Answer: 3528.25
Step-by-step explanation:Make a sideview sketch
you should have 2 triangles, one right-angled containing the height and a scalene triangle with angles 24° , 153° (the supplement of 27°) and 3°
the side opposite the 3° angle is 1000
by let the side opposite the 24° be x, (also the hypotenuse of the right-angled triangle)
x/sin24 = 1000/sin3
x = 1000sin24/sin3
let the height of the mountain be h
sin 27 = h/x
h = x sin27 = (1000sin24/sin3)(sin27)
= 3528.25
describe an infinite list of decimals. all of which are greater than 3.514, but get closer and closer to 3.514
Which set of numbers may represent the lengths of the sides of a triangle? (A) {2,5,9} (B) {6,6,7} (C) {6,4,2} (D) {7,8,1}
Answer:
B {6, 6, 7}
Step-by-step explanation:
Which set of numbers may represent the lengths of the sides of a triangle? (A) {2,5,9} (B) {6,6,7} (C) {6,4,2} (D) {7,8,1}
For a given triangle with 3 sides, the sun of the length of any two sides must be greater Than the third side. This can be expressed mathematically as;
Let the side be ;
x, y and z
Then:
x > (y + z) or
y > (x + z) or
z > (x + y)
For A{2,5,9}
(2 + 5) < 9 (does not meet criteria)
For B {6,6,7}
(6 +6) > 7
(7 +6) > 6
Meets all criteria
For C {6,4,2}
(4 +2) is not greater Than 6 (does not meet criteria)
For D {7,8,1}
(7 +1) is not greater Than 8 ( does not meet criteria)
Find the exact area of the surface obtained by rotating the curve about the x-axis. y = sin πx 3 , 0 ≤ x ≤ 3
Answer:
[tex]\mathbf{S =6 \sqrt{1 + \dfrac{\pi^2}{9} }+ \dfrac{18}{\pi} In (\dfrac{\pi}{3}+ \sqrt{1+ \dfrac{\pi^2}{9}})}[/tex]
Step-by-step explanation:
Given that
curve [tex]y = \dfrac{\pi x}{3}, 0 \leq x \leq 3[/tex]
The objective is to find the area of the surface obtained by rotating the above curve about the x-axis.
Suppose f is positive and posses a continuous derivative,
the surface is gotten by the rotating the curve about the x-axis is:
[tex]S = \int ^b_a 2 \pi f (x) \sqrt {1 + (f' (x))^2 } \ dx[/tex]
The derivative of the function [tex]y' = \dfrac{\pi}{3} cos \dfrac{\pi x}{3}[/tex]
As such, the surface area is:
[tex]S = \int ^3_0 2 \pi sin \dfrac{\pi x}{3} \sqrt {1 +(\dfrac{\pi}{3}cos \dfrac{\pi x}{3})^2 } \ dx[/tex]
Suppose ;
[tex]u = \dfrac{\pi}{3}cos \dfrac{\pi x}{3}[/tex]
[tex]du = -( \dfrac{\pi}{3})^2 sin \dfrac{\pi x}{3} \ dx[/tex]
If x = 0 , then [tex]u = \dfrac{\pi}{3}cos \dfrac{\pi (0)}{3} = \dfrac{\pi}{3}[/tex]
If x = 3 , then [tex]u = \dfrac{\pi}{3}cos \dfrac{\pi (3)}{3}[/tex]
[tex]u = \dfrac{\pi}{3}(-1)[/tex]
[tex]u = -\dfrac{\pi}{3}[/tex]
The equation for S can now be rewritten as:
