Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters and measure the duration of their fall. He found a plane with an incline of 12 degrees that he could climb until he could get to an altitude of 100 m. How far should Galileo walk up the inclined plane? Round your final answer to the nearest hundredth.
Answers
We have to find the value of the hypotenuse.
For this we use the following trigonometric relationship:
senx = C.O / h
Where
x: angle
C.O: opposite leg
h: hypotenuse.
Substituting the values we have:
sen (12) = 100 / h
We cleared h:
h = 100 / sin (12)
h = 480.97 m
Answer:
Galileo should walk 480.97 m up the inclined plane
Galileo walk 480.97 meters up the inclined plane if Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters and measure the duration of their fall.
What is the trigonometric ratio?The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
We have:
Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters.
Let's suppose Galileo walked x meters up the inclined plane.
The plane with an inclined a 12°
As we can see in the right angle triangle the sin ratio:
[tex]\rm sin24\° = \frac{100}{x}[/tex]
[tex]\rm x = \frac{100}{sin24\°}[/tex]
x = 480.97 meters (Sin12° = 0.20791)
Thus, Galileo walk 480.97 meters up the inclined plane if Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters and measure the duration of their fall.
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Related Questions
Choose the correct product of (7x − 3)(7x + 3). 49x2 + 9 49x2 − 42x + 9 49x2 − 9 49x2 + 42x + 9
Answers
(7x - 3)(7x + 3) // Given
7x * (7x + 3) // First Outside
49x^2 + 21x // Distribute (remember this)
-3 * (7x + 3) // Inside Last
-21x - 9 // Distribute (remember this)
49x^2 + 21x - 21x - 9 // Add both answers (the one from Outside and the one from Inside)
49x^2 - 9 // Simplify. This is your answer
You can do this, or you can remember that this is a factor for a difference of squares, where
a^2 - b^2 = (a + b)(a - b)
Plug in “7x” for a, “3” for b
Final answer:
The product of the binomials (7x - 3)(7x + 3) is calculated using the difference of squares formula, resulting in 49x² - 9.
Explanation:
To find the correct product of the binomials (7x − 3)(7x + 3), we use the difference of squares formula, a² - b² = (a - b)(a + b). In this case, a is 7x and b is 3. Thus, the product is:
(7x − 3)(7x + 3) = (7x)² - (3)²
= 49x² - 9
Therefore, the correct product is 49x² - 9.
The formula v =sqrt 64h can be used to find the velocity, v, in feet per second, of an object that has fallen h feet. Find the velocity of an object that has fallen 75 feet. Round to the nearest tenth.,
Answers
The following sequence is an arithmetic sequence what comes next ? 7,___,17
Answers
Since this is an arithmetic sequence, you can conclude that the addition to the number is constant.
Let x = the number asked
k = constant number added to the sequence
7 + k = x
x + k = 17
Solve the system of equation:
7 + k + k = 17
7 + 2k = 17
2k = 10
k = 5
Therefore, the missing number is 12 (7 + 5).
What is the value of x? The figure shows 2 right triangles, triangle K L J with right angle J and triangle L J M with right angle M. The measure of angle L K J is 30 degrees. The measure of angle L J M is 45 degrees. The length of side K L is 8 square root 2. The length of side L M is x. Enter your answer in the box.
Answers
In triangle KLJ, the hypotenuse is 8 square roots of 2. The side opposite the 30 degree angle is half of that amount. Therefore, it is only 4 square roots of 2.
That side is also the hypotenuse in the 45 45 90 triangle. To find the leg, we simply divide by the square root of 2. We will end of with legs that are 4.
Which of the following statements is true about the given function?
