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loris [4]
3 years ago
10

Jennifer is putting together a selection of flowers that has at most 12 flowers in it. She is choosing either roses or carnation

s. She wants to pick at least three roses and at least two carnations. Let r be the number of roses she uses and let c be the number of carnations she uses. Write a system of inequality’s that represents this scenario.
Mathematics
1 answer:
ohaa [14]3 years ago
7 0

Answer:

r + c ≤12

r > 3

c > 2

Step-by-step explanation:

Jennifer is putting together a selection of flowers that has at most 12 flowers in it.

r = number of roses she uses

c = the number of carnations

At also means Less than or equal to.

It is represented by ≤

She is choosing either roses or carnations. She wants to pick at least three roses

r > 3

and at least two carnations.

= c > 2

Therefore, the system of inequality that represents this scenario is written as:

r + c ≤ 12

r > 3

c > 2

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Evaluate the Riemann sum for f(x) = 3x − 1, −6 ≤ x ≤ 4, with five subintervals, taking the sample points to be right endpoints.
Verdich [7]

Answer:

The Riemann sum equals -10.

Step-by-step explanation:

The right Riemann Sum uses the right endpoints of a sub-interval:

\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f(x_1)+f(x_2)+f(x_3)+...+f(x_{n-1})+f(x_{n})\right)

where

\Delta{x}=\frac{b-a}{n}

To find the Riemann sum for \int\limits^{4}_{-6} {3x-1} \, dx with n = 5 rectangles, using right endpoints you must:

We know that a = -6, b = 4 and n = 5, so

\Delta{x}=\frac{4-\left(-6\right)}{5}=2

We need to divide the interval −6 ≤ x ≤ 4 into n = 5 sub-intervals of length \Delta{x}=2

a=\left[-6, -4\right], \left[-4, -2\right], \left[-2, 0\right], \left[0, 2\right], \left[2, 4\right]=b

Now, we just evaluate the function at the right endpoints:

f\left(x_{1}\right)=f\left(-4\right)=-13=-13

f\left(x_{2}\right)=f\left(-2\right)=-7=-7

f\left(x_{3}\right)=f\left(0\right)=-1=-1

f\left(x_{4}\right)=f\left(2\right)=5=5

f\left(x_{5}\right)=f(b)=f\left(4\right)=11=11

Finally, just sum up the above values and multiply by 2

2(-13-7-1+5+11)=-10

The Riemann sum equals -10

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