Determine the Sin for K and P Determine el pecado para Ky P Tanluso 14/ 48 48

3. Jack buys a bicycle on sale for $59.

Semmy [17]

Answer:

One 50$, one 5$, and four 1$ bills

6 0

3 years ago

Read 2 more answers

Sid and Libby are planning to sell pies at a local fair. They spend $200 to rent a table at the fair. Their costs for ingredient

pychu [463]

Sid and Libby are planning to sell pies at a local fair.
=> $200 to rent a table at the fair.
=> $3.00 per pie costs for ingredients, other supplies, baking, and packaging
They plan to sell the pies for $8 each.
Let's find out how many pies will they be selling inorder to gain profit
=> 200 + 3.00(n) = 8(n), where n is the number of pie.
Let's try 40
=> 200 + 3(40) = 8 (40)
=> 320 = 320
=> 200 + 3(41) = 8 (41)
=> 323 = 328
Thus, in their 41st pie, they will get a profit

4 0

3 years ago

Calculus Problem

Roman55 [17]

The two parabolas intersect for

$8-x^2 = x^2 \implies 2x^2 = 8 \implies x^2 = 4 \implies x=\pm2$

and so the base of each solid is the set

$B = \left\{(x,y) \,:\, -2\le x\le2 \text{ and } x^2 \le y \le 8-x^2\right\}$

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, $|x^2-(8-x^2)| = 2|x^2-4|$ . But since -2 ≤ x ≤ 2, this reduces to $2(x^2-4)$ .

a. Square cross sections will contribute a volume of

$\left(2(x^2-4)\right)^2 \, \Delta x = 4(x^2-4)^2 \, \Delta x$

where ∆x is the thickness of the section. Then the volume would be

$\displaystyle \int_{-2}^2 4(x^2-4)^2 \, dx = 8 \int_0^2 (x^2-4)^2 \, dx \\\\ = 8 \int_0^2 (x^4-8x^2+16) \, dx \\\\ = 8 \left(\frac{2^5}5 - \frac{8\times2^3}3 + 16\times2\right) = \boxed{\frac{2048}{15}}$

where we take advantage of symmetry in the first line.

b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

$\dfrac\pi8 \left(2(x^2-4)\right)^2 \, \Delta x = \dfrac\pi2 (x^2-4)^2 \, \Delta x$

We end up with the same integral as before except for the leading constant:

$\displaystyle \int_{-2}^2 \frac\pi2 (x^2-4)^2 \, dx = \pi \int_0^2 (x^2-4)^2 \, dx$

Using the result of part (a), the volume is

$\displaystyle \frac\pi8 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{256\pi}{15}}}$

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

$\dfrac{\sqrt3}4 \left(2(x^2-4)\right)^2 \, \Delta x = \sqrt3 (x^2-4)^2 \, \Delta x$

and using the result of part (a) again, the volume is

$\displaystyle \int_{-2}^2 \sqrt 3(x^2-4)^2 \, dx = \frac{\sqrt3}4 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{512}{5\sqrt3}}$

7 0

2 years ago

Samaria has 6 more than three times as many pieces of candy as sydney. samaria has 36 pieces of candy. how many does sydney have

lesya [120]

For this case we have:

x: Number of candies that Sydney has

The equation to find the amount of Sydney sweets is given by:

$3x + 6 = 36$

We want to clear x:

$3x = 36-63x = 30$

$x = \frac{30}{3}$

$x = 10$

So, Sydney has 10 candies

Answer:

Sydney has 10 candies

4 0

2 years ago

Read 2 more answers

And here is the other one.

LUCKY_DIMON [66]

Since BD bisects angle ABC, that means angle ABD and angle CBD are equal to each other. With that set up the equation to solve for x like this:

-4x+33 = 2x+81
-2x -2x
————————
-6x +33 = 81
-33 -33
————————
-6x = 48
————- (divide by -6)
-6

x = -8

Now substitute that to ABD
-4(-8) +33
32 +33
=65

here’s CBD
2(-8) + 81
-16 + 81
=65

Finally angle ABC will be double the amount of ABD or CBD so 65 times 2 is 130.

ANSWERS: (angles)
ABD and CBD: 65
ABC: 130

3 0

3 years ago