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2 years ago

How many solutions does the equation 4s + 8 = 3 + 5 + 4s have?

Mathematics

2 answers:

cluponka [151]2 years ago

5 0

Answer:

The answer is none.

Step-by-step explanation:

MAXImum [283]2 years ago

3 0

Answer:

none

Step-by-step explanation:

You might be interested in

Which two ordered pairs would represent points on a graph of 5x + 6y = 12?

skelet666 [1.2K]

B. (0,2) and D. (6,-3)

4 0

3 years ago

I have 4 times as much money as my brother has. our total is $55.how much does each of us have?

babymother [125]

Answer:

You have 44$, your brother has 11$.

Step-by-step explanation:

Let $x$ be the amount of money your brother has.

Since you have four times the amount of money your brother has, we can call the amount of money you have $4x$ .

$x+4x=55,\\5x=55,\\x=\boxed{\$11}$

Thus, you have:

$4(11)=\boxed{\$44}$

5 0

2 years ago

Read 2 more answers

Evaluate the integral, show all steps please!

Aloiza [94]

Answer:

$\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x=\dfrac{x}{9\sqrt{9-x^2}} +\text{C}$

Step-by-step explanation:

Fundamental Theorem of Calculus

$\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))$

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

$\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x$

Rewrite 9 as 3² and rewrite the 3/2 exponent as square root to the power of 3:

$\implies \displaystyle \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x$

Integration by substitution

$\boxed{\textsf{For }\sqrt{a^2-x^2} \textsf{ use the substitution }x=a \sin \theta}$

$\textsf{Let }x=3 \sin \theta$

$\begin{aligned}\implies \sqrt{3^2-x^2} & =\sqrt{3^2-(3 \sin \theta)^2}\\ & = \sqrt{9-9 \sin^2 \theta}\\ & = \sqrt{9(1-\sin^2 \theta)}\\ & = \sqrt{9 \cos^2 \theta}\\ & = 3 \cos \theta\end{aligned}$

Find the derivative of x and rewrite it so that dx is on its own:

$\implies \dfrac{\text{d}x}{\text{d}\theta}=3 \cos \theta$

$\implies \text{d}x=3 \cos \theta\:\:\text{d}\theta$

Substitute everything into the original integral:

$\begin{aligned}\displaystyle \int \dfrac{1}{(9-x^2)^{\frac{3}{2}}}\:\:\text{d}x & = \int \dfrac{1}{\left(\sqrt{3^2-x^2}\right)^3}\:\:\text{d}x\\\\& = \int \dfrac{1}{\left(3 \cos \theta\right)^3}\:\:3 \cos \theta\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{\left(3 \cos \theta\right)^2}\:\:\text{d}\theta \\\\ & = \int \dfrac{1}{9 \cos^2 \theta} \:\: \text{d}\theta\end{aligned}$

Take out the constant:

$\implies \displaystyle \dfrac{1}{9} \int \dfrac{1}{\cos^2 \theta}\:\:\text{d}\theta$

$\textsf{Use the trigonometric identity}: \quad\sec^2 \theta=\dfrac{1}{\cos^2 \theta}$

$\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta$

$\boxed{\begin{minipage}{5 cm}\underline{Integrating $\sec^2 kx$}\\\\$\displaystyle \int \sec^2 kx\:\text{d}x=\dfrac{1}{k} \tan kx\:\:(+\text{C})$\end{minipage}}$

$\implies \displaystyle \dfrac{1}{9} \int \sec^2 \theta\:\:\text{d}\theta = \dfrac{1}{9} \tan \theta+\text{C}$

$\textsf{Use the trigonometric identity}: \quad \tan \theta=\dfrac{\sin \theta}{\cos \theta}$

$\implies \dfrac{\sin \theta}{9 \cos \theta} +\text{C}$

$\textsf{Substitute back in } \sin \theta=\dfrac{x}{3}:$

$\implies \dfrac{x}{9(3 \cos \theta)} +\text{C}$

$\textsf{Substitute back in }3 \cos \theta=\sqrt{9-x^2}:$

$\implies \dfrac{x}{9\sqrt{9-x^2}} +\text{C}$

Learn more about integration by substitution here:

brainly.com/question/28156101

brainly.com/question/28155016

4 0

2 years ago

4. Which equation in point-slope form contains the point (-3, 5) and has slope -1? 100%

Flura [38]

ʕ•ﻌ•ʔ $\huge\bold\pink{hello!!!}$ ʕ•ﻌ•ʔ

HERE IS UR ANSWER

_____________________

(x-(-3)) = -1(y-5)

(x+3)= -y+5

x+y+3-5=0

x+y-2=0

3 0

2 years ago

Can someone please explain how to do this.

lutik1710 [3]

Set the to equal:

x^2 - 4x+4 = 2x-4
solve for X

subtract 2x from each side:
x^2 -6x + 4 = -4

subtract 4 from each side:

x^2 -6x = -8

add 8 to both sides:

x^2 -6x +8 = 0

factor the polynomial:

x = 4 and x = 2

using the line equation replace x with 2 and 4 and solve for y

y = 2(2) - 4 = 0
y = 2(4)-4 = 4

so the 2 points the line crosses the curve is (2,0) and (4,4)

using those 2 points you can calculate the length:
distance = sqrt((x2-x1)^2 +(y2-y1)^2

distance = sqrt( (4-2)^2 + (4-0)^2)

distance = sqrt (2^2 + 4^2)
distance = sqrt (4+16)
= sqrt 20
= 2 sqrt(5) EXACT LENGTH

4 0

3 years ago