MATHEMATICS HIGH SCHOOL

The sycamore grove contains 30 sycamoretrees. That's 75 percent of all the sycamore
trees in the park. How many sycamore trees
are in the park?
​

Answers

Answer 1
Answer:

Answer:

40 sycamore trees

Step-by-step explanation:

We can use the following equation to calculate the total number of sycamore trees in the park:

75% of Total sycamore tree = 30 sycamore tree

0.75 of Total sycamore tree = 30 sycamore tree

\textsf{ Total sycamore tree = $\sf (30)/(0.75) $ sycamore tree}

\textsf{ Total sycamore tree = $\sf 40 $ sycamore tree}

Therefore, there are 40 sycamore trees in the park.
Answer 2
Answer:

Let’s assume that the number of sycamore trees in the park is x. According to the problem statement, 30 sycamore trees make up 75% of all sycamore trees in the park. This can be expressed as:

30 = 0.75 * x

Solving for x, we get:

x = 30 / 0.75

x = 40

Therefore, there are 40 sycamore trees in the park.

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If p varies directly with q, and p = 10 when q = 5, what is the value of p when q = 20? A.p = 40

B.p = 1

C.p = 100

D.p = 28

Answers

A. p=40 because if you look at your question carefully q is half of p so if q=20 which is half of 40 then that means p=40

Write the Riemann sum to find the area under the graph of the function f(x) = x3 from x = 2 to x = 5.

Answers

Answer: The answer is 152.25 sq units.


Step-by-step explanation: Given function to be integrated is

f(x)=x^3,~~x=2~~\textup{to}~~x=5.

To find the area of the given curve from x = 2 to 5, first we need to integrate the function and we will put the boundary values and subtract the smallest from largest value.

The Riemann sum and the formula to find the area is given by

A=\int_(x=2)^(5)f(x)dx\n\n\Rightarrow A=\int_(2)^(5)x^3dx\n\n\Rightarrow A=[(x^4)/(4)]_2^5=(1)/(4)(625-16)=152.25

Thus, the required area is 152.25 sq units.

The area under the graph of the function f\left( x \right) = {x^3} from x = 2 to x = 5 is \boxed{152.25{\text{ unit}}{{\text{s}}^2}}.

Further explanation:

Given:

The function is f\left( x \right) = {x^3}.

The function is defined in the interval from x = 2 to x = 5.

Explanation:

The given function is f\left( x \right) = {x^3}.

Integrate the given function with respect x.

\begin{aligned}Area &= \int\limits_2^5 {f\left( x \right)dx} \n&= \int\limits_2^5 {{x^3}dx}\n&= \left[ {\frac{{{x^4}}}{4}} \right]_2^5\n&= \left( {\frac{{{5^4}}}{4} - \frac{{{2^4}}}{4}} \right)\n\end{aligned}

Further solve the above equation to obtain the area under the curve,

\begin{aligned}{\text{Area}} &= \frac{{625}}{4} - \frac{{16}}{4}\n&= \frac{{625 - 16}}{4}\n&= 152.25\n\end{aligned}\n

The area under the graph of the function f\left( x \right) = {x^3} from x = 2 to x = 5 is \boxed{152.25{\text{ unit}}{{\text{s}}^2}}.

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Riemann function

Keywords: Riemann, sum, area, graph function, Riemann sum, area under the curve, function, f(x) -= x3, x = 2, x = 5.

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