[tex]S = \int^3_0 2 \pi sin \dfrac{\pi x}{3} \sqrt{1+(\dfrac{\pi}{3} cos \dfrac{\pi x}{3})^2 }\ dx[/tex]
[tex]S = 2 \pi \int ^{-\frac{\pi}{3} }_{\frac{\pi}{3}}(-\dfrac{9 \ du }{\pi^2} ) \sqrt{1+u^2}[/tex]
[tex]S = 18 \pi * \dfrac{1}{\pi ^2 } \int ^{-\frac{\pi}{3}}_{\frac{\pi}{3}} \sqrt{1+u^2} \ du[/tex]
[tex]S = \dfrac{18} {\pi} \int ^{-\frac{\pi}{3}}_{\frac{\pi}{3}} \sqrt{1+u^2} \ du[/tex]
[tex]S = \dfrac{18} {\pi} (2 \int ^{-\frac{\pi}{3}}_{0} \sqrt{1+u^2} \ du)[/tex]
since [tex](\int ^a_{-a} fdx = 2\int^a_0 fdx , f= \sqrt{1+u^2} \ is \ even )[/tex]
Applying the formula:
[tex]\int {\sqrt{1+x^2}} \ d x= \dfrac{x}{2} \sqrt{1+x^2}+ \dfrac{1}{2} In ( x + \sqrt{1+x^2})[/tex]
[tex]S = \dfrac{36}{x}[ \dfrac{u}{2} \sqrt{1+u^2}+ \dfrac{1}{2} \ In (u+ \sqrt{1+u^2}) ] ^{\frac{\pi}{3}}_{0}[/tex]
[tex]S = \dfrac{36}{x}[ \dfrac{\dfrac{\pi}{3}}{2} \sqrt{1+\dfrac{\pi^2}{9}}+ \dfrac{1}{2} \ In (\dfrac{\pi}{3}+ \sqrt{1+\dfrac{\pi^2}{9}})-0 ][/tex]
[tex]S =6 \sqrt{1 + \dfrac{\pi^2}{9} }+ \dfrac{18}{\pi} In (\dfrac{\pi}{3}+ \sqrt{1+ \dfrac{\pi^2}{9}})[/tex]
Therefore, the exact area of the surface is [tex]\mathbf{S =6 \sqrt{1 + \dfrac{\pi^2}{9} }+ \dfrac{18}{\pi} In (\dfrac{\pi}{3}+ \sqrt{1+ \dfrac{\pi^2}{9}})}[/tex]
The area of the surface is,[tex]S = 6\sqrt{1+\dfrac{\pi ^2}{3}} + \dfrac{18}{3}\ ln (\dfrac{\pi }{3}+\sqrt{1+\dfrac{\pi ^2} {9}})[/tex].
Given that,
The exact area of the surface obtained by rotating the curve about the x-axis. y = sin πx\3 , 0 ≤ x ≤ 3.
We have to determine,
Area of the surface obtained by rotating the curve.
According to the question,
Suppose f is positive and posses a continuous derivative,
The surface is gotten by the rotating the curve about the x-axis is:
Area of the surface is given by,
[tex]S = \int\limits^b_a {2\pi f(x) .\sqrt{1+ (f'(x))} } \, dx[/tex]
The given curve is x-axis,
[tex]y = \dfrac{sin\pi x}{3}[/tex]
The derivative of the function is,
[tex]\dfrac{dy}{dx} =\dfrac{\pi }{3} \dfrac{ cos\pi x}{3}[/tex]
The surface area is,
[tex]S = \int\limits^b_a {2\pi f(x) .\sqrt{1+(\dfrac{\pi }{3} \dfrac{ cos\pi x}{3})^2} }}} \, dx[/tex]
Substitute the value of f(x),
[tex]S = \int\limits^3_0{2\pi\dfrac{sin\pi x}{3} .\sqrt{1+(\dfrac{\pi }{3} \dfrac{ cos\pi x}{3})^2} }}} \, dx[/tex]
Suppose;
[tex]u = \dfrac{\pi }{3}cos\dfrac{\pi x}{3}dx\\\\\du =( \dfrac{-\pi }{3})^2 sin\dfrac{\pi x}{3}dx\\\\if \ x = 0, \ then \ u = \dfrac{\pi }{3}cos\dfrac{\pi (0)}{3} = \dfrac{\pi }{3}\\\\if \ x = 3, \ then \ u = \dfrac{\pi }{3}cos\dfrac{\pi (3)}{3} = \dfrac{\pi }{3}(-1)= \dfrac{-\pi }{3}[/tex]
Then,
