Answers
Answer:
Step-by-step explanation:
when you break a vector into its parts, those parts are called its components. For example, in the vector (4, 1), the x-axis (horizontal) component is 4, and the y-axis (vertical) component is 1. Typically, a physics problem gives you an angle and a magnitude to define a vector; you have to find the components yourself using a little trigonometry.
Suppose you know that a ball is rolling on a flat table at 15 degrees from a direction parallel to the bottom edge at a speed of 7.0 meters/second. You may want to find out how long the ball will take to roll off the edge 1.0 meter to the right.
Define your axes so the ball is at the origin initially and the x-axis is parallel to the bottom edge of the table (refer to the figure). Therefore, the problem breaks down to finding out how long the ball will take to roll 1.0 meter in the x direction. To find the time, you first need to know how fast the ball is moving in the x direction.
The problem tells you that the ball is rolling at a speed of 7.0 meters/second at 15 degrees to the horizontal (along the positive x-axis), which is a vector: 7.0 meters/second at 15 degrees gives you both a magnitude and a direction. What you have here is a velocity — the vector version of speed. The ball’s speed is the magnitude of its velocity vector, and when you include a direction to that speed, you get the velocity vector v.
To find out how fast the ball is traveling toward the table edge, you need not the ball’s total speed but the x component of the ball’s velocity. The x component is a scalar (a number, not a vector), and you write it like this: vx. The y component of the ball’s velocity vector is vy. Therefore, you can say that
v = (vx, vy)
That’s how you express breaking a vector up into its components. So what’s vx here? And for that matter, what’s vy, the y component of the velocity? The vector has a length (7.0 meters/second) and a direction
And you know that the edge of the table is 1.0 meter to the right.
As you can see in the figure, you have to use some trigonometry to resolve this vector into its components. No sweat. The trig is easy after you get down the angles you see in the figure.
The magnitude of a vector v is expressed as v, and from the figure, you can see that the following is true:
The two vector-component equations are worth knowing because you see them a lot in any beginning physics course. Make sure you know how they work, and always have them at your fingertips.
Of course, if you forget these equations, you can always retrieve them from basic trigonometry. You may remember that the sine and cosine of an angle in a right triangle are defined as the ratio of the opposite side and the adjacent side to the hypotenuse, like so:
By multiplying both sides of these equations by v, you can express the x and y components of the vector as
You can go further by relating each side of the triangle to each other side (and if you know that
you can derive all these from the previous two equations as required; no need to memorize all these):
You know that
so you can find the x component of the ball’s velocity, vx, this way:
Plugging in the numbers gives you
You now know that the ball is traveling at 6.8 meters/second to the right. And because you also know that the table’s edge is 1.0 meter away, you can divide distance by speed to get the time:
Because you know how fast the ball is going in the x direction, you now know the answer to the problem: The ball will take 0.15 seconds to fall off the edge of the table. What about the y component of the velocity? That’s easy to find, too:
Related Questions
What is the mode of the following numbers?
1
,
2
,
4
,
6
,
4
Answers
Answer:
4 because mode is always the number that occurs the most. If there were two sixes and two fours, then there would be two modes.
Answer:
4
Step-by-step explanation:
The mode of the data set (a set of distinct values, at least) is the value which appears the most often. In this set, that number is 4.
D 0,1 of x is?
A. (4,0)
B. (4,1)
C. (5,1)
*20 points!!!*
Answers
Answer:
4,0
Step-by-step explanation:
Answer:
i can confirm it is 4,0
Step-by-step explanation:
Two forces act on an object. The first force has a magnitude of 360 newtons and acts at an angle of 30° as measured from the horizontal. The second force has a magnitude of 240 newtons and acts at an angle of 135° as measured from the horizontal. Determine the vector v that represents the resultant force.
