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3 years ago

Anthony Drew plans for a triangle porch determine if the triangle can be made justify your response

Mathematics

1 answer:

garik1379 [7]3 years ago

3 0

The triangle cannot be made.

Solution:

Given sides of a triangle are 8 ft, 20 ft and 8 ft.

To determine if the triangle can be made:

Let us first define the triangle inequality theorem.

Triangle inequality theorem:

The sum of the lengths of the any two sides of a triangle is greater than the length of the third side.

Using this theorem, we can determine if the triangle can be made or not.

8 ft + 20 ft = 28 ft > 8 ft

20 ft + 8 ft = 28 ft > 8 ft

8 ft + 8 ft = 16 ft < 20 ft

Here the sum of the two sides is less than 20 ft.

This is not satisfy the triangle inequality theorem.

Therefore, the triangle cannot be made.

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A rectangle has its base on the x axis and its upper two vertices on the parabola y = 9 − x2. (a) Draw a graph of this problem.

gtnhenbr [62]

Answer:

(a) see attached
(b) width: 2x; height: y = 9-x²
(c) A=2x(9-x²) . . . 0 ≤ x ≤ 3
(d) dA/dx = -6x² +18; x=±√3
(e) 12√3 units²

Step-by-step explanation:

(a) The attachment shows the graph of the parabola in blue. It also shows an inscribed rectangle in black.

(b) The upper right point of the rectangle is shown in the attachment as (x, y). The dimension y is the height of the rectangle. The x-dimension is half the width of the rectangle, which is symmetrical about the y-axis. Hence the width is 2x.

(c) As with any rectangle, the area is the product of length and width:

... A = (2x)(9 -x²) . . . . . the attachment shows a graph of this

... A = -2x³ +18x . . . . . expanded form suitable for differentiation

A suitable domain for A is where both x and A are non-negative: 0 ≤ x ≤ 3.

(d) The derivative of A with respect to x is ...

... A' = -6x² +18

This is defined everywhere, so the critical values will be where A' = 0.

... 0 = -6x² +18

... 3 = x² . . . . . . . divide by -6, add 3

... √3 = x . . . . . . . -√3 is also a solution, but is not in the domain of A

(e) The rectangle will have its largest area where x=√3. That area is ...

... A = 2x(9 -x²) = 2√3(9 -(√3)²) = 2√3(6)

... A = 12√3 . . . . square units . . . . ≈ 20.785 units²

7 0

3 years ago

To create a unique house paint color, Melton mixes together a sample that is 12 gallons of red, 2.5 gallons of yellow and 0.5 ga

Mariana [72]

Answer:

180

Step-by-step explanation:

total ratio is 15

gallons of red =

$\frac{12}{15} \times 6 \times \frac{15}{0.5 } \\ \\ = 144$

gallons of yellow

$30$

gallons of blue

$\frac{0.5}{15} \times 30 \times \frac{15}{2.5} \\ \\ = 6$

total =144+30+6

=180

4 0

2 years ago

Read 2 more answers

Suppose the time a child spends waiting at for the bus as a school bus stop is exponentially distributed with mean 7 minutes. De

Gala2k [10]

Answer:

The probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.

Step-by-step explanation:

Let the random variable X represent the time a child spends waiting at for the bus as a school bus stop.

The random variable X is exponentially distributed with mean 7 minutes.

Then the parameter of the distribution is, $\lambda=\frac{1}{\mu}=\frac{1}{7}$ .

The probability density function of X is:

$f_{X}(x)=\lambda\cdot e^{-\lambda x};\ x>0,\ \lambda>0$

Compute the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning as follows:

$P(6\leq X\leq 9)=\int\limits^{9}_{6} {\lambda\cdot e^{-\lambda x}} \, dx$

$=\int\limits^{9}_{6} {\frac{1}{7}\cdot e^{-\frac{1}{7} \cdot x}} \, dx \\\\=\frac{1}{7}\cdot \int\limits^{9}_{6} {e^{-\frac{1}{7} \cdot x}} \, dx \\\\=[-e^{-\frac{1}{7} \cdot x}]^{9}_{6}\\\\=e^{-\frac{1}{7} \cdot 6}-e^{-\frac{1}{7} \cdot 9}\\\\=0.424373-0.276453\\\\=0.14792\\\\\approx 0.148$

Thus, the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.

6 0

3 years ago

A snail climbs to the top of a coconut tree 18 meters high. In an hour it will climb 2 meters. But if it go 2 meters, it will sl

kumpel [21]

Answer:

The snail will reach the top of the coconut in 18 hours.

Step-by-step explanation:

If the snail will climb 2 meters in 1 hour but it will slip down one meter for every 2 meters climbed, then the distance traveled will be:

$d = 2 m - 1 m = 1 m$

Since in 1 hour, it climbs 2 meters minus 1 meter, the time in which the snail will reach the top is:

$t = \frac{1 h}{1 m}*18 m = 18 h$

Therefore, the snail will reach the top of the coconut in 18 hours.

I hope it helps you!

5 0

3 years ago

Three consecutive even integers have a sum of -126. What is the smallest integer ?

SSSSS [86.1K]

Answer:

-40, - 42 and -44

Step-by-step explanation:

The fastes way here is trying. Lets pick a number, intelligently, and then work on it.

We need three even integers that sum -126. These will be all negative numbers and as they are consecutive they will be very similar (for example, -33 and -35 and -37). Thus, lets start by 1/3 of -126, which is -42:

(-42)+ (-44) + (-46) = - 132, so -42 no.

Lets go a step back: -40

(-40) + (-42) + (-44) = -126

So, the integers are -40, -42 and -44

5 0

3 years ago

Anthony Drew plans for a triangle porch determine if the triangle can be made justify your response​

Anthony Drew plans for a triangle porch determine if the triangle can be made justify your response