If the radius of the planet is given by R, and the height above the surface is given by h, use the figure below, and the Pythagorean Theorem to derive the formula for the distance, d, to the horizon tangent point, assuming that the triangle is a right triangle.
Please answer the second one too
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Applying the pythagroean theorem, the formula to find the horizontal distance, d, is: [tex]\mathbf{d = \sqrt{h^2 - R^2} }[/tex]
What is the Pythagorean Theorem?The pyhagroean theorem is given as, c² = a² + b², where h is the longest side of the right triangle.
Given the following:
c = ha = db = RThe formula derived would be:
h² = d² + R²
Make d the subject fo the formula
[tex]\mathbf{d = \sqrt{h^2 - R^2} }[/tex]
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Related Questions
What is the length of the missing leg? If necessary, round to the nearest tenth
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Answer: 48
Step-by-step explanation:
1. Find two numbers that...
a. multiply to -40 and add to -6.
b. multiply to -40 and add to 6.
c. multiply to -36 and add to 9.
d. multiply to -36 and add to -5.
If you get stuck, try listing all the factors of the first number.
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Answer:
a. +34 b. +46 c. +45 d. +31
Step-by-step explanation: use a number line
Which of the following is a geometric series? 0.1 0.3 0.5 0.7 1 3 9 27 19 17 15 13 0.4 0.9 1.5 2.2
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Geometric series have the same ratio. The series which is a geometric series is 1, 3, 9, 27.
What is a geometric series?A series of numbers is a geometric series if the quotient of any two consecutive numbers is the same.
A series of numbers is a geometric series if the quotient of any two consecutive numbers is the same.
A.) 0.1 0.3 0.5 0.7
To check if the series is geometric series, find the quotient.
[tex]r_1=\dfrac{0.3}{0.1} = 3\\\\r_2 = \dfrac{0.5}{0.3} = 1.66[/tex]
Since the ratio is different this is not a geometric series.
B.) 1 3 9 27
To check if the series is geometric series, find the quotient.
[tex]r_1=\dfrac{3}{1} = 3\\\\r_2 = \dfrac{9}{3} = 3[/tex]
Since the ratio is the same this is a geometric series.
C.) 19 17 15 13
To check if the series is geometric series, find the quotient.
[tex]r_1=\dfrac{17}{19} = 0.8947\\\\r_2 = \dfrac{15}{17} = 0.8823[/tex]
Since the ratio is different this is not a geometric series.
D.) 0.4 0.9 1.5 2.2
To check if the series is geometric series, find the quotient.
[tex]r_1=\dfrac{0.4}{0.9} = 0.4444\\\\r_2 = \dfrac{0.9}{1.5} = 0.6[/tex]
Since the ratio is different this is not a geometric series.
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Answer:
its b 1 + 3 + 9 + 27
Step-by-step explanation:
How many cups of flour would be needed to make all of the cookie recipes that use 2 3/4 cups of flour?
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I’m very confused please help:)
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Answer:
b=20°, c=160°
Step-by-step explanation:
b=20° [vertically opposite angle]
c+b=180° [angle at same line ]
c=180° - 20°
c = 160°
Find the measure of <1
Please answer ASAP!!!!
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PLEASE HELP 20 POINTS!
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Answer:
Step-by-step explanation:
Translate the point A (-3,4) right 5 up 1
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Answer:
(2,5)
Step-by-step explanation:
-3+5=2 and 4+1=5
what is the slope of a line
(a) where the line crosses at the y-axis
(b) the amount the line rises on the y-axis over the amount it moves horizontally on the x-axis
(c) where the line crosses at the x-axis
(d) where the line begins
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Answer:
the answer is (b), because
Step-by-step explanation:
rise over run
Answer:
B
because I
saw someone else say it was b
Step-by-step explanation:
I'm smart
only question 5 parts a and b PLEASE HELP!!
Answers
Answer:
slope = 3/2
the plant grows 3 centimeters every 2 weeks
Step-by-step explanation:
Which is the equation of a hyperbola with directrices at x = ±2 and foci at (6, 0) and (−6, 0)? x squared over 12 minus y squared over 24 equals 1 x squared over 12 minus y squared over 48 equals 1 y squared over 12 minus x squared over 24 equals 1 y squared over 48 minus x squared over 12 equals 1
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The equation of a hyperbola with directrices at x = ±2 and foci at (6, 0) and (−6, 0) is y squared over 48 minus x squared over 12 equals 1.
