Evaluate −b2−2bx2−x when x=−2.

A 5 1/2 quart pot is filled 2/3 of the way with water. How many more quarts of water can the pot hold?

Inessa [8989]

The pot has the capability to hold 1/3 more than its current level. Therefore, 1/3 of 5 1/2 quarts equals:

(1/3)(11/2) = 11/6 quarts. Thus, the total capacity of the pot is 11/6 quarts.

8 0

29 days ago

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Jane is organizing a fundraiser to buy a ping-pong table for the community center. The table costs $500.00. Jane is asking contr

babunello [8402]

The function representing the cost per share, C, relative to the number of contributors, n, is C = 500 / n. For the contribution to be $20 each, Jane must gather 20 additional contributors, totaling 25. With just 5 currently, she needs 20 more to reach this goal.

4 0

6 days ago

1. X^4(dy/dx) +x^3y =- sec (xy)<br><br>Integral by separation of variables? <br>

PIT_PIT [9101]

Answer:

Step-by-step explanation:

Considering the differential equation x^4(dy/dx) + x^3y = -sec(xy). We will solve it employing the method of separation of variables;

$x^{4} \frac{dy}{dx} +x^{3}y = -sec(xy)\\x^{3}(x\frac{dy}{dx} + y) = -sec(xy)\\let \ v=xy\\\frac{dv}{dx} = x\frac{dy}{dx} + y(implicit \ in\ nature)\\$

By substituting v and dv/dx into the previous equation, we acquire;

$x^{3}\frac{dv}{dx} = -secv$

We then separate the variables:

$-\frac{dv}{secv} = \frac{dx}{x^{3} }$

$-cosvdv = x^{-3}dx\\ integrating\ both\ sides\\-\int\limits {cosv} \, dv = \int\limits {x^{-3} } \, dx\\-sinv = \frac{x^{-2} }{-2} + C\\since\ v = xy\\-sinxy = \frac{x^{-2} }{-2} + C\\2sin(xy) = x^{-2} -2C\\2 sin(xy) = \frac{1}{x^{2} } -K (where\ K = 2C)\\$

The end expression provides the solution to the differential equation.

8 0

27 days ago

Ax+16=b−3x what is a= and what does b= ?

PIT_PIT [9101]

Response:

Slope=4

x−intercept=−

4

16

=−4

b−intercept=

1

16

=16.0000

Detailed breakdown:

7 0

18 days ago

Brenda is cooking couscous. The recipe says she requires 480 grams of couscous for 4 people. How many will she need for 14?

AnnZ [9071]

1,680 grams

To determine this, we can set up a proportion as follows:

grams/people=grams/people

The recipe requires 480 grams for 4 individuals and we need to find how many grams (x) are necessary for 14 individuals.

480 grams/4 people=x grams/14

480/4=x/14

Now, let's isolate x, the grams necessary for 14 people. Currently, x is divided by 14, so we will multiply both sides by 14 as multiplication is the inverse of division.

14(480/4)=(x/14)14

14(480/4)=x

14*120=x

1680=x

Thus, she requires 1,680 grams of couscous to serve 14 individuals.

8 0

10 days ago