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3 years ago

Find the value of p3- q3, if p-q = -7 and pq= -10

Mathematics

1 answer:

sergiy2304 [10]3 years ago

5 0

<h3>Answer: -133</h3>

===================================================

Work Shown:

p-q = -7

(p-q)^2 = (-7)^2

p^2-2pq+q^2 = 49

p^2-2(-10)+q^2 = 49

p^2+20+q^2 = 49

p^2+q^2 = 49-20

p^2+q^2 = 29

By the difference of cubes formula, we can say,

p^3 - q^3 = (p-q)*(p^2+pq+q^2)

p^3 - q^3 = (p-q)*(p^2+q^2+pq)

p^3 - q^3 = (-7)*(29-10)

p^3 - q^3 = -133

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Here's another way to solve:

p-q = -7

p = q-7

pq = -10

(q-7)*q = -10

q^2-7q = -10

q^2-7q+10 = 0

(q-5)(q-2) = 0

q-5 = 0 or q-2 = 0

q = 5 or q = 2

If q = 5, then p = q-7 = 5-7 = -2

If q = 2, then p = q-7 = 2-7 = -5

We can see that no matter what we pick for q, we'll get p*q = -10

Also, you should find that p^3-q^3 is equal to -133 for either case as well.

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Answer: The quotient is (x-2).

Step-by-step explanation:

Since we have given that

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Now, we have to find the quotient of the above expression.

So, here we go:

$Factorise\ (x^3+3x^2-4x-12)\\\\=\left(x^3+3x^2\right)+\left(-4x-12\right)\\\\=-4\left(x+3\right)+x^2\left(x+3\right)\\\\=\left(x+3\right)\left(x^2-4\right)$

Now, we will divide the above simplest form with g(x):

$\frac{\left(x+3\right)\left(x^2-4\right)}{\left(x+2\right)\left(x+3\right)}\\\\=\frac{x^2-4}{x+2}\\\\=\frac{\left(x+2\right)\left(x-2\right)}{x+2}\ using\ (a^2-b^2)=(a+b)(a-b)\\\\=x-2$

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3 years ago

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An arc on a circle measures 250 degrees. Within range which range is the radian measure of the central angle?

blondinia [14]

If the arc measures 250 degrees then the range of the central angle lies from π to 1.39π.

Given that the arc of a circle measures 250 degrees.

We are required to find the range of the central angle.

Range of a variable exhibits the lower value and highest value in which the value of particular variable exists. It can be find of a function.

We have 250 degrees which belongs to the third quadrant.

If 2π=360

x=250

x=250*2π/360

=1.39 π radians

Then the radian measure of the central angle is 1.39π radians.

Hence if the arc measures 250 degrees then the range of the central angle lies from π to 1.39π.

Learn more about range at brainly.com/question/26098895

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Answer:

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Step-by-step explanation:

The 95% confidence interval is given by the interval

$\bf [ \bar x-z^*\frac{s}{\sqrt n}, \bar x+t^*\frac{s}{\sqrt n}]$

where

$\bf \bar x$ = 26.7 is the sample mean

s = 17.7 is the sample standard deviation

n = 180 is the sample size

Since the sample size is big enough, we can use the Normal N(0,1) to compute $\bf z^*$ and it would be 1.96(*) (a value such that the area under the Normal curve outside the interval [-z, z] is 5% (0.05))

and our 95% confidence interval is

$\bf [26.7-1.96*\frac{17.7}{\sqrt{180}}, 26.7+1.96*\frac{17.7}{\sqrt{180}}]=\boxed{[24.114,29.2858]}$

(*)

This value can be computed in Excel with

<em>NORMINV(1-0.025,0,1)</em>

and in OpenOffice Calc with

<em>NORMINV(1-0.025;0;1)</em>

Since 30 is not in the 95% confidence interval, there is a 95% probability that 30 is not the true mean WEP

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