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3 years ago

The average height of two forwards

Mathematics

1 answer:

Gelneren [198K]3 years ago

5 0

Answer:

the other 2 guards must be 6 feet 3 inches

Step-by-step explanation:

$\frac{3(6.8)+2x}{5} =6.6$

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If a/b < c/d with b > 0, d > 0, prove that a+c / b+d lies between the two fractions a/b and c/d .

Tems11 [23]

Divide through everything by b :

$\dfrac{a+c}{b+d} = \dfrac{\dfrac ab + \dfrac cb}{1 + \dfrac db}$

Since a/b < c/d, it follows that

$\dfrac{a+c}{b+d} < \dfrac{\dfrac cd+\dfrac cb}{1 + \dfrac db}$

Multiply through everything on the right side by b/d to get

$\dfrac{a+c}{b+d} < \dfrac{\dfrac{bc}{d^2}+\dfrac cd}{\dfrac bd+1} = \dfrac{\dfrac cd\left(\dfrac bd+1\right)}{\dfrac bd+1} = \dfrac cd$

and so (a + c)/(b + d) < c/d.

For the other side, you can do something similar and divide through everything by d :

$\dfrac{a+c}{b+d} = \dfrac{\dfrac ad + \dfrac cd}{\dfrac bd + 1}$

and a/b < c/d tells us that

$\dfrac{a+c}{b+d} > \dfrac{\dfrac ad + \dfrac ab}{\dfrac bd + 1}$

Then

$\dfrac{a+c}{b+d} > \dfrac{\dfrac ab + \dfrac{ad}{b^2}}{1 + \dfrac db} = \dfrac{\dfrac ab\left(1+\dfrac db\right)}{1 + \dfrac db} = \dfrac ab$

and so (a + c)/(b + d) > a/b.

Then together we get the desired inequality.

5 0

2 years ago

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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Given:

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

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

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

Asked:

$p_{max} = ?$

Solution:

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

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

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

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

$v = -128t + 24$

$0 = -128t + 24$

$128t = 24$

$t = 24 \div 128$

$t = 3 \div 16$

$t = 0.1875 \texttt{ s}$

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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

Read 2 more answers

EN LOS PUEBLOS DE AYLLÓN, RIAZA Y CANTALEJO DE 1200, 2100 Y 3500 HABITANTES, RESPECTIVAMENTE, SE HA SOLICITADO LA PARTICIPACIÓN

MAVERICK [17]

Answer:

???

Step-by-step explanation:

6 0

3 years ago

Capon City has 5 more than 3 times as many residents as Harbor City.

sergey [27]

Answer:

3r+5

Step-by-step explanation:

6 0

2 years ago

What is the greatest common factor (gcf) of 40 and 75?

Reil [10]

Answer:

the greatest common factor of 75 and 40 is 5

4 0

2 years ago