What two equivalent ratios for 30 to 6

What is the solution to 2/3a - 1/6 = 1/3

konstantin123 [22]

The solution would be: a = 3/4

4 0

2 years ago

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A baseball is thrown in a parabolic arc. It's position above the ground at a given point in time

FinnZ [79.3K]

If the ball was thrown straight up at 24 ft/sec when it was 5 ft above the ground, the ball reached a maximum height of 7.25 m

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<h3>Further explanation</h3>

Discriminant of quadratic equation ( ax² + bx + c = 0 ) could be calculated by using :

From the value of Discriminant , we know how many solutions the equation has by condition :

D < 0 → No Real Roots

D = 0 → One Real Root

D > 0 → Two Real Roots

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An axis of symmetry of quadratic equation y = ax² + bx + c is :

$\large {\boxed {x = \frac{-b}{2a} } }$

Let us now tackle the problem!

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<u>Given:</u>

$p(t) = 3gt^2 + v_ot + p_o$

$p(t) = 3(-32)t^2 + 24t + 5$

$p(t) = -64t^2 + 24t + 5$

<u>Asked:</u>

$p_{max} = ?$

<u>Solution:</u>

<em>At the maximum height , velocity is 0 m/s:</em>

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

$v = \frac{d}{dt} ( -64t^2 + 24t + 5 )$

$v = (-64)(2)t^{2-1} + 24$

$v = -128t + 24$

$0 = -128t + 24$

$128t = 24$

$t = 24 \div 128$

$t = 3 \div 16$

$t = 0.1875 \texttt{ s}$

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$p(t) = -64t^2 + 24t + 5$

$p(0.1875) = -64(0.1875)^2 + 24(0.1875) + 5$

$p(0.1875) = 7.25 \texttt{ m}$

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<h3>Learn more</h3>

Solving Quadratic Equations by Factoring : brainly.com/question/12182022
Determine the Discriminant : brainly.com/question/4600943
Formula of Quadratic Equations : brainly.com/question/3776858

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<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Quadratic Equations

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Keywords: Quadratic , Equation , Discriminant , Real , Number

#LearnWithBrainly

3 0

3 years ago

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5 2/3 divided by 2 im terrible at fractions

Degger [83]

You can make the mixed number 5 2/3 an improper fraction, which is the number in the numerator is larger than the number in the denominator.
Multiply, Add, and Keep the denominator are the steps you need to take.
Multiply the denominator by the whole number and then add the number in the numerator, while keeping the denominator. 5*3+2=17>>> 17/3 is the improper fraction.
17/3 ÷ 2 is the resulting equation.
When you divide fractions, you have to multiply by the reciprocal. 2/1 is the whole number 2, but in fraction form. The reciprocal is 1/2 because your just flipping the numerator and the denominator.
17/3 * 1/2 is the new equation.
When you multiply fractions, you multiply straight across.
17/3 * 1/2 = 17/6 or 2 5/6 is your answer.

8 0

3 years ago

If the bottom of the ladder is 3ft from a wall and the top of the ladder is 4ft from the ground, then how long is the ladder?

statuscvo [17]

Answer:

5ft

Step-by-step explanation:

$4^{2} +3^{2} =c^{2} \\16+9=25\\\sqrt{25} =5$

6 0

3 years ago

A motorboat takes 3 hours to travel 108 kilometers going upstream. The return trip takes 2 hours going

IRISSAK [1]

Answer:

45 km/h and 9 km/h

Step-by-step explanation:

Let the rate of boat in still water be b and the speed of the current be c

Speed downstream = b + c
Speed upstream = b - c

<u>We got equations for time:</u>

108/(b - c) = 3 ⇒ b - c = 36
108/(b + c) = 2 ⇒ b + c = 54

<u>Add up the equations:</u>

b - c + b + c = 36 + 54
2b = 90
b = 45 km/h

<u>Then finding the values of c</u>

c = 45 - 36 = 9 km/h

6 0

3 years ago