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3 years ago

Which of the following is a solution to 3x^2 = 36?

Mathematics

1 answer:

aleksklad [387]3 years ago

6 0

Answer:

x = √12

Step-by-step explanation:

Easy:

3x^2 = 36

Cancel out the 3 so it is only x^2; you can do this by dividing each side by 3 which gives you:

x^2 = 12

Square root the entire thing to get rid of the square and you get the answer

x = √12

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Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = e^−2

Mekhanik [1.2K]

Answer:

x=1

y=s

z=1

Step-by-step explanation:

(x, y, z)=(1, 0, 1)

Substitute 0 for y

$y = e^{-2t} *sin 4t\\0 = e^{-2t} *sin 4t\\\\0 = e^{-2t} *(\frac{e^{4t}-e^{-4t}}{2j} )\\0 = e^{-2t} *(e^{4t}-e^{-4t} )\\0 = e^{-2t} *e^{4t}*(1-e^{-8t} )\\\\0 = e^{2t}*(1-e^{-8t} )\\\\\\Either \\0 = e^{2t}\\t = -inf\\or\\0 = (1-e^{-8t} )\\(e^{-8t} ) = 1\\ -8t = ln(1) =0\\t=0\\\\$

Confirming if t=0 satisfy the other equation

x = e^−2t cos 4t = e^−2(0)cos(4*0)

= e^(0)cos(0) = 1

z = e^−2t = e^−2(0) = 0

Therefore t=0 satisfies the other equation

Finding the tangent vector at t=0

$\frac{dx}{dt}=-2te^{-2t} cos4t + e^{-2t}(-4sin4t)=-2(0)e^{-2(0)} cos4(0) + e^{-2(0)}(-4sin4(0))=0\\\\ \frac{dy}{dt} =-2te^{-2t} sin4t + e^{-2t}(4cos4t)=-2(0)e^{-2(0)} sin4(0)+ e^{-2(0)(4cos4(0)) }= 1\\\\\frac{dz}{dt} = -2te^{-2t} = -2(0)e^{-2(0)} = 0$

The vector equation of the tangent line is

(1, 0, 1) +s(0,1,0)= (1, s, 1)

The parametric equations are:

x=1

y=s

z=1

6 0

3 years ago

Consider the proof. Given: In △ABC, BD ⊥ AC Prove: the formula for the law of cosines, a2 = b2 + c2 – 2bccos(A) Statement Reason

loris [4]

Solution: The missing reason in Step 8 is substitution of $x=c\cos (A)$ .

Explanation:

The given steps are used to prove the formula for law of cosines.

From step 5 it is noticed that our equation is

$a^2=b^2-2bx+c^2$ ..... (1)

From step 7 it is noticed that the value of $x$ is $c\cos (A)$ .

So by substituting $c\cos (A)$ for $x$ in equation (1) we get the equation of step 8, i.e.,

$a^2=b^2-2bc\cos (A)+c^2$

Hence, the missing reason in Step 8 is substitution of $x=c\cos (A)$ .

5 0

3 years ago

Read 2 more answers

Whats 17×3297÷47+70=

ANTONII [103]

Answer:

1,262.5

according to the calculator lol

7 0

3 years ago

Read 2 more answers

Need help badly don’t have answer to this problem.

NikAS [45]

There are a couple of ways to tackle this one, using the 45-45-90 rule or just using the pythagorean theore, let's use the pythagorean theorem.

the angle at A is 45°, and its opposite side is BC, the angle at C is 45° as well, and its opposite side is AB, well, the angles are the same, thus BC = AB.

hmmm le'ts call hmmm ohh hmmm say z, thus BC = AB = z.

$\bf \textit{using the pythagorean theorem}
\\\\
c^2=a^2+b^2 \implies (6\sqrt{2})^2=z^2+z^2
\qquad 
\begin{cases}
c=\stackrel{6\sqrt{2}}{hypotenuse}\\
a=\stackrel{z}{adjacent}\\
b=\stackrel{z}{opposite}\\
\end{cases}\\\\\\ 6^2(\sqrt{2})^2=2z^2\implies 36(2)=2z^2\implies \cfrac{36(2)}{2}=z^2\implies 36=z^2
\\\\\\
\sqrt{36}=z\implies 6=z$

4 0

3 years ago

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You can walk 1.75 miles in 30 minutes. What is your average speed?

Varvara68 [4.7K]

Answer:

The answer is 3.5 mph

Step-by-step explanation:

30 x 2 = 60 minutes = 1 hour

1.75 x 2 = 3.5 miles

So 3.5 miles in 1 hour

3.5 mph

3 0

3 years ago