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3 years ago

Use synthetic division and the remainder theorem to find p(a) = 2x3 -x2 + 10x; = a = 1/2

Mathematics

1 answer:

sergey [27]3 years ago

8 0

Answer:

p(1/2) = 5

Step-by-step explanation:

Find the value of p(1/2) if p(x) = 2x^3 -x^2 + 10x

Set up synthetic div.:

1/2 ) 2 -1 10 0

1 0 5

------------------------

2 0 10 5

The remainder is 5, so we conclude that p(x) = 2x^3 -x^2 + 10x = 5 when x = 1/2.

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List all the factors of the composite number 146

Temka [501]

1 and 146
2 and 73
and that's about it

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3 years ago

23 and 25 how do you do the work? find the areas of each

stiks02 [169]

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Answer:

23) 35.77 in²

25) 48.19 cm²

Step-by-step explanation:

Use the appropriate area formula with the given information.

23) The area of a triangle is given by the formula ...

A = 1/2bh . . . . . base b, height h

A = 1/2(9.8 in)(7.3 in) = 35.77 in²

25) The area of a parallelogram is given by the formula ...

A = bh . . . . . . base b, height h

A = (7.9 cm)(6.1 cm) = 48.19 cm²

_____

The height in each figure is measured perpendicular to the base. This tells you that the length 10.6 cm of the diagonal side of the triangle is not relevant to finding the area.

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3 years ago

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Find the median for the following set of numbers: 12, 15, 15, 16, 19, 21, 25

Hoochie [10]

The median is the number in the middle of the data set.

There are 7 numbers, so the 4th number is the median.

(Another method is to eliminate a number on each side until you get to the middle number)

<h2>Answer:</h2>

The median is 16.

I hope this helps :)

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3 years ago

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For right triangle , triangle rst shown below, what is tan r

-Dominant- [34]

You know, it would really be helpful if we could have a peek at
the picture that's "shown below". Just a peek would be enough.
Right now, the only thing I see below is my dog.

Now ... follow me here ... if you're looking for tan(r), then 'r' is
one of the angles in the triangle, and I'm guessing that all three
of those letters are angles.

tan(r) is going to be the ratio of two of the sides ... I mean

(one side) divided by (another side).

There's no way to go any farther, because you haven't given us
any names for the sides, or any way to describe them.

Betcha the names of the sides are on that picture that's supposed
to be shown below.

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3 years ago

The height (in meters) of a projectile shot vertically upward from a point 4 m above ground level with an initial velocity of 25

Assoli18 [71]

Answer:

(a) The velocity after 2 second is 5.9 m/s

The velocity after 4 second is -13.7 m/s.

(b) The projectile reaches its maximum height after 2.60 s of projection.

(c)The maximum height that is attained by the projectile is 37.18 m.

(d)Therefore the projectile hits the ground after 5.36 seconds of projection.

(e)The velocity of the projectile when it hits the ground is 27.03 m/s

Step-by-step explanation:

Given that, a projectile shot vertically upward from a point 4 m above the ground with a initial velocity of 25.5 m/s.

The height of the projectile after t seconds is

$h=4+25.5t-4.9t^2$

where h is in meter.

(a)

We use the formula

v=u+at

V= final velocity

u = initial velocity = 25.5 m/s

a = acceleration= acceleration due to gravity= 9.8 m/s²

Since the object moves upward direction and acceleration due to gravity is downward direction. So here a= -9.8 m/s.

v(2)= 25.5+(-9.8)×2

=25.5-19.6

=5.9 m/s

And when t= 4

v(4)= 25.5+(-9.8)×4

=25.5-39.2

= -13.7 m/s

The velocity after 2 second is 5.9 m/s

The velocity after 4 second is -13.7 m/s.

(b)

At its maximum height,the velocity of the projectile is zero. i.e v=0

∴0=25.5+(-9.8)t

⇒9.8t=25.5

$\Rightarrow t=\frac{25.5}{9.8}$

⇒t = 2.60 s

The projectile reaches its maximum height 2.60 s after projection.

(c)

To find the maximum height, we are putting t= 2.60 in this equation $h=4+25.5t-4.9t^2$ .

$\therefore h= 4+(25.5\times 2.60)-(4.9\times 2.60^2)$

=37.18 m

The maximum height that is attained by the projectile is 37.18 m.

(d)

When the projectile hits the ground the height will be zero i.e h=0

From the equation of height we get

$\therefore h=0=4+25.5t-4.9t^2$

$\Rightarrow 4+25.5t-4.9t^2=0$

$\Rightarrow t=\frac{-25.5\pm\sqrt{25.5^2-4(-4.9).4}}{2(-4.9)}$

⇒t= -0.15 ,5.36

Therefore it hits the ground after 5.36 seconds of projection.

(e)

To find the velocity we use the formula v=u+at

Here v = final velocity=?

u=25.5 m/s,

t = 5.36 s

a= -9.8m/s²

v=25.5+(-9.8)5.36

= -27.03 m/s

Negative sign denoted that the motion of the projectile is downward direction.

The velocity of the projectile when it hits the ground is 27.03 m/s.

6 0

3 years ago