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2 years ago

Use the following triangle to find Sec theta.

Mathematics

1 answer:

makkiz [27]2 years ago

7 0

Answer:

$\frac{\sqrt{41}}{4}$

Step-by-step explanation:

sec(theta) is defined as: $sec(\theta)=\frac{1}{cos(\theta)} = \frac{hypotenuse}{adjacent}$

In the diagram you provided the hypotenuse of the triangle is sqrt(41) and the opposite side is 5, using these two sides, we can solve for the adjacent side by using the Pythagorean Theorem: $a^2+b^2=c^2$

So this gives us the equation where a=adjacent side:

$a^2+5^2=\sqrt{41}^2$

$a^2+25=41$

Subtract 25 from both sides

$a^2=16$

Take the square root of both sides

$a=4$

So now plug this into the definition of sec(theta) and you get: $\frac{\sqrt{41}}{4}$ . This is in most simplified form since 41, has no factors besides 41 and 1.

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What is the identity property

Montano1993 [528]

The identity property shows us that any number that adds zero to itself stays itself. The identity for multiplication tells us that any number multiplied by one is itself.

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3 years ago

Consider the function g(x) = (x-e)^3e^-(x-e). Find all critical points and points of inflection (x, g(x)) of the function g.

Elden [556K]

Answer:

The answer is " $cirtical\ points \ (x,g(x))\equiv (e,0),(e+3,\frac{27}{e^3})$ "

Step-by-step explanation:

Given:

$g(x) = (x-e)^3e^{-(x-e)}$

Find critical points:

$g(x) = (x-e)^3e^{(e-x)}$

differentiate the value with respect of x:

$\to g'(x)= (x-e)^3 \frac{d}{dx}e^{e-r} +e^{e-r} \frac{d}{dx}(x-e)^3=(x-e)^2 e^{(e-x)} [-x+e+3]$

critical points $g'(x)=0$

$\to (x-e)^2 e^{(e-x)} [e+3-x]=0\\\\\to e^{(e-x)}\neq 0 \\\\\to (x-e)^2=0\\\\ \to [e+3-x]=0\\\\\to x=e\\\\\to x=e+3\\\\\to x= e,e+3$

So,

The critical points of $(x,g(x))\equiv (e,0),(e+3,\frac{27}{e^3})$

7 0

3 years ago

2. A group of activists wants to raise money for a good cause, so they decide to sponsor a bicycle race. It receives $60 per cyc

Scorpion4ik [409]

Answer

Step-by-step explanation:

The number of cyclists the group needs to raise at least $57,000 must be at least 1000 cyclists
Let x represent the number of cyclists.
Since, the activists receive $60 per cyclist entry and $15,000 in donations, hence:
Revenue = 60x + 15000
Also, the cost of the race is $18 per entry, hence:
Cost = 18x
They need to raise at least $57,000, hence:
Profit ≥ 57000
Revenue - Cost ≥ 57000
(60x + 15000) - 18x ≥ 57000
42x ≥ 42000
x ≥ 1000
Therefore the number of cyclists the group needs to raise at least $57,000 must be at least 1000 cyclists

5 0

2 years ago

Simplify the expression 4x^3/28x^4

KIM [24]

1/7x

Factorize the numbers (4 and 28) as they have a common factor of 4 so you can simplify it to 1/7. Cancel out the 3 in the x (numerator) from the denominator and you will have x^1 remaining in the denominator. That is also the same as x, therefore making it 1/(7x)

5 0

2 years ago

Look at the rectangle and the square

Komok [63]

Answer:

NO. Ada is not correct.

Step-by-step explanation:

Using Pythagorean Theorem, find the length of the diagonal of the rectangle and the square, respectively.

✔️Diagonal of the Rectangle:

$a^2 + b^2 = c^2$