To find the maximum of a function we always use the derivative of the function and we set it equal zero to find the critical points.

To find the maximum height and when it occurs, we set the velocity function equal to 0 and solve for t.

$-32t+208=0\\\\-32t+208-208=0-208\\\\-32t=-208\\\\\frac{-32t}{-32}=\frac{-208}{-32}\\\\t=\frac{13}{2}$

Next, we substitute this value into the equation of motion to find the maximum height

$s(\frac{13}{2})= -16(\frac{13}{2})^2+208(\frac{13}{2})+156\\\\s(\frac{13}{2})=-676+1352+156)=832$

The maximum height is 832 ft and it occurs when $t=\frac{13}{2}$

6 0

3 years ago

How to find the total areas of two states. One state is 82,144 square miles and the other is 145, 552

romanna [79]

Add them together since they're already in area unit

8 0

3 years ago

Read 2 more answers

Write problem out please

Gekata [30.6K]

Answer:

21.25 m

Step-by-step explanation:

y = Ax² + Bx + C

Set the origin at the middle of the span so that the point (0, 0) is on the curve

0 = A(0)² + B(0) + C means C = 0

The points (200, 85) and (-200, 85) are on the curve

85 = A(200)² + B(200)

85 = A(-200)² + B(-200)

85 - 40000A - B(200) = 85 - 40000A + B(200)

- B(200) = B(200)

-400B = 0

B = 0

85 = A(200)²

A = 85/40000

y = 85x²/40000

y = 85(100)²/40000 = 21.25 m

5 0

3 years ago

Gold fish or cheez its

babymother [125]

Answer: gold fish

Step-by-step explanation:

4 0

4 years ago

Read 2 more answers

In a certain Algebra 2 class of 29 students, 7 of them play basketball and 14 of them

Mariulka [41]

Answer:

Two possible answers below

Step-by-step explanation:

Probability and Sets

We are given two sets: Students that play basketball and students that play baseball.

It's given there are 29 students in certain Algebra 2 class, 10 of which don't play any of the mentioned sports.

This leaves only 29-10=19 players of either baseball, basketball, or both sports. If one student is randomly selected, then the propability that they play basketball or baseball is:

$\displaystyle P=\frac{19}{29}$

P = 0.66

Note: if we are to calculate the probability to choose one student who plays only one of the sports, then we proceed as follows:

We also know 7 students play basketball and 14 play baseball. Since 14+7 =21, the difference of 21-19=2 students corresponds to those who play both sports.

Thus, there 19-2=17 students who play only one of the sports. The probability is:

$\displaystyle P=\frac{17}{29}$

P = 0.59

3 0

3 years ago