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3 years ago

PLEASE HELP!! I NEED THIS ASAP

Mathematics

1 answer:

Leona [35]3 years ago

7 0

Answer:

54√3 +18√91 units²

Step-by-step explanation:

The regular hexagon base is comprised of 6 equilateral triangles, each having a side length of 6. That means the internal right triangle shown having a face edge as its hypotenuse has side lengths of 6 and 8. The face edge length is then ...

face edge = √(6² +8²) = 10 . . . . . double the hypotenuse of a 3-4-5 right triangle, as expected

So, each of the 6 base triangles is an equilateral triangle with side length 6, and each of the 6 face triangles is an isosceles triangle with side lengths 10 and base length 6.

In each case, the altitude of the triangle can be figured from the Pythagorean theorem:

face slant height = √(10² -3²) = √91

base apothem = √(6² -3²) = 3√3

The area of each of these triangle is half the product of its base width and height. The total area of the pyramid is 6 times the sum of the areas of these two triangles.

total surface area = 6·(1/2·6·√91 +1/2·6·3√3) = 18(√91 +3√3)

total surface area = 18√91 +54√3 . . . units²

You might be interested in

How are rational functions similar to linear, quadratic, or exponential functions? How are they different? When are these simila

jeyben [28]

Answer:

See explanation below for further details.

Step-by-step explanation:

A rational consist of two real numbers such that:

$\frac{a}{b} =c$

If c is a polynomial with a certain grade, then, both the numerator and the denominator must be also polynomials and the grade of the numerator must be greater than denominator.

If c is linear function, that is, a first order polynomial, then a must be a (n+1)-th polynomial and b must be a n-th polynomial.

Example:

If $a = x^{2}$ and $b = x$ , then:

$c = \frac{x^{2}}{x}$

$c = x$

If c is a quadratic function, that is, a second order polynomial, then a must be a (n+1)-th polynomial and b must be a n-th polynomial.

Example

If $a = 3\cdot x^{3}$ and $b = x$ , then:

$c = \frac{3\cdot x^{3}}{x}$

$c = 3\cdot x^{2}$

But if c is an exponential, both the numerator and the denominator must be therefore exponential function and grade of each exponential function must different to the other.

Example

If $a = 10^{2x}$ and $b = 3\cdot 10^x$ , then:

$c = \frac{10^{2\cdot x}}{3\cdot 10^{x}}$

$c = \frac{1}{3}\cdot 10^{2\cdot x -x}$

$c = \frac{1}{3}\cdot 10^x$

Otherwise, c would be equal to a constant function, that is, a polynomial with a grade 0.

If $a = 5\cdot e^{x}$ and $b = -3\cdot e^{x}$ , then:

Example

$c = \frac{5\cdot e^{x}}{-3\cdot e^{x}}$

$c = -\frac{5}{3}$

It is worth to add that exponential functions can be a linear combination of single exponential function, similar to polynomials.

Example

$5\cdot a^2\cdot x -9$

7 0

3 years ago

8. Select all the numbers that irrational

Snowcat [4.5K]

Answer:

Answers are square root of 2, square root of 7,

Step-by-step explanation:

Irational is a number that is never ending.

Square root of 2 is irrational since there is no pattern to the number after the decimal.

10/ sqrt of 100. Sqrt of 100 is 10. 10/10 = 1 so this is not a irrational.

Sqrt of 7 does not have a pattern after the decimal point so it is irrational.

5.87 with a dash on top is rational since it means it has a pattern of continues 87's.

Last one it is equal to 2 so it is rattional.

4 0

3 years ago

Read 2 more answers

Let the number of chocolate chips in a certain type of cookie have a Poisson distribution. We want the probability that a cookie

ludmilkaskok [199]

Answer:

$\lambda \geq 6.63835$

Step-by-step explanation:

The Poisson Distribution is "a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event".

Let X the random variable that represent the number of chocolate chips in a certain type of cookie. We know that $X \sim Poisson(\lambda)$

The probability mass function for the random variable is given by:

$f(x)=\frac{e^{-\lambda} \lambda^x}{x!} , x=0,1,2,3,4,...$

And f(x)=0 for other case.

For this distribution the expected value is the same parameter $\lambda$

$E(X)=\mu =\lambda$

On this case we are interested on the probability of having at least two chocolate chips, and using the complement rule we have this:

$P(X\geq 2)=1-P(X$

Using the pmf we can find the individual probabilities like this:

$P(X=0)=\frac{e^{-\lambda} \lambda^0}{0!}=e^{-\lambda}$

$P(X=1)=\frac{e^{-\lambda} \lambda^1}{1!}=\lambda e^{-\lambda}$

And replacing we have this:

$P(X\geq 2)=1-[P(X=0)+P(X=1)]=1-[e^{-\lambda} +\lambda e^{-\lambda}[]$

$P(X\geq 2)=1-e^{-\lambda}(1+\lambda)$

And we want this probability that at least of 99%, so we can set upt the following inequality:

$P(X\geq 2)=1-e^{-\lambda}(1+\lambda)\geq 0.99$

And now we can solve for $\lambda$

$0.01 \geq e^{-\lambda}(1+\lambda)$

Applying natural log on both sides we have:

$ln(0.01) \geq ln(e^{-\lambda}+ln(1+\lambda)$

$ln(0.01) \geq -\lambda+ln(1+\lambda)$

$\lambda-ln(1+\lambda)+ln(0.01) \geq 0$

Thats a no linear equation but if we use a numerical method like the Newthon raphson Method or the Jacobi method we find a good point of estimate for the solution.

Using the Newthon Raphson method, we apply this formula:

$x_{n+1}=x_n -\frac{f(x_n)}{f'(x_n)}$

Where :

$f(x_n)=\lambda -ln(1+\lambda)+ln(0.01)$

$f'(x_n)=1-\frac{1}{1+\lambda}$

Iterating as shown on the figure attached we find a final solution given by:

$\lambda \geq 6.63835$

4 0

3 years ago

How do I solve the following system of equations? <br>-5x-3y=7<br>-3x-4y=2

garri49 [273]

Answer:

(-2, 1)

Step-by-step explanation:

Systems of equations can be solved using different methods. For this set of systems, you can multiply each equation by a factor in order to eliminate a variable and solve for the other variable:

-3(-5x - 3y = 7) or 15x + 9y = -21

5(-3x - 4y = 2) or <u>-15x -20y = 10</u>

-11y = -11

y = 1

Solve for x: -5x - 3 = 7

Add 3 to both sides: -5x -3 + 3 = 7 + 3 or -5x = 10

Solve for x: x = -2

(-2, 1)

6 0

3 years ago

Find the value of x and the value of y

erik [133]

The triangle is an isosceles triangle with exactly two congruent angles.
Since the two 45-deg angles are congruent, their opposite sides are also congruent. That makes y = 5.

This triangle is a 45-45-90 triangle. In a 45-45-90 triangle, the legs are congruent and the hypotenuse is sqrt(2) times the length of the legs.
The hypotenuse has length x, so x = 5 * sqrt(2) = 5sqrt(2)

Answer: B. x = 5sqrt(2), y = 5

5 0

3 years ago