Triangle ABC is similar to Triangle QRS. What is the degree measure of angle B?

A pigpen is to be enclosed using 640 m of fencing along three of its sides, the fourth side being a barn. Determine the dimensio

Basile [38]

Answer:

$W_{max}=480m\\ L_{max}=160m$

Step-by-step explanation:

Since we know we only have 640 feet of fence available, we know that L + W + L = 640, $\implies$ 2L + W = 640. This allows us to represent the width, W, in terms of L: W = 640 – 2L

Remember, the area of a rectangle is equal to the product of its width and length, therefore,

$A_{\rm pigpen}=L(640-2L)\implies 640L-2L^2$

Notice that, quadratic has been vertically reflected, since the coefficient on the squared term is negative, so the graph will open downwards, and the vertex will be a maximum value for the area.

recall,

$x_{max}=-b/2a$
$f(x)_{max}=f(x_{max})$

Since our function is A(L)=640L-2L², we get

a=-2
b=640

plug in the value of a and b into the first formula:

$L_{max}=-(640)/2(-2)\implies 160$

$A(L)_{max}=640(160)-2(160)^2\implies 76800$

hence,the dimensions of the pen that will maximize the area are L=160m and W=76800/160=480m

and we're done!

3 0

3 years ago

To which set or sets does the number 12 belong? real numbers and natural numbers only real numbers, whole numbers, and integers

almond37 [142]

First off, let's take a look at what these numbers are:

Real numbers: It can be any numbers,both rational and irrational.

Natural numbers: The number has to be integer and positive.

Integers: A number without fraction or demical place.

Whole number: The number has to be natural and cannot be negative.

Therefore, as 12 is a positive number with no demical place or fraction, it is real numbers,integers, whole numbers, and natural numbers.

Hope it helps!

5 0

3 years ago

Items produced by a manufacturing process are supposed to weigh 90 grams. The manufacturing procon

Annette [7]

Using the normal distribution, it is found that 0.26% of the items will either weigh less than 87 grams or more than 93 grams.

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

It measures how many standard deviations the measure is from the mean.

After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem:

The mean is of 90 grams, hence $\mu = 90$ .

The standard deviation is of 1 gram, hence $\sigma = 1$ .

We want to find the probability of an item differing more than 3 grams from the mean, hence:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{3}{1}$

$Z = 3$

The probability is P(|Z| > 3), which is 2 multiplied by the p-value of Z = -3.

Looking at the z-table, Z = -3 has a p-value of 0.0013.

2 x 0.0013 = 0.0026

0.0026 x 100% = 0.26%

0.26% of the items will either weigh less than 87 grams or more than 93 grams.

For more on the normal distribution, you can check brainly.com/question/24663213

4 0

3 years ago

What does 3n-10=b+4???

Rufina [12.5K]

You cant solve but u can simplify which would be 2b=14

4 0

3 years ago

Whats the volume of a cone? Lengths: 9cm, 5cm

abruzzese [7]

Answer:

B) 75π cm³

Step-by-step explanation:

The volume of a cone is given by the formula ...

V = (1/3)πr²h

Your cone has r = 5 cm and h = 9 cm. Putting these values into the formula gives ...

V = (1/3)π(5 cm)²(9 cm) = 75π cm³

3 0

4 years ago