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d1i1m1o1n [39]
3 years ago
9

A polynomial function has roots –5 and 1. Which of the following could represent this function?

Mathematics
2 answers:
sesenic [268]3 years ago
6 0

Answer:

D

Step-by-step explanation:

just did it on edge:)

wel3 years ago
5 0

Answer:

Option D is correct .i.e., f(x) = ( x + 5 ) ( x - 1 )

Step-by-step explanation:

Given: Roots of Polynomial are -5 and 1

To find: Polynomial function

We substitute given value of roots in each polynomial and check

if for both value polynomial given 0 then that our required polynomial

A). f(x) = ( x + 5 ) ( x + 1 )

for x = -5

f(-5) = ( -5 + 5 ) ( -5 + 1 )

       = 0 × (-4) = 0

for x = 1

f(1) = ( 1 + 5 ) ( 1 + 1 )

     =  6 × 2 = 12 ≠ 0

Thus, It is not required polynomial

B). f(x) = ( x - 5 ) ( x - 1 )

for x = -5

f(-5) = ( -5 - 5 ) ( -5 - 1 )

       = -10 × (-6) = 60 ≠ 0

for x = 1

f(1) = ( 1 - 5 ) ( 1 - 1 )

     =  -4 × 0 = 0

Thus, It is not required polynomial

C). f(x) = ( x - 5 ) ( x + 1 )

for x = -5

f(-5) = ( -5 - 5 ) ( -5 + 1 )

       = -10 × (-4) = 40 ≠ 0

for x = 1

f(1) = ( 1 - 5 ) ( 1 + 1 )

     =  -4 × 2 = -8 ≠ 0

Thus, It is not required polynomial

D). f(x) = ( x + 5 ) ( x - 1 )

for x = -5

f(-5) = ( -5 + 5 ) ( -5 - 1 )

       = 0 × (-6) = 0

for x = 1

f(1) = ( 1 + 5 ) ( 1 - 1 )

     =  6 × 0 = 0

Thus, It is required polynomial

Therefore, Option D is correct .i.e., f(x) = ( x + 5 ) ( x - 1 )

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Find the direction cosines and direction angles of the vector. (Give the direction angles correct to the nearest degree.) 5, 1,
Dahasolnce [82]

Answer:

The direction cosines are:

\frac{5}{\sqrt{42} }, \frac{1}{\sqrt{42} }  and  \frac{4}{\sqrt{42} }  with respect to the x, y and z axes respectively.

The direction angles are:

40°,  81° and  52° with respect to the x, y and z axes respectively.

Step-by-step explanation:

For a given vector a = ai + aj + ak, its direction cosines are the cosines of the angles which it makes with the x, y and z axes.

If a makes angles α, β, and γ (which are the direction angles) with the x, y and z axes respectively, then its direction cosines are: cos α, cos β and cos γ in the x, y and z axes respectively.

Where;

cos α = \frac{a . i}{|a| . |i|}               ---------------------(i)

cos β = \frac{a.j}{|a||j|}               ---------------------(ii)

cos γ = \frac{a.k}{|a|.|k|}             ----------------------(iii)

<em>And from these we can get the direction angles as follows;</em>

α =  cos⁻¹ ( \frac{a . i}{|a| . |i|} )

β = cos⁻¹ ( \frac{a.j}{|a||j|} )

γ = cos⁻¹ ( \frac{a.k}{|a|.|k|} )

Now to the question:

Let the given vector be

a = 5i + j + 4k

a . i =  (5i + j + 4k) . (i)

a . i = 5         [a.i <em>is just the x component of the vector</em>]

a . j = 1            [<em>the y component of the vector</em>]

a . k = 4          [<em>the z component of the vector</em>]

<em>Also</em>

|a|. |i| = |a|. |j| = |a|. |k| = |a|           [since |i| = |j| = |k| = 1]

|a| = \sqrt{5^2 + 1^2 + 4^2}

|a| = \sqrt{25 + 1 + 16}

|a| = \sqrt{42}

Now substitute these values into equations (i) - (iii) to get the direction cosines. i.e

cos α = \frac{5}{\sqrt{42} }

cos β =  \frac{1}{\sqrt{42} }              

cos γ =  \frac{4}{\sqrt{42} }

From the value, now find the direction angles as follows;

α =  cos⁻¹ ( \frac{a . i}{|a| . |i|} )

α =  cos⁻¹ ( \frac{5}{\sqrt{42} } )

α =  cos⁻¹ (\frac{5}{6.481} )

α =  cos⁻¹ (0.7715)

α = 39.51

α = 40°

β = cos⁻¹ ( \frac{a.j}{|a||j|} )

β = cos⁻¹ ( \frac{1}{\sqrt{42} } )

β = cos⁻¹ ( \frac{1}{6.481 } )

β = cos⁻¹ ( 0.1543 )

β = 81.12

β = 81°

γ = cos⁻¹ ( \frac{a.k}{|a|.|k|} )

γ = cos⁻¹ (\frac{4}{\sqrt{42} })

γ = cos⁻¹ (\frac{4}{6.481})

γ = cos⁻¹ (0.6172)

γ = 51.89

γ = 52°

<u>Conclusion:</u>

The direction cosines are:

\frac{5}{\sqrt{42} }, \frac{1}{\sqrt{42} }  and  \frac{4}{\sqrt{42} }  with respect to the x, y and z axes respectively.

The direction angles are:

40°,  81° and  52° with respect to the x, y and z axes respectively.

3 0
3 years ago
The number of girls in the Middle School Cyber Club was 6 more than double the number of boys, and in total there were 48 middle
Wittaler [7]

Answer:

g = number of girls;

b= number of boys

we know that: g= 6+2b

     and that: g+b= 156 kids in total

so we may write  g+b=(6+2b)+b=6+3b

                 but g+b= 156

so 6+3b = 156 => 3b= 156-6=150 =>   b=150/3=50 => b = 50 (number of boys)

g= 6+2b= 6+2 x 50= 106 => g =106 (number of girls)  

Step-by-step explanation:

5 0
3 years ago
Evaluate if a=2, b=5, C=1<br> b(4a + c²)​
kipiarov [429]

Answer:

45

Step-by-step explanation:

5(4(2)+ 1²)

5(8 + 1²)

40 + 5

45

5 0
3 years ago
Solve for the difference <br><br><br><br><br><br> `7.2-3.67`
storchak [24]
The correct answer is 3.53
7 0
2 years ago
Whats the simpilest form of the ratio <br>48 min to 3 hours.​
MArishka [77]

15:4.

Step-by-step explanation:

1 hour = 60 min

3 hours = 60 x 3 = 180 min

Ratio:

180/48

Simplest form 15/4

Therefore, the simplest form of the ratio will be 15:4

7 0
3 years ago
Read 2 more answers
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