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3 years ago

The length of a side of an equilateral triangle is 40cm. what is the length of the altitude of the triangle?

Mathematics

1 answer:

podryga [215]3 years ago

4 0

Answer:

20√3 cm

Step-by-step explanation:

Altitude of an equilateral triangle splits it into 2 equal right triangles, it bisects the base and the angle opposite to the base.

<u>Let the altitude be x. Then as per Pythagorean theorem:</u>

x² = 40² - (40/2)²
x²= 1600 -400
x²= 1200
x= √1200
x= 20√3 cm

<u>Correct choice is</u> the second one

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Consider the kth iteration of the simplex method as defined in Algorithm 4.2 of the textbook. (a) Show that the matrix Ak+1, def

trasher [3.6K]

Answer:

The solution and complete explanation for the above question and mentioned conditions is given below in the attached document.i hope my explanation will help you in understanding this particular question.

Step-by-step explanation:

7 0

2 years ago

The forecast for week 13 is 747. (Enter your response rounded to the nearest whole number.) Specify the mean absolute deviatio

son4ous [18]

Answer:

a) MAD without the forecast = 43.71

MAD with the forecast = 45.59

b) MAPE = 0.097 = 9.7%

Step-by-step explanation:

642 602 656 747 663 618 731 726 679 737 664 740

Mean Absolute deviation is given as

MAD = [Σ|x - μ|]/N

We first calculate the mean

Mean = Σx/N

Mean = (642+602+656+747+663+618+731+726+679+737+664+740)/12

Mean = (8205/12) = 683.75

absolute deviations from the mean

|642-683.75| + |602-683.75| + |656-683.75| + |747-683.75| + |663-683.75| + |618-683.75| + |731-683.75| + |726-683.75| + |679-683.75| + |737-683.75| + |664-683.75| + |740-683.75|

Absolute deviations from the mean

41.75+81.75+27.75+63.25+20.75+65.75+47.25+42.25+4.75+53.25+19.75+56.25

= 524.5

MAD = [Σ|x - μ|]/N

MAD = (524.5/12)

MAD = 43.71

If we include the forecast on the 13th week

642 602 656 747 663 618 731 726 679 737 664 740 747

Mean = (8205+747)/13

Mean = 688.62

absolute deviations from the mean

|642-688.62| + |602-688.62| + |656-688.62| + |747-688.62| + |663-688.62| + |618-688.62| + |731-688.62| + |726-688.62| + |679-688.62| + |737-688.62| + |664-688.62| + |740-688.62| + |747-688.62|

Absolute deviations from the mean

= 46.62+86.62+32.62+58.38+25.62+70.62+42.38+37.38+9.62+48.38+24.62+51.38+58.38

= 592.62

MAD = (592.62/13)

MAD = 45.59.

b) MAPE is used to check forecast errors

MAPE = (1/N) Σ [|x-f|/x]

where N = Sample size = 12

x = each variable

f = the forecasted value = 747

x = 642, 602, 656, 747, 663, 618, 731, 726, 679, 737, 664, 740

Σ [|x-f|/x]

= 0.164+0.241+0.139+0+0.112+0.209+0.022+0.029+0.100+0.014+0.125+0.009

Σ [|x-f|/x] = 1.164

MAPE = (1.164/12)

MAPE = 0.097 = 9.7%

Hope this Helps!!!

7 0

3 years ago

The Table below gives you The population of Texas since 1970. Find the average rate if change from 1970 to 1090

ruslelena [56]

Answer:

Average rate of change = 0.29 million per year

Step-by-step explanation:

Average rate of change in the population from year 1970 to year 1900 is given by the formula,

Average rate of change = $\frac{\text{Population in year 1990-Population in year 1970}}{1990-1970}$

= $\frac{17-11.2}{1990-1970}$

= $\frac{5.8}{20}$

= 0.29 million per year

Therefore, average rate of change in the population from 1970 to 1990 will be 0.29 million per year.

8 0

3 years ago

Please help with this maths question!??

tia_tia [17]

Answer:

2.44746×10⁶

Step-by-step explanation:

R=(3.8×10⁵)²/5.9×10⁴

=3.8²×10¹⁰/5.9×10⁴

=1.444×10¹¹/5.9×10⁴

=1.444×10⁷/5.9

=361×10⁷/1475

=2.44746×10⁶

4 0

2 years ago

How do you construct a regular polygon inside a circle?

Tresset [83]

You could use a ruler, think about how you want the polygon inside of the circle or how you want the circle to surround the polygon. When you use a ruler, make sure your co-ordinates inside of the circle are correct though before drawing the line.

I hope this info helps! :3

7 0

3 years ago