Line segment CT contains the point C(−2, 5) and a midpoint at A(1, −3). What is the location of endpoint T?

Given f(x) = x^3 + kx + 2, and x + 1 is a factor of f(x), then what is the value of k?

Aleks [24]

Answer:

k = 1

Step-by-step explanation:

Given that,

$f(x) = x^3 +kx + 2$

If (x+1) is a factor of (x), we need to find the value of k.

Using remainder theorem to find it.

Put (x+1) = 0

x = -1

Put x = -1 in equation below.

$x^3 + kx + 2=0\\\\(-1)^3+k(-1)+2=0\\\\-1-k+2=0\\\\1-k=0\\\\k=1$

So, the value of k is 1.

4 0

3 years ago

Evaluate the line integral, where c is the given curve. (x + 9y) dx + x2 dy, c c consists of line segments from (0, 0) to (9, 1)

viktelen [127]

$\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=\int_C\langle x+9y,x^2\rangle\cdot\underbrace{\langle\mathrm dx,\mathrm dy\rangle}_{\mathrm d\mathbf r}$

The first line segment can be parameterized by $\mathbf r_1(t)=\langle0,0\rangle(1-t)+\langle9,1\rangle t=\langle9t,t\rangle$ with $0\le t\le1$ . Denote this first segment by $C_1$ . Then

$\displaystyle\int_{C_1}\langle x+9y,x^2\rangle\cdot\mathbf dr_1=\int_{t=0}^{t=1}\langle9t+9t,81t^2\rangle\cdot\langle9,1\rangle\,\mathrm dt$
$=\displaystyle\int_0^1(162t+81t^2)\,\mathrm dt$
$=108$

The second line segment ( $C_2$ ) can be described by $\mathbf r_2(t)=\langle9,1\rangle(1-t)+\langle10,0\rangle t=\langle9+t,1-t\rangle$ , again with $0\le t\le1$ . Then

$\displaystyle\int_{C_2}\langle x+9y,x^2\rangle\cdot\mathrm d\mathbf r_2=\int_{t=0}^{t=1}\langle9+t+9-9t,(9+t)^2\rangle\cdot\langle1,-1\rangle\,\mathrm dt$
$=\displaystyle\int_0^1(18-8t-(9+t)^2)\,\mathrm dt$
$=-\dfrac{229}3$

Finally,

$\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=108-\dfrac{229}3=\dfrac{95}3$

5 0

4 years ago

I need help please i’ll give u a brainliest

Feliz [49]

Answer:

12

Step-by-step explanation:

c = sqrt(a^2+b^2)

Imput numbers and solve for b!

4 0

3 years ago

Read 2 more answers

5 + 2n2 when n = 3. (The 2 after the n is an exponent)

Pani-rosa [81]

Answer:

23

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Kim and Danielle each improved their yards by planting hostas and ivy. They bought their supplies from the same store. Kim spent

svetlana [45]

Answer:

The cost of one hosta is $6

Step-by-step explanation:

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.

In this case, the variables are:

x = price of a hosta .
y = price of a pot of ivy.

If Kim spent $62 on 5 hostas and 4 pots of ivy, t his is represented by the equation: 5*x +4*y= 62

If Danielle spent $144 on 8 hostas and 12 pots of ivy, t his is represented by the equation: 8*x +12*y=144

So, the system of equations to solve is:

$\left \{ {{5*x+4*y=62} \atop {8*x+12*y=144}} \right.$

One way to solve a system of equations is through the substitution method, which consists of solving or isolating one of the unknowns (for example, x) and substituting its expression in the other equation. In this way, you obtain an equation of the first degree with the other unknown, and. Once solved, you calculate the value of x by substituting the already known value of y.

Isolating y from the first equation:

$y=\frac{62-5*x}{4}$

and replacing this expression in the second equation you get:

$8*x +12*\frac{62-5*x}{4}=144$

Solving:

$8*x +\frac{12}{4}*(62-5*x)=144$

8*x + 3*(62-5*x)=144

8*x + 3*62 - 3*5*x=144

8*x + 186 - 15*x=144

8*x - 15*x=144 -186

(-7)*x= -42

x= (-42)÷ (-7)

x= 6

The cost of one hosta is $6

8 0

3 years ago