Answers
Answer:377.46 N
Step-by-step explanation:
Given
Vector 1 has a magnitude of [tex]360\ N[/tex] and makes an angle of [tex]30^{\circ}[/tex]
vector 2 has a magnitude of [tex]240\ N[/tex] and makes an angle of [tex]135^{\circ}[/tex]
Net Horizontal force
[tex]\sum F_h=360\cos 30+240\cos 135[/tex]
[tex]\sum F_h=311.769-169.70[/tex]
[tex]\sum F_h=142.069\ N\quad \ldots(i)[/tex]
Net vertical force
[tex]\sum F_v=360\sin 30+240\sin 135[/tex]
[tex]\sum F_v=180+169.705[/tex]
[tex]\sum F_v=349.705\ N\quad \ldots(ii)[/tex]
Net resultant force
[tex]F_{net}=\sqrt{F_h^2+F_v^2}[/tex]
[tex]F_{net}=\sqrt{(142.069)^2+(349.705)^2}[/tex]
[tex]F_{net}=377.46\ N[/tex]
angle which resultant make with x-axis
[tex]\tan \theta =\frac{\sum F_v}{\sum F_h}[/tex]
[tex]\tan \theta =\frac{349.705}{142.069}[/tex]
[tex]\tan \theta =2.461[/tex]
[tex]\theta =67.88^{\circ}[/tex]
Thus vector v is given by
[tex]\vec{v}=377.46[\cos 67.88+\sin 67.88][/tex]
Answer:
B) [tex]v=(180\sqrt{3} -120\sqrt{2})i+(18 0+120\sqrt{2} )j[/tex]
Step-by-step explanation:
I just did the test and this is the correct answer.
What is the least common denominator of 1/12 and 5/8
Answers
A professional soccer player buys 16 acers of land. he plans to build a house on the land but wants to use 2/8 of the land to put his own soccer field and facility on. how many acres of land will the soccer player need for his soccer field and facility?
Answers
Answer:
Step-by-step explanation:
The professional soccer player buys 16 acres of land.
He wants to use [tex]\frac{2}{8}[/tex] of the land to put his own soccer field and facility on.
All we have to do is find [tex]\frac{2}{8}[/tex] of 16 acres.
[tex]\frac{2}{8}[/tex] of 16 acres:
[tex]\frac{2}{8}[/tex] * 16 = 4 acres
He will need 4 acres out of the 16 acres for his soccer field and facility.
The local grocery store will purchase food items and mark them up 115%. If the wholesale price of an item was $3.50, what price will the customer pay for the item?
Answers
Answer:
5
Step-by-step explanation:
The customer paid $7.53 for the item
Markup is the difference between a product's selling price and cost as a percentage of the cost. It is given by:
[tex]Markup=\frac{selling\ price-cost\ price}{cost\ price} \\\\[/tex]
Markup = 115% = 1.15, cost price = $3.50, hence:
[tex]Markup=\frac{selling\ price-cost\ price}{cost\ price} \\\\1.15=\frac{selling\ price-3.5}{3.5} \\\\Selling\ price=\$7.53[/tex]
Hence the customer paid $7.53 for the item.
Find out more at: https://brainly.com/question/20548779
What is the radius of the circle with the following equation (x+1)²+ (y-3)²= 64? *
Answers
The center-radius form is: (x−h)^2+(y−k)^2=r^2
Knowing this, all we need to do is square root the 64 to get 8 as your radius.
can someone plzzzzzzz help me
A spinner and two cards are shown below.
Which table correctly identifies the sample space of spinning the spinner and then selecting a card? (5 points)
Group of answer choices
Results of the spin
Card Color Orange Yellow Red
Purple Orange, Purple Yellow, Green Red, Green
Green Green, Green Yellow, Yellow Red, Red
Results of the spin
Card Color Orange Yellow Red
Purple Orange, Green Yellow, Yellow Red, Red
Green Green, Purple Yellow, Green Red, Green
Results of the spin
Card Color Orange Yellow Red
Purple Orange, Purple Yellow, Purple Red, Purple
Green Green, Green Yellow, Yellow Red, Red
Results of the spin
Card Color Orange Yellow Red
Purple Orange, Purple Yellow, Purple Red, Purple
Green Orange, Green Yellow, Green Red, Green
Answers
Answer:
it the last one
Step-by-step explanation:
only the last option has all the possible combinations
Answer:
Sample space:
{Yellow Purple,
Yellow Green,
Orange Purple
Orange Green,
Red Purple,
Red Green}
A box is filled with 9 red crayons, 5 blue crayons, and 8 yellow crayons. A crayon is chosen at random from the box. Find the probability that it is a blue or a yellow crayon.
