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
Evgen [1.6K]
2 years ago
11

Add x^3 - 4x^2 + 1 to 3x^2 + x Show Your work!

Mathematics
1 answer:
Sladkaya [172]2 years ago
6 0

\qquad \qquad\huge \underline{\boxed{\sf Answer}}

Let's solve ~

\qquad \sf  \dashrightarrow \: (x {}^{3}  - 4x {}^{2}  + 1) + (3 {x}^{2}  + x)

\qquad \sf  \dashrightarrow \:  {x}^{3}  - 4 {x}^{2}  + 1 + 3 {x}^{2}  + x

\qquad \sf  \dashrightarrow \:  {x}^{3}  - 4 {x}^{2}  + 3x {}^{2}  + x + 1

\qquad \sf  \dashrightarrow \:  {x}^{3}  -  {x}^{2}  + x + 1

You might be interested in
Paul wants to deposit $600 today for a vacation he plans to take after graduation. Which formula should he use to determine the
Vitek1552 [10]

Answer:

Future value of a single amount

Step-by-step explanation:

Future value of a single amount - it is referred to as the amount of money that received after n year when money is deposit at the rate interest of i from the initial time. we can say that the total amount is the sum of principal money and interest value.

The formula used to calculate the Future Value of a single amount

Future value = Present value *[Future value factor]

6 0
3 years ago
Can someone please help
Masja [62]

Answer:

3 or c

Step-by-step explanation:

5 0
3 years ago
99 POINT QUESTION, PLUS BRAINLIEST!!!
VladimirAG [237]
First, we have to convert our function (of x) into a function of y (we revolve the curve around the y-axis). So:


y=100-x^2\\\\x^2=100-y\qquad\bold{(1)}\\\\\boxed{x=\sqrt{100-y}}\qquad\bold{(2)} \\\\\\0\leq x\leq10\\\\y=100-0^2=100\qquad\wedge\qquad y=100-10^2=100-100=0\\\\\boxed{0\leq y\leq100}

And the derivative of x:

x'=\left(\sqrt{100-y}\right)'=\Big((100-y)^\frac{1}{2}\Big)'=\dfrac{1}{2}(100-y)^{-\frac{1}{2}}\cdot(100-y)'=\\\\\\=\dfrac{1}{2\sqrt{100-y}}\cdot(-1)=\boxed{-\dfrac{1}{2\sqrt{100-y}}}\qquad\bold{(3)}

Now, we can calculate the area of the surface:

A=2\pi\int\limits_0^{100}\sqrt{100-y}\sqrt{1+\left(-\dfrac{1}{2\sqrt{100-y}}\right)^2}\,\,dy=\\\\\\= 2\pi\int\limits_0^{100}\sqrt{100-y}\sqrt{1+\dfrac{1}{4(100-y)}}\,\,dy=(\star)

We could calculate this integral (not very hard, but long), or use (1), (2) and (3) to get:

(\star)=2\pi\int\limits_0^{100}1\cdot\sqrt{100-y}\sqrt{1+\dfrac{1}{4(100-y)}}\,\,dy=\left|\begin{array}{c}1=\dfrac{-2\sqrt{100-y}}{-2\sqrt{100-y}}\end{array}\right|= \\\\\\= 2\pi\int\limits_0^{100}\dfrac{-2\sqrt{100-y}}{-2\sqrt{100-y}}\cdot\sqrt{100-y}\cdot\sqrt{1+\dfrac{1}{4(100-y)}}\,\,dy=\\\\\\ 2\pi\int\limits_0^{100}-2\sqrt{100-y}\cdot\sqrt{100-y}\cdot\sqrt{1+\dfrac{1}{4(100-y)}}\cdot\dfrac{dy}{-2\sqrt{100-y}}=\\\\\\

=2\pi\int\limits_0^{100}-2\big(100-y\big)\cdot\sqrt{1+\dfrac{1}{4(100-y)}}\cdot\left(-\dfrac{1}{2\sqrt{100-y}}\, dy\right)\stackrel{\bold{(1)}\bold{(2)}\bold{(3)}}{=}\\\\\\= \left|\begin{array}{c}x=\sqrt{100-y}\\\\x^2=100-y\\\\dx=-\dfrac{1}{2\sqrt{100-y}}\, \,dy\\\\a=0\implies a'=\sqrt{100-0}=10\\\\b=100\implies b'=\sqrt{100-100}=0\end{array}\right|=\\\\\\= 2\pi\int\limits_{10}^0-2x^2\cdot\sqrt{1+\dfrac{1}{4x^2}}\,\,dx=(\text{swap limits})=\\\\\\

