Please help for this question

A 4 foot tree was planted in 2012 outside a high school. The tree grew continuously by 22% each year from that point. Find out w

Brut [27]

Answer:

The height of the tree in 2020 was of 19.63 feet.

Step-by-step explanation:

Exponential equation for growth:

The exponential equation for the growth of an amount has the following format:

$H(t) = H(0)(1+r)^t$

In which H(t) is the amount after t years, H(0) is the initial amount and r is the growth rate, as a decimal.

A 4 foot tree was planted in 2012 outside a high school.

This means that $H(0) = 4$

The tree grew continuously by 22% each year from that point.

This means that $r = 0.22$

Find out what the height of the tree was in 2020.

2020 is 2020 - 2012 = 8 years after 2012, so this is H(8).

$H(t) = H(0)(1+r)^t$

$H(t) = 4(1+0.22)^t$

$H(4) = 4(1.22)^t$

$H(4) = 4(1.22)^8 = 19.63$

The height of the tree in 2020 was of 19.63 feet.

6 0

3 years ago

Write the first four terms of a geometric sequence with a first term of 81 and a ratio of 1/3

zaharov [31]

Answer:

Huh?

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

A. 6x^3+18x b.6x^2+3 c.36x^2+18 d. 36x^2+3

zzz [600]

The answer: 6x^3+18x

The Explanation: You need to uses distributive property to 6x to x^2+3 which will be 6x^3+18x

6 0

3 years ago

Find, correct to four decimal places, the length of the curve of intersection of the cylinder 4x2 1 y2 − 4 and the plane x 1 y 1

charle [14.2K]

Answer- Length of the curve of intersection is 13.5191 sq.units

Solution-

As the equation of the cylinder is in rectangular for, so we have to convert it into parametric form with

x = cos t, y = 2 sin t (∵ 4x² + y² = 4 ⇒ 4cos²t + 4sin²t = 4, then it will satisfy the equation)

Then, substituting these values in the plane equation to get the z parameter,

cos t + 2sin t + z = 2

⇒ z = 2 - cos t - 2sin t

∴ $\frac{dx}{dt} = -\sin t$

$\frac{dy}{dt} = 2 \cos t$

$\frac{dz}{dt} = \sin t-2cos t$

As it is a full revolution around the original cylinder is from 0 to 2π, so we have to integrate from 0 to 2π

∴ Arc length

$= \int_{0}^{2\pi}\sqrt{(\frac{dx}{dt})^{2}+(\frac{dy}{dt})^{2}+(\frac{dz}{dt})^{2}$

$=\int_{0}^{2\pi}\sqrt{(-\sin t)^{2}+(2\cos t)^{2}+(\sin t-2\cos t)^{2}$

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$

Now evaluating the integral using calculator,

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$ $= 13.5191$

8 0

3 years ago

The measures of 6 of the interior angles of a heptagon are: 120°, 150°, 135°, 170°, 90°, and 125°. What is the measure of the la

Lilit [14]

1. consider one angle of a (convex) heptagon. From that angle you can construct 7-3=4 diagonals. (-3 because we cannot create diagonals with the adjacent vertices and the angle itself )

2. 4 diagonals create 5 triangular regions. (check the picture)

3. So the sum of the measures of the interior angles of the heptagon is 180°*5=900°.

4. The measure of the remaining 7th interior angle is 900°-(120+150+135+170+90+125)°=110°.

5. The largest exterior angle is when the interior angle is the smallest.

6. The smallest interior angle is 90°, so the largest exterior angle is 180°-90°=90°

Answer: 90°

7 0

3 years ago