Answers
x = (-b plus or minus √b² - 4ac)/2a
Therefore, the other answer would be √7 - 5i
Most flat screen TVs today are made with an aspect ratio (ratio of the length to the height) of 16:9. Xenock Electronics' top selling TV is their 28-inch model, whose viewing area has a length of 24 inches and a height of 13.5 inches. This TV costs $226.99. They have three main competitors that claim to offer a better deal per viewing area. Phil's Supercenter claims their 18-inch model, whose viewing area length is of the length of Xenock's 28-inch model, is a better deal per viewing area at $152.99. Tyler's Electronics claims their 33-inch model, whose viewing area height is 20% taller than Xenock's 28-inch model, is a better deal per viewing area at $276.99. Beltre's Superstore claims their 82-inch model, whose viewing area dimensions are 300% as large as Xenock's 28-inch model, is a better deal per viewing area at $2,079.99. List the TV's in order of best deal per viewing area. Assume all TV's have the same aspect ratio.
Answers
1. Phil's Supercenter: 24 inches in length x 13.5 inches in height = 324 inches in viewing area for $152.99 or $0.47/inch
2. Tyler's Electronics: 28.8 inches in length x 16.2 inches in height = 466.56 inches in viewing area for $276.99 or $0.59/inch
3. Xenock Electronics: 24 inches in length x 13.5 inches in height = 324 inches in viewing area for $226.99 or $0.70/inch
4. Beltre's Superstore: 72 inches in length x 40.5 inches in height = 2,916 inches in viewing area for $2,079.99 or $0.71/inch
Which of the following is true for the angular momentum of a rotating bicycle wheel?
(Points : 1)
It is a vector that points in the direction the bike would travel.
It is a vector that points along the axis of rotation perpendicular to the wheel.
It is a vector pointing radially outward from the center to the edge of the wheel.
It is a scalar.,
Answers
The diameter of a sphere is 21.6 cm. What is the sphere's volume? Round to the nearest tenth, if necessary.
Answers
[tex]V = \frac{4}{3} (\pi) (r ^ 3) [/tex]
Where,
r: sphere radio
Substituting values we have:
[tex] V = \frac{4}{3}(3.14)(( \frac{21.6}{2} ) ^ 3) [/tex]
[tex]V = 5273.99424 [/tex] Rounding the result to the nearest tenth:
[tex]V = 5274.0 cm ^ 3 [/tex] Answer:
the sphere's volume is:
[tex]V = 5274.0 cm ^ 3 [/tex]
simplify 8v + W + 7 - 8v + 2w
Answers
= 3w + 7
8v +-8v is just 0. That is why it is not included in the equation.
When a number is divided by -3, the result is 12 more than the number what is the number?
Answers
Final answer:
To find the number that, when divided by -3, the result is 12 more than the number, we set up an equation and solve it to get the answer, which is -9.
Explanation:
When a number is divided by -3, and the result is 12 more than the number itself, we can set up the following equation to find the number: number / -3 = number + 12. Following division and multiplication rules for signs, and executing proper algebraic manipulations, we can solve this equation.
First, we multiply both sides by -3 to get rid of the fraction:
-3 * (number / -3) = -3 * (number + 12),
which simplifies to:
number = -3(number) - 36.
Next, we add 3(number) to both sides to get:
4(number) = -36.
Finally, we divide both sides by 4 to isolate the 'number':
number = -36 / 4
number = -9.
Therefore, the number in question is -9.
I’m not sure how to use integration to solve this question (4)
Answers
[tex]Area= \frac{16}{3}=2*( k*\sqrt{k}- \int\limits^{\sqrt{k}}_{0} {x^2} \, dx )\\\\ \dfrac{8}{3}=k ^\frac{3}{2}- \frac{1}{3}* [x^3]^{\sqrt{^k}}_0\\\\ 2* k ^\frac{3}{2}=8\\\\ k = \sqrt[3]{16}\\ [/tex]
Think it’s b not sure though
Answers
A1 = 30.25pi cm ^ 2
We now look for the area of the triangle, which by definition is:
A2 = (1/2) * (b) * (h)
Where,
b: base
h: height
Substituting the values:
A2 = (1/2) * (11) * (11)
A2 = 60.5 cm ^ 2
The area of the shaded region will be given by the subtraction of both areas:
A1-A2 = (30.25pi - 60.5) cm ^ 2
Answer:
A1-A2 = (30.25pi - 60.5) cm ^ 2
option 3
Cara muffin recipe calls for 1 1/2 cups of flour for the muffins and 1/4 cup flour for the topping.If she makes 1/2 of the original recipe.How much flour will she use.
Answers
The amount of flour she is using for the muffins is 6/8,
and the amount of flour she is using for the topping is 1/8.
Hope this helps
The amount of cups of flour needed to make 1/2 of the original recipe is 7/8 cups.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Recipe:
Amount of flour for muffins = [tex]1\frac{1}{2}[/tex] = 3/2 cups
Amount of flour for toppings = [tex]\frac{1}{4}[/tex] = 1/4 cups
The total amount of flour:
= 3/2 + 1/4
= (12 + 2) / 8
= 14 / 8
= 7/4 cups
We see that the total amount of flour needed to make one Cara muffin recipe is 7/4 cup of flour.
To make 1/2 of the original recipe.
The amount of flour needed:
1 recipe = 7/4 cups
Divide both sides by 2.
1/2 recipe = 1/2 x 7/4 cups
1/2 recipe = 7/8 cups
Thus,
The amount of cups of flour needed to make 1/2 of the original recipe is 7/8 cups.
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John bikes for 2 hours at a speed of 15 miles per hour. How many hours will it take Shannon to cover the same distance at a speed of 10 mi/h?
Answers
if john bikes for two hours 15 miles per hour two hours is thirty miles of biking
D=RT
Distance= 30 miles
Rate= 10 miles per hour
Time= t
plug numbers in
30 = 10t
divide each side by ten to get t by itself
t= 3
time = 3
3 hours to travel 30 miles biking at 10mph
Answer:
3 hours to travel 30 miles biking at 10mph
Step-by-step explanation:
hope this helps... :)
identify a counterexample for the following conditional: if you live in Springfield, then you Iive in Illinois.
Answers
2. Solve 10^6x = 93. Round to the nearest ten-thousandth. (1 point)
11.8109
1.0986
13.3801
0.3281
3. Use a graphing calculator. Solve 5.5^3x = 805 by graphing. Round to the nearest hundredth. (1 point)
2.91
3.92
1.31
0.97,
Answers
3. 1.31
2. 10^(6x) = 93
For this problem, using a calculator makes it quite simple. What you want is the power that you can raise 10 to that gives you 93. That value is the logarithm of 93 to base 10. So
10^(6x) = 93
log(10^(6x)) = log(93)
6x = 1.968482949
x = 0.328080491
x = 0.3281
3. This problem is both trickier and easier than the previous. All you need to do is plot the function on your calculator and look for the answer that's nearest which is 1.31, you could also get a more precise answer by calculating the logarithm to base 5.5 of 805. You won't find such a logarithm function on your calculator, but that isn't a major problem since you can easily convert a logarithm from any base to any other base by simply dividing by the logarithm of the desired base. So:
5.5^(3x) = 805
log(5.5^(3x)) = log(805)
log(5.5^(3x))/log(5.5) = log(805)/log(5.5)
log to base 5.5 of 5.5^(3x) = log(805)/log(5.5)
3x = 2.90579588/0.740362689
3x = 3.92482755
x = 1.30827585
x = 1.31
1. B
2. D
3. C
4. A
5. B
ESKETIT
Calculate the difference 12.0875 – 7.50 using significant digits.
A. 4.5
B. 4.587
C. 4.59
D. 4.6
Answers
C. 4.59
Step-by-step explanation:Significant digits are digits expressing precision of a measurement. Non-zero digits are always significant but zeroes can be either included or ignored. For instance, zeroes that comes before other digits aren't significant. For example 0.058 has two significant digits. In this exercise, we have two numbers:
12.0875
7.50
The number 12.0875 has five significant digits while 7.50 has three significant digits. If we add or subtract two numbers, the least number of decimal places (that isn't the same as significant digits) in any of the two numbers must be the same as the number of decimal places in the result. Hence, for 12.0875 we have four decimal places and for 7.50 we have two decimal places. Therefore, the result must have two decimal places:
12.0875 - 7.50 = 4.59
The following is the correct way to begin solving for the quotient of 39.538 divided by 5.3 using the standard method:
True
False
ILL GIVE BRAINLIEST IF U GET IT RIGHT!!