=2\pi\int\limits_0^{10}2x^2\cdot\sqrt{1+\dfrac{1}{4x^2}}\,\,dx= 4\pi\int\limits_0^{10}\sqrt{x^4}\cdot\sqrt{1+\dfrac{1}{4x^2}}\,\,dx=\\\\\\= 4\pi\int\limits_0^{10}\sqrt{x^4+\dfrac{x^4}{4x^2}}\,\,dx= 4\pi\int\limits_0^{10}\sqrt{x^4+\dfrac{x^2}{4}}\,\,dx=\\\\\\= 4\pi\int\limits_0^{10}\sqrt{\dfrac{x^2}{4}\left(4x^2+1\right)}\,\,dx= 4\pi\int\limits_0^{10}\dfrac{x}{2}\sqrt{4x^2+1}\,\,dx=\\\\\\=\boxed{2\pi\int\limits_0^{10}x\sqrt{4x^2+1}\,dx}

Calculate indefinite integral:

\int x\sqrt{4x^2+1}\,dx=\int\sqrt{4x^2+1}\cdot x\,dx=\left|\begin{array}{c}t=4x^2+1\\\\dt=8x\,dx\\\\\dfrac{dt}{8}=x\,dx\end{array}\right|=\int\sqrt{t}\cdot\dfrac{dt}{8}=\\\\\\=\dfrac{1}{8}\int t^\frac{1}{2}\,dt=\dfrac{1}{8}\cdot\dfrac{t^{\frac{1}{2}+1}}{\frac{1}{2}+1}=\dfrac{1}{8}\cdot\dfrac{t^\frac{3}{2}}{\frac{3}{2}}=\dfrac{2}{8\cdot3}\cdot t^\frac{3}{2}=\boxed{\dfrac{1}{12}\left(4x^2+1\right)^\frac{3}{2}}

And the area:

A=2\pi\int\limits_0^{10}x\sqrt{4x^2+1}\,dx=2\pi\cdot\dfrac{1}{12}\bigg[\left(4x^2+1\right)^\frac{3}{2}\bigg]_0^{10}=\\\\\\= \dfrac{\pi}{6}\left[\big(4\cdot10^2+1\big)^\frac{3}{2}-\big(4\cdot0^2+1\big)^\frac{3}{2}\right]=\dfrac{\pi}{6}\Big(\big401^\frac{3}{2}-1^\frac{3}{2}\Big)=\boxed{\dfrac{401^\frac{3}{2}-1}{6}\pi}

Answer D.
6 0
3 years ago
Read 2 more answers
Amys age is 6 years less than 3 times marys age. if the sum of their ages is greater than 46, find the youngest possible age of
Anarel [89]
I hope this helps you

5 0
3 years ago
What is the solution for the following equation?<br> x^2-6x+9=11
tankabanditka [31]
Make one side equal zero
minus 11 to both sides
x^2-6x-2=0
another quadratic equation

if you hahve
ax^2+bx+c=0
x=\frac{-b+/- \sqrt{b^{2}-4ac} }{2a}

1x^2-6x-2=0
a=1
b=-6
c=-2

x=\frac{-(-6)+/- \sqrt{(-6)^{2}-4(1)(-2)} }{2(1)}
x=\frac{6+/- \sqrt{36+8} }{2}
x=\frac{6+/- \sqrt{44} }{2}
x=\frac{6+/- 2\sqrt{11} }{2}
x=3+/- \sqrt{11}
x=3+ \sqrt{11} or 3- \sqrt{11}

aprox
x=6.31662 or -0.316625
4 0
3 years ago
Other questions:
  • In the diagram, AB = 10 and AC = 2√10. What is the perimeter of △ABC?
    10·1 answer
  • Find the indicated term of the given arithmetic sequence. a1=45, d= -3, n=10
    15·2 answers
  • What is the answer of 3[4(2³)-5²+7(8+4²)-16]?
    7·1 answer
  • An ice cream cone is 3 inches wide at the widest point, and is 6 inches tall. what is the volume of the cone in cubic inches?
    6·1 answer
  • I=$26.25I=$26.25, P=$500P=$500, t=18 t=18 months
    11·1 answer
  • Write an inequality that represents the graph.
    5·1 answer
  • What’s the correct answer for this?
    11·2 answers
  • Q÷ 6 = 4 plzzzz helppp I need answerss ASAP
    14·1 answer
  • Timed Test Please Help.
    6·1 answer
  • 3v+4(v-2)= -29 solve for v​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!