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3 years ago

15

What percentage of the distance covered by an Olympic triathlon do athletes cycle if they swim 3%, run for 20% and cycle the rem

ainder?

2 answers:

Igoryamba3 years ago

7 0

cycling=100%-22%=78%

Please mark me as brainiest

alexgriva [62]3 years ago

4 0

Cycling = 100% -3% -20%
Cycling = 100% -23%
Cycling = 77%

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In a circle, a 90degrees sector has area 144pi in2. What is the radius of the circle?

RUDIKE [14]

Answer:

The radius of the circle is 24 inches.

Step-by-step explanation:

Central angle in a sector is 90 degrees

Area of a sector is $144\pi\ \text{inch}^2$

The area of sector is given by the formula as follows :

$A=\dfrac{\theta}{360}\pi r^2$

r is the radius of circle

$r=\sqrt{\dfrac{360 A}{\theta \pi}} \\\\r=\sqrt{\dfrac{360 \times 144\pi }{90\times \pi}} \\\\r=24\ \text{inch}$

So, the radius of the circle is 24 inches.

6 0

4 years ago

Find the critical numbers of the function f(x) = x6(x − 2)5.x = (smallest value)x = x = (largest value)(b) What does the Second

Marrrta [24]

Answer:

$a) x=0, x=\frac{12}{11}, x=2 \:$ b) The 2nd Derivative test shows us the change of sign and concavity at some point. c) At which point the concavity changes or not. This is only possible with the 2nd derivative test.

Step-by-step explanation:

a) To find the critical numbers, or critical points of:

$f(x)=x^{6}(x-2)^{5}$

1) The procedure is to calculate the 1st derivative of this function. Notice that in this case, we'll apply the <em>Product Rule</em> since there is a product of two functions.

$f(x)=x^{6}(x-2)^{5}\Rightarrow f'(x)=(f*g)'(x)\\=f'g+fg'\Rightarrow (fg)'(x)=6x^{5}(x-2)^{5}+5x^{6}(x-2)^{4} \Rightarrow 6x^{5}(x-2)^{5}+5x^{6}(x-2)^{4}=0\\f'(x)=6x^{5}(x-2)^{5}+5x^{6}(x-2)^{4}$

2) After that, set this an equation then find the values for x.

$x^{5}(x-2)^{4}[6(x-2)+5x]=0\Rightarrow x^{5}(x-2)^{4}[11x-12]=0\Rightarrow x_{1}=0\\(x-2)^{4}=0\Rightarrow \sqrt[4]{(x-2)}=\sqrt[4]{0}\Rightarrow x-2=0\Rightarrow x_{2}=2\\(11x-12)=0\Rightarrow x_{3}=\frac{12}{11}$

$x=0\:(smallest\:value)\:x_{3}=\frac{12}{11}\:x=2 (largest value)$

b) The Second Derivative Test helps us to check the sign of given critical numbers.

Rewriting f'(x) factorizing:

$f'(x)=(11x-12)(x-2)^4x^{5}$

Applying product Rule to find the 2nd Derivative, similarly to 1st derivative:

$f''(x)>0 \Rightarrow Concavity\: Up\\\\f''(x)$

$f''(x)=11\left(x-2\right)^4x^5+4\left(x-2\right)^3x^5\left(11x-12\right)+5\left(x-2\right)^4x^4\left(11x-12\right)\\f''(x)=10\left(x-2\right)^3x^4\left(11x^2-24x+12\right)$

1) Setting this to zero, as an equation:

$10\left(x-2\right)^3x^4\left(11x^2-24x+12\right)=0\\\\$

$10\left(x-2\right)^3x^4\left(11x^2-24x+12\right)=0\\(x-2)^{3}=0 \Rightarrow x_1=2\\x^{4}=0 \therefore x_2=0\\11x^{2}-24x+12=0 \Rightarrow x_3=\frac{12+2\sqrt{3}}{11}\:,x_4=\frac{12-2\sqrt{3}}{11}\cong 0.78$

2) Now, let's define which is the inflection point, the domain is as a polynomial function:

$D=(-\infty$

Looking at the graph.

Plugging these inflection points in the original equation $f(x)=x^{6}(x-2)^{5}$ to get y coordinate:

We have as Inflection Points and their respective y coordinates (Converting to approximate decimal numbers)

$(1.09,-1.05)$ Inflection Point and Local Minimum

$(2,0)$ Inflection Point and Saddle Point

$(0,0)$ Inflection Point Local Maximum

(Check the graph)

c) At which point the concavity changes or not. This is only possible with the 2nd derivative test.

At

$x=\frac{12}{11}\cong1.09$ Local Minimum

$At\:x=0,\:Local \:Maximum$

$At\:x=2, \:neither\:a\:minimum\:nor\:a\:maximum$ (Saddle Point)

5 0

3 years ago

What is the complete factorization of the polynomial below?

Hunter-Best [27]

The complete factorisation of the polynomial given; x³ + 2x² + 4x + 8 as in the task content can be factorised and determined as; Choice D; (x+2)(x+2i)(x-2i).

<h3>What is the complete factorisation of the given polynomial; x³ + 2x² + 4x+8?</h3>

It follows from the given task content that the polynomial whose factors are to be determined by means of factorisation is; x³ + 2x² + 4x+8.

It follows from observation that one of the zeros of the polynomial expression is at; x = -2.

Consequently, one of the factors of the polynomial in discuss is; (x+2).

x³ + 2x² + 4x+8 = (x+2) (x² - 4i²)

= (x+2)(x+2i)(x-2i)

Consequently, it follows that the complete factorisation of the polynomial is; (x+2)(x+2i)(x-2i).

Read more on polynomial factorisation;

brainly.com/question/11434122

#SPJ1

8 0

2 years ago

Pls tell the answer for 50 points!

White raven [17]

Answer:

7*11^5

Explanation:

(the photo)

5 0

3 years ago

Can someone answer this question please answer it correctly if it’s corect I will mark you brainliest

____ [38]

19) 3/8

24 - 15 = 9

9/24 = 3/8

20) 3/28

8 total people running. We want to know the probability that both the president and vice-president are girls, so we have to assume that the president is a girl first.

3/8 x 2/7 = 6/56 = 3/28

21) Travis should play the game where he has to pick either an A or B out of a hat which contains letters A, B, C, D, and E. The probability of him drawing an A or B and winning is 2/5, or 0.4. If he plays the other game, then the probability of him winning is only 1/3, or 0.33.

Probability of rolling a 2 or 3 on a die = 2/6 = 1/3 (0.33)

Probability of picking an A or B = 2/5 (0.4)

6 0

4 years ago