Answers
so it is False. Hope it helps
Answer:the answer is false
Which is an example of the associative property?
A) x + 5 = 5 + x
B) (x + 3) + 7 = x + (3 + 7)
C) 3 • (x + 5) = 3 • x + 15
D) If x = a, and a = 7, then x =
Answers
Associative property Property that is fulfilled if, given any three elements of a given set, it is verified that there is an operation that verifies equality
An expression that meets the definition is:
(x + 3) + 7 = x + (3 + 7)
We observe that both members of equality are identical, but written in different ways.
Answer:
B) (x + 3) + 7 = x + (3 + 7)
When the town of Bradyville first started its voluntary recycling program, 1500 of the town’s residence participated. The town predicts that the number of people participating in the recycling program will increase by 15% each year.
Which explicit rule can be used to determine the number of people participating in the program in the fifth year?
an=1500(1.15)^n−1
an=1500(0.15)^n
an=1500(1.15)n
an=1500(0.15)^n−1
Answers
This is an example of an exponential equation.
These types of equations are in the form: y = ab^x
A is the starting amount, b is the rate and x is the number of years.
All you have to do is put the pieces in place. Since it is a 15% increase, we are using 1.15 for the rate. And the starting value (a) is 1500.
Answer:
Here you go. :)
A circle of radius 1 centered at (4, 0) is rotated about the y-axus. Draw a picture of the three-dimensional shape that is produced when the circle is rotated about the y-axis. In two or more complete sentences, describe the three-dimensional shape. Upload both parts A and B as your final answer.
Answers
Imagine taking a knife and cutting a slice in a donut. The cross-section of where you cut would be a circle. This is what would happen if you rotated the circle around the y-axis. It would be like that cross-section of the donut going around the entire circle.
When a circle rotates around the y-axis, it forms a three-dimensional object known as a cylinder. The cylinder will have a radius of 1 and height equal to the diameter of the circle, which is 2.
Explanation:When a circle of radius 1 centered at (4,0) is rotated about the y-axis, the three-dimensional shape that is produced is known as a cylinder.
This cylinder would have a radius of 1, and its height would be equal to the length of the diameter of the original circle, which is 2 units (from -1 to 1 along the x-axis).In terms of the visual representation, imagine a circle on a piece of paper, now pick up the paper and rotate it about the line that is the y-axis. The paper, on which the circle is drawn, forms a cylindrical shape when rotated. The edges of the paper represent the bases of the cylinder and the surface of the paper forms the curved surface of the cylinder.Learn more about 3D Shapes after Rotation here:
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If △STU ~ △XYZ, which statements must be true? Check all that apply. ∠S ≅ ∠X ∠T ≅ ∠Y ST = XY SU = XZ
Answers
A.) ST/XY = TU/YZ
C.) <S congruent to <X
D.) <T congruent to <Y
Two triangles are similar if and only if there corresponding angles are congruent and the ratio of there corresponding sides are equal. Triangle STU is similar to triangle XYZ than [tex]\rm \angle S \cong \angle X[/tex] , [tex]\rm \angle T \cong \angle Y[/tex] and [tex]\rm \dfrac{ST}{XY}=\dfrac{TU}{YZ}=\dfrac{SU}{XZ}[/tex].
Given :
[tex]\rm \Delta STU \sim \Delta XYZ[/tex]
Two triangles are similar if and only if there corresponding angles are congruent and the ratio of there corresponding sides are equal.
Now, it is given that triangle STU is similar to triangle XYZ. This condition is only true when:
[tex]\rm \angle S \cong \angle X[/tex][tex]\rm \angle T \cong \angle Y[/tex][tex]\rm \dfrac{ST}{XY}=\dfrac{TU}{YZ}=\dfrac{SU}{XZ}[/tex]It can be conclude that if triangle STU is similar to triangle XYZ than [tex]\rm \angle S \cong \angle X[/tex] , [tex]\rm \angle T \cong \angle Y[/tex] and [tex]\rm \dfrac{ST}{XY}=\dfrac{TU}{YZ}=\dfrac{SU}{XZ}[/tex] . Therefore, the correct option is A), C) and D).
