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ASHA 777 [7]
3 years ago
14

An obtuse triangle with area 12 has two sides of lengths 4 and 10. Find the length of the third side. (There are two answers.) (

Use law of cosines) ...?
Mathematics
1 answer:
mart [117]3 years ago
3 0
This question can be solved using the Herons equation where 
A = SQRT [s*(s-a)*(s-b)*(s-c)]

A = area of the triangle
a, b and c are the sides of the triangle

s = (a+b+c)/2

Since we are given the area, we can express "s" as a function of the third side c. This can be substituted in the original equation so as to obtain an expression to solve for the third side c

s = (4+10+c)/2 = (14+c)/2

using the solver function of the calculator or MS Excel, the third side is 7.21 units
You might be interested in
Seven less than one-fourth of a numer is -1.
zavuch27 [327]

Answer:

The number is 24.

Step-by-step explanation:

-1+7=6

6*4=24

4 0
3 years ago
Read 2 more answers
The following observations were made on fracture toughness of a base plate of 18% nickel maraging steel (in ksi √in, given in in
Grace [21]

Answer:

A 90% confidence interval for the standard deviation of the fracture toughness distribution is [4.06, 6.82].

Step-by-step explanation:

We are given the following observations that were made on fracture toughness of a base plate of 18% nickel maraging steel below;

68.6, 71.9, 72.6, 73.1, 73.3, 73.5, 75.5, 75.7, 75.8, 76.1, 76.2,  76.2, 77.0, 77.9, 78.1, 79.6, 79.8, 79.9, 80.1, 82.2, 83.7, 93.4.

Firstly, the pivotal quantity for finding the confidence interval for the standard deviation is given by;

                             P.Q.  =  \frac{(n-1) \times s^{2} }{\sigma^{2} }  ~ \chi^{2} __n_-_1

where, s = sample standard deviation = \sqrt{\frac{\sum (X - \bar X^{2}) }{n-1} } = 5.063

            \sigma = population standard deviation

            n = sample of observations = 22

Here for constructing a 90% confidence interval we have used One-sample chi-square test statistics.

<u>So, 90% confidence interval for the population standard deviation, </u>\sigma<u> is ;</u>

P(11.59 < \chi^{2}__2_1 < 32.67) = 0.90  {As the critical value of chi at 21 degrees  

                                                  of freedom are 11.59 & 32.67}  

P(11.59 < \frac{(n-1) \times s^{2} }{\sigma^{2} } < 32.67) = 0.90

P( \frac{ 11.59}{(n-1) \times s^{2}} < \frac{1}{\sigma^{2} } < \frac{ 32.67}{(n-1) \times s^{2}} ) = 0.90

P( \frac{(n-1) \times s^{2} }{32.67 } < \sigma^{2} < \frac{(n-1) \times s^{2} }{11.59 } ) = 0.90

<u>90% confidence interval for</u> \sigma^{2} = [ \frac{(n-1) \times s^{2} }{32.67 } , \frac{(n-1) \times s^{2} }{11.59 } ]

                                     = [ \frac{21 \times 5.063^{2}  }{32.67 } , \frac{21 \times 5.063^{2}  }{11.59 } ]

                                     = [16.48 , 46.45]

<u>90% confidence interval for</u> \sigma = [\sqrt{16.48} , \sqrt{46.45} ]

                                                 = [4.06 , 6.82]

Therefore, a 90% confidence interval for the standard deviation of the fracture toughness distribution is [4.06, 6.82].

5 0
3 years ago
What is the center of the dot plot 2 2.5 3 5
gizmo_the_mogwai [7]

I would say the answer is 2.5 sorry if it's incorrect! :) ✨

4 0
2 years ago
A cone has a radius of 8 inches and a height of 12 inches. What is the exact volume of the cone? A. 32π in3 B. 96π in3 C. 256π i
balu736 [363]
I believe the answer is c. 256 pi in 3. <span />
6 0
3 years ago
Read 2 more answers
Please help me solve this
DochEvi [55]

9514 1404 393

Answer:

  a) q = 15 at minimum average cost; q = 10 at minimum marginal cost

  b) marginal cost = average cost = 225 at q = 15

Explanation:

The average cost is the total cost divided by the number of units.

  A = C/q = 300 -10q +1/3q^2

The marginal cost is the derivative of the total cost.

  M = 300 -20q +q^2

__

a) The minimum average cost is where its derivative is zero.

  A' = 0 = -10 +2/3q   ⇒   q = 15

The minimum marginal cost is where its derivative is zero.

  M' = -20 +2q   ⇒   q = 10

__

b) The average cost for 15 units produced is ...

  A(15) = 300 -10(15) +1/3(15^2) = 225

The marginal cost at that same production level is ...

  M(15) = 300 -20(15) +15^2 = 225

The average cost and marginal cost are equal at the minimum average cost.

6 0
3 years ago
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