[tex]\large\underline{\sf{Solution-}}[/tex]
Given that:
[tex]\sf p(y) = 2y^3+my^2+11y+m+3 [/tex]
We are also given that, p(y) is divisible by 2y - 1.
So, 2y - 1 is a factor of p(y).
[tex]\sf\longmapsto 2y-1=0[/tex]
[tex]\sf\longmapsto y=\dfrac{1}{2}[/tex]
So, 1/2 is a zero of p(y).
[tex]\sf\longmapsto p(1/2) =0 [/tex]
[tex]\sf\longmapsto p(y) = 2y^3+my^2+11y+m+3 [/tex]
[tex]\sf\longmapsto p\left(\dfrac{1}{2}\right) = 2\left(\dfrac{1}{2}\right)^3+m\left(\dfrac{1}{2}\right)^2+11\left(\dfrac{1}{2}\right)+m+3 [/tex]
So,
[tex]\sf\longmapsto p\left(\dfrac{1}{2}\right) = 2\left(\dfrac{1}{8}\right)+m\left(\dfrac{1}{4}\right)+11\left(\dfrac{1}{2}\right)+m+3 [/tex]
[tex]\sf\longmapsto p\left(\dfrac{1}{2}\right) = \dfrac{1}{4}+\dfrac{m}{4}+\dfrac{11}{2}+m+3 [/tex]
[tex]\sf\longmapsto p\left(\dfrac{1}{2}\right) =\dfrac{1}{4}+\dfrac{m}{4}+\dfrac{22}{4}+\dfrac{4m}{4}+\dfrac{12}{4} [/tex]
[tex]\sf\longmapsto 0 =\dfrac{1+m+22+4m+12}{4} [/tex]
[tex]\sf\longmapsto 0 =\dfrac{5m+35}{4}[/tex]
[tex]\sf\longmapsto 5(m+7)=4\times0[/tex]
[tex]\sf\longmapsto 5(m+7)=0[/tex]
[tex]\sf\longmapsto m+7=0[/tex]
[tex]\longmapsto\bf m=-7[/tex]
Therefore, the value of m is -7.
Prove that: (sin x - 2 sin³ x)/(2 cos³ x - cos x) = tan x
[tex]\large\underline{\sf{Solution-}}[/tex]
We have to prove that:
[tex]\rm\longmapsto \dfrac{ \sin(x) - 2 \sin^{3} (x) }{2 \cos^{3} (x) - \cos(x) } = \tan(x) [/tex]
Taking LHS, we get:
[tex]\rm = \dfrac{ \sin(x) - 2 \sin^{3} (x) }{2 \cos^{3} (x) - \cos(x) }[/tex]
We can take sin(x) as common from numerator part. We get:
[tex]\rm = \dfrac{ \sin(x) \{1- 2 \sin^{2} (x) \}}{2 \cos^{3} (x) - \cos(x) }[/tex]
Similarly, we can take cos(x) as common from first two terms. We get:
[tex]\rm = \dfrac{ \sin(x) \{1- 2 \sin^{2} (x) \}}{ \cos(x) \{ 2 \cos^{2} (x) -1\}}[/tex]
[tex]\rm = \dfrac{ \sin(x) }{ \cos(x) } \cdot \dfrac{\{1- 2 \sin^{2} (x) \}}{\{ 2 \cos^{2} (x) -1\}}[/tex]
As we know that:
[tex]\rm\longmapsto \dfrac{ \sin(x) }{ \cos(x) } = \tan(x) [/tex]
We get:
[tex]\rm = \tan(x) \cdot \dfrac{\{1- 2 \sin^{2} (x) \}}{\{ 2 \cos^{2} (x) -1\}}[/tex]
Now, we will expand the terms in fraction:
[tex]\rm = \tan(x) \cdot \dfrac{\{1- \sin^{2} (x) - { \sin }^{2}(x) \}}{\{\cos^{2} (x) + \cos^{x}(x) -1\}}[/tex]
As we know that:
[tex]\rm \longmapsto \sin^{2}(x)+cos^{2}(x)=1[/tex]
[tex]\rm \longmapsto\cos^{2}(x)=1-sin^{2}(x)[/tex]
[tex]\rm \longmapsto\cos^{2}(x) - 1=-sin^{2}(x)[/tex]
Now substitute the values in the expression, we get:
[tex]\rm = \tan(x)\cdot \dfrac{ \cos^{2} (x)-{ \sin }^{2}(x)}{\cos^{2} (x) - \sin^{2} (x) }[/tex]
[tex]\rm = \tan(x)\cdot1[/tex]
[tex]\rm = \tan(x)[/tex]
Here, we notice that LHS = RHS
Proved.
