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3 years ago

You are given g(x)=4x^2 + 2x and

Mathematics

1 answer:

Strike441 [17]3 years ago

4 0

Answer:

324

Step-by-step explanation:

Given:

$g(x)=4x^2+2x\\ \\f(x)=\int\limits^x_0 {g(t)} \, dt$

Find:

$f(6)$

First, find f(x):

$f(x)\\ \\=\int\limits^x_0 {g(t)} \, dt\\ \\=\int\limits^x_0 {(4t^2+2t)} \, dt\\ \\=\left(4\cdot \dfrac{t^3}{3}+2\cdot \dfrac{t^2}{2}\right)\big|\limits^x_0\\ \\=\left(\dfrac{4t^3}{3}+t^2\right)\big|\limits^x_0\\ \\= \left(\dfrac{4x^3}{3}+x^2\right)-\left(\dfrac{4\cdot 0^3}{3}+0^2\right)\\ \\=\dfrac{4x^3}{3}+x^2$

Now,

$f(6)\\ \\=\dfrac{4\cdot 6^3}{3}+6^2\\ \\=288+36\\ \\=324$

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What is the period of the function y=3/2con(3/5x)+5

jeyben [28]

Answer:

$y = \frac{3}{2} cot( \frac{3x}{5} ) + 5 \\ \\ \pi \div \frac{3}{5} \\ \ \\ = \frac{5\pi}{3} is \: period$

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3 years ago

I WILL GIVE YOU BRAINLIEST, AND 30 POINTS SO PLEASE HELP ME, IT'S URGENT!

IRINA_888 [86]

Answer:

Answer is option b)

${(x - 3)}^{2} + {(y - 4)}^{2} = 400$

Your guess was right.

Step-by-step explanation:

$the \: question \: states \: that \: \\ distance \: between \: two \: points \: is \: 20 \: units \: \\ and \: the \: two \: points \: are \: (x,y) \: \: and \: \: (3 ,- 4) \\ distance \: formula \\ = \sqrt{ {(x1 - x2) }^{2} + {(y1 - y2)}^{2} } \\ on \: substituting \: the \: values \: in \: formula \\ 20 = \sqrt{ {(x - 3)}^{2} + {(y - ( - 4))}^{2} } \\ 20 = \sqrt{ {(x - 3)}^{2} + {(y + 4)}^{2} } \\ now \: squaring \: on \: both \: sides \\ 400 = {(x - 3)}^{2} + {(y + 4)}^{2} \\ hence \: the \: answer \: is \: option \: b)$

HAVE A NICE DAY!

THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION. 

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3 years ago

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3 years ago

Read 2 more answers

Two cones have their heights in the ratio 1 : 3 and the radius of their bases in the ratio 3 : 1, show that their volumes are in

Nuetrik [128]

<h2> $\large\bold{\underline{\underline{Question:-}}}$ </h2>

Two cones have their heights in the ratio 1 : 3 and the radius of their bases in the ratio 3 : 1 show that their volumes are in the ratio 3 : 1.

<h2> $\large\bold{\underline{\underline{Solution:-}}}$ </h2>

⇒ Ratio of heights of two cones = 1 : 3

⇒ Ratio of radius of their bases = 3 : 1

⇒ We know that V = 1/3πr²h

⇒ Ratio of their volume = V1 : V2

$\underline{ \underline{ \sf{Let's \: find \: the \: ratio \: of \: their \: volumes:}}}$

${ \implies{ \sf {V _{1} : V_{2}}}}$

${ \implies{ \sf{ \frac{1}{3} \pi \: { r_{1}}^{2} h_{1} : \frac{1}{3} \pi \: { r_{2} }^{2} h_{2}}}}$

${ \implies{ \sf{ {r_{1}}^{2} h_{1} : { r_{2}}^{2} h_{2}}}}$

${ \implies{ \sf{ \frac{ { r_{1} }^{2} }{ { r_{2} }^{2} } : \frac{ h_{2} }{ h_{1} } }}} \\$

${ \implies{ \sf{ \frac{ {3}^{2} }{ {1}^{2} } : \frac{3}{1} }}} \\$

${ \implies{ \sf{ \frac{9}{1} : \frac{3}{1} }}} \\$

${ \implies{ \sf{3 : 1}}} \\$

${ \therefore{ \sf{ \green{Ratio \: of \: their \: volumes = 3 : 1}}}}$

4 0

3 years ago

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in s

sergij07 [2.7K]

Answer:

The polynomial function is $P(x) = x^4-35x^2+180x-416.$

Step-by-step explanation:

A polynomial function is completely determined by its roots, up to a constant factor. So, if we want that $x_1=4$ , $x_2=-8$ and $x_3=2+3i$ be roots of the polynomial P, we can write it as

$P(x)= (x-x_1)(x-x_2)(x-x_3)=(x-4)(x+8)(x-(2+3i)) = (x^2+4x-32)(x-(2+3i)).$

Now, notice that the factor $x^2+4x-32$ has real coefficients, while the other one don't. So, we need to ‘‘eliminate’’ the complex coefficients that will appear. This can be done adding other complex root to the polynomial: the conjugate of $x_3$ : 2-3i. Then,

$P(x) = (x^2+4x-32)(x-(2+3i))(x-(2-3i)).$

Expanding the above expression we obtain the desired polynomial

$P(x) = x^4-35x^2+180x-416.$

Recall that P(x) must have three roots, and this implies that P has at least degree 3. As we had to add a new root in order to obtain real coefficients, the degree of P must be at least 4. With this reasoning we assure the minimal degree.

7 0

3 years ago