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Vikki [24]
4 years ago
10

Every 5 1/2 cups of flour weighs 1 9/16 pounds. Use a unit rate to show how you could determine if there are more than or less t

han 35 cups of flour in a 10-pound bag of flour.
Mathematics
1 answer:
chubhunter [2.5K]4 years ago
5 0
1 9/16 pounds /  5 1/2 cups will tell you the unit rate of 25/88 pound per 1 cup.  So if you take 25/88 times 35 cups, you will find that it is 9 83/88 pounds.  This is less than a 10-pound bag of flour.
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Find the solution of the problem (1 3. (2 cos x - y sin x)dx + (cos x + sin y)dy=0.
lakkis [162]

Answer:

2*sin(x)+y*cos(x)-cos(y)=C_1

Step-by-step explanation:

Let:

P(x,y)=2*cos(x)-y*sin(x)

Q(x,y)=cos(x)+sin(y)

This is an exact differential equation because:

\frac{\partial P(x,y)}{\partial y} =-sin(x)

\frac{\partial Q(x,y)}{\partial x}=-sin(x)

With this in mind let's define f(x,y) such that:

\frac{\partial f(x,y)}{\partial x}=P(x,y)

and

\frac{\partial f(x,y)}{\partial y}=Q(x,y)

So, the solution will be given by f(x,y)=C1, C1=arbitrary constant

Now, integrate \frac{\partial f(x,y)}{\partial x} with respect to x in order to find f(x,y)

f(x,y)=\int\  2*cos(x)-y*sin(x)\, dx =2*sin(x)+y*cos(x)+g(y)

where g(y) is an arbitrary function of y

Let's differentiate f(x,y) with respect to y in order to find g(y):

\frac{\partial f(x,y)}{\partial y}=\frac{\partial }{\partial y} (2*sin(x)+y*cos(x)+g(y))=cos(x)+\frac{dg(y)}{dy}

Now, let's replace the previous result into \frac{\partial f(x,y)}{\partial y}=Q(x,y) :

cos(x)+\frac{dg(y)}{dy}=cos(x)+sin(y)

Solving for \frac{dg(y)}{dy}

\frac{dg(y)}{dy}=sin(y)

Integrating both sides with respect to y:

g(y)=\int\ sin(y)  \, dy =-cos(y)

Replacing this result into f(x,y)

f(x,y)=2*sin(x)+y*cos(x)-cos(y)

Finally the solution is f(x,y)=C1 :

2*sin(x)+y*cos(x)-cos(y)=C_1

7 0
3 years ago
14 = 2y/5 what is the solution?
Gnom [1K]

Answer:

y=35

Step-by-step explanation:

y in (-oo:+oo)

14 = (2*y)/5 // - (2*y)/5

14-((2*y)/5) = 0

(-2/5)*y+14 = 0

14-2/5*y = 0 // - 14

-2/5*y = -14 // : -2/5

y = -14/(-2/5)

y = 35

y = 35

5 0
3 years ago
Let x be the middle integer of three consecutive integers. What is the sum of these three integers
ololo11 [35]

Answer:

because x is the middle integer of three consecutive integers

=> The remaining 2 numbers respectively are x - 1 and x + 1

=> the sum of these three integers is

x - 1 + x + x + 1 = 3x

8 0
3 years ago
Question 1 (Essay Worth 10 points)
zysi [14]

$394.51 is future value of money after 2 years.

What future value means?

  • A current asset's future value (FV), which is based on an estimated rate of growth, is its value at a later time.
  • Investors and financial planners use the future value to project how much an investment made now will be worth in the future.

The method that results in more money after 2 years is Peggy's investment.

Which method results in more money in 2 years?

The formula for calculating the future value of an investment:

FV = P (1 + r)^nm

FV = Future value

P = Present value

R = interest rate

m = number of compounding

N = number of years

Future value of Larry's investment: $350 x [1 + (0.04/4)]^(4 x 2) = $379

Future value of Peggy's investment: $350 x [1 + (0.06/12)]^(12 x 2) = $394.51

Learn more about future value

brainly.com/question/14860893

#SPJ13

4 0
1 year ago
Jaxson buys ice cream and apples at the store. He pays a total of $24.81. He pays a total of $3.60 for the ice cream. He buys 7
Vadim26 [7]

Answer:

$3.03

Step-by-step explanation:

7x + $3.60 = $24.81

Subtract $3.60 from both sides of the equation:

7x + $3.60 - $3.60 = $24.81 - $3.60

7x = $24.81 - $3.60

7x = $21.21

Divide each side by 7:

(7x/7) = ($21.21/7)

x = ($21.21/7)

x = $3.03

3 0
3 years ago
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