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3 years ago

(1.) decide if function f is invertible.

1 answer:

4 0

a) f(n) is the number of students in your calculus class whose birthday is on the nth day of the year.

f(n) is not invertible because several different days, n, may have the same number of students, f(n). Then for one specific f(n) you cannot determine a unique n.

b) f(x) is the volume in litters of x kilograms of water at 4 degrees celsius.?

f(x) is invertible because each x gives a different f(x), then you can determine unambiguously which f(x) corresponds to each x.

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In ΔBCD, the measure of ∠D=90°, the measure of ∠C=77°, and CD = 41 feet. Find the length of BC to the nearest foot.

OLga [1]

Answer:

182 ft

Step-by-step explanation:

When you are not given a diagram, always draw one for yourself (see diagram).

When you have a right triangle (triangle with 90° angle), you can use the trigonometry ratios, You can remember them using SohCahToa. It is read like this:

sinθ = opposite/hypotenuse Soh

cosθ = adjacent/hypotenuse Cah

tanθ = opposite/adjacent Toa

"θ" means the angle of reference (the angle you are talking about).

We are looking for the length of BC, which is the hypotenuse. I labelled it "d" (lowercase D) because it is opposite to ∠D.

We know ∠C = 77°. This will be our angle of reference (replace θ).

The side we know is DC, also known as "b" (lowercase B) because it's opposite to ∠B. "b" is the adjacent side when θ = C because "b" is touching ∠C.

Take the general trig. formula that has hypotenuse and adjacent: (cosine ratio)

cosθ = adjacent/hypotenuse

Substitute the variables specific for this problem.

cosC = b/d

Substitute the values you know.

cos77° = (41 ft) / d

Isolate "d" to the left side

dcos77° = $d*\frac{41ft}{d}$ Multiply both sides by "d"

dcos77° = 41 ft

dcos77° / cos77° = 41 ft / cos77° Divide both sides by cos77°

d = 41 ft / cos77° Input into calculator

d = 182.261874....... ft Unrounded answer

d ≈ 182 ft Rounded to nearest foot (whole number)

Remember d = BC. It's often easier to use one letter for calculations.

Therefore the length of BC is about 182 feet.

8 0

3 years ago

Adiya said that the first step to solving the quadratic equation x2 + 6 = 20x by completing the square was to divide 6 by 2, squ

Anit [1.1K]

No, actually the method is not correct. Adiya needed to take x2 and subtract it from 20x. she would then get 6 = 18x. Have in mind also that she needed to divide 18. So 6 = 18x turns into 6=X. That is why is incorrect

7 0

3 years ago

Read 2 more answers

What number is 3.4 more than 7.3?

Westkost [7]

Answer:

10.7

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Find the slope of the line tangent to the

g100num [7]

Ln(xy) - 2x =0

slope of the tangent line = derivative of the function

[ln(xy)]' = [2x]'

[1/(xy)] [y + xy'] = 2

y + xy' = 2(xy)

xy' = 2xy - y =y(2x-1)

y' = y(2x-1)/x

Now use x = -1 to find y and after to find y'

ln(xy) = 2x
x=-1
ln(-y) =-2

-y = e^-2

y = - e^-2

y' = [-e^-2][2(-1)-1]/(-1) = [e^-2](-2-1)= [e^-2](-3) = - 3e^-2

Answer: option 6. from the list

8 0

3 years ago

What is the range of this function?*

Mamont248 [21]

Answer:

Hey there!

The range of this function is all numbers to three.

Thus, this can be expressed as (-∞, 3]

Let me know if this helps :)

7 0

3 years ago