I would really appreciate it if you could help me solve this thing. Thanks!

How do you graph y=2/3x-4

Masja [62]

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▹ Answer

You can use a graphing calculator.

▹ Step-by-Step Explanation

Attached is a screenshot.

Hope this helps!

CloutAnswers ❁

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8 0

4 years ago

Read 2 more answers

Find the average rate of change for problems 1-3: X. X^2+7 2. 11 3. 16 4. 23 5. 32 6. 43 1) what is the average rate of change b

miv72 [106K]

Answer:

(1)7 (2)9 (3)6

Step-by-step explanation:

$\left|\begin{array}{c|cc}X&f(X)=X^2+7\\--&-----\\2&11\\3&16\\4&23\\5&32\\6&43\end{array}\right|$

(1)The average rate of change between x=2 and x=5

$\dfrac{dy}{dx} =\dfrac{f(5)-f(2)}{5-2} =\dfrac{32-11}{3} =\dfrac{21}{3} =7$

(2)The average rate of change between x=3 and x=6

$\dfrac{dy}{dx} =\dfrac{f(6)-f(3)}{6-3} =\dfrac{43-16}{3} =\dfrac{27}{3} =9$

(3)The average rate of change between x=2 and x=4

$\dfrac{dy}{dx} =\dfrac{f(4)-f(2)}{4-2} =\dfrac{23-11}{2} =\dfrac{12}{2} =6$

7 0

3 years ago

Find the minimum and maximum of f(x,y,z)=x^2+y^2+z^2 subject to two constraints, x+2y+z=4 and x-y=8.

Alika [10]

The Lagrangian for this function and the given constraints is

$L(x,y,z,\lambda_1,\lambda_2)=x^2+y^2+z^2+\lambda_1(x+2y+z-4)+\lambda_2(x-y-8)$

which has partial derivatives (set equal to 0) satisfying

$\begin{cases}L_x=2x+\lambda_1+\lambda_2=0\\L_y=2y+2\lambda_1-\lambda_2=0\\L_z=2z+\lambda_1=0\\L_{\lambda_1}=x+2y+z-4=0\\L_{\lambda_2}=x-y-8=0\end{cases}$

This is a fairly standard linear system. Solving yields Lagrange multipliers of $\lambda_1=-\dfrac{32}{11}$ and $\lambda_2=-\dfrac{104}{11}$ , and at the same time we find only one critical point at $(x,y,z)=\left(\dfrac{68}{11},-\dfrac{20}{11},\dfrac{16}{11}\right)$ .

Check the Hessian for $f(x,y,z)$ , given by

$\mathbf H(x,y,z)=\begin{bmatrix}f_{xx}&f_{xy}&f_{xz}\\f_{yx}&f_{yy}&f_{yz}\\f_{zx}&f_{zy}&f_{zz}\end{bmatrix}=\begin{bmatrix}=\begin{bmatrix}2&0&0\\0&2&0\\0&0&2\end{bmatrix}$

$\mathbf H$ is positive definite, since $\mathbf v^\top\mathbf{Hv}>0$ for any vector $\mathbf v=\begin{bmatrix}x&y&z\end{bmatrix}^\top$ , which means $f(x,y,z)=x^2+y^2+z^2$ attains a minimum value of $\dfrac{480}{11}$ at $\left(\dfrac{68}{11},-\dfrac{20}{11},\dfrac{16}{11}\right)$ . There is no maximum over the given constraints.

7 0

4 years ago

The common ratio of a geometric series is 1/4 and the sum of the first 4 terms is 170.

Illusion [34]

Answer: the first term of the series is 128

Step-by-step explanation:

In a geometric sequence, the consecutive terms differ by a common ratio. The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as

Sn = a(1 - r^n)/(1 - r)

Where

n represents the number of term in the sequence.

a represents the first term in the sequence.

r represents the common ratio.

From the information given,

r = 1/4 = 0.25

n = 4

S4 = 170

Therefore, the expression for the sum of the 4 terms, S4 is

170 = a(1 - 0.25^4)/(1 - 0.25)

170 = a(1 - 0.00390625)/(1 - 0.25)

170 = a(0.99609375)/(0.75)

170 = 1.328125a

a = 170/1.328125

a = 128

5 0

3 years ago

En una camioneta se pueden transportar 28.5 kilogramos. ¿ Cuántas camionetas se necesitan para transportar 484.5 Kg?

r-ruslan [8.4K]

Answer:

The number of trucks required is 17.

Step-by-step explanation:

28.5 kilograms can be transported in a van. How many trucks are needed to transport 484.5 Kg?

For the transportation of 28.5 kg, one truck is required.

Total mass = 484.5 kg

The number of trucks required is

n = total mass/ mass of one

$n=\frac{484.5}{28.5}\\\\n = 17$

3 0

3 years ago