1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
VashaNatasha [74]
3 years ago
10

The height of the tunnel at the center is 54 ft, and the vertical clearance must be 18 ft at a point 8 ft from the center. Find

an equation for the ellipse.
Mathematics
1 answer:
IrinaVladis [17]3 years ago
8 0

the standard form for a horizontal ellipse is

X^2/a^2 + y^2/b^2 = 1

Substitute 54 for b and and use (8,18) as the

point to find a

x=8

y=18

8^2/a^2 + 18^2/54^2 =1

64/a^2 +  324/2916 = 1

324/2916 reduces to 1/9

64/a^2 + 1/9 = 1

64/a^2= 1-1/9

64/a^2 = 8/9

64*9/8 = a^2

576/8 = 72

A^2 = 72

A = square root(72) = 8.485

 So formula

would be x^2/72 + y^2/2916 =1

You might be interested in
You deposit $600 in a savings account. The account earns 10% simple interest per year. a. What is the interest earned after 10 y
Mrac [35]

Answer:

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
The least-squares regression model y =−3.4+5.2x and correlation coefficient r=−0.66 were calculated for a set of bivariate data
Makovka662 [10]

Answer:

r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}  

For this case the value of r = -0.66

Now we can calculate the determination coeffcient:

r^2 = (-0.66)^2 = 0.4356

And then we can conclude that 43.56% of the variation in y can be explained by the explanatory variable

And then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variable

Step-by-step explanation:

For this case we need to calculate the slope with the following formula:

m=\frac{S_{xy}}{S_{xx}}

Where:

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}

\bar x= \frac{\sum x_i}{n}

\bar y= \frac{\sum y_i}{n}

And we can find the intercept using this:

b=\bar y -m \bar x

And the model obtained for this case is:

y = -3.4 +5.2 x

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:  

r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}  

For this case the value of r = -0.66

Now we can calculate the determination coeffcient:

r^2 = (-0.66)^2 = 0.4356

And then we can conclude that 43.56% of the variation in y can be explained by the explanatory variable

And then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variable

8 0
2 years ago
Recall that rational numbers are numbers that can be represented as the ratio, or fraction, of two integers. When expressed as d
fredd [130]

Answer:

Repeating

Terminating

Repeating

Repeating

Step-by-step explanation:

5 2/7 as improper fraction is 37/7 and it equals 5.28571428571 which makes it repeating because the numbers don't stop.

7/16 is equal to 0.4375 making it terminate because the numbers stop.

14 5/9 as an improper fraction is 131/9 and 131/9 is 14.5555555556 and that is a never ending pattern so it is repeating.

3/22 is equal to 0.13636363636 it is repeating because the numbers never stop.

3 0
11 months ago
What are the next 3 numbers in the number sequence?<br> 23,31,41, 53?
aksik [14]

Answer:

61, 71, 83

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Which expression is equivalent to -8 - (-12)<br> 8 - 12 <br> -8 + 12<br> -8 - 12<br> -8 (8+12)
aleksley [76]

I need help with this too it’s confusing and I don’t understand it.

8 0
3 years ago
Read 2 more answers
Other questions:
  • How do you solve this?
    12·1 answer
  • I will mark brainliest!!
    9·1 answer
  • The US Department of Transportation requires tire manufacturers to provide tire performance information on the sidewall of the t
    7·1 answer
  • NEED HELP QUCKILY PLZ HURRY
    9·2 answers
  • Diane purchased a prepaid phone card for $15. Long distance calls cost 17 cents a minute using this card. Diane used her card on
    8·1 answer
  • What is the value of x?
    5·2 answers
  • Turn the sentence into an expression <br><br> 5.three times the sum of two consecutive<br> integers
    10·1 answer
  • What is the genaral term of this number pattern ? 45,41,37,33,29​
    15·2 answers
  • Simplify each algebraic axpression 4y+6y+5x-2y<br><br><br>​
    10·2 answers
  • How to plot and graph y1 = 17,105 + 1.31x
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!