hi po pahelp ito pls pls pls pls pls pls pls
conversion of temperature
buying groceries
checking weight
measuring length
Plz help I need help
Answer:
The ratios are proportional ratios
Answer:
Step-by-step explanation:
The ratios are proportional
[tex]\dfrac{5}{12}=\dfrac{5*2}{12*2}=\dfrac{10}{24}[/tex]
Find the sum of A.5 B.3 C.4 D.1
Answer:
D. Maybe? brainliest suggested
Step-by-step explanation:
Find the value of x in the figure below:
Answer:
x = 25
Step-by-step explanation:
The interior angle adjacent to the 123° angle is supplementary to it.
Its measure is 180° - 123° = 57°
The sum of the measures of the interior angles of a polygon is
(n - 2)180° = (4 - 2)180° = 2(180°) = 360°
3x + 7 + 96 + 5x + 57 = 360
8x + 160 = 360
8x = 200
x = 25
find the value of 3x^3y-2xy^2 when x=3 and y=-2
Answer:
sorry I don't remember bye I will try to remember
Determine the domain and the range of the relation, and tell whether the relation is
a function.
{(13,2), (18, – 5), (39,2), (13,4), (51,4)}
--
What is the domain and range?
Step-by-step explanation:
it is NOT a function, because one x value (13) has more than one associated result value (2 and 4). that violates the basic principle of a function.
anyway, the domain is the interval or set of the valid values for x, and the range the interval or set of the valid values for y.
the domain is {13, 18, 39, 51}
the range is {-5, 2, 4}
the square root of a negative number is known as an _______ number
Positive number is a square root
Select True or False for each statement pls.
Statement 1: False
Statement 2: True
Statement 3: True
please help me with this sum
Answer:
Step-by-step explanation:
2. 3 × 12 = 3 × 2 × 6 = 3 × 2 × 2 × 3
3. 4 × 9 = 2 × 2 × 3 × 3
4. 6 × 6 = 2 × 3 × 2 × 3
please give me a brainliest answer
Step-by-step explanation:
2. 36 = 3 × 12 = 3 × 2 × 6 = 3 × 2 × 2 × 3
3. 36 = 4 × 9 = 2 × 2 × 3 × 3
4. 36 = 6 × 6 = 2 × 3 × 2 × 3
Two trains leave stations 420 miles apart at the same time and travel toward each other. One train travels at 65 miles per hour while the other travels at 85
miles per hour. How long will it take for the two trains to meet?
Do not do any rounding.
Answer:
2hr 48 minutes
Step-by-step explanation:
65t + 85t = 420
150t = 420
t = 2 120/150 = 2 4/5 = 2hr 48 minutes
Time taken by two trains to cover 420 miles is 2hr 48 minutes.
Given, that two trains are travelling towards each other.
Relation between speed, time and distance:
Distance = Speed × Time
When the two trains are travelling towards each other the speeds of two trains are added.
When the two trains are moving in same direction then the relative speed is difference of the two.
So, here the trains are moving towards each other.
65t + 85t = 420
150t = 420
t = 420/150
t = 42/15
t = 2hr 48 minutes
Therefore total time required by two trains to meet is 2hr 48 minutes.
Know more about speed, time and distance,
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Suppose z varies directly with x and inversely with the square of y . If z=18 when x=6 and y=5 , what is z when x=11 and y=10?
Patrick ate 540 apples in 9 hours. at that rate, how many apples could he eat in 4 minutes?
Answer:
He could eat 4 apples in 4 minutes
Step-by-step explanation:
If he eats 1 apple per minute (which I dont know how he does) then in 4 minutes he will have eaten 4 apples.
632 16/25 +32 3/10 answer in decimal
Answer:
664.94
Step-by-step explanation:
Give me brainlyest please
Answer:
664.94 is the answer to this question. I hope this helps.
ANSWER LAST QUESTION PLZZZ
Step-by-step explanation:
what ask you ask you not ask any question please write your question please mark me brainlist
List all subsets of the set {A, B, C} using proper notation
Answer:
subset of {A, B, C} = { }, {A}, {B}, {C}, {A,B}, {B,C},{C,A}
Hope that my answer is helpful to you
Round off the numbers then add to find the estimated difference.
