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3 years ago

Find the average of e^-x over [0,3]

1 answer:

8 0

The average value of a continuous function f(x) over an interval [a, b] is given by the integral,

$\displaystyle \frac1{b-a}\int_a^b f(x)\,\mathrm dx$

Compute the integral for f(x) = e ⁻ˣ over [0, 3] :

$\displaystyle \frac1{3-0}\int_0^3e^{-x}\,\mathrm dx=\frac13(-e^{-x})\bigg|_0^3=\frac13(-e^{-3}-(-e^{-0})) = \frac13 \left(1-\frac1{e^3}\right) = \boxed{\frac{e^3-1}{3e^3}}$

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The Boyd corporation would like to donate 10 computers and 15 printers to local schools. The corporation would like to make sure

anyanavicka [17]

GCF of 10 and 15 is 5

10/5 = 2
15/5 = 3

so it can donate to 5 schools, each receiving 2 computers and 3 printers

8 0

3 years ago

Mahni plans to spend the next 12 weeks saving some of her income. She will save $x a week for the first 6 weeks and then $(2x −

Ulleksa [173]

$x=213$

For first six weeks she saved 213$

Now

For next 6weeks

$\\ \sf\longmapsto 2x-30=2(213)-30=426-30=396\$$

Total savings:-

. $\\ \sf\longmapsto 396+213=609\$$

4 0

3 years ago

Read 2 more answers

Filipe was playing with a triangle on a coordinate plane. The triangle's area is 24 square units. The largest circle he can fit

pickupchik [31]

Answer:

52.36%

Step-by-step explanation:

First, you need to find the radius of the circle. You can do this by using the Pythagorean theorem, which states a^2+b^2=c^2. In this case, a and b are equal to 1.2 and 1.6, and c is the radius of the circle. Plugging in we get 1.2^2+1.6^2=c^2 or 1.44+2.56=c^2 or 4=c^2. Finding the square root of both sides of the equation, we find that 2=c. Now that we have the radius, we can find the area of the circle. The area of a circle is expressed as πr^2, and plugging in 2 for r we get an area of 4π, or ~12.56637. Now all we do is divide 12,56637 by 24 and get what percentage of the area of the triangle the circle covers, which is roughly 0.5236, or 52.36%

4 0

3 years ago

Operations with rational expressions

Scorpion4ik [409]

$$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}=-\frac{w+7}{9}$

Solution:

Given expression:

$$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}$

To solve the given expression:

First simplify: $\frac{50-2 w^{2}}{3 w^{2}+9 w-30}$

$$\frac{50-2 w^{2}}{3 w^{2}+9 w-30}=-\frac{2(w+5)(w-5)}{3(w-2)(w+5)}$

Cancel the common factor (w + 5).

$$=-\frac{2(w-5)}{3(w-2)}$

Now substitute this in the given expression.

$$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}=-\frac{2(w-5)}{3(w-2)} \cdot \frac{w^{2}+5 w-14}{6 w-30}$

Multiply the fractions $\frac{a}{b} \cdot \frac{c}{d}=\frac{a \cdot c}{b \cdot d}$

$$=-\frac{2(w-5)\left(w^{2}+5 w-14\right)}{3(w-2)(6 w-30)}$

Factor the denominator $3(w-2)(6 w-30) =18(w-2)(w-5)$

$$=-\frac{2(w-5)\left(w^{2}+5 w-14\right)}{18(w-2)(w-5)}$

Cancel the common factor 2(w – 5).

$$=-\frac{w^{2}+5 w-14}{9(w-2)}$

Factor the numerator $w^{2}+5 w-14=(w-2)(w+7)$

$$=-\frac{(w-2)(w+7)}{9(w-2)}$

Cancel the common factor (w – 2).

$$=-\frac{w+7}{9}$

$$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}=-\frac{w+7}{9}$

3 0

3 years ago

Kayla’s work to find the surface area of a composite solid formed when a rectangular prism and rectangular pyramid are joined at

docker41 [41]

Answer:

Option B

Step-by-step explanation:

The reason is because the surface area is not including the base of the pyramid and the top of the prism.

Option b. she left out one of the faces of the solid she should have simplified 2((5)(7))+2((6)(7))+2[1/2(5)(9.3)]+2[1/2(6)(9.2)]+(5)(6)

Step-by-step explanation:

we know that

The surface area of the composite figure is equal to the surface area of the pyramid not including the base plus the surface area of the prism not including the top

SA= 285.7 units squared

5 0

4 years ago