[tex]S = \int\limits^3_0{2\pi\dfrac{sin\pi x}{3} .\sqrt{1+(\dfrac{\pi }{3} \dfrac{ cos\pi x}{3})^2} }}} \, dx\\\\S = 2\pi \int\limits^{\frac{-\pi}{3}}_ \frac{\pi }{3} (\dfrac{-9du}{\pi ^2})\sqrt{1+u^2} \ du\\\\S = 18\pi \times \dfrac{1}{\pi ^2}\int\limits^{\frac{-\pi}{3}}_ \frac{\pi }{3} \sqrt{1+u^2} \ du\\\\S = \dfrac{18}{\pi}\int\limits^{\frac{-\pi}{3}}_ {0} 2\sqrt{1+u^2} \ du\\\\\\[/tex]
Since,
[tex](\int\limits^a_{-a}{f} \, dx = 2\int\limits^a_0 {f} \, dx , \ f = \sqrt{1+u^2}\ is \ even)[/tex]
By applying the formula to solve the given integration,
[tex]\int {\sqrt{1+x^2} } \, dx = \dfrac{x}{2}\sqrt{1+x^2} + \dfrac{1}{2} \ ln(x+\sqrt{1+x^2})\\\\S = \dfrac{36}{2} [ \dfrac{u}{2} \sqrt{1+u^2} + \dfrac{1}{2} \ ln(u+\sqrt{1+u^2})}]^{\frac{\pi }{3}}_0\\\\[/tex]
[tex]S = \dfrac{36}{2} [ \dfrac{\dfrac{\pi }{3}}{2} \sqrt{1+\dfrac{\pi^2 }{9}} + \dfrac{1}{2} \ ln(\dfrac{\pi }{3}+\sqrt{1+\dfrac{\pi ^2} {9}}-0)]\\\\S = 6\sqrt{1+\dfrac{\pi ^2}{3}} + \dfrac{18}{3}\ ln (\dfrac{\pi }{3}+\sqrt{1+\dfrac{\pi ^2} {9}})[/tex]
Hence, The area of the surface is,[tex]S = 6\sqrt{1+\dfrac{\pi ^2}{3}} + \dfrac{18}{3}\ ln (\dfrac{\pi }{3}+\sqrt{1+\dfrac{\pi ^2} {9}})[/tex]
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What is the leading coefficient in the polynomial 5x - 6 + 3x2 ?
(HINT: The polynomial must be written in standard form)
6
5
3
-6
According to the same report, the 28.5 million passengers in 2018 represented a 6.7% increase in cruise passengers since 2017. How many cruise passengers must there have been in 2017
Answer:
approximately 26.7 million
Step-by-step explanation:
Let x be the number of cruise passengers in 2017.
6.7% increase of x gives us 28.5 m cruise passengers in 2018.
Thus, 106.7 % of x = 28.5
[tex] \frac{106.7}{100} * x = 28.5 [/tex]
[tex] \frac{106.7x}{100} = 28.5 [/tex]
Multiply both sides by 100
[tex] \frac{106.7x}{100} * 100 = 28.5*100 [/tex]
[tex] 106.7x = 2850 [/tex]
Divide both sides by 106.7
[tex] \frac{106.7x}{106.7} = \frac{2850}{106.7} [/tex]
[tex] x = 26.7 [/tex] (approximated)
Number of passengers in 2017 must have been approximately 26.7 million
consider the ratio of 153 per 108. write this ratio in different forms. a ratio written as a reduced fraction and as a decimal rounded to the hundredths.
Answer:
153:108
1.42
1 [tex]\frac{5}{12}[/tex]
1.42 is the approximate value of the ratio [tex]\frac{153}{108}[/tex].
What is the ratio?The ratio is the number of times one value contains or is contained within the other in a quantitative relationship between two numbers.
What is the required answer?The ratio of 153:108 is given.
Other forms of the ratio are
[tex]\frac{153}{108}=\frac{17}{12}[/tex]
[tex]=1.41666...\approx 1.42[/tex] (rounded to the hundredth place.
