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3 years ago

What happens to the volume of a sphere when its diameter is tripled?

1 answer:

8 0

V = 4/3 pi r^3

r is directly proportional to the diameter

and v is proportional to r^3

so

v is proportional to d^3

for d tripled

v is (3)^3 = 27 times original

You might be interested in

If m = 7x + 7, m = 4y, and m = 112, find the values of x and y

tester [92]

<span>If m = 7x + 7, m = 4y, and m = 112

since m = 112

112 = 7x + 7
112 - 7 = 7x
105= 7x
x = 15

112 = 4y
y = 28</span>

6 0

3 years ago

Read 2 more answers

Find the smallest positive $n$ such that \begin{align*} n &\equiv 3 \pmod{4}, \\ n &\equiv 2 \pmod{5}, \\ n &\equiv

Alex777 [14]

4, 5, and 7 are mutually coprime, so you can use the Chinese remainder theorem right away.

We construct a number $x$ such that taking it mod 4, 5, and 7 leaves the desired remainders:

$x=3\cdot5\cdot7+4\cdot2\cdot7+4\cdot5\cdot6$

Taken mod 4, the last two terms vanish and we have

$x\equiv3\cdot5\cdot7\equiv105\equiv1\pmod4$

so we multiply the first term by 3.

Taken mod 5, the first and last terms vanish and we have

$x\equiv4\cdot2\cdot7\equiv51\equiv1\pmod5$

so we multiply the second term by 2.

Taken mod 7, the first two terms vanish and we have

$x\equiv4\cdot5\cdot6\equiv120\equiv1\pmod7$

so we multiply the last term by 7.

Now,

$x=3^2\cdot5\cdot7+4\cdot2^2\cdot7+4\cdot5\cdot6^2=1147$

By the CRT, the system of congruences has a general solution

$n\equiv1147\pmod{4\cdot5\cdot7}\implies\boxed{n\equiv27\pmod{140}}$

or all integers $27+140k$ , $k\in\mathbb Z$ , the least (and positive) of which is 27.

3 0

3 years ago

4.50 to a percent form?

Degger [83]

4.50 is 450 percent
because it is greater than 1, we know it is more than 100%

6 0

4 years ago

Read 2 more answers

COMPRÉ 30 LIBROS A 40 BS CADA UNO ; VENDÍ UNOS CUANTOS A 360 BS, A 36 BS CADA UNO. ¿ EN CUANTO DEBO VENDER CADA UNO DE LOS RESTA

Ksenya-84 [330]

Answer:

28BS

Step-by-step explanation:

Compré 30 libros a 40 bs cada uno;

Precio de costo = 30 × 40BS

= 1200 BS

Vendí unos pocos a 360 Bs, a 36 Bs cada uno.

Número de libros vendidos = 360 BS / 36 BS

= 10 libros

Número de libros restantes = 40 BS - 10 BS

= 30 BS

¿Cuánto debo vender cada uno de los libros restantes para no perder ni ganar nada?

Para no ganar ni perder nada, la cantidad total que queda para vender los libros =

1200BS - 360 BS = 840 BS

La cantidad para vender cada uno de los libros restantes sin ganar ni perder nada se calcula como:

840BS / Número de libros restantes

= 840BS / 30BS

= 28BS

8 0

3 years ago

Tina had a job during her summer vacation. She earned $6.50 per hour. She worked 20 hours per week for 8 weeks. How much money d

frozen [14]

6.50 x 20 = 130 and then times by the number of weeks that is 8 so 130 x 8 = 1,040 :)

7 0

3 years ago

Read 2 more answers