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3 years ago

9

What is the value of x in log2 (x) – 3 = 1?

1 answer:

USPshnik [31]3 years ago

6 0

Answer:

2

Step-by-step explanation:

because 2-3=1

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Duffy was analyzing the trajectory made after throwing a football. his coach was able to measure that his throw reached a maximu

gregori [183]

Answer:

4.35 seconds.

Step-by-step explanation:

Let x represent the time the independent variable and y be dependent variable (height of the ball).

We are told that Duffy figured that the ball left his hand at a height of 5 feet. This means at x equals 0, y was 5 or initial height of ball is 5 feet.

We have been given that Duffy's coach measured that his throw reached a maximum height of 18 feet after 2 seconds. This means that at x equals 2 y was 18.

As point (2,18) represents maximum height of ball, so it will be vertex of parabola.

Since initial height of ball is less than maximum height, so our parabola will be downward opening and leading coefficient will be negative.

We know that vertex form of a downward opening parabola is in form: $y=-a(x-h)^2+k$

$y=-a(x-2)^2+18$

Let us find value of a using point (0,5).

$5=-a(0-2)^2+18$

$5=-a*4+18$

$5-18=-a*4+18-18$

$-13=-4a$

$\frac{-13}{-4}=\frac{-4a}{-4}$

$\frac{13}{4}=a$

Therefore, the equation $y=-(\frac{13}{4})(x-2)^2+18$ can be used to find the height of ball after x seconds.

To find the time it will take the ball to hit the ground, we will substitute y equals 0 in our equation.

$0=-(\frac{13}{4})(x-2)^2+18$

$0-18=-(\frac{13}{4})(x-2)^2+18-18$

$0-18=-(\frac{13}{4})(x-2)^2$

$-18*(\frac{4}{13})=-(x-2)^2$

$\frac{72}{13}=(x-2)^2$

Taking square root of both sides of our equation we will get,

$\sqrt{\frac{72}{13}}=x-2$

$x-2\pm 2.35339$

$x-2=2.35339\text{ (or) } x-2=2.35339$

$x-2+2=2.35339+2\text{ (or) } x-2+2=-2.35339+2$

$x=4.35339\text{ (or) } x=-0.35339$

$x\approx 4.35\text{ (or) } x\approx -0.35$

Since time can not be negative, therefore, the ball will hit the ground approximately after 4.35 seconds.

7 0

3 years ago

Simplify<br><br> b - 3 + 6 - 2b

Mariulka [41]

Answer:

-b+3

Step-by-step explanation:

B-2b=-b

-3+6=3

8 0

2 years ago

Read 2 more answers

The two lines y=2/5x+9 and y= -2/5x-9 are: <br> a) parallel <br> b) perpendicular <br> c)neither

irakobra [83]

Answer:

neither

Step-by-step explanation:

parallel lines have the same slope and different y-intercept

perpendicular lines have the reciprocal as slopes( 2/5 and 5/2)

as these slopes have neither the answer in NEITHER

8 0

3 years ago

Solve for e.<br> 0.75(8 + e) = 2 - 1.25e

timofeeve [1]

Answer:

e = -2

Step-by-step explanation:

Well to solve for e in the following equation,

.75(8 + e) = 2 - 1.25e

We need to distribute and use the communicative property to find <em>e</em>.

6 + .75e = 2 - 1.25e

-2 to both sides

4 + .75e = -1.25e

-.75 to both sides

4 = -2e

-2 to both sides

e = -2

<em>Thus,</em>

<em>e is -2.</em>

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<em>Hope this helps :)</em>

3 0

3 years ago

An ice cream cone has a height of 14 cm and

sergejj [24]

Answer:

height of cone(h)=14cm

volume of cone(v)=528cm³

radius of cone =?

now,

by using formula

v=1/3πr²h
528=1/3A×r²×14
r²=113.14
r=4.83cm

hope it helps.

6 0

2 years ago