Answers
Answer:
13/22
Step-by-step explanation:
The total number of crayons in the box
9 red crayons, 5 blue crayons, and 8 yellow crayons = 22
The number that are blue or yellow = 5+8 = 13
P (blue or yellow) = number that are blue or yellow / total
= 13/22
Answer:
13/22
Step-by-step explanation:
Total: 9 + 5 + 8 = 22
Blue or yellow: 5 + 8 = 13
P(Blue or yellow) = 13/22
Why is it important to describe the variable in an expression?
Answers
Answer: They show numerical value. You have to make them clear.
Step-by-step explanation:
Answer:
you define it, and it lets you know how to properly write the equation. ... If you want to solve for the unknowns using mathematical equations it is necessary to define the unknown variables i.e. what they represent in the real world so that the known relationships can be expressed in equation form
Step-by-step explanation:
its basically a value that can hold and amount depending on the value you give it
This pizza has a radius of 4 inches . Which measurement is closest to the area of this pizza in inches?
Answers
Answer:
The area is 50.24
Step-by-step explanation:
Area of a circle is
A = πr²
A = 3.14 x 4²
A = 3.14 x 16
A = 50.24
If I do this with 4 and 5 - I get 29. If I do the same thing with 4 and 6 - I get 40. Thesame thing again to 8 and 9 gives me 89. What do I get if I do the same thing to 5 and 8?
Answers
Answer: 69
Step-by-step explanation:
If I do this with 4 and 5 - I get 29.
This can be explained as this:
4 + (5^2) = 4 + 25 = 29
If I do the same thing with 4 and 6 - I get 40. This can be explained as:
4 + (6^2) = 4 + 36 = 40
Thesame thing again to 8 and 9 gives me 89. This can be explained as:
8 + (9^2) = 8 + 81 = 89
What do I get if I do the same thing to 5 and 8. This will be:
5 + (8^2) = 5 + 64 = 69
Lindsay shot a model rocket over an area that consists of two grassy areas shown in green and an area without grass, shown in white. What is the probability that his rocket landed in the area WITHOUT grass?
A. 3/5
B. 4/5
C. 3/4
D.3/10
Answers
Anika buys a pair of shin guards for $8.58 and several pairs of soccer socks for $4.29 per pair. If she spends $25.74 before taxes, how many pairs of socks does Anika buy?
Answers
Answer:
4
Step-by-step explanation:
easier answer
The Thompson family borrowed $120,000
to buy a house. Over thirty years, they had
to repay 230% of what they borrowed. Find
the total cost of the house.
Answers
Answer:
27,600
Step-by-step explanation:
WHAT IS THIS ANSWER
Answers
Answer:
15
Step-by-step explanation:
I beleive you just count the dots thats what i did
Answer:
ahskdhdidjdujdjdjej
miguel drove 355 miles using 17 gallons. at this rate , how many gallons of gas would he need to drive 284 miles
Answers
Answer:
14.2
Step-by-step explanation:
Answer:
It should be somewhere around 13.6
Step-by-step explanation:
What is 1,289,845 rounded to the nearest thousand?
Answers
Answer:
1,290,000
Step-by-step explanation:
Answer:
1,290,000
Step-by-step explanation:
If we are rounding to the nearest thousand, then we are finding the number in the hundredth's and rounding it.
From 1-9 If it's less than 5, round down. If it's 5 or more, round up.
At this case, it is 8 in the hundredths and nine in the thousandths. Since 8 is 5 or greater, you round it up to 1000, but the thousandth's place has a nine, which nine plus 1 is 10.
Therefore, 1,289,845 rounded up is 1,290,000.
I hope this helped! :)
a theater has 44 seats in the first row,46 seats in the second row,48 seats in the third row,and so on. how many seats are there in row 18?
Answers
Step-by-step explanation:
Total rows = 18
This is a even number sequence so
44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78
So 78 seats are in row 18
Leon verified that the side lengths 21, 28, 35 form a Pythagorean triple using this procedure. Step 1: Find the greatest common factor of the given lengths: 7 Step 2: Divide the given lengths by the greatest common factor: 3, 4, 5 Step 3: Verify that the lengths found in step 2 form a Pythagorean triple: 3 squared + 4 squared = 9 + 16 = 25 = 5 squared Leon states that 21, 28, 35 is a Pythagorean triple because the lengths found in step 2 form a Pythagorean triple. Which explains whether or not Leon is correct?