What is the equation of hyperbola?The equation of the hyperbola is the equation which is used to represent the hyperbola in the algebraic equation form, with the value of center point in the coordinate plane and foci.
The standard form of the equation of the hyperbola can be given as,
[tex]\dfrac{(y-k)^2}{b^2}-\dfrac{(x-h)^2}{a^2}=r^2[/tex]
Here (h,k) is the center of the hyperbola, (b) is the transverse axis, and (a) is the conjugate axis.
The foci of the hyperbola is,
[tex](h,k\pm c)[/tex]
The directrix is,
[tex]y=k\pm \dfrac{a^2}{c}[/tex]
A hyperbola is given with directrices at x = ±2 and foci at (6, 0) and (−6, 0). Thus, the directrix is,
[tex]y=k\pm \dfrac{a^2}{c}\\\pm 2=k\pm \dfrac{a^2}{c}\\\dfrac{a^2}{6}=2\\a^2=12\\[/tex]
It is known that,
[tex]a^2+b^2=c^2\\[/tex]
Put the value of a and c,
[tex](12)+b^2=6^2\\b^2=36-12\\b^2=24[/tex]
The value of center is (0,0). Thus, the equation of hyperbola is,
[tex]\dfrac{(y-0)^2}{24^2}-\dfrac{(x-0)^2}{12^2}=1\\\dfrac{y^2}{24^2}-\dfrac{x^2}{12^2}=1[/tex]
Thus, the equation of a hyperbola with directrices at x = ±2 and foci at (6, 0) and (−6, 0) is y squared over 48 minus x squared over 12 equals 1.
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Jose is starting a word-processing business out of his home. He plans to charge $15 per hour. He anticipates his monthly expenses to be $490 for equipment rental, $45 for materials, and $65 for phone usage. What is the minimum number of hours he must work in a month to make a profit of at least $600?
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Answer:
80
Step-by-step explanation:
profit = revenue - expenses
revenue = $15 per hour = $15 * number of hours (n) = $15 * n
expenses = $490 + $45 + $65 = $600
we want profit to be 600 or more
15 * n - 600 = profit
profit ≥ 600
15 * n - 600 ≥ 600
add 600 to both sides to isolate the variable and its coefficient
15 * n ≥ 1200
divide both sides by 15 to isolate the variable
n ≥ 80
Jose must therefore work 80 or more hours, for a minimum of 80
help pleaseeeeee will ark brainliest
Answers
Answer:40
Step-by-step explanation:
Your correct and final answer for this question is 40
(✿◕‿◕✿) Pls mark me Brainiest (✿◕‿◕✿)
Which statement describes the expression 20+ ½ x (4 + 6) ?
A. Half of 4 added to six, Plus 20
B. The sum of 4 and 6 plus half of 20
C. Half the sum of 4 and 6 added to 20.
D. The sum of 4 and 6 plus 20 divided by 2
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This is for my Iready and I’m super confused the story problem reads ""Lola rode her bike for 7/10 of an hour on Saturday and 3/5 of an hour on Sunday. How much longer did she ride her bike on Saturday than Sunday?
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7/10 is 7 divided by 10 so:
= 0.70
3/5 is 3 divided by 5 so:
= 0.60
60 minutes is one hour (since the question said that Lola rides the bike for 7/10 and 3/5 of an hour)
Now we use these to find how many minutes:
To find 0.70 (or 7/10) of 60 minutes, you multiply 60 x 0.70
= 42 minutes on Saturday
To find 0.60 (or 3/5) of 60 minutes, you multiply 60 x 0.60
= 36 minutes on Sunday
Now to find how much longer she rode her bike on Saturday than Sunday, you subtract the two numbers:
42 - 36
= 6
Therefore, Lola rode her bike for 6 minutes more on Saturday than on Sunday.
Help me on this inequality please!
Answers
Answer:
w ≤ 5
Step-by-step explanation:
-2w ≥ -10
-2w / -2 ≥ -10 / -2
The -2 cancels each other out and -10 divided by -2 is 5. When divding an inequality by a negative number you MUST flip the sign.
w ≤ 5
△ACE, B is the midpoint of AC and D is the midpoint of EC.
Answers
Answer:
See below
Step-by-step explanation:
[tex]1.\:\:\overline{BD}||\overline{AE}[/tex]
(By Midsegment theorem)
[tex]2.\:\:m\angle 1=48\degree\implies m\angle 4=48\degree [/tex]
([tex]\angle 1\: \&\:\angle 4[/tex] are alternate angles)
[tex]3.\:\:m\angle 3=25\degree\implies m\angle 2=25\degree [/tex]
([tex]\angle 2\: \&\:\angle 3[/tex] are vertical angles)
[tex]4.\:\:\overline {AE}=17\: cm\implies BD = 8.5\: cm [/tex]
(By midsegment theorem: [tex]BD=\frac{1}{2}AE[/tex]
[tex]5.\:\: BD=\frac{1}{2}AE\\\\\implies (3x+10)=\frac{1}{2}\times (12x+2)\\\\\implies 2(3x +10) = 12x+2\\\\\implies 6x +20= 12x+2\\\\\implies 6x - 12x = 2-20\\\\\implies -6x =-18\\\\\implies x =\frac{-18}{-6}\\\\\implies x = 3\\\\\implies \overline{BD}= (3\times 3 + 10)\\\\=(9+10)\\\\\implies \overline{BD}= (9 + 10)\\\\\implies \huge{\purple{\overline{BD}=19}}[/tex]
A circle is centered at (7,8). The point (11,8) is located on the lip of the circle. Write the equation for this circle.
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The center of the circle is (7,8) and the equation of the given circle is (x- 7)^2 + (y - 8)^2 = 16
How to determine the equation of the circle?The given parameters are:
Center (a,b) = (7,8)
Point (x,y) = (11,8)
Calculate the radius (r) using:
[tex]r = \sqrt{(x- a)^2 + (y - b)^2}[/tex]
So, we have:
[tex]r= \sqrt{(11- 7)^2 + (8 - 8)^2}[/tex]
Evaluate the expression
[tex]r = 4[/tex]
The circle equation is then calculated using:
[tex](x- a)^2 + (y - b)^2 =r^2[/tex]
So, we have:
[tex](x- 7)^2 + (y - 8)^2 = 4^2[/tex]
Evaluate the exponent
[tex](x- 7)^2 + (y - 8)^2 = 16[/tex]
Hence, the equation of the given circle is (x- 7)^2 + (y - 8)^2 = 16
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Drag each pair of rates to the correct location on the table.
Identify the pairs of rates as equivalent or not equivalent
hand
18/3 and 9/1
20/5 and 3/1
36/6 and 6/1
32/4 and 8/1
35/7 and 5/1
100/10 and 5/1
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1/8 is in it 3/2 if that is it
For what value of x does 3 superscript 2 x baseline = 9 superscript 3 x minus 4?
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Equations are expressions separated by equal sign. The value of x that make the expression equal is 2
Equation and expressionsGiven the equation expressed as:
3^2x = 9^3x - 4
This can be further simplified as:
3^2x = 3^2(3x-4)
2x = 2(3x - 4)
x = 3x - 4
x - 3x = -4
-2x = -4
x = 2
Hence the value of x that make the expression equal is 2
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Answer: its 2
Step-by-step explanation: just took test on chrome 2022, and got 100%
Mr.Santino needs A total of 406 Forks restaurant. He currently has 302 forks. If each cell has 12 forks which is the minimum number of sets of forks you should buy?
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Abby used the law of cosines for trianglekmn to solve for k. k2 = 312 532 – 2(31)(53)cos(37°) triangle k n m is shown. the length of k n is 53, the length of n m is k, and the length of k m is n. law of cosines: a2 = b2 c2 – 2bccos(a) what additional information did abby know that is not shown in the diagram? manglek = 37° and n = 31 manglek = 37° and k = 31 manglen = 37° and n = 31 manglen = 37° and k = 31
Answers
Answer:
(A) mK = 37° and n = 31.
Step-by-step explanation:
The following are A of ed.
Which statement about the function is true? the domain of the function is all real numbers less than or equal to −2. the domain of the function is all real numbers less than or equal to 9. the range of the function is all real numbers less than or equal to −2. the range of the function is all real numbers less than or equal to 9.
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The statement which is true about the function is the range of the function is all real numbers less than or equal to 9.
What is domain and range of function?
The Domain of a function is the set of all the possible input values which are valid for that function.
Range of a function is the set of all the possible output values which are valid for that function.
The function shown in the graph can be given as,
[tex]f(x)=-x^2-4x+5[/tex]
The one coordinate point of this equation is -2, 9, which is shown in the graph. At the value of x as -2, the value of f(x) is 9,
[tex]f(-2)=-(-2)^2-4(-2)+5\\f(-2)=-4+8+5\\f(-2)=9[/tex]
Here, the input value is -2 and the output value is 9. The domain for this function is all real number, but the range of this function is (-∞,9).
Hence, the statement which is true about the function is the range of the function is all real numbers less than or equal to 9.
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Answer:
its literally D bro on edge
Step-by-step explanation:
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
help! (answers needed fast and will give brainliest)
Answers
Answer:
13/20
Step-by-step explanation:
Note that:
Difference is the same meaning as subtract.
Given:
1 ¼ - ⅗
We first have to change 1 ¼ into a improper fraction:
1 ¼ = 5/4
5/4 - ⅗
Since the denominator are different we have to find common denominator.
25/20 - 12/20
Subtracting: 25 - 12 = 13
13/20
Hence, the different of these fractions is 13/20
Kavinsky
Is 10/12 greater less or equal to 3/8 also it's the same question for 1/7 4/11 and 2/6 5/8
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Answer:
10/12 is greater and for the second one, 4/11 is greater and 5/8 is greater
help pls!!!! ASAPPPPPP
Answers
Answer:eht sistep 2 and step 4 is the correct answer
Step-by-step explanation:
Sean asked 10 of his classmates the amount of their weekly allowance. He recorded the information in this table. $15 $15 $22 $14 $12$24 $16 $25 $15 $15 Match the measures with their values. 13 12 22 15 7 third quartile interquartile range first quartile range
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The interquartile range = Third quartile - First quartile = 22 - 15 = 7
The range = 25 - 12 = 13
What is the Interquartile Range (IQR) and Range ofa Data?Range = largest data value - the least data value
Interquartile range = Q3 - Q1
Given the following weekly allowance of Sean's classmates as, 15, 15, 22, 14, 12, 24, 16, 25, 15, 15:
Third quartile (Q3) = 22
First quartile (Q1) = 15
Interquartile range = 22 - 15 = 7
Range = 25 - 12 = 13
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The area of a parallelogram is given by the formula A=bh. The area of the parallelogram is 85 sq. Units. Find it’s base and height.
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Answer:
the height is 5 and the base is 17.
Step-by-step explanation:
X + 1 is the height and 4x + 1 is the base, so we can substitute this into an equation:
( x + 1 ) (4x + 1) = 85
{apply the distributive law}
4x² + x + 4x + 1 =
4x² + 5x + 1 = 85
Take 85 to the other side by -85 each side:
4x² + 5x + 1 - 85 = 85 - 85
4x² + 5x - 84 = 0
{Now we have a quadratic equation}
The roots are either -5.25 or 4. X must be 4 since it must be positive as it is a side length.
Substitute x into the base and height to get the answers.
X + 1 = 4 + 1 = 5
4x + 1 = 16 + 1 = 17
Therefore the height is 5 and the base is 17.
Find the missing length of the triangle.
a= in.
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Answer:
9 in.
Step-by-step explanation:
a^2 + 5.6^2 = 10.6^2
a^2 + 31.36 = 112.36
Subtract 31.36 from both sides
a^2 = 81
Squart Root both sides
a = 9 inches
Answer:
a = 11.9883 in
Step-by-step explanation:
Sides:
a = 5.6 in
b = 11.9883 in
c = 10.6 in
Angles:
A = 27.8476 °
B = 90 °
C = 62.1524 °
Other:
P = 28.1883 in
s = 14.0942 in
K = 29.68 in2
r = 2.10584 in
R = 5.99416 in
SAS is Side, Angle, Side
Given the size of 2 sides (c and a) and the size of the angle B that is in between those 2 sides, you can calculate the sizes of the remaining 1 side and 2 angles. Use The Law of Cosines to solve the remaining side.
Law of Cosines
If a, b and c are the lengths of the legs of a triangle opposite to the angles A, B and C respectively; then the law of cosines states:
a^2 = c^2 + b^2 - 2bc cos A, solving for cos A, cos A = ( b^2 + c^2 - a^2 ) / 2bc
b^2 = a^2 + c^2 - 2ca cos B, solving for cos B, cos B = ( c^2 + a^2 - b^2 ) / 2ca
c^2 = b^2 + a^2 - 2ab cos C, solving for cos C, cos C = ( a^2 + b^2 - c^2 ) / 2ab
Solving, for example, for an angle, A = cos^-1 [ ( b^2 + c^2 - a^2 ) / 2bc ]
FIND THE SLOPE OF A LINE THAT PASSES THROUGH THE POINT (-3-3) AND (-4-4)
Answers
Answer:
m=1
Step-by-step explanation:
y2-y1/x2-x1
-4+3/-4+3
-1/-1
1