A rectangle has a perimeter of 150 feet and a base of 45 feet. What is the height?

Divide 1.75 × 10^-2 by -7.3 × 10^-8. Express your answer in scientific notation. Round the coefficient to two decimal places.

viva [34]

Answer:

-2.4 · $10^{5}$

Step-by-step explanation:

4 0

3 years ago

At the beginning of a musical, four-fifths of the seats in the theater were filled. During intermission, 18 people left. If ther

Roman55 [17]

Answer:

there are 380 seats in total

Step-by-step explanation:

286 + 18 = 304 which is four-fifths of the seat. since 304 seats is 80% of the total seats then if you divide it by 80 then multiply it by 100 you get 380.

so one fifth would be 76 seats and if you multiply it by 4 you get 304 which is four fifths of the seat.

8 0

3 years ago

A forestry company hopes to generate credits from the carbon sequestered in its plantations.The equation describing the forest w

Dmitry [639]

Answer:

Explanation:

Given:

The equation describing the forest wood biomass per hectare as a function of plantation age t is:

y(t) = 5 + 0.005t^2 + 0.024t^3 − 0.0045t^4

The equation that describes the annual growth in wood biomass is:

y ′ (t) = 0.01t + 0.072t^2 - 0.018t^3

To find:

a) The year the annual growth achieved its highest possible value

b) when does y ′ (t) achieve its highest value?

a)

To determine the year the highest possible value was achieved, we will set the derivative y'(t) to zero. The values of t will be substituted into the second derivative to get the highest value

$\begin{gathered} 0\text{ = 0.01t + 0.072t}^2\text{ - 0.018t}^3 \\ using\text{ a graphing tool,} \\ t\text{ = -0.1343} \\ \text{t = 0} \\ t\text{ = 4.1343} \\ \\ Since\text{ we can't have time as a negative value, t = 0 or t = 4.1343} \end{gathered}$ $\begin{gathered} To\text{ ascertain which is the maximum, we take a second derivative} \\ y^{\prime}\text{'\lparen t\rparen = 0.01 + 0.144t - 0.054t}^2 \\ \\ substitute\text{ t = 0 and t = 4.13 respectively} \\ when\text{ t = 0 } \\ y^{\prime}\text{'\lparen t\rparen= 0.01 + 0.144\lparen0\rparen - 0.054\lparen0\rparen}^2 \\ y^{\prime}\text{'\lparen t\rparen= 0.01 + 0 - 0} \\ y^{\prime}\text{'\lparen t\rparen= 0.01 > 0} \\ \\ y^{\prime}\text{'\lparen t\rparen= 0.01 + 0.144\lparen4.13\rparen - 0.054\lparen4.13\rparen}^2 \\ y^{\prime}\text{'\lparen t\rparen= -0.316 < 0} \\ \\ if\text{ }y^{\prime}\text{'\lparen t\rparen > 0 , then it is minimum, } \\ if\text{ }y^{\prime}\text{'\lparen t\rparen < 0, then it is maximum} \end{gathered}$

SInce t = 4.13, gives y ′' (t) = -0.316 (< 0). This makes it the maximum value of t

The year the annual growth achieved its highest possible value to the nearest whole number will be

year 4

b) y ′ (t) will achieve its highest value, when we substitute the value of t that gives into the initial function.

Initial function: y(t) = 5 + 0.005t^2 + 0.024t^3 − 0.0045t^4

$undefined$

6 0

1 year ago

What happens when you multiply both numerator and denominator by 4?

Roman55 [17]

Answer:

The answer stays the same.

Step-by-step explanation:

For example, if you have 1/2 and multiply the numerator and the denominator by 4, you get 4/8. 4 divided by 8 still gives you 1/2.

6 0

3 years ago

2 point) what is the height of a d-heap that contains n elements? the height should be a function of n and

belka [17]

Assuming a d-heap means the order of the tree representing the heap is d.
Most of the computer applications use binary trees, so they are 2-heaps.

A heap is a complete tree where each level is filled (complete) except the last one (leaves) which may or may not be filled.

The height of the heap is the number of levels. Hence the height of a binary tree is Ceiling(log_2(n)), for example, for 48 elements, log_2(48)=5.58.
Ceiling(5.58)=6. Thus a binary tree of 6 levels contains from 2^5+1=33 to 2^6=64 elements, and 48 is one of the possibilities. So the height of a binary-heap with 48 elements is 6.

Similarly, for a d-heap, the height is ceiling(log_d(n)).

6 0

3 years ago