ANSWERS ARE INCORRECT
Answer:
500, 300
Step-by-step explanation:
Assuming the rounding is for nearest 100,
635-124
600-100
500
864-612
900-600
300
Solve 3x + 4x = 2.
+
Answer: [tex]\frac{-2+\sqrt{10}}{3}[/tex]
Step-by-step explanation:
Evaluate -8x+5-2x-4+5x
Answer:
The value of the expression is - 9.
Evaluating the expression before simplifying is preferred because you only have to substitute once instead of substituting three times.
Step-by-step explanation:
x = 2
- 8x + 5 - 2x - 4 + 5x
= - 8x - 2x + 5x + 5 - 4
= - 10x + 5x + 1
= - 5x + 1
= - 5 ( 2 ) + 1
= - 10 + 1
= - 9
Translate this sentence into an equation.
70 is the product of Han's savings and 5.
Use the variable h to represent Han's savings.
Có 2 chuông gà: chuồng 1 có 5 trống 10 mái ,chuồng 2 có 6 trống 14 mái. Có 1 con ở chuồng 2 nhảy sang chuồng 1 . từ chuồng 1 bắt ngẫu nhiên ra 2 con. Tính xác suất bắt được
a . 2 con trống
Add the denominate numbers and simplify if necessary. 3 hr 55 min 40 sec + 5 hr 28 min 20 sec
Answer:
3hr 26min 25src
Step-by-step explanation:
The lengths of the worms (in inches) are listed here.
Which line plot shows this data?
Answer:
Top Left
Step-by-step explanation:
The numbers all coordinate to that plot
Answer:
Plot #1Step-by-step explanation:
The easy way is to look for exceptions. The first and last plots missing 7/8 and same with data set.
There are 4 1's in the set which is correct with the first plot.
b. What is the number that is halfway between the two values?
7 and 11
Submit
Answer:
9
Step-by-step explanation:
It would be 9 because 7 +2 is 9 and 11 - 2 is 9.
Isn't way to hard.
Good luck on whatever you are doing.
9514 1404 393
Answer:
9
Step-by-step explanation:
The midpoint between two values is their average. The average is half their sum.
(7 +11)/2 = 18/2 = 9
The number 9 is halfway between 7 and 11.
_____
Check
The distance from 7 to 9 is 9-7 = 2. The distance from 9 to 11 is 11-9 = 2. The distances are the same, so 9 is halfway between 7 and 11.
The cost for one ticket to a jazz concert is $7.50. Two tickets cost $15. Write an equation in point-slope form to represent the total cost y for x tickets.
An equation in the point-slope form to represent the total cost y for x tickets is [tex]y-15 = 2(x-2)\\[/tex]
Let the cost of ticket be C
Let the number of tickets be x
The coordinate for the cost of a ticket will be written as: (x, C)
If the cost for one ticket to a jazz concert is $7.50, this is represented in coordinate form as (1, 7.50)
If two tickets cost $15, his is represented in coordinate form as (2, 15)
Get the slope of the equation
[tex]m =\frac{15-7.5}{2-1}\\m=\frac{7.5}{1}\\m = 7.5\\[/tex]
Get the equation in point-slope form
[tex]y-y_1 = m(x-x_1)\\[/tex]
Substitute the slope and one of the point into the formula:
[tex]y-15 = 2(x-2)\\[/tex]
Hence an equation in the point-slope form to represent the total cost y for x tickets is [tex]y-15 = 2(x-2)\\[/tex]
Learn more here: https://brainly.com/question/13075635
There are twice as many gray kittens than white
kittens. There are 4 white kittens. How many gray
kittens are there?
Answer:
8 gray kittens
Step-by-step explanation:
There are double the amount of grey kittens compared to white kittens so, you would do 4 × 2 which is 8. There are 8 grey kittens.
Hope this helps!
What cross sections might you see when a plane intersects a cone that you would not see when a plane intersects a prism or a pyramid
Answer:
the long They speaker by my parents waving the firstpassword of their TainQuestion Choice Worth 2 points)
(02.06Derek has a bird that weighs 4 pounds. Use the double fine diagram below to help you determine approximately how many kilograms this bird weighs
3 5 7
Pounds
1 2 3
Kilograms
15 klograms
O2 xilogram
5 kilograms
7 kilograms
is -5.25 greater than -3
Answer:
False -5.25 is < (less than) -3
Step-by-step explanation:
Given matrices A and B shown below, find (−3)A+(−5)B.
Answer:
i don't understand this
Step-by-step explanation:
I don't understand this at all I have no been getting this in school
