All categories

3 years ago

Use a graph to solve the equation on the interval

1 answer:

3 0

$sec(x)=-\sqrt{2}\qquad 
\begin{cases}
sec(\theta)=\cfrac{1}{cos(\theta)}
\end{cases}
\\ \quad \\
\cfrac{1}{cos(x)}=-\sqrt{2}\implies \cfrac{1}{-\sqrt{2}}=cos(x)
\\ \quad \\
cos^{-1}\left( \cfrac{1}{-\sqrt{2}} \right)=cos^{-1}[cos(x)]
\\ \quad \\
cos^{-1}\left(- \cfrac{1}{\sqrt{2}} \right)=x
\\ \quad \\
\textit{now, check your Unit Circle for those }\measuredangle x$

You might be interested in

A bike is bought for $1200 and sold 10 months later for $940.

Stolb23 [73]

Value

Depreciation is defined as the reduction in value of an asset over time. In this case, value reduction is due to wear and tear of an equipment (bicycle).

a. The depreciation value would simply be the difference in initial and salvage value divided by time in years.

Depreciation = (Initial value – Salvage value) / Number of years

b. Substituting the given values into the equation where:

Initial value = $1200

Salvage value = $940

Number of years = 10 months = 10/12 years

Calculating:

Depreciation = ($1200 - $940) / (10/12 years)

Depreciation = $312 / year

<span>Depreciation = $26 / month</span>

7 0

3 years ago

A rectangular prism has a volume of 60 cubic centimeters. The height of the prism is 3 centimeters. What is the area of the base

victus00 [196]

Answer: The area of the base would be 20 sq cm

Step-by-step explanation:

Hope this helps :)

8 0

3 years ago

What are the zeros of the polynomial function f(x) = x3 + 10x2 + 24x?

Amiraneli [1.4K]

X^3 + 10x^2 + 24x

divide by x
x(x^2 + 10x + 24)

factor it
x(x+4)(x + 6)

now solve for x

the answer is -6,0,-4

8 0

3 years ago

Identify the vertex, the axis of symmetry, the maximum or minimum value, and the range of the parabola for y=x^2+6x+13

charle [14.2K]

Answer:

Step-by-step explanation:

First we can determine the x value of our vertex via the equation:

$x=\frac{-b}{2a}$

Note that in general a quadratic equation is such that:

$ax^2+bx+c$

In this case a,b and c are the coefficients and so a=1, b=6 and c=13.

Therefore we can determine the x component of the vertex by plugging in the values known and so:

$x=\frac{-b}{2a}=\frac{-6}{2(1)}=\frac{-6}{2}=-3$

Now we can determine the y-component of our vertex by plugging in the x-component to the equation and so:

$f(x)=x^2+6x+13\\\\f(-3)=(-3)^2+6(-3)+13\\\\f(-3)=4$

Therefore our vertex is (-3,4). Now in vertex our x component determines is the axis of symmetry so the equation for axis of symmetry is:

x=-3

Similarly, the y-component of our vertex is the minimum or maximum. In this case it is the minimum you can determine this because a is positive meaning that the parabola will point up, and so the equation for the minimum is:

y=4

The range of the formula is the smallest y-value meaning the minimum y=4 and all real numbers that are more than 4, mathematically:

Range = All real numbers greater than or equal to 4.

4 0

3 years ago

Simplify the radical expression by rationalizing the denominator.

artcher [175]

$\frac{4}{\sqrt{21}} = \frac{4}{\sqrt{21}} \times \frac{\sqrt{21}}{\sqrt{21}} =\boxed{ \frac{4\sqrt{21}}{21}}$

4 0

3 years ago