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user100 [1]
3 years ago
13

Sketch the region enclosed by y=e3x,y=e5x and x=1. Decide whether to integrate with respect to x or y, and then find the area of

the region.
Mathematics
1 answer:
Lina20 [59]3 years ago
4 0

The area of the region is \text { Area } \approx 23.12

Explanation:

The area of the region is given by

\text { Area }=\int_{0}^{1}\left(e^{5 x}-e^{3 x}\right) d x

Integrating the terms inside the bracket, we get,

\left[\frac{e^{5 x}}{5}-\frac{e^{3 x}}{3}\right]

Now, applying the limits for x for the integrated term,

Area=\frac{e^{5}}{5}-\frac{e^{3}}{3}-\frac{e^{0}}{5}+\frac{e^{0}}{3}

Any number to the power of zero is one. Thus, substituting the values, we get,

Area=\frac{e^{5}}{5}-\frac{e^{3}}{3}-\frac{1}{5}+\frac{1}{3}

Adding the like terms,

Area=\frac{e^{5}}{5}-\frac{e^{3}}{3}+\frac{2}{15}

Simplifying the terms, we get,

\text { Area } \approx 23.12

Thus, The area of the region is \text { Area } \approx 23.12

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Aleksandr [31]

Answer:

1620

Step-by-step explanation:

0.36*4500=1620

7 0
3 years ago
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Please help me!!!! You only have to answer number 1!!!
mrs_skeptik [129]

Given : A social media website has currently = 1,000 members.

           In each month number of members gets triple.

To find: Equation that represents number of members m belongs to site.

Solution: Because we are given, each month the number of members gets triple, that means each month we can multiply by 3 to the number of members of previous month.

For first month, we would multiply 1,000 by 3.

For second month, we would multiply 1,000 by 3 *3.

For second month, we would multiply 1,000 by 3*3*3.

Each month one factor of 3 is being increasing.

We could write those 3's as exponents of 3.

Like 1000*3 = 1000*3^1

1000 * 3^2.

1000 * 3^3.

As many months as many 3's are there.

So, the exponent of 3 is represnts the number of months.

Let us take a variable for number of month by n.

So, we could setup an equation for number of members m belongs to site on a particular month n as

m= 1000 (3)^n

This is our final equation.

7 0
3 years ago
A hotel has 30 floors with 40 rooms per floor. The rooms on one side of the hotel face the water, while rooms on the other side
Ket [755]

A) Choosing a <em>stratified random sample</em> might be preferable to an <em>SRS </em>because;

<em><u>Stratified random sampling would divide the population into stratas but the </u></em>

<em><u>SRS would not do so. The strata would be the type of room namely those </u></em>

<em><u>with water view and those with golf view.</u></em>

B) The reason why a cluster sample would be a simpler option is because;

<u><em>It will divide the population into multiple clusters that makes it easier to </em></u>

<u><em>work with unlike the SRS that generalizes. The clusters would be each of </em></u>

<u><em>the 30 floors.</em></u>

We are told that the manager wanted to select 120 rooms and carry out a survey on each registered guest by asking how satisfied they were with the hotel. He decided to use a sampling method called SRS which means Simple Random Sampling.

Simple random sampling is defined as a sampling method where individuals or objects are selected randomly from a population thereby given each person or object an equal chance of selection.

A) Stratified Random sampling is a method of sampling that divides the population into smaller groups known as objects/stata. In this case Stratified random sampling would be preferred to SRS because the hotel rooms are divided into two types namely those that can view the water and those that can view the golf course and as such the Stratified random sampling would divide the population but the SRS would not do so.

B) Cluster sampling is when the population is divided into multiple groups known for assessment. The reason why it would be a simpler option is because there are 30 floors and they can be classified as clusters and surveyed per floor.

Read more at; brainly.com/question/15932504

7 0
3 years ago
Alan drives 20.4 miles in 17 minutes.He passes a sign which gives the speed limit as 60mph.By how much in mph did Alan exceed th
Rzqust [24]
12 miles over the speed limit
7 0
2 years ago
7 + 2y^2<br><br> Evaluate the expression for <br> Y = 5.<br><br><br> Please help me
garik1379 [7]

Answer:

107

Step-by-step explanation:

We first need to input the values of the variables.

7 + 2 x 5^2

7+10^2

7+100 = 107

4 0
3 years ago
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