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3 years ago

46 lbs of apples cost $414. How much would 29 lbs cost?

1 answer:

7 0

You first divide 414 by 46 to see how much it costs for 1 lb. After the calculation, you get 9 lb. Then you multiply that by 29 to get 261.

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Suppose f(x,y)=xy, P=(−4,−4) and v=2i+3j. A. Find the gradient of f. ∇f= i+ j Note: Your answers should be expressions of x and

mart [117]

Answer:

a) The gradient of a function is the vector of partial derivatives. Then

$\nabla f=(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y})=(y,x)=y\hat{i} + x\hat{j}$

b) It's enough evaluate P in the gradient.

$\nabla f(P)=(-4,-4)=-4\hat{i} - 4 \hat{j}$

c) The directional derivative of f at P in direction of V is the dot produtc of $\nabla f(P)$ and v.

$\nabla f(P) v=(-4,-4)\left[\begin{array}{ccc}2\\3\end{array}\right] =(-4)2+(-4)3=-20$

d) The maximum rate of change of f at P is the magnitude of the gradient vector at P.

$||\nabla f(P)||=\sqrt{(-4)^2+(-4)^2}=\sqrt{32}=4\sqrt{2}$

e) The maximum rate of change occurs in the direction of the gradient. Then

$v=\frac{1}{4\sqrt{2}}(-4,-4)=(\frac{-1}{\sqrt{2}},\frac{-1}{\sqrt{2}})= \frac{-1}{\sqrt{2}}\hat{i}-\frac{1}{\sqrt{2}}\hat{j}$

is the direction vector in which the maximum rate of change occurs at P.

6 0

3 years ago

Which of the following is the inverse of f(x)=4x-10?

Anastasy [175]

Injective- (one-to-One)
so
Replace the f(x) with y
10-4x
Interchange the variables
x=10-4y
Solv for y.
y= 5/2 - x/4
So solve for y and replace with f-1 (x).
and it equals
f-1 (x)=5/2- x/4

5 0

2 years ago

When 605,000 is written in scientific notation, what will be the value of the exponent?

postnew [5]

6.05 x 10^5 would be your answer.

I hope this helps!

3 0

3 years ago

Simplify the expression. -4k^4j^5^3 - -64% 33,30 -64 -64% 17,18 64% 33,36

Degger [83]

Answer:

D)There are limited resources and unlimited wants and demands.

Step-by-step explanation:

5 0

3 years ago

se vendieron 144 boletos. 2 pesos por adulto y un peso por niño, si se gastaron 207 pesos cuantos boletos de adulto se vendieron

natulia [17]

Answer:

Se vendieron 81 boletos de niños y 63 boletos de adultos.

Step-by-step explanation:

La cantidad de boletos vendidos es igual a:

$144 = a + n$ (1)

En donde a es por adultos y n por niños

A su vez, el dinero gastado equivale:

$207 = 2*a + 1*n$ (2)

Resolviendo la ecuación (1) para a:

$a = 144 - n$ (3)

Introduciendo (3) en la ecuación (2) tenemos:

$207 = 2*(144 - n) + n$

$n = 81$

Ahora podemos calcular el numero de boletos de adultos vendidos introduciendo n en la ecuación (3):

$a = 144 - n = 144 - 81 = 63$

Entonces, se vendieron 81 boletos de niños y 63 boletos de adultos.

Espero que te sea de utilidad!

5 0

2 years ago