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3 years ago

What substitution should be used to rewrite 4x^4-21x^2+20=0 as a quadratic function?

Mathematics

2 answers:

pogonyaev3 years ago

3 0

Answer:

see explanation

Step-by-step explanation:

Let u = x² ( choice of variable is flexible ), then

4u² - 21u + 20 = 0 ← expressed as a quadratic

This can now be solved for u and converted back into terms of x

Ipatiy [6.2K]3 years ago

3 0

Answer:

refer the explanation

Step-by-step explanation:

this question can be written as

X^2=y

so,x^4=y^2

so it will be 4y^2-21y+20=0

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Been stuck on this question for 20 minutes, can someone please help.

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3 years ago

Fill in Sin, Cos, and tan ratio for angle x. <br> Sin X = 4/5 (28/35 simplified)

Fantom [35]

Answer:

Given: $\sin(x) = (4/5)$ .

Assuming that $0 < x < 90^{\circ}$ , $\cos(x) = (3/5)$ while $\tan(x) = (4/3)$ .

Step-by-step explanation:

By the Pythagorean identity $\sin^{2}(x) + \cos^{2}(x) = 1$ .

Assuming that $0 < x < 90^{\circ}$ , $0 < \cos(x) < 1$ .

Rearrange the Pythagorean identity to find an expression for $\cos(x)$ .

$\cos^{2}(x) = 1 - \sin^{2}(x)$ .

Given that $0 < \cos(x) < 1$ :

$\begin{aligned} &\cos(x) \\ &= \sqrt{1 - \sin^{2}(x)} \\ &= \sqrt{1 - \left(\frac{4}{5}\right)^{2}} \\ &= \sqrt{1 - \frac{16}{25}} \\ &= \frac{3}{5}\end{aligned}$ .

Hence, $\tan(x)$ would be:

$\begin{aligned}& \tan(x) \\ &= \frac{\sin(x)}{\cos(x)} \\ &= \frac{(4/5)}{(3/5)} \\ &= \frac{4}{3}\end{aligned}$ .

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2 years ago

What is the completely factored form of p4 – 16? (p – 2)(p – 2)(p 2)(p 2) (p – 2)(p – 2)(p – 2)(p – 2) (p minus 2) (p 2) (p squa

n200080 [17]

The completely factored form of the provided polynomial is (p -2) (p+ 2) (p² +4). The option 4 is the correct option.

<h3>What is polynomial?</h3>

Polynomial equations is the expression in which the highest power of the unknown variable is n (n is a real number).

The polynomial equation given in the problem is,

$p^4 - 16$

Let the factor form of the polynomial is f(p). Thus,

$f(p)=p^4 - 16\\f(p)=p^4 - 2^4\\f(p)=(p^2)^2- (2^2)^2$

Using the formula of difference of squares, we get,

$f(p)=(p^2-4)(p^2+4)\\f(p)=(p^2-2^2)(p^2+4)\\f(p)=(p-2)(p+2)(p^2+4)$

Thus, the completely factored form of the provided polynomial is (p -2) (p+ 2) (p² +4). The option 4 is the correct option.

Learn more about polynomial here;

brainly.com/question/24380382

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2 years ago

Helppp i need help on this question on my hw

yaroslaw [1]

Answer:

B)m^2/3n^5/3

Step-by-step explanation:

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3 years ago

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A submarine started at 750 meters below sea level. It rose 50 meters per hour over a 4-hour period. Which expression represents

Cerrena [4.2K]

Answer:

$y(t) = 750 -50t$

Step-by-step explanation:

We want to model the position of the submarine as a function of time.

Notice that we have a constant amount. The initial depth: 750 meters

Then we have a factor that varies over time. Every hour the submarine ascends 50 meters. therefore as t increases the depth y(t) of the submarine decreases. Then the factor is:

-50t.

Where t represents the time in hours.

Then the equation that represents the new position of the submarine in relation to the level of the sea:

$y(t) = 750 -50t$

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3 years ago

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