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3 years ago

Help please! This is a Calculus AB question!

Mathematics

1 answer:

Lynna [10]3 years ago

7 0

Answer:

½ ln 3

Step-by-step explanation:

∫ sec²x / tan x dx

If u = tan x, then du = sec²x dx.

∫ du / u

ln|u| + C

ln|tan x| + C

Evaluate between π/4 and π/3.

ln|tan(π/3)| + C − (ln|tan(π/4)| + C)

ln|√3| + C − ln|1| − C

ln(√3)

½ ln 3

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The cost y to rent a tent is proportional to x days. if it costs $56 to rent a tent for 7 days what is the formula

Alona [7]

Probably y = 8x. 56 = 8(7), so that works. Without more data, I couldn't say if it could be something else, so that's what I go with.

4 0

2 years ago

Find the area of the triangle below.

gulaghasi [49]

Answer:

Gọi AH là đường cao kẻ từ A đến BC

Xét tam giác AHC vuông tại H

Suy ra AH = HC. cotA= 9.cot35° = 12,9

Xét tam giác AHB vuông tại H

Suy ra BH = AH.tanA = 12,9.tan61°=23,37

Ta có BC= HC+ HB= 9+23,27 =32,27

Diện tích tam giác ABC = 1/2 × AH ×BC= 1/2 ×12,9×32,27=208,1415

8 0

2 years ago

Is it C or no? Can u help please

Westkost [7]

the answer is Probably C.

7 0

3 years ago

Find area round to nearest tength I’ll mark brainest

Vadim26 [7]

Answer:

12.5 sq. units

Step-by-step explanation:

Divide the blue triangle into two smaller triangles.

The length of their common base = 5 units

The height of the <u>yellow</u> triangle = 2 units

The height of the <u>red</u> triangle = 3 units

The area of the yellow triangle

= (5×2)÷2

= 5 sq. units

The area of the red triangle

= (5×3)÷2

= 7.5 sq. units

The total area

= 5+7.5

= 12.5 sq. units

6 0

2 years ago

The volume of a cone of radius r and height h is given by V=πr²h³. If the radius and the height both increase at a constant rate

Aloiza [94]

Answer:

The volume of cone is increasing at a rate 1808.64 cubic cm per second.

Step-by-step explanation:

We are given the following in the question:

$\dfrac{dr}{dt} = 12\text{ cm per sec}\\\\\dfrac{dh}{dt} = 12\text{ cm per sec}$

Volume of cone =

$V = \dfrac{1}{3}\pi r^2 h$

where r is the radius and h is the height of the cone.

Instant height = 9 cm

Instant radius = 6 cm

Rate of change of volume =

$\dfrac{dV}{dt} = \dfrac{d}{dt}(\dfrac{1}{3}\pi r^2 h)\\\\\dfrac{dV}{dt} = \dfrac{\pi}{3}(2r\dfrac{dr}{dt}h + r^2\dfrac{dh}{dt})$

Putting values, we get,

$\dfrac{dV}{dt} = \dfrac{\pi}{3}(2(6)(12)(9) + (6)^2(12))\\\\\dfrac{dV}{dt} =1808.64\text{ cubic cm per second}$

Thus, the volume of cone is increasing at a rate 1808.64 cubic cm per second.

5 0

3 years ago