Hank bought 2.4 pounds of apples . Each pound cost $1.95. How much did hank spend ont the apples ?

A small island is 4 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a

True [87]

Answer:

a) t(x) = [ √ (4)² + (x)²]/ 4 + 7/5 - x/5

b) x = 0,97 miles

c) t (min) = 1,24 hours

Step-by-step explanation: See Annex

Figure in annex shows a clear description of the situation

Let x be distance in miles between point P and where boat lands

A woman has to row a distance L

L = √ (4)² + (x)²

and the part to get to the town (which she has to walk)

d = ( 7 - x)

But we are required to give time as a function of x

distance = speed * time ⇒ t = distance / speed

Therefore

t(x) = [ √ (4)² + (x)²]/ 4 + ( 7 - x ) / 5

t(x) = [ √ (4)² + (x)²]/ 4 + 7/5 - x/5

Taking derivatives both sides of the equation

t¨(x) = ( 2x)*4 / 16√ (4)² + (x)²] - 5/25

t¨(x) = x/ 2√ (4)² + (x)²] - 1/5

t¨(x) = 0 x/ 2√ (4)² + (x)²] - 1/5 = 0

[ 5 x - 2√ (4)² + (x)²] = 0 ⇒ 5x = 2√ (4)² + (x)²] or

25 x² = 4 ( 4 + x²)

25 x² = 16 + 8x²

17x² = 16

x² = 16/17

x² = 0,941

x = 0,97 miles

And the distance walking to get to town

d = 7 - x d = 7 - 0,97

d = 6,03 miles

The least travel time is t(x) = [ √ (4)² + (x)²]/ 4 + 7/5 - x/5

t (min) = √ 16 + 0,94) /4 + 1,4 - 0,97/5

t (min) = 1,03 + 1,4 - 0,194

t (min) = 1,24 hours

7 0

2 years ago

Consider the initial value problem: 2ty′=8y, y(−1)=1. Find the value of the constant C and the exponent r so that y=Ctr is the s

VikaD [51]

The correct question is:

Consider the initial value problem

2ty' = 8y, y(-1) = 1

(a) Find the value of the constant C and the exponent r such that y = Ct^r is the solution of this initial value problem.

b) Determine the largest interval of the form a < t < b on which the existence and uniqueness theorem for first order linear differential equations guarantees the existence of a unique solution.

c) What is the actual interval of existence for the solution obtained in part (a) ?

Step-by-step explanation:

Given the differential equation

2ty' = 8y

a) We need to find the value of the constant C and r, such that y = Ct^r is a solution to the differential equation together with the initial condition y(-1) = 1.

Since Ct^r is a solution to the initial value problem, it means that y = Ct^r satisfies the said problem. That is

2tdy/dt - 8y = 0

Implies

2td(Ct^r)/dt - 8(Ct^r) = 0

2tCrt^(r - 1) - 8Ct^r = 0

2Crt^r - 8Ct^r = 0

(2r - 8)Ct^r = 0

But Ct^r ≠ 0

=> 2r - 8 = 0 or r = 8/2 = 4

Now, we have r = 4, which implies that

y = Ct^4

Applying the initial condition y(-1) = 1, we put y = 1 when t = -1

1 = C(-1)^4

C = 1

So, y = t^4

b) Let y = F(x,y)................(1)

Suppose F(x, y) is continuous on some region, R = {(x, y) : x_0 − δ < x < x_0 + δ, y_0 −ę < y < y_0 + ę} containing the point (x_0, y_0). Then there exists a number δ1 (possibly smaller than δ) so that a solution y = f(x) to (1) is defined for x_0 − δ1 < x < x_0 + δ1.

Now, suppose that both F(x, y)

and ∂F/∂y are continuous functions defined on a region R. Then there exists a number δ2

(possibly smaller than δ1) so that the solution y = f(x) to (1) is

the unique solution to (1) for x_0 − δ2 < x < x_0 + δ2.

c) Firstly, we write the differential equation 2ty' = 8y in standard form as

y' - (4/t)y = 0

0 is always continuous, but -4/t has discontinuity at t = 0

So, the solution to differential equation exists everywhere, apart from t = 0.

The interval is (-infinity, 0) n (0, infinity)

n - means intersection.

7 0

1 year ago

A farmer is estimating the surface area of his barn to find how much paint he needs to buy. One part of the barn is triangular a

Nady [450]

We know the triangle is an isosceles triangle. So, we use the Pythagorean Theorem.

a^2+b^2=c^2

The c would be 22, because it's the longest edge. Now find a or b. They are the same, that is how you find the two sides of the triangle for part A.

To find the area of the triangle, the forumla is a=hb/2

Plug in the numbers for that formula and the answer would be found for part B.

I hope I helped.

7 0

2 years ago

Fredrick and Kate have 1713 cups of flour. They want to make loaves of banana bread for a bake sale. Fredrick has a recipe for b

Mariana [72]

Answer:

Fredrick's recipe will make 10 whole loaves.

There will be less flour left over if Frederick's recipe is used.

Step-by-step explanation:

Fredrick and Kate have 17 1/3 cups of flour. They want to make loaves of banana bread for a bake sale. Fredrick has a recipe for banana bread that calls for 1 5/8 cups of flour. Kate has a recipe that calls for 1 3/4 cups of flour. Select all the statements that are true about the recipes.

1. Fredrick's recipe will make 10 whole loaves.

2. Kate's recipe will make 11 whole loaves.

3. There will be less flour left over if Frederick's recipe is used.

4. There will be less flour left over if Kate's recipe is used.

5. More loaves of bread can be made using Frederick's recipe than Kate's recipe.

Solution:

Total cups of flour = 17 1/3

Fredrick recipe = 1 5/8 cups of flour

Kate = 1 3/4 cups of flour

Number of banana bread made with Fredrick's recipe = Total flour / flour per Fredrick's recipe

= 17 1/3 ÷ 1 5/8

= 52/3 ÷ 13/8

=52/3 × 8/13

= 416 / 39

= 10.67 loaves of banana bread

Number of banana bread made with Kate's recipe = Total flour / flour per Kate's recipe

= 17 1/3 ÷ 1 3/4

= 52/3 ÷ 7/4

= 52/3 × 4/7

= 216 / 21

= 10.29 loaves of banana bread

The true statements are:

Fredrick's recipe will make 10 whole loaves.

There will be less flour left over if Frederick's recipe is used

5 0

2 years ago

A store is advertising a sale with 15% off all prices in the store. Sales tax is 8%. Which equation will correctly determine the

ICE Princess25 [194]

Answer: 15%-8%=C

Step-by-step explanation:

4 0

2 years ago

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