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galina1969 [7]
3 years ago
5

Two similar pyramids have base edges 3 and 5. Find the following (use a colon between the numbers):

Mathematics
1 answer:
egoroff_w [7]3 years ago
5 0

Step-by-step explanation:

a) the ratio between their altitudes = 3:5

b) the ratio between their base areas = 9:25

c) the ratio between their lateral edges = 3:5

d) the ratio between their volumes = 27:125

e) the ratio between their lateral areas =9:25

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Hey there! :D

So you're wondering if you can make a new ten in this problem, right? Well, lets find out! We can simply do<span> 59 + 17 = 59 + 1 + 16 = 60 + 16 = 76. When we did 59 + 1, that is a new ten then we added to 16. So yes, we did make a new ten in this problem. </span>

<span>Hope it helps! ;)</span>

4 0
3 years ago
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Which expressions are equivalent to -6z+ (-5.5) +3.5z + 5y - 2.5?
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Answer:

what the heck its too much to me

Step-by-step explanation:

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2 years ago
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You invested $11,000 in two accounts paying 3% and 7% annual interest, respectively. If the total interest earned for the year w
Trava [24]

Answer:

I invested $ 10,000 at 7% per year, and $ 1,000 at 3% per year.

Step-by-step explanation:

Given that I invested $ 11,000 in two accounts paying 3% and 7% annual interest, respectively, if the total interest earned for the year was $ 730, to determine how much was invested at each rate, the following calculation must be performed:

5,000 x 0.07 + 6,000 x 0.03 = 530

8,000 x 0.07 + 3,000 x 0.03 = 650

10,000 x 0.07 + 1,000 x 0.03 = 730

Therefore, I invested $ 10,000 at 7% per year, and $ 1,000 at 3% per year.

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3x^2(4x^3-2x^2+7x-4)
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▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄

<h3>>> Given Question :</h3>

3x²(4x³ - 2x² + 7x - 4)

<h3>>> Required Solution :</h3>

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6 0
2 years ago
Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x4 ln(x) (a) Find the interval on which f is incre
Ainat [17]

Answer: (a) Interval where f is increasing: (0.78,+∞);

Interval where f is decreasing: (0,0.78);

(b) Local minimum: (0.78, - 0.09)

(c) Inflection point: (0.56,-0.06)

Interval concave up: (0.56,+∞)

Interval concave down: (0,0.56)

Step-by-step explanation:

(a) To determine the interval where function f is increasing or decreasing, first derive the function:

f'(x) = \frac{d}{dx}[x^{4}ln(x)]

Using the product rule of derivative, which is: [u(x).v(x)]' = u'(x)v(x) + u(x).v'(x),

you have:

f'(x) = 4x^{3}ln(x) + x_{4}.\frac{1}{x}

f'(x) = 4x^{3}ln(x) + x^{3}

f'(x) = x^{3}[4ln(x) + 1]

Now, find the critical points: f'(x) = 0

x^{3}[4ln(x) + 1] = 0

x^{3} = 0

x = 0

and

4ln(x) + 1 = 0

ln(x) = \frac{-1}{4}

x = e^{\frac{-1}{4} }

x = 0.78

To determine the interval where f(x) is positive (increasing) or negative (decreasing), evaluate the function at each interval:

interval                 x-value                      f'(x)                       result

0<x<0.78                 0.5                 f'(0.5) = -0.22            decreasing

x>0.78                       1                         f'(1) = 1                  increasing

With the table, it can be concluded that in the interval (0,0.78) the function is decreasing while in the interval (0.78, +∞), f is increasing.

Note: As it is a natural logarithm function, there are no negative x-values.

(b) A extremum point (maximum or minimum) is found where f is defined and f' changes signs. In this case:

  • Between 0 and 0.78, the function decreases and at point and it is defined at point 0.78;
  • After 0.78, it increase (has a change of sign) and f is also defined;

Then, x=0.78 is a point of minimum and its y-value is:

f(x) = x^{4}ln(x)

f(0.78) = 0.78^{4}ln(0.78)

f(0.78) = - 0.092

The point of <u>minimum</u> is (0.78, - 0.092)

(c) To determine the inflection point (IP), calculate the second derivative of the function and solve for x:

f"(x) = \frac{d^{2}}{dx^{2}} [x^{3}[4ln(x) + 1]]

f"(x) = 3x^{2}[4ln(x) + 1] + 4x^{2}

f"(x) = x^{2}[12ln(x) + 7]

x^{2}[12ln(x) + 7] = 0

x^{2} = 0\\x = 0

and

12ln(x) + 7 = 0\\ln(x) = \frac{-7}{12} \\x = e^{\frac{-7}{12} }\\x = 0.56

Substituing x in the function:

f(x) = x^{4}ln(x)

f(0.56) = 0.56^{4} ln(0.56)

f(0.56) = - 0.06

The <u>inflection point</u> will be: (0.56, - 0.06)

In a function, the concave is down when f"(x) < 0 and up when f"(x) > 0, adn knowing that the critical points for that derivative are 0 and 0.56:

f"(x) =  x^{2}[12ln(x) + 7]

f"(0.1) = 0.1^{2}[12ln(0.1)+7]

f"(0.1) = - 0.21, i.e. <u>Concave</u> is <u>DOWN.</u>

f"(0.7) = 0.7^{2}[12ln(0.7)+7]

f"(0.7) = + 1.33, i.e. <u>Concave</u> is <u>UP.</u>

4 0
3 years ago
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