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3 years ago

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Natalie made blueberry muffins for a bake sale. Each muffin cost her about $0.25 to make. She spent $8.75 to make all of the muf

fins. Natalie sold each muffin for $0.50 more than it cost her to make. How much money did Natalie receive from selling all of the muffins? Enter your answer in the box.

1 answer:

Scilla [17]3 years ago

5 0

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Evaluate the Riemann sum for f(x) = 3 - 1/2 times x between 2 and 14 where the endpoints are included with six subintervals taki

Digiron [165]

Answer:

-6

Step-by-step explanation:

Given that :

we are to evaluate the Riemann sum for $f(x) = 3 - \dfrac{1}{2}x$ from 2 ≤ x ≤ 14

where the endpoints are included with six subintervals, taking the sample points to be the left endpoints.

The Riemann sum can be computed as follows:

$L_6 = \int ^{14}_{2}3- \dfrac{1}{2}x \dx = \lim_{n \to \infty} \sum \limits ^6 _{i=1} \ f (x_i -1) \Delta x$

where:

$\Delta x = \dfrac{b-a}{a}$

a = 2

b =14

n = 6

∴

$\Delta x = \dfrac{14-2}{6}$

$\Delta x = \dfrac{12}{6}$

$\Delta x =2$

Hence;

$x_0 = 2 \\ \\ x_1 = 2+2 =4\\ \\ x_2 = 2 + 2(2) \\ \\ x_i = 2 + 2i$

Here, we are using left end-points, then:

$x_i-1 = 2+ 2(i-1)$

Replacing it into Riemann equation;

$L_6 = \lim_{n \to \infty} \sum \imits ^{6}_{i=1} \begin {pmatrix}3 - \dfrac{1}{2} \begin {pmatrix} 2+2 (i-1) \end {pmatrix} \end {pmatrix}2$

$L_6 = \lim_{n \to \infty} \sum \imits ^{6}_{i=1} 6 - (2+2(i-1))$

$L_6 = \lim_{n \to \infty} \sum \imits ^{6}_{i=1} 6 - (2+2i-2)$

$L_6 = \lim_{n \to \infty} \sum \imits ^{6}_{i=1} 6 -2i$

$L_6 = \lim_{n \to \infty} \sum \imits ^{6}_{i=1} 6 - \lim_{n \to \infty} \sum \imits ^{6}_{i=1} 2i$

$L_6 = \lim_{n \to \infty} \sum \imits ^{6}_{i=1} 6 - 2 \lim_{n \to \infty} \sum \imits ^{6}_{i=1} i$

Estimating the integrals, we have :

$= 6n - 2 ( \dfrac{n(n-1)}{2})$

= 6n - n(n+1)

replacing thevalue of n = 6 (i.e the sub interval number), we have:

= 6(6) - 6(6+1)

= 36 - 36 -6

= -6

5 0

3 years ago

Need help please<br> need help please<br> need help please<br> need help please

nexus9112 [7]

Hi! I’ll help you in just a moment when I’m done with my walk

7 0

2 years ago

What is the solution of 2|2x-1|-8=18?

Maurinko [17]

Solve for $|2x-1|$ :

$2|2x-1|-8=18\implies2|2x-1|=26\implies|2x-1|=13$

Now if $2x-1\ge0$ , we have $|2x-1|=2x-1$ and

$2x-1=13\implies2x=14\implies x=7$

On the other hand, if $2x-1$ , then $|2x-1|=-(2x-1)=1-2x$ and

$1-2x=13\implies-2x=12\implies x=-6$

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A classroom can accommodate less than 24 students.

Effectus [21]

The answer is c because it’s asking for less than so it goes left and the dot isn’t filled so it means less than

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At which angle will the hexagon rotate so that it maps

Viefleur [7K]

Answer:

60

Step-by-step explanation:

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