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2 years ago

For the function y= -1+6cos(2pi/7(x-5)) what is the maximum value?

1 answer:

4 0

The maximum value is actually the maximum of y

So, you don't need to care about the stuff inside cosine function,

Cosine function is always within the range of [-1,1]

So here, ymax = -1 + 6* 1 = 5

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Alice and Briana each participate in a 5 kilometer race. Alice's distance covered, in kilometers, after t minutes can be modeled

Pavel [41]

Answer:

a. Alice

b. Briana

c. 0.51 minutes

Step-by-step explanation:

a. Alice formula is valid for any t > 0 minutes, but Briana formula is only valid for

2t - 1 > 0

2t > 1

t > 1/2 minutes

b. They finish when their covered distance is equal to 5 kilometers. For Alice:

t/4 = 5

t = 5*4 = 20 minutes

For Briana:

√(2t - 1) = 5

2t - 1 = 5²

2t = 25 + 1

t = 26/2

t = 13 minutes

c. They are side by side when they have covered the same distance, that is:

t/4 = √(2t - 1)

(t/4)² = 2t - 1

t²/16 = 2t - 1

t² = 16*(2t - 1)

t² = 32t - 16

t² - 32t + 16 = 0

Using quadratic formula:

$t = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)}$

$t = \frac{32 \pm \sqrt{-32^2 - 4(1)(16)}}{2(1)}$

$t = \frac{32 \pm 30.98}{2}$

$t_1 = \frac{32 + 30.98}{2}$

$t_1 = 31.49$

$t_2 = \frac{32 - 30.98}{2}$

$t_2 = 0.51$

Only the second answer has sense for this problem because the race already finished before they spent 31.49 minutes in it.

4 0

2 years ago

Read 2 more answers

A rectangular sheet of metal has identical squares cut from each corner. The sheet is then bent along the dotted lines to form a

Reika [66]

The correct answer is:

3 inches.

Explanation:

We will use the Rational Roots Theorem to solve this.

First we can divide both sides of the equation by 4 in order to simplify it:

$\frac{4x^3-72x^2+320x}{4}=\frac{420}[4} \\ \\x^3-18x^2+80=105$

In order to solve this, we want the polynomial set equal to 0. To do this, subtract 105 from both sides:

$x^3-18x^2+80x-105=105-105 \\x^3-18x^2+80x-105=0$

The Rational Roots Theorem says that if p/q is a root of the polynomial, then p is a factor of the constant term and q is a factor of the leading coefficient. The constant term is -105. Drawing a factor tree, we find that the factors of this number are 1, -1, 3, -3, 5, -5, 7, -5, 15, -15, 21, -21. The leading coefficient is 1; its only factor is 1. This means p/q must be a whole number, and can be any of the factors of 105.

Using synthetic division, we try 1 in the box:

1 | 1 -18 80 -105

_______ 1__ -17___63__

1 -17 63 -42

Since there is a remainder, this is not a root. Trying -1,

-1 | 1 -18 80 -105

_______-1__ 19 _-99_

1 -19 99 -204

This is not a root; in fact, it shows us that none of the negatives will be a factor, as the absolute values increase as we complete the synthetic division.

Trying 3,

3 | 1 -18 80 -105

________3__-45___105_

1 -15 35 0

Since there is no remainder, 3 is a root, and is the answer we are looking for.

3 0

2 years ago

Read 2 more answers

ΔABC is dilated from the origin at a scale factor of 3 to create ΔA′B′C′. Select the option that completes the statement: The tr

Angelina_Jolie [31]

Answer:

The triangle's corresponding angles are congruent and their corresponding sides are proportional therefore, the triangles are similar

Step-by-step explanation:

we know that

If two figures are similar, then their corresponding angles are congruent and their corresponding sides are proportional. The ratio of its corresponding sides is called the scale factor

An dilatation is a transformation that does not modify the internal angles of the figure or the proportion of its measurements.

In this problem ΔABC and ΔA′B′C′ are similar

therefore

The triangle's corresponding angles are congruent and their corresponding sides are proportional therefore, the triangles are similar

6 0

2 years ago

Read 2 more answers

What is the value of y in the following system y= 3x-5 6x+3y=15

Misha Larkins [42]

X=2. You use substitution to put the y=3x-5 into 6x+3y=15.
So you get 6x+3(3x-5)=15
=6x+9x-15=15
add 15 on both sides to get the x's alone and add the x's together.
6+9=15 -- 15+15=30
15x=30
30/15 =2
x=2

7 0

2 years ago

Read 2 more answers

The graph shows the relationship between the number of minutes Maria spent jogging on a treadmill and the distance she jogged.

alina1380 [7]

Answer:

0.1 miles per minute

Step-by-step explanation:

The line goes through (0, 0), so Maria's speed is the ratio of miles to minutes:

(4.5 mi)/(45 min) = 0.1 mi/min

4 0

2 years ago