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This is a word problem where you have to create an equation and a solution to.
"Michaela and Aleah play on the same basketball team. In one game Michaela scored one fifth of the team's points and Aleah scored one tenth's of the teams points. Together they scored a total of 42 points. How many points did the team score?"
(I might find an equation for it, but I doubt it so if anyone is good with creating equations for word problems please help me!!)
-matty
Answers
.. Michaela scored s/5 . . . . . one fifth of the team's points
.. Aleah scored s/10 . . . . . . . one tenth o the team's points
These scores together are (s/5 +s/10) and that amount is 42 points.
.. s/5 +s/10 = 42
.. s(2/10 +1/10) = 42 . . . . . factor out s
.. s(3/10) = 42 . . . . . . . . . . form the sum of the numbers in parentheses
.. s = 42*10/3 = 140 . . . . . multiply by the inverse of the coefficient of s
The team scored 140 points.
______
Michaela scored 140/5 = 28 points; Aleah scored 140/10 = 14 points.
To solve this word problem, set up the equation (1/5) x + (1/10) x = 42 and solve for x. The team scored 140 points.
Explanation:To solve this word problem, we can start by letting the total number of points scored by the team be represented by 'x'. Since Michaela scored one-fifth of the team's points, her score can be represented as (1/5)x. Similarly, Aleah's score can be represented as (1/10)x. Together, their scores add up to 42 points, so we can set up the equation:
(1/5)x + (1/10)x = 42
To simplify the equation, we can find a common denominator of 10:
(2/10) x + (1/10) x = 42
Combining like terms, we get:
(3/10) x = 42
To isolate x, we can multiply both sides of the equation by 10/3:
x = 42 * (10/3)
Simplifying further, we get:
x = 140
Therefore, the team scored 140 points.
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What is the value of n? Enter you answer in the box.
Please help! Even just explaining how to do it will help a lot.
Answers
Answer:
The value of n is [tex]n=4[/tex]
Step-by-step explanation:
we know that
The intersecting chords theorem states that the products of the lengths of the line segments on each chord in a circle are equal
so
In this problem
[tex](n+2)16=(n+8)8[/tex]
solve for n
[tex]16n+32=8n+64[/tex]
[tex]16n-8n=64-32[/tex]
[tex]8n=32[/tex]
[tex]n=4[/tex]
Expand the logarithmic expression.
log5(7)a^5
A. log57 • 5log5a
B. log57 + 5log5a
C. 7log5a^5
D. log57 – 5log5a
Answers
B. log5(7)+5log5(a)
The explanation of the problem is shown below:
1. You have the following expression given in the problem above:
log5(7)(a^5)
2. To expand it, you must use the logaritms properties, as following:
log5(7)(a^5)
log5(7)+log5(a^5)
log5(7)+5log5(a)
3. Therefore, as you can see, the answer is the option B.
Answer: is b. log57 + 5log5a
Solve the system by substitution.
x - 2y = 4
2x - 6y = 8
Answers
2.) 2x - 6y = 8, Add 6y to both sides, then divide both sides by 2. --> answer is, X = 3y + 4
To solve this system with substitution, we need to set x equal to [its value] and plug it into the second equation.
x = 2y + 4
2(2y + 4) - 6y = 8
4y + 8 - 6y = 8
-2y + 8 = 8
-2y = 0
y = 0
Now, we plug y into the equation and solve for x.
x = 4
Hope this helps!
what is: 2/3 X 5/6 X 14 =
this is so that i can help a 5th grader. and i am horrible at fractions. please show work and or explain how to do it. so that i can show her how to do it as well.,
Answers
pls help me with this one question
Answers
This should m=be the answer, but i am 51.1111%sure
Which of the following values are zeros of
x(x+5)(x-3)?
SELECT ALL THAT APPLY.
A. -5
B. -3
C. 0
D. 3
E. 5
Answers
Selections A, C, D apply.
The radius of a circle is equal to half of its diameter. What is the RADIUS of this circle?