(cosecx+2)(2cosx-1)=0

The values of a and b using the factor theorem for the polynomial f(x), we set f(1) and f(-1) equal to zero. Solving the resulting system of equations, we find that a = 12 and b = -1.

To find the values of a and b using the factor theorem, we need to use the given factors (x - 1) and (x + 1) and the fact that they are roots of the polynomial f(x).
The factor theorem states that if (x - c) is a factor of a polynomial, then f(c) = 0. Therefore, we can set x = 1 and x = -1 in the polynomial f(x) to get two equations.
First, let's substitute x = 1 into f(x):
f(1) = (1)^3 + a(1)^2 + b(1) - 12
f(1) = 1 + a + b - 12
Next, let's substitute x = -1 into f(x):
f(-1) = (-1)^3 + a(-1)^2 + b(-1) - 12
f(-1) = -1 + a - b - 12
Since (x - 1) and (x + 1) are factors, f(1) and f(-1) must equal zero. Therefore, we can set the two equations equal to zero and solve for a and b:
1 + a + b - 12 = 0
-1 + a - b - 12 = 0
Rearraning the equations, we have:
a + b = 11
a - b = 13
Now, we can solve this system of equations. Adding the two equations, we get:
2a = 24
a = 12
Substituting the value of a into one of the equations, we find:
12 - b = 13
b = -1
Therefore, the values of a and b are 12 and -1 respectively.

For more such questions on polynomial

https://brainly.com/question/1496352

#SPJ8

Answer:

378.33 minutes

Step-by-step explanation:

From the question, we're told that

Length of the side of the square, l = 4 m

Then the current volume of water = (4 m)³ = 64 m³3 = 64,000 Liters

64,000 + [∫(20 - t) dt from 0 to t] = 0, solving the integral, we have

20t - (t^2)/2 = -64,000, multiplying all by 2 so as to eliminate the fraction

40t - t^2 + 128,000 = 0

t^2 - 40t - 128,000 = 0, on solving the quadratic equation(using general formula), we find that

t = 378.33 minutes

The equation of the line with slope 1/3 and y-intercept as -1 is y = x/3-1 in slope-intercept form.

According to the question,

We have the following information:

Slope of the line = 1/3

We know that the slope of the line is denoted by m.

y-intercept of the line = -1

We know that the y-intercept is denoted by b.

We have the following equation for the line in slope-intercept form:

y = mx+b

Putting the above values in this equation:

y = x/3-1

Hence, the equation of the line with slope 1/3 and y-intercept as -1 is y = x/3-1 in slope-intercept form.

To know more about equation of the line here

https://brainly.com/question/402319

#SPJ1

Answer:

6 = u

Step-by-step explanation:

54 / u = 9

We have to isolate "u" all by itself;

54 = 9*u

54 / 9 = u

6 = u

Hope this helps!

Answer:

6

Step-by-step explanation:

We need to find of u value such that , 54 divided by u = 9. Converting it into equation ,

Equation :-

→ 54/u = 9

→ 1/u = 9 × 1/54

→ 1/u = 1/6

→ u = 6

using SOH CAH TOA

Tan 85.144 =h/130

h=tan 85.144*130

h=1530.19 fr

the value of the test statistic for testing whether there is a linear relationship between the and the estimated number is 0.3506905

Using a correlation Coefficient calculator, the correlation Coefficient, r for the data = 0.127

The test statistic :

T = r² / √(1 - r²) / (n - 2)

Sample size, n = 10

Hence,

T = 0.127² / √(1 - 0.127²) / (10 - 2)

T = (0.016129 / 0.3506905)

T = 0.3506905

The value of the test statistic to 2 decimal places is 0.35

learn more about of statistic here

https://brainly.com/question/23382433

#SPJ4

Answer:

100°

Step-by-step explanation:

tThe sum of all arc measures that make up that circle is 360 degrees.

QS + RQ + RS = 360

QS = 360 - 120 - 140 = 100

An arc angle is the degree measurement of that angle inside the circle, opposite the arc

m∠R = arc QS = 100°

Answer:

∠ R = 50°

Step-by-step explanation:

the inscribed angle R is half the measure of its intercepted arc QS

the sum of the arcs on a circle is 360° , that is

RQ + QS + SR = 360°

120° + QS + 140° = 360°

QS + 260° = 360° ( subtract 260° from both sides )

QS = 100°

Then

∠ R = \(\frac{1}{2}\) × 100° = 50°

Answer:

~ 17.4

Step-by-step explanation:

The number of students per teacher in 1999 is approximately 17.4  

Answer:

Step-by-step explanation:

To write y as a function of x using the given functions, we can substitute the value of "a" in the first equation with the expression "-5x + 1" from the second equation.

