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3 years ago

Evaluate f(x) = -2x squared - 4 for x = 3

Mathematics

1 answer:

damaskus [11]3 years ago

7 0

$f(x)=-2x^2-4;\ \text{for}\ x=3\\\\\text{substitute:}\\\\f(3)=-2\cdot3^2-4=-2\cdot9-4=-18-4=-22$

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Sebastian swam laps every day in the community swimming pool. He swam 45 minutes each day, 5 days each week, for 12 weeks. In th

lord [1]

Answer:

$\text{Average rate}=\frac{\text{40 laps}}{\text{ hour}}$

Step-by-step explanation:

Please consider the complete question.

Sebastian swan laps every day in the community swimming pool. He swam 45 minutes each day, 5 days each week, for 12 weeks. In that time, he swam 1800 laps. What was his average rate in laps per hour?

Let us convert time taken into hours as:

$\text{Days}=5\times 12=60$

$\text{Minutes}=60\times 45$

1 hour = 60 minutes. To convert minutes into hours, we will divide total minutes by 60.

$\text{Hours}=\frac{60\times 45}{60}=45$

Now, we will divide 1800 by 45 to find average rate in laps per hour as:

$\text{Average rate}=\frac{\text{1800 laps}}{\text{45 hours}}$

$\text{Average rate}=\frac{\text{40 laps}}{\text{ hour}}$

Therefore, Sebastian's average rate is 40 laps per hour.

6 0

3 years ago

Find the measures of the angles of the triangle whose vertices are A = (-3,0) , B = (1,3) , and C = (1,-3).A.) The measure of ∠A

alekssr [168]

Answer:

$\theta_{CAB}=128.316$

$\theta_{ABC}=25.842$

$\theta_{BCA}=25.842$

Step-by-step explanation:

A = (-3,0) , B = (1,3) , and C = (1,-3)

We're going to use the distance formula to find the length of the sides:

$r= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}$

$AB= \sqrt{(-3-1)^2+(0-3)^2}=5$

$BC= \sqrt{(1-1)^2+(3-(-3))^2}=9$

$CA= \sqrt{(1-(-3))^2+(-3-0)^2}=5$

we can use the cosine law to find the angle:

it is to be noted that:

the angle CAB is opposite to the BC.

the angle ABC is opposite to the AC.

the angle BCA is opposite to the AB.

to find the CAB, we'll use:

$BC^2 = AB^2+CA^2-(AB)(CA)\cos{\theta_{CAB}}$

$\dfrac{BC^2-(AB^2+CA^2)}{-2(AB)(CA)} =\cos{\theta_{CAB}}$

$\cos{\theta_{CAB}}=\dfrac{9^2-(5^2+5^2)}{-2(5)(5)}$

$\theta_{CAB}=\arccos{-\dfrac{0.62}}$

$\theta_{CAB}=128.316$

Although we can use the same cosine law to find the other angles. but we can use sine law now too since we have one angle!

To find the angle ABC

$\dfrac{\sin{\theta_{ABC}}}{AC}=\dfrac{\sin{CAB}}{BC}$

$\sin{\theta_{ABC}}=AC\left(\dfrac{\sin{CAB}}{BC}\right)$

$\sin{\theta_{ABC}}=5\left(\dfrac{\sin{128.316}}{9}\right)$

$\theta_{ABC}=\arcsin{0.4359}\right)$

$\theta_{ABC}=25.842$

finally, we've seen that the triangle has two equal sides, AB = CA, this is an isosceles triangle. hence the angles ABC and BCA would also be the same.

$\theta_{BCA}=25.842$

this can also be checked using the fact the sum of all angles inside a triangle is 180

$\theta_{ABC}+\theta_{BCA}+\theta_{CAB}=180$

$25.842+128.316+25.842$

$180$

6 0

3 years ago

Read 2 more answers

A hockey player strikes a hockey puck. The height of the puck increases until it reaches a maximum height of 3 feet, 55 feet awa

MariettaO [177]

Answer:

The maximum height of the second pluck is greater than that of the first pluck, hence the second pluck travels further

Also the distance of the maximum height of first pluck from the player is less than the distance of the second pluck from the player hence the second pluck travels further

Step-by-step explanation:

From the question we are told that

The maximum height of the first pluck is $h_1 = 3 \ ft$

The height of the second height is mathematically represented as

$$y=x\left(0.15-0.001x\right)$

=> $y=0.15x -0.001x^2$

Generally at maximum height $y' = 0$

$y'=0.15 -0.002 x = 0$

=> $x = 75 \ ft$

Here 75 ft is the horizontal distance the second pluck traveled at maximum height

So the maximum height of the second pluck is mathematically represented as

$y=0.15(75) -0.001(75)^2$

=> $y= 5.625 \ ft$

So comparing the maximum height of the first and the second pluck we see that the maximum height of the second pluck is greater than that of the first pluck, hence the second pluck travels father

3 0

3 years ago

HELP ASAP PLEASE!!! WILL MARK BRAINLIEST!!!

LuckyWell [14K]

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3 years ago

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trapecia [35]

Answer:

Step-by-step explanation: