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3 years ago

Part 3 please help

Mathematics

1 answer:

aleksandr82 [10.1K]3 years ago

6 0

I'm taking "part 3" to mean the 3rd of the posted questions.

If $f(x)=(x^3+2x)\ln x$ , then

$f'(x)=(x^3+2x)'\ln x+(x^3+2x)(\ln x)'=(3x^2+2)\ln x+\dfrac{x^3+2x}x$

$\implies f'(x)=(3x^2+2)\ln x+x^2+2$

Then when $x=1$ , we get $f'(1)=3$ .

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What is the perimeter of the triangle? Round to the nearest tenth.

Cerrena [4.2K]

Answer: 19.8 Units

Step-by-step explanation:

The triangle is shown in the attached figure, and have three vertices: $AB$ , $AC$ and $BC$ .

Each vertice represents a point in the cartesian plane and the length of each side of the triangle is the modulus of each vector.

In this sense, the modulus $m$ is calculated as shown:

$m=\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}$

Hence, for each vector:

$AB=\sqrt{(-2-3)^{2} + (3-0)^{2}}=\sqrt{34}$

$AC=\sqrt{(-2-(4))^{2} + (3-(-3))^{2}}=\sqrt{40}$

$BC=\sqrt{(-4-3)^{2} + (-3-0)^{2}}=\sqrt{58}$

Now, the perimeter of a triangle is the sum of its three sides:

$AB+AC+BC=\sqrt{34} + \sqrt{40} + \sqrt{58}$

Finally:

$AB+AC+BC=19.77 \approx 19.8$

6 0

4 years ago

Angle DOF and angle GOH are vertical angles. What's the measure of angle DOF if the measure of angle GOH is 58°? A. 122° B. 302°

natulia [17]

Answer: C

<u>Step-by-step explanation:</u>

1. DOF and GOH are vertical angles 1. Given

2. m∠DOF = m∠GOH 2. Vertical Angles Theorem

3. ∠DOF = 58° 3. Given

4. 58° = m∠GOH 4. Substitution

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3 years ago

The admission fee at the fair is $1.50 for children and $4 for adults. On a certain day, a total pf 2200 people entered the fair

mash [69]

Answer:

the answer and explanation is in the picture I hope this helps

Step-by-step explanation:

8 0

3 years ago

A diamond can be classified as either gem-quality or industrial-grade. 80% of diamonds are classified as industrial-grade.

mote1985 [20]

Answer:

a) 0.64

b) 0.21

c) 0.79

Step-by-step explanation:

Percentage of industrial-grade diamonds = 80%

This means, if one diamond is chosen at random, there is 80% chance that it will be of industrial-grade. So,

P(Industrial grade) = 80% = 0.80

Part a)

Probability that 1st diamond is industrial-grade = 0.80

Since, selection of diamonds in independent, the probability that 2nd diamond is also industrial grade = 0.80

The overall probability of both diamonds being industrial-grade will be the product of their individual probabilities, according to the fundamental rule of counting.

So, if two diamonds are chosen at random, the probability that both are industrial grade = 0.80 x 0.80 = (0.80)² = 0.64

Part b)

Following the same logic as we followed in the previous part.

The probability of each of the 7 diamonds being industrial-grade is 0.80, so the probability that all 7 are industrial grade will be:

Probability = 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 = $(0.80)^{7}$ = 0.21

So, if 7 diamonds are chosen at random, the probability that all 7 are industrial grade is 0.21.

Part c)

The event "at least one" is complement of event "none". So, the event "at least one of 7" will be complement of "none of the 7"

If none of the selected diamonds is gem quality, this means all 7 of the diamonds are industrial-grade. So,

The probability that none of the diamonds is gem-quality = The probability that all 7 are industrial-grade = 0.21

So,

The probability that at least one of the 7 selected diamonds is gem-quality = 1 - Probability that none is gem-quality

= 1 - 0.21

= 0.79

Since the probability that atleast one of the 7 randomly selected diamonds is gem-quality is greater than 0.05, it won't be unusual event.

3 0

4 years ago

Lines

xeze [42]

Answer:

x=27, y=18

Step-by-step explanation:

Angle CB is 128, which means angle AC is 72. We can confirm angle O is also 72, since the lines are straight. Angle AM is 27, because AN is a right angle. 63+72+27= 162 180-162=18 Angle ND is 18.

6 0

4 years ago

Read 2 more answers

Part 3 please help ​

Part 3 please help