1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
nirvana33 [79]
3 years ago
12

How many different whole numbers will divide into 168 without a remainder

Mathematics
1 answer:
Fiesta28 [93]3 years ago
3 0

Answer:

16

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168

You might be interested in
a $1,000 savings account earns 2.3% interest compounded monthly. how long will it take to double the original investment?
Rudik [331]
It will take a total of 44 months
3 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
Four times the square of a certain number increased by 6 times the number equals 108.find the number
slamgirl [31]
To effectively determine the correct answer, it would be helpful to write this into an algebraic expression. We let x as the number. We do as follows:

<span>Four times the square of a certain number increased by 6 times the number equals 108.

4x^2 + 6x = 108

The numbers can be either of the following since the equation generated was a quadratic equation which has two roots.
x = 4.5
x = -6 </span>
5 0
3 years ago
Read 2 more answers
An individual needs a daily supplement of at least 420 units of vitamin C and 170 units of vitamin E and agrees to obtain this s
Ierofanga [76]

Answer:

To obtain equivalent amount from both foods we can eat 10 ounces of Food I and 5 Ounces of food II

To obtain minimum cholesterol, the individual should eat only 21 ounces of food II and zero ounce of food for the daily supplement of the individual

Step-by-step explanation:

Food I contains 32×C + 10×E per ounce

Food II contains 20×C + 14×E  

Here we have X × (Food I) + Y × (Food II) = 420 C + 170 E

32·X + 20·Y = 420 C

10·X + 14·Y = 170 E

Therefore

X = 10 and Y = 5

To minimize the cholesterol, we can increase amount of Food II to get

21 ounces of food II gives

420 units of vitamin E and 294 units of vitamin E with 273 units of cholesterol.

 

                     

3 0
3 years ago
Expand.
liraira [26]

Answer:

2z^3 - 5z^2 + 4z - 1

Step-by-step explanation:

(2z - 1)(z^2 – 2z+ 1) =

= 2z^3 - 4z^2 + 2z - z^2 + 2z - 1

= 2z^3 - 5z^2 + 4z - 1

8 0
2 years ago
Other questions:
  • Lines
    15·1 answer
  • Put into scientific notation 2910000
    9·1 answer
  • 6(x+8)=5x+4 <br><br> Please help me
    10·2 answers
  • What is the value of -9(2)-7
    5·1 answer
  • -y=15-4x divide to make y positive
    9·2 answers
  • Mia hired a moving company. The company charged \$500$500dollar sign, 500 for its services, and mia gives the movers a 16\%16%16
    10·2 answers
  • Which property is illustrated by the equation 2+8=8+2?
    11·2 answers
  • Sophie is buying 3 outfits (shirt and shorts) to wear to volleyball practice. The shirts are $10.00 each, and the total cost is
    12·1 answer
  • Please answer !! thanks
    10·1 answer
  • a 18-inch candle is burning at the rate of 1 inch per hour and 1 15-inch candle is burning at half of an inch per hour. How long
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!