Given:

y = -3a + 3

a = -5x + 1

Substituting the value of "a" in the first equation:

y = -3(-5x + 1) + 3

Now, let's simplify this expression:

y = 15x - 3 + 3

y = 15x

Therefore, y can be expressed as a function of x as:

y = 15x

Answer:

c

Step-by-step explanation:

it's a property of powers, when the base is the same (-5) , you need to

sum the powers when both terms are multiplyng

subtract the powers when both terms are dividing (numerator power minus denominator power, in that order)

Answer:

150 units woild fill the volume of the prism.

Answer:

4*(x+y)=20

Step-by-step explanation:

sum means add all together. and sum of a number means number added all together.

The given statement "Four times the sum of a number x and a number y is equal to 20" is written in the form of an expression as 4(x+y)=20.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given statement "Four times the sum of a number x and a number y is equal to 20" can be written in the form of an expression as,

Hence, The given statement "Four times the sum of a number x and a number y is equal to 20" is written in the form of an expression as 4(x+y)=20.

Learn more about Expression here:

https://brainly.com/question/13947055

#SPJ2

Answer:

28.26

Step-by-step explanation:

The formula for calculating diameter is πd (pi times the diameter), so 3.14 times 9 is 28.26.

Answer:

click the picture for see all anwer

Step-by-step explanation:

I hope it help.

Answer:

520 - 10x = 380

Step-by-step explanation:

x= 14

Answer:

520-10x=380

x = 14

Step-by-step explanation:

Answer:

Step-by-step explanation:

The adjacent angle to the missing angle must sum to 180 degrees. So a=180-74=106 degrees. The sum of the three angles of the triangle must also sum to 180.

x+49+106=180

x+155=180

x=25

Answer:

106

Step-by-step explanation:

x+49=74

x=74-49=25

y=74=180

y=180-74=106

im sorry im late if u see this yw!

Answer:

16

Step-by-step explanation:

Step 1: Write down the function \(f(x)=7x^2+2x+3.\)

Step 2: Write down the limit definition of the derivative:
\(f'(x)= lim_{h0} \frac{f(x+h)=f(x)}{h} .\)

Step 3: Substitute the function \(f(x)\) into the limit definition:
\(f'(x)=lim_{h0} \frac{(7(x+h)^2+2(x+h)+3)-(7x^2+2x+3)}{h}.\)

Step 4: Simplify the expression inside the limit:
\(f'(x)=lim_{h0}\frac{7x^2+14xh+7h^2+2x+2h+3-7x^2-2x-3}{h} .\)

Step 5: Combine like terms:
\(f'(x)=lim_{h0} \frac{14xh+7h^2+2h}{h} .\)

Step 6: Factor out an \(h\) from the numerator:
\(f'(x)=lim_{h0} \frac{h(14x+7h+2h}{h} .\)

Step 7: Cancel out the \(h\) in the numerator and denominator:
\(f'(x)=lim_{h0}(14x+7h+2).\)

Step 8: Evaluate the limit as \(h\) approaches 0:
\(f'(x)=14x+2.\)

Step 9: Substitute \(x=1\) into the derivative:
\(f'(1)=14(1)+2=14+2=16.\)

The Slope of the tangent line to the curve \(f(x)=7x^2+2x+3\) at \(x=1\) would be \(16.\)

Using the method of Lagrange multipliers: the Lagrangian is

\(L(x,y,z,\lambda) = (x-4)^2+(y-5)^2+(z-6)^2 - \lambda (z-4x^2-4y^2)\)

Fix λ > 0.

That is, we are minimizing the squared distance of a point (x, y, z) on the paraboloid to the point (4, 5, 6). We can use the squared distance in place of the proper Euclidean distance because both f(x) and √f(x) have critical points at the same point x ; plus the math works out much more easily.

Find the critical points of the Lagrangian:

\(\dfrac{\partial L}{\partial x} = 2(x-4) + 8\lambda x = 0 \\\\ \dfrac{\partial L}{\partial y} = 2(y-5) + 8\lambda y = 0 \\\\ \dfrac{\partial L}{\partial z} = 2(z-6) - \lambda = 0 \\\\ \dfrac{\partial L}{\partial\lambda} = -z+4x^2+4y^2 = 0\)

Solving for λ in terms of x, y, or z gives

\(\displaystyle \lambda = \frac1x-\frac14 = \frac5{4y} - \frac14 = 2z-12\)

so right away, we get

\(\dfrac5{4y} - \dfrac14 = \dfrac1x - \dfrac14 \implies y=\dfrac{5x}4 \\\\ 2z-12 = \dfrac1x-\dfrac14 \implies z = \dfrac1{2x} + \dfrac{47}8\)

Substitute these into the constraint and solve for x, then for y and z :

\(\dfrac1{2x} + \dfrac{47}8 = 4x^2 +4\left(\dfrac{5x}4\right)^2 \implies 82x^3 - 47x - 4 = 0\)

This has 3 roots, but we take the lone positive solution for x because otherwise λ would be negative. This root is x ≈ 0.7965.

