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Trig: Solve Quadratic Equations by Factoring help with 3c and 3d

MissTica

Answer:

3c) x = 1/4, x = 6

3d) t = 0, t = 4

Step-by-step explanation:

3c).....................................

6x² - 15x + 2 = 2x² + 10x - 4
4x² -25x + 6 = 0
4x² - 24x - (x - 6) = 0
4x(x -6) - (x - 6) = 0
(4x - 1)(x - 6) =0
4x - 1 = 0 ⇒ 4x = 1 ⇒ x = 1/4
x - 6 = 0 ⇒ x = 6

==============================

3d).....................................

- 16t² + 76t + 5 = 12t + 5
-16t² + 64t = 0
t² - 4t = 0
t(t - 4) = 0
t = 0
t - 4 = 0 ⇒ t = 4

8 0

3 years ago

Find the local maximum and minimum values of f using both the first and second derivative tests. f(x) = 6 9x2 − 6x3 local maximu

olga55 [171]

The local minimum value of the function f(x) = 6 + 9x² - 6x³ is 6 and the local maximum value of the function f(x) = 6 + 9x² - 6x³ is 9.

For given question,

We have been given a function f(x) = 6 + 9x² - 6x³

We need to find the local maximum and local minimum of the function f(x)

First we find the first derivative of the function.

⇒ f'(x) = 0 + 18x - 18x²

⇒ f'(x) = - 18x² + 18x

Putting the first derivative of the function equal to zero, we get

⇒ f'(x) = 0

⇒ - 18x² + 18x = 0

⇒ 18(-x² + x) = 0

⇒ x (-x + 1) = 0

⇒ x = 0 or -x + 1 = 0

⇒ x = 0 or x = 1

Now we find the second derivative of the function.

⇒ f"(x) = - 36x + 18

At x = 0 the value of second derivative of function f(x),

⇒ f"(0) = - 36(0) + 18

⇒ f"(0) = 0 + 18

⇒ f"(0) = 18

Here, at x=0, f"(x) > 0

This means, the function f(x) has the local minimum value at x = 0, which is given by

⇒ f(0) = 6 + 9(0)² - 6(0)³

⇒ f(0) = 6 + 0 - 0

⇒ f(0) = 6

At x = 1 the value of second derivative of function f(x),

⇒ f"(1) = - 36(1) + 18

⇒ f"(1) = - 18

Here, at x = 1, f"(x) < 0

This means, the function f(x) has the local maximum value at x = 1, which is given by

⇒ f(1) = 6 + 9(1)² - 6(1)³

⇒ f(1) = 6 + 9 - 6

⇒ f(1) = 9

So, the function f(x) = 6 + 9x² - 6x³ has local minimum at x = 0 and local maximum at x = 1.

Therefore, the local minimum value of the function f(x) = 6 + 9x² - 6x³ is 6 and the local maximum value of the function f(x) = 6 + 9x² - 6x³ is 9.

Learn more about the local minimum value and local maximum value here:

brainly.com/question/15437371

#SPJ4

3 0

2 years ago

While visiting Crimson Lake, Sally decided to go Kayaking. The rangers charge $8.50 per hour in addition to a $25.00 deposit to

salantis [7]

The total cost to rent the Kayak will be $50.50

Step-by-step explanation:

Let h be the number of hours

Given

Charges per hour = $8.50

Renting Charges = $25.00

The renting charges are constant and will be used only once while the per hour charges will be calculated as number of hours change.

The function will be written as:

$f(h) = 8.50h +25.00$

Here h is the number of hours.

From 11:30 AM to 02:30 PM makes three hours. So, to find the cost for 3 hours we have to put h = 3

$f(h) = 8.5(3) + 25.00\\= 25.5+25.00\\= 50.5$

Hence,

The total cost to rent the Kayak will be $50.50

Keywords: Linear functions,, slope

Learn more about linear function at:

#LearnwithBrainly

6 0

3 years ago

With gasoline prices increasing, drivers are more concerned with their cars’ gasoline consump- tion. For the past 5 years, a dri

polet [3.4K]

Answer:

The calculated chi -square value =5.7356 Is less than12.01 at 0.1level of significance .

The null hypothesis is accepted.

The past 5 years, a driver has tracked the gas mileage of his car and found that the variance from fill-up to fill-up was σ2 = 23 mpg^2.

Step-by-step explanation:

Step:-(1)

Given data 28 25 29 25 32 36 27 24

Sample size 'n' = 8

mean of the sample (x⁻) = ∑x /n = $\frac{28+ 25+ 29 +25 +32 +36 + 27 + 24}{8}$

mean of the sample (x⁻) = 28.25

x x- x⁻ (x-x⁻ )²

28 28 - 28.25 = -0.25 0.0625

25 25 -28.25 = -3.25 10.56

29 29-28.25 = 0.75 0.5625

25 25-28.25 = -3.25 10.56

32 32-28.25 = 3.75 14.06

36 36-28.25 = 7.75 60.06

27 27-28.25 = -1.25 1.5625

24 24-28.25 = -4.25 18.06

∑(x-x⁻)² = 115.4875

Step:-(2)

The sample standard deviation

S² = ∑(x-x⁻)²/n-1 = $\frac{115.4875 }{7}$ = 16.49

By using χ² distribution

χ² = $\frac{ns^2 }{variance}$

By above test can be applied only if the population from which sample is drawn normal.

Given data For the past 5 years, a driver has tracked the gas mileage of his car and found that the variance from fill-up to fill-up was σ2 = 23 mpg^2.

Population variance σ² = 23

Step:-(3)

Null hypothesis :H₀:σ² = 23

Alternative hypothesis :H₁:≠23

$X^{2} = \frac{8 (16.49)}{23}=5.7356$

The calculated chi -square value =5.7356

The degrees of freedom γ=n-1 =8-1=7

The tabulated value of chi -square = 12.01 at 0.1level of significance (check table)

The calculated chi -square value =5.7356 Is less than12.01 at 0.1level of significance .

The null hypothesis is accepted.

Conclusion:-

The null hypothesis is accepted.

The past 5 years, a driver has tracked the gas mileage of his car and found that the variance from fill-up to fill-up was σ2 = 23 mpg^2.

5 0

3 years ago

A very surveyed 240 people about their favorite type of movie if 15% of the people chose documentaries how many of the people ch

taurus [48]

Step-by-step explanation:

If the library surveyed 240 people and only 15% chose documentaries, then only 36 people chose documentaries and the other 204 chose something else other than documentaries. You had to get 15% into decimal form and to do that you move the "." in 15.0% left 2 places so you get 0.15. Then you multiply 240 by 0.15 and you get 36.

5 0

3 years ago

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