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3 years ago

Is y + 5x^2=-4 a quadratic function? yes or no

Mathematics

2 answers:

devlian [24]3 years ago

7 0

Answer:

Yes

Step-by-step explanation:

In standard form, this function is written as:

$y = - 5 {x}^{2} - 4$

Because it has the parent function of:

$y = {x}^{2}$

It is a quadratic function.

Arlecino [84]3 years ago

5 0

Answer: Yes

Step-by-step explanation:

When you rearrange the equation it would be y=-5x^2-4, and since it is a 2nd degree we can easily say it is a quadratic function.

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HELP :Write the expression as the sine or cosine of an angle.

Reptile [31]

Answer:

sin(4π/21)

Step-by-step explanation:

Step 1: Rearrange expression

sin(π/3)cos(π/7) - cos(π/3)sin(π/7)

Step 2: Use sin(A ± B)

sin(π/3 - π/7)

Step 3: Evaluate

sin(4π/21)

And we have our answer!

5 0

3 years ago

A skier is trying to decide whether or not to buy a season ski pass. a daily pass is $75. A season ski pass is $350. The skier w

pishuonlain [190]

Since the skier has to rent skis for 30 dollars per day with both passes, we can ignore it while solving the question.

A season pass is 350, while a daily pass is 75.

$\frac{350}{75} = \frac{25\times 14}{25\times 3} = \frac{14}{3} = 4 \frac{2}{3}$

So a seasonal pass is equivalent to having 4.6667 daily passes. And you can't buy 0.6667 of a pass.

So, if you went at least 5 days with a seasonal pass, then the seasonal pass would be less expensive than a daily pass.

6 0

2 years ago

Express the complex number in trigonometric form -6 + 6sqrt3i

marusya05 [52]

$\large\begin{array}{l}\\\\ \textsf{This is a complex number in }\mathsf{a+bi}\textsf{ form:}\\\\ \mathsf{z=-6+6\sqrt{3}\,i}\\\\ \textsf{where }\mathsf{a=-6~~and~~b=6\sqrt{3}.} \end{array}$

$\large\begin{array}{l}\\\\ \bullet~~\textsf{1}\mathsf{^{st}}\textsf{ step: Find the absolute value of z (complex modulus of z):}\\\\ \mathsf{|z|=\sqrt{a^2+b^2}}\\\\ \mathsf{|z|=\sqrt{(-6)^2+(6\sqrt{3})^2}}\\\\ \mathsf{|z|=\sqrt{36+36\cdot 3}}\\\\ \mathsf{|z|=\sqrt{36\cdot 108}}\\\\ \mathsf{|z|=\sqrt{144}}\\\\ \mathsf{|z|=12} \end{array}$

$\large\begin{array}{l}\bullet~~\textsf{2}\mathsf{^{nd}}\textsf{ step: Find the argument }\mathsf{\theta}\textsf{ of z:}\\\\ \mathsf{arg(z)=\theta}\\\\ \textsf{is an angle that satisfies the following conditions:}\\\\ \begin{cases} \mathsf{cos\,\theta=\dfrac{a}{|z|}=\dfrac{a}{\sqrt{a^2+b^2}}}\\\\ \mathsf{sin\,\theta=\dfrac{b}{|z|}=\dfrac{b}{\sqrt{a^2+b^2}}} \end{cases}\qquad\quad-\pi$

$\large\begin{array}{l}\textsf{For }\mathsf{z=-6+6\sqrt{3}\,i,}\\\\ \begin{cases} \mathsf{cos\,\theta=\dfrac{-6}{12}=-\,\dfrac{1}{2}}\\\\ \mathsf{sin\,\theta=\dfrac{6\sqrt{3}}{12}=\dfrac{\sqrt{3}}{2}} \end{cases}\\\\\\ \textsf{Since}\\\\ \mathsf{cos\,\theta0,}\\\\ \theta\textsf{ lies in the 2}\mathsf{^{nd}}\textsf{ quadrant.}\\\\\\\textsf{Therefore,}\\\\ \mathsf{\theta=\dfrac{2\pi}{3}~rad~~(120^\circ)} \end{array}$

$\large\begin{array}{l}\bullet~~\textsf{3}\mathsf{^{rd}}\textsf{ step: Express z in the trigonometric form:}\\\\ \begin{array}{rcl} \mathsf{z}&\!\!=\!\!&\mathsf{|z|\cdot (cos\,\theta+i\,sin\,\theta)}\\\\ \mathsf{-6+6\sqrt{3}\,i}&\!\!=\!\!&\mathsf{12\cdot \left(cos\, \dfrac{2\pi}{3}+i\,sin\,\dfrac{2\pi}{3}\right)\qquad\quad\checkmark} \end{array} \end{array}$

If you're having problems understanding this answer, try seeing it through your browser: brainly.com/question/2154167

$\large\textsf{I hope it helps.}$

Tags: complex number trigonometric form trig absolute value modulus argument angle

4 0

3 years ago

Tina has an old fish tank in the shape of a circular cylinder. The tank is 2 feet in diameter and 6 feet high. How many cubic fe

yanalaym [24]

Answer:

The tank can hold 18.84 cubic feet

Step-by-step explanation:

Given

Shape: Cylinder

$D = 2ft$ -- Diameter