Answers
Answer: Leon was wrong by using the greatest common factor to determine that the numbers are a Pythagorean triple.
Step-by-step explanation: The numbers that Leon used in his calculations which are, 21, 28, and 35 are actually a Pythagorean triple and this can be determined by using the Pythagoras' theorem which states that,
AC² = AB² + BC²
Where AC is the longest side, and AB and BC are the other two sides.
Substituting for the given values, we now have
35² = 28² + 21²
1225 = 784 + 441
1225 = 1225
Since both sides of the equation are equal, we can conclude that the numbers form a Pythagorean triple.
However, dividing the numbers by their greatest common factor does not prove that it is a Pythagorean triple. This process cannot be successfully applied to other Pythagorean triples, and is best described as a chance event.
For example, the numbers 21, 20 and 29 are Pythagorean triples and they have no common factor. Similarly, 6, 8 and 10 are also Pythagorean triples and their greatest common factor is 2. This too is not sufficient to prove that they form a Pythagorean triple.
The only prove that is sufficient enough is to substitute the numbers into the Pythagoras theorem as stated in the calculation above, and the result must show the left hand side of the equation to be equal to the right hand side of the equation.
Answer:
it’s C tell me if I’m right or wrong
Step-by-step explanation:
The following graph shows the low temperatures for the past six nights. Which night had a low temperature of 26°F?
1. Thursday
2.Wednesday
3.Monday
4. Tuesday
Answers
Answer:
thursday
Step-by-step explanation:
A public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes. Karen took bus number 14 during peak hours on 18 different occasions. Her mean waiting time was 7.8 minutes with a standard deviation of 2.5 minutes. At the 0.01 significance level, test the claim that the mean is less than 10 minutes.
Answers
Answer:
We conclude that the mean waiting time is less than 10 minutes.
Step-by-step explanation:
We are given that a public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes.
Karen took bus number 14 during peak hours on 18 different occasions. Her mean waiting time was 7.8 minutes with a standard deviation of 2.5 minutes.
Let [tex]\mu[/tex] = mean waiting time for bus number 14.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 10 minutes {means that the mean waiting time is more than or equal to 10 minutes}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 10 minutes {means that the mean waiting time is less than 10 minutes}
The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean waiting time = 7.8 minutes
s = sample standard deviation = 2.5 minutes
n = sample of different occasions = 18
So, test statistics = [tex]\frac{7.8-10}{\frac{2.5}{\sqrt{18} } }[/tex] ~ [tex]t_1_7[/tex]
= -3.734
The value of t test statistics is -3.734.
Now, at 0.01 significance level the t table gives critical value of -2.567 for left-tailed test.
Since our test statistic is less than the critical value of t as -3.734 < -2.567, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the mean waiting time is less than 10 minutes.
Using the t-distribution, it is found that since the test statistic is less than the critical value for the left-tailed test, it is found that there is enough evidence to support the claim that the mean is less than 10 minutes.
At the null hypothesis, it is tested if the mean is of at least 10 minutes, that is:
[tex]H_0: \mu \geq 10[/tex]
At the alternative hypothesis, it is tested if it is less than 10 minutes, that is:
[tex]H_1: \mu < 10[/tex]
We have the standard deviation for the sample, thus, the t-distribution is used. The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. s is the standard deviation of the sample. n is the sample size.For this problem, the values of the parameters are: [tex]\overline{x} = 7.8, \mu = 10, s = 2.5, n = 18[/tex]
Hence, the value of the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{7.8 - 10}{\frac{2.5}{\sqrt{18}}}[/tex]
[tex]t = -3.73[/tex]
The critical value for a left-tailed test, as we are testing if the mean is less than a value, with a 0.01 significance level and 18 - 1 = 17 df is of [tex]t^{\ast} = -2.57[/tex]
Since the test statistic is less than the critical value for the left-tailed test, it is found that there is enough evidence to support the claim that the mean is less than 10 minutes.
A similar problem is given at https://brainly.com/question/13873630
The graph of which function has a y-intercept of 3? Picture A, B, C, or D?
Answers
Answer:
A
Step-by-step explanation:
A is the only one that intersects with the y axis at the value 3.
hope this helps :)
Answer:
The answer is the first graph!