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Simplify 8 + 10a - 3 + 5a when a=3
Answer:
50
Step-by-step explanation:
8 + 10a - 3 + 5a when a=3
8+10(3)-3+5(3)=
8+30-3+15=
38+15-3=50
Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.
Answer:
2 works
-3 is extraneous
Step-by-step explanation:
sqrt(x + 7) - 1 = x Add 1 to both sides
sqrt(x + 7) = x + 1 Square both sides
(x + 7) = (x + 1 )^2
x + 7 = x^2 + 2x + 1 Subtract x from both sides
0 = x^2 + x + 1 -7
0 = x^2 + x - 6 This will factor
(x + 3)(x - 2) = 0 Find the values for x
x + 3 = 0
x = - 3
x - 2 = 0
x = 2
Now you must check this to see if both values work
sqrt(-3 + 7) - 1 = -3
sqrt(4) - 1 = -3
2 - 1 =? - 3
1 does not equal - 3. Therefore - 3 is extraneous. Try x = 2
sqrt(2 + 7) - 1 = 2
sqrt(9) - 1 = 2
3 - 1 = 2
2 = 2
Write a verbal expression for 3n-8
Answer: Pick anyone that suits you
8 is subtracted from 3 times a numberThrice a number minus 8Step-by-step explanation:
Answer:
[tex]\large \boxed{\mathrm{Eight \ subtracted \ from \ the \ product \ of \ three \ and \ a \ number.}}[/tex]
Step-by-step explanation:
[tex]\sf 3n-8[/tex]
n is a number.
8 is subtracted from the product of 3 and a number.
The verbal expression would be :
Eight subtracted from the product of three and a number.
How do you perform this: 2x+3y=25 3x+4y=22
Answer:
x = -34 , y = 31
Step-by-step explanation suing Gaussian elimination:
Solve the following system:
{2 x + 3 y = 25
3 x + 4 y = 22
Express the system in matrix form:
(2 | 3
3 | 4)(x
y) = (25
22)
Write the system in augmented matrix form and use Gaussian elimination:
(2 | 3 | 25
3 | 4 | 22)
Swap row 1 with row 2:
(3 | 4 | 22
2 | 3 | 25)
Subtract 2/3 × (row 1) from row 2:
(3 | 4 | 22
0 | 1/3 | 31/3)
Multiply row 2 by 3:
(3 | 4 | 22
0 | 1 | 31)
Subtract 4 × (row 2) from row 1:
(3 | 0 | -102
0 | 1 | 31)
Divide row 1 by 3:
(1 | 0 | -34
0 | 1 | 31)
Collect results:
Answer: {x = -34 , y = 31
which of the following expression has more than one term? t-t, 18, dz, or 4q
Answer:
t-t
Step-by-step explanation:
What’s 11 + 9/35 make sure answer is a mixed number
Answer: 11 9/35
Step-by-step explanation: just add the whole number to the fraction.
Answer & Step-by-step explanation:
[tex]11+\frac{9}{35}[/tex]
Add the whole number to the fraction:
[tex]11 \frac{9}{35}[/tex]
:Done
Please I need help! ❤️
Answer:
8,0
8,-9
2,1
Step-by-step explanation:
It is always going to be the opposite.
Answer:
see explanation
Step-by-step explanation:
Under a reflection in the y- axis
a point (x, y ) → (- x, y ) , thus
L(- 8, 0 ) → L'(8, 0 )
M(- 8, 9 ) → M'(8, 9 )
N(- 2, - 1 ) → N'(2, - 1 )
A.$454.75
B.$502.75
C.$327.75
D.$327.25
E.None of These
Answer:
D. 327.25
Step-by-step explanation:
You start out with a gross pay of $415.00. When you have a deduction from your gross pay, it means it gets subtracted. So subtract the deductions of 48, 31.25, and 8.50 from 415 and it leaves you with 327.25.
415 48-31.25-8.50 = 327.25
Evaluate 12(20 - 17) - 3•6
A.18
B.205
C.1320
D.198
Answer:
A. 18
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out expression
12(20 - 18) - 3(6)
Step 2: Multiply parenthesis
12(20 - 18) - 18
Step 3: Parenthesis
12(3) - 18
Step 4: Multiply
36 - 18
Step 5: Subtract
18
Water is not a liquid if its temperature is above 100 °C or below 0 °C.
0
40
80
120
160
Write a compound inequality to show the levels that are within the range described
above.
Answer:
[tex]0 \leq x \leq 100[/tex]
0, 40, and 80 are the values that work for this compound inequality.
Step-by-step explanation:
To create a compound inequality, we have to examine the conditions for [tex]x[/tex] to work.
Since [tex]x[/tex] can not be below 0° C, that means that [tex]x[/tex] must be greater than or equal to 0.
Which is represented as [tex]x\geq 0[/tex], or [tex]0\leq x[/tex].
Since [tex]x[/tex] can not be above 100° C, that means [tex]x[/tex] must be less than 100.
Which is represented as [tex]x \leq 100[/tex].
We can combine both inequalities into one, where [tex]x[/tex] is shared between the two. This creates [tex]0\leq x \leq 100[/tex].
Let's test each value of [tex]x[/tex] .
0 is equal to 0 and less than 100, so it works.
40 is greater than 0 and less than 100, so it works.
80 is greater than 0 and less than 100, so it works.
120 is greater than 0 and greater than 100, so it doesn't work.
160 is greater than 0 and greater than 100, so it doesn't work.
Hope this helped!
The formula for the area of a triangle is a=1/2bh . If the base of the triangle is 6x units and has a height of x+3, write a simplified algebraic expression for the area of the triangle in terms of x
Answer:
a = 3x^2 +9x
Step-by-step explanation:
Put the given dimensions in the formula and simplify. The distributive property is useful.
a = (1/2)bh
a = (1/2)(6x)(x+3) = 3x(x +3)
a = 3x^2 +9x
The diameter of a strand of rope is 1.2 × 10^ -3 inch. The diameter of a strand of floss is 2.0 × 10^ -4 inch. How much longer is the diameter of the strand of rope than the diameter of the strand of floss? A. 2.0 × 10^ -7 inch B. 1.0 × 10^ -7 inch C. 2.0 × 10^ -3 inch D. 1.0 × 10^ -3 inch
Answer:
D
Step-by-step explanation:
I answer this already. XD
Answer:
D
Step-by-step explanation:
sorry i needed these points XD
Which 2 statements are true
Answer:
B
Good luck in Geometry my guy!
If there are 132 stamps on a total of 12 pages in a collector's book, what the unit rate of stamps per page ?
Answer: 11 stamps per page
Step-by-step explanation: 132 divided by 12
Write an algebraic expression for the phrase.
the product of d and 4
An expression is a combination of numbers, variables, and functions such as addition, subtraction, multiplication or division, etc.
The expression for the product of d and 4 is d x 4.
What is an expression?An expression is a combination of numbers, variables, and functions such as addition, subtraction, multiplication or division, etc.
Example:
3 added to 2 will be 3 + 2.
4 times 3 is 4 x 3.
4 less than 6 is 6 - 4.
We have,
The product of d and 4.
This can be written as:
= d x 4
Thus the expression for the product of d and 4 is d x 4.
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4/5 = 5/4 =
Your answer
Answer:
not equal
Step-by-step explanation:
Answer:
4/5 is not equal to 5/4.
4/5 x 4 = 16/20
5/4 x 5 = 25/20
25/20 > 16/20
Provide two examples that show that all square roots are not irrational numbers ?
Answer:
[tex]\sqrt{4}, \ \sqrt{9} \text{ are rational numbers.}[/tex]
Step-by-step explanation:
Hello,
[tex]\sqrt{n^2}=n \ for \ n\geq 0\\\\\text{For instance}\\\\\sqrt{2^2}=2=\sqrt{4}\\\\\sqrt{3^2}=3=\sqrt{9}[/tex]
Find the area of the triangle below. Be sure to include the correct unit in your answer.
When given the base of and height of a triangle, you can use this formula:
[tex]area = \frac{1}{2} bh[/tex]
Plug in the known values:
[tex]area = \frac{1}{2} (18)(6)[/tex]
Solve:
[tex]area = \frac{1}{2} \times 108[/tex]
[tex]area = 54[/tex]
Add units:
[tex]area = 54cm^{2} [/tex]
Which pair of numbers have a greatest common factor of 7? Select each correct answer. 21 and 3 7 and 14 28 and 7 7 and 1
Answer:
Hey there!
There are actually multiple answers.
7 and 14 have a GCF (greatest common factor) of 7, and so do 7 and 7.
Let me know if this helps :)
Answer:
answers are:
7 and 14
The factors of 7 is: 1, 7
The factors of 14 is: 1, 2, 7, 14
28 and 7
Factors of 28: 1, 2, 4, 7, 14, 28
Facotrs of 7: 1, 7
Step-by-step explanation:
others:
21, 3 is GCF is 3
The factors of 3 are: 1, 3
The factors of 21 are: 1, 3, 7, 21
7, 1 is GCF is 1
The factors of 1 are: 1
The factors of 7 are: 1, 7
The problem is attached.
Answer:
Cosec θ = – 25/24
Step-by-step explanation:
From the question given, we obtained the following information:
Tan θ = – 24/7
Cosec θ =?
Tan θ is negative in the forth quadrant.
Please see attached photo.
Tan θ = Opposite /Adjacent
Opposite = – 24
Adjacent = 7
Hypothenus = x
Thus, we can obtain the value of x by using the pythagoras theory as illustrated below:
x² = (–24)² + 7²
x² = 576 + 49
x² = 625
Take the square root of both side
x = √625
x = 25
Next, we shall determine Sine θ. This can be obtained as follow:
Opposite = – 24
Hypothenus = 25
Sine θ = ?
Sine θ = Opposite /Hypothenus
Sine θ = –24/25
Finally, we shall determine the Cosec θ. This can be obtained as follow:
Cosec θ = 1 /Sine θ
Sine θ = –24/25
Cosec θ = 1 ÷ –24/25
Cosec θ = 1 × – 25/24
Cosec θ = – 25/24
the temperature at 5:00 PM is 4 degrees. By midnight, the temperature had dropped 12 degrees. What was the temperature at midnight?
Answer:
-8 degrees
Step-by-step explanation:
4-12 = -8
It dropped 12 degrees in 7 hours.
Answer: -8°
Step-by-step explanation:
4 - 12
One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the third angle is 10 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.
Answer:
Step-by-step explanation:
x + x + 10 + 3x = 180
5x + 10 = 170
5x = 170
x = 36°
3(36)= 108° the largest angle
Which is a real world example of two planes intersecting?
One example is the idea of two parts of a book that open up. Each flat part is a plane and the two planes intersect along the spine of the book.
Another example would be a wall intersecting with the floor. Both are flat surfaces.
A third example would be a laptop's screen as one plane and the keyboard as the other plane. They intersect at the hinge of the laptop.
For each example, the surface has a finite amount of area and it doesn't extend forever in all four directions. Theoretically, a plane is where the flat surface extends in all four directions infinitely. Though of course, real life has limitations but the idea is still applicable in a way.
Note how for each example, the two planes intersect to form a line. Also, each plane must be flat without bending or curving in any way.
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is 29 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
Answer:
x = 45°, y = 53°, z = 82°
Step-by-step explanation:
x is the first angle, y is the second, and z is the third.
The sum of the second and third, which is denoted by y + z, is 3 times the measure of the first, which is just x. So, we have:
y + z = 3 * x
Additionally, the third angle, z, is 29 more than the second, y, so:
z = 29 + y
We also know that the sum of the three is 180, so:
x + y + z = 180
Let's substitute y + z in the last equation with 3 * x:
x + y + z = 180
x + 3x = 180
4x = 180
x = 45
Now, we know that y + z = 3 * 45 = 135. We also know that z = 29 + y, so substitute 29 + y in for z in y + z = 135:
y + z = 135
y + (29 + y) = 135
2y + 29 = 135
2y = 106
y = 53
Finally, use this value of y to solve for z:
z = 29 + y
z = 29 + 53 = 82
Thus, the angles are x = 45°, y = 53°, and z = 82°.
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