Then it follows that the closest point on the paraboloid to (4, 5, 6) is the critical point (0.7965, 0.9956, 6.5028).

Answer:

cot (x) ; D

Step-by-step explanation:

Mathematically;

cosec is 1/sin

So if cosec is 14/10 , then sin is 10/14

Sine refers to opposite/hypotenuse

So to get the adjacent, we use the pythagoras theorem.

According to this, the square of the hypotenuse equals the sum of the squares of the opposite and adjacent

Hence to get the value of the adjacent, we have;

14^2 - 10^2 = O^2

O^2 = 196-100

O^2 = 96

O = square root of 96

Now, mathematically, we know that Tan is opposite/ adjacent

So in this case tan = 10/√96

But cot is 1/tan

Thus cot = √96/10

So cot is our answer

Answer:

A. cos(x)

Step-by-step explanation:

Answer:

x ≤ -9 and x ≤ 5

Step-by-step explanation:

2x² + 4x - 85 ≤ -4x +5

2x² + 8x - 85 ≤ 5

2x² + 8x - 90 ≤ 0

x² + 8x -180 ≤ 0

(x + 18)(x - 10) ≤ 0

(x + 9)(x - 5) ≤ 0

x + 9 ≤ 0

x ≤ -9

x - 5 ≤ 0

x ≤ 5

Answer:

20.3

Step-by-step explanation:

Answer:

Step-by-step explanation:

u=6i-j

v=7i-4j

u.v=|6i-j||7i-4j| cos α,where α is the angle between u & v.

(6i-j).(7i-4j)=√(6²+(-1)²)√(7²+(-4)²) cos α

(6)(7)+(-1)(-4)=√37√65 cos α

42+4=√37√65  cos α

\(\cos \alpha =\frac{46}{\sqrt{37} \sqrt{65} } \\\alpha =\cos^{-1}\frac{46}{\sqrt{37} \sqrt{65} } \approx 20.28^\circ \approx 20.3^\circ\)

The expression is,

Put x=5 and y=-3 in the above expression.

Therefore, the answer is 22.

Answer:

1/6

Step-by-step explanation:

I dunno, I put this into a calculator and that's the answer it gave me.

In the equation y = 10 - 0.1x, the coefficient 0.1 represents the slope of the line.

it represents the rate of change of y with respect to x, which is the amount by which y changes for every unit increase in x.

In this case, the slope is negative (-0.1), which means that as the number of minutes on hold (x) increases by 1 unit, the level of satisfaction (y) decreases by 0.1 units.

In other words, the longer a customer spends on hold, the lower their level of satisfaction is likely to be. The slope is a key parameter in the equation and provides valuable information about the relationship between the two variables.

To Know more about variables, visit:

https://brainly.com/question/17344045

#SPJ1

Step-by-step explanation:

\(-2(-9x + 6y)\) is factored, use the Distributive Property to un factor this expression.

Work:

\(-2(-9x + 6y) \\=-2(-9x)+-2(6y)\\=18x-12y\)

Answer:

12.9

Step-by-step explanation:

Since the degree of the 10 is 1, move the decimal point of 1.29 to the right once.

Hi!

Your answer should be: 12.9.

Hope this helps!

Yours truly,

Answer:

Step-by-step explanation:

(a)

well since they can lay 7 miles of track every day, the formula i make for the amount of track there is left to lay is:

L=196-Ld

where l is the length of track remaining, L is the length of track they can lay in one day and d is the number of days.

so we replace L for 7 and d for 17 and we get:

L=196-7x17

which works out to be 77 miles of track remaining to lay.

(b)

well since we want them to have 0 length of track remaining, and they can lay 7 miles of track a day, we can work out d. let's give the formula a bash to get:

d=196-l/L

we then replace l with 0 and L with 7 and get:

d=196/7

which works out to be 28. so it will take 28 days or 4 weeks for the railroad crew to lay 196 miles of track.

Answer:

33.33%

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

so we add 1 and 3 together becuase since there are equal parts, we need to add to get the whole. so since the ration is 1:3, there are 1/4x cats thereate the show

Answer:

the value of expression is 58

Step-by-step explanation:

3(2x-y)+(3+x)²

substitute x =4 and y=5

3(2(4)-5)+(3+4)²

3(8-5)+(7)²

3(3)+49

9+49

58