Jen rode her bike 1/5 of a mile to her friend's house. It took her 5 minutes to get there. What was Jen's speed?
Answers
Jen's speed is 0.04 miles per minute.
Explanation:To find Jen's speed, we need to divide the distance she traveled by the time it took her to get there. In this case, Jen traveled 1/5 of a mile and it took her 5 minutes. To find her speed in miles per minute, we divide the distance (1/5 mile) by the time (5 minutes):
Speed = Distance ÷ Time
Speed = 1/5 mile ÷ 5 minutes
To simplify the calculation, we can convert 1/5 mile to a decimal by dividing 1 by 5:
1/5 = 0.2
Now we can divide 0.2 by 5 to find Jen's speed:
0.2 ÷ 5 = 0.04
Therefore, Jen's speed is 0.04 miles per minute.
you have 4 4/5 cups of rice. each serving of rice takes 2/5 of a cup. how many servings can you make?
Answers
Answer:
12 cups
Step-by-step explanation:
2/5 times 12 =4 4/5
Sorry, this answer was wrong.
What steps should be taken to calculate the volume of the right triangular prism? Select three options.
A triangular prism. The triangular base has a base of 8 meters and height of 14 meters. The height of the prism is 7 meters.
A. Use the formula A = one-half b h to find the area of the base.
B. Use the formula A = b h to find the area of the base.
C. The area of the base, A, is One-half (7) (8) = 28 meters squared.
D. The area of the base, A, is One-half (8) (14) = 56 meters squared.
E. The volume of the prism, V is (56) (7) = 392 meters cubed.
Answers
Answer:
Options A, D and E.
Step-by-step explanation:
Formula to calculate the volume of the triangular prism is,
Volume of the triangular prism = (Area of the triangular base)×(height)
= B × h
Area of the right triangular base = [tex]\frac{1}{2}(\text{Base})(\text{height})[/tex]
= [tex]\frac{1}{2}(8)(14)[/tex]
= 56 m²
Volume of the prism = [tex](56)(7)[/tex]
= 392 cubic meter
Therefore, from the given options correct options are Option A, Option D and Option E.
Answer:
a,d, and e
Step-by-step explanation:
Do the following lengths form a right triangle?
45, 117, and 125
Answers
Answer:
NOTStep-by-step explanation:
[tex]\text{If}\ a\leq b<c\ \text{and}\ a^2+b^2=c^2,\ \text{then}\ a,\ b\ \text{and}\ c\ \text{form a right triangle.}\\\\\text{We have:}\\\\a=45,\ b=117,\ c=125\\\\\text{substitute}\\\\a^2+b^2=45^2+117^2=2025+13689=15714\\\\c^2=125^2=15625\\\\a^2+b^2\neq c^2\\\\\text{Therefore your answer is}\ \bold{NO}[/tex]
Gracie has 1/2 of a cantaloupe that she wants to divide. How many 1/10 's of a cantaloupe are there in 1/2 of a cantaloupe?
Answers
To find out how many 1/10's of a cantaloupe are there in 1/2 of a cantaloupe, you divide 1/2 by 1/10. The answer is 5.
Explanation:To find out how many 1/10's of a cantaloupe are there in 1/2 of a cantaloupe, we can divide 1/2 by 1/10. Dividing fractions involves multiplying the first fraction by the reciprocal of the second fraction. So, we have (1/2) * (10/1) = 10/2 = 5. Therefore, there are 5 1/10's of a cantaloupe in 1/2 of a cantaloupe.
Learn more about Dividing fractions here:https://brainly.com/question/18511795
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The product of 12 and k is 84. Solve for k
Answers
Answer:
k=7
Step-by-step explanation
This is the same as 12 x k = 84. To solve, put it into a division problem which is 84 divided by 12. 84 divided by 12 is 7.
How many 1/3 cm cubes can fit in a rectangular prism with a length of 5 1/3 cm, a width of 2/3 cm and a height of 1 1/3 cm. PLEASE REPLY QUICKLY I HAVE TO SUBMIT THIS IN 30 MINUTES
Answers
Answer:
You could fit 48 cubes with side lengths of 1/3 cm inside a rectangular prism with dimensions of 1 cm X 2 2/3 cm X 2/3 cm.
Step-by-step explanation: