All categories

3 years ago

P is directly proportional to the cube of q

Mathematics

1 answer:

Molodets [167]3 years ago

3 0

Answer:

p=q^3

Step-by-step explanation:

You might be interested in

Find all the zeros of the polynomial function p(x) = x3 – 5x2 + 33x – 29

hram777 [196]

Answer:

$\large \boxed{\sf \ \ x=1, \ \ x=2+5i, \ \ x=2-5i \ \ }$

Step-by-step explanation:

Hello,

I assume that we are working in $\mathbb{C}$ , otherwise there is only one zero which is 1. Please consider the following.

First of all, <u>we can notice that 1 is a trivial solution</u> as

$p(1) = 1^3-5\cdot 1^2 + 33\cdot 1-29=1-5+33-29=0$

It means that (x-1) is a factor of p(x) so we can find two real numbers, a and b, so that we can write the following.

$p(x)=(x-1)(x^2+ax+b)=x^3+ax^2+bx-x^2-ax-b=x^3+(a-1)x^2+(b-a)x-b$

Let's identify like terms as below.

a-1 = -5 <=> a = -5 + 1 = -4

b-a = 33

-b = -29 <=> b = 29

$\boxed{ \ p(x)=(x-1)(x^2-4x+29) \ }$

Now, we need to find the zeroes of the second factor, meaning finding x so that:

$x^2-4x+29=0 \ \text{ complete the square, 29 = 25 + 4} \\ \\ x^2-2\cdot 2 \cdot x+2^2+25=0 \\ \\ (x-2)^2=-25=(5i)^2 \ \text{ take the root } \\ \\x-2=\pm 5i \ \text{ add 2 } \\ \\ x = 2+5i \ \text{ or } \ x = 2-5i$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

5 0

3 years ago

A sphere has a decimeter of 12 ft what is the volume of the sphere? Give the exact value in terms of

meriva

Answer: 904.78 cu. ft

Step-by-step explanation:

Volume of sphere = 4/3 pi r^3

Assuming 12 ft. is the diameter of the sphere.

6 0

2 years ago

HELP PLEASE!!! i do not understand

mel-nik [20]

Answer:

a)-3>-7

b)3>-4 The symbol was preserved.

c)-6<8 The symbol was reversed.

Step-by-step explanation:

Hope this helps! :)

5 0

2 years ago

A scale on a map shows that 2 inches equals 25 miles how many inches on the map represents 60 miles?? I NEED HELP ASAP

irakobra [83]

Answer:

60 miles is equal to 4.8 inches.

Step-by-step explanation:

To find the answer to this question, we need divide 60 by 25 to find out how much to multiply 2 by so its equal.

60/25=2.4

2*2.4=4.8

60 miles is equal to 4.8 inches.

Hope this helps!

6 0

2 years ago

Read 2 more answers

Hernando ate StartFraction 2 Over 8 EndFraction of a pizza for a dinner. He gave his 6 friends the rest of the pizza and told th

ozzi

Answer:

Yes, they are correct. Hernando divided 6 by 6.

Step-by-step explanation:

Given that:

Hernando ate 2/8 of a pizza for dinner.

Let the pizza be x. Then:

Hernando ate $\dfrac{2}{8} \ \ o f \ \ x$

Then he gave the rest of the pizza to his friends

Hernando now carried out the following calculations to support his activities;

$\dfrac{6}{8} \div 6= \dfrac{6 \div 6}{8}= \dfrac{1}{8}$

$\dfrac{6}{8} \times \dfrac{1}{6}= \dfrac{6 \div 6}{8}= \dfrac{1}{8}$

From the above calculation; we will see that Hernando divided 6 by 6 in both cases to get $\dfrac{1}{8}$ .

Thus, the correct answer is:

Yes, they are correct. Hernando divided 6 by 6.

3 0

2 years ago

Read 2 more answers