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3 years ago

Please help me answer these questions

Mathematics

1 answer:

Triss [41]3 years ago

5 0

Discussed why 2 is the answer

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One of the roots of the quadratic equation dx^2+cx+p=0 is twice the other, find the relationship between d, c and p

scZoUnD [109]

Answer:

$c^2 = 9dp$

Step-by-step explanation:

Given

$dx^2 + cx + p = 0$

Let the roots be $\alpha$ and $\beta$

So:

$\alpha = 2\beta$

Required

Determine the relationship between d, c and p

$dx^2 + cx + p = 0$

Divide through by d

$\frac{dx^2}{d} + \frac{cx}{d} + \frac{p}{d} = 0$

$x^2 + \frac{c}{d}x + \frac{p}{d} = 0$

A quadratic equation has the form:

$x^2 - (\alpha + \beta)x + \alpha \beta = 0$

So:

$x^2 - (2\beta+ \beta)x + \beta*\beta = 0$

$x^2 - (3\beta)x + \beta^2 = 0$

So, we have:

$\frac{c}{d} = -3\beta$ -- (1)

and

$\frac{p}{d} = \beta^2$ -- (2)

Make $\beta$ the subject in (1)

$\frac{c}{d} = -3\beta$

$\beta = -\frac{c}{3d}$

Substitute $\beta = -\frac{c}{3d}$ in (2)

$\frac{p}{d} = (-\frac{c}{3d})^2$

$\frac{p}{d} = \frac{c^2}{9d^2}$

Multiply both sides by d

$d * \frac{p}{d} = \frac{c^2}{9d^2}*d$

$p = \frac{c^2}{9d}$

Cross Multiply

$9dp = c^2$

$c^2 = 9dp$

Hence, the relationship between d, c and p is: $c^2 = 9dp$

8 0

3 years ago

If marching bands vary from 21 to 49 player, which numbers of players can be arranged in the greatest number of rectangles?

ANEK [815]

Hmm. a rectangle?ok then, least number of rectangles needed-6.
. . .
. . . ( rectangle)
so, 6 x 8=48(greatest multiple of 6 from between 21 and 49)
48 players are most, so 8 rectangles

5 0

3 years ago

If F ( x ) = 2 x - 1, find the zero of F -1( x ). A) -1 B) 1/2 C) 1

tigry1 [53]

Answer:

Step-by-step explanation:

7 0

3 years ago

Five more than four times a number is greater than seven

kolezko [41]

Answer:

5+ 4x > 7, x > 1/2

Step-by-step explanation:

8 0

3 years ago

Simplify The Expression: 1/8h+7-3/4h Thank you!

ivann1987 [24]

Answer:

-5/8h + 7

Step-by-step explanation:

First you need to combine like terms (1/8h and -3/4h)

So 1/8h - 3/4h is -5/8h

Then we have our 7 left over

So the answer is -5/8h + 7

4 0

3 years ago