Final Answer:
The magnitude of the resultant force when two 10 pound forces act on the same object 135° apart is approximately 18.47 pounds.
Explanation:
To find the magnitude of the resultant force when two forces are acting at an angle to each other, we can use the law of cosines. In this scenario, we have two forces each of 10 pounds acting on an object with an angle of 135° between them. Let's denote the forces as F1 and F2, both of which have magnitudes of 10 pounds. The angle between them is θ = 135°.
The formula for the resultant force R when two forces act at an angle θ is:
[tex]\[ R = \sqrt{F1^2 + F2^2 + 2 \cdot F1 \cdot F2 \cdot \cos(θ)} \][/tex]
In our case:
[tex]\[ F1 = F2 = 10 \, \text{pounds} \][/tex]
[tex]\[ θ = 135° \][/tex]
Plugging these values into the formula, we get:
[tex]\[ R = \sqrt{10^2 + 10^2 + 2 \cdot 10 \cdot 10 \cdot \cos(135°)} \][/tex]
[tex]\[ R = \sqrt{100 + 100 + 200 \cdot \cos(135°)} \][/tex]
The cosine of 135° is -√2/2 (since 135° is in the second quadrant where the cosine is negative):
[tex]\[ R = \sqrt{200 - 200 \cdot \frac{-\sqrt{2}}{2}} \][/tex]
[tex]\[ R = \sqrt{200 + 100\sqrt{2}} \][/tex]
[tex]\[ R = \sqrt{200 + 100 \cdot 1.414} \] (Since √2 is approximately 1.414)[/tex]
[tex]\[ R = \sqrt{200 + 141.4} \][/tex]
[tex]\[ R = \sqrt{341.4} \][/tex]
[tex]\[ R \approx 18.47 \text{ pounds} \][/tex]
Therefore, the magnitude of the resultant force when two 10 pound forces act on the same object 135° apart is approximately 18.47 pounds.
The list shows the number of contacts six people each have stored in the their cell phone: 68, 72, 77, 64, 69, 76. What is the mean absolute deviation for this set of data? will mark brainliest if correct
a- 71
b- 24
c- 4
d- 13
Final answer:
This answer explains how to calculate the Mean Absolute Deviation (MAD) for a given data set and determines the MAD for the provided set of numbers.
Explanation:
Mean Absolute Deviation (MAD) measures the average difference between each data point and the mean of the data set.
To calculate MAD:
Find the mean of the data set: (68 + 72 + 77 + 64 + 69 + 76) / 6 = 72.67
Find the absolute difference for each data point: |68 - 72.67|, |72 - 72.67|, |77 - 72.67|, |64 - 72.67|, |69 - 72.67|, |76 - 72.67|
Add up all the absolute differences and divide by the total number of data points: (4.67 + 0.67 + 4.33 + 8.67 + 3.67 + 3.33) / 6 = 4.67
The Mean Absolute Deviation for the given data set is 4.67. Therefore, option c- 4 is the correct answer.
Jennifer has three times as many books as her friend Jeremy. Together they have 60 novels. How many books does Jennifer have? answer ASAP
Answer:
Jennifer has 45 books and Jeremy has 15.
Step-by-step explanation:
15x3=45
45+15=60
The 53 students go to a nearby Italian restaurant for lunch. Each table holds 5 people. How many tables will the group need
Answer:
They will need 11 tables
Step-by-step explanation:
The first 10 will seat 5, the 11th will seat the final 3.
Answer:
The group will need 11 tables.
Step-by-step explanation:
Think: How many times does 5 go into 53?
We know that 5 goes into 50, 10 times. The extra 3 students must sit at a seperate table. That means they need 10 tables plus another. Therefore, the group will need 11 tables.
What is the area of the following circle?
Either enter an exact answer in terms of it or use 3.14 for IT and enter your answer as a decimal.
r = 7
Answer:
A =153.86
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
We know pi = 3.14 and the radius is 7
A = 3.14 * 7^2
A =153.86
Ned scored 84 points in the first 6 games of the basketball season . How many points per game has Ned scored ?
Answer:
he scored 14 points per game :)
Step-by-step explanation:
Write the next two numbers in the sequence: 1, 2, 4, 8, 16...
Answer:
32
Step-by-step explanation:
Answer:
Step-by-step explanation:
hello :
32 , 64 ( geometric-sequence) when the common ratio is : 2
Write
44
51
in lowest terms
Answer:44=11/25 and 51=then its 51/100
Step-by-step explanation:if its frcations.hope it helps.
Answer:
44/51
Step-by-step explanation:
Laney builds a tower with wooden cubes. The bottom cube's edges are 8 centimeters long. The middle cube's edges are 2 centimeters shorter than the bottom cube. The top cube's edges are 2 centimeters shorter than the middle cube. What is the total volume of the cubes in the tower?
Answer: The total volume of the the cubes in the tower is 792 cubic centimetres (792 cm³)
Step-by-step explanation: We shall call the volume of the cube at the bottom VB, the volume of the cube at the middle VM, and the volume of the cube at the top VT. The tower is made up of cubes at different levels and at the bottom the cube measures 8 centimetres. The cube at the middle measures 2 cm less than the bottom cube, hence middle cube equals 8 minus 2 which equals 6 cm. The top cube measures 2 cm less than the middle cube, hence the top cube equals 6 minus 2 which equals 4 cm. The volume of each cube is given as;
Volume = L³
The length of a cube measures the same on all sides, that is, length, width and height. The length on all sides therefore of the bottom cube is 8 cm. The volume equals;
VB = 8³
VB = 512 cm³
The length on all sides of the middle cube is 6 cm (measures 2 cm shorter than the bottom cube). The volume of the middle cube equals;
VM = L³
VM = 6³
VM = 216 cm³
The length on all sides of the top cube is 4 cm (measures 2 cm shorter than the middle cube). The volume of the top cube equals;
VT = L³
VT = 4³
VT = 64
From the calculations shown, the total volume of the cubes in the tower is given as;
Total volume = VB + VM + VT
Total volume = 512 + 216 + 64
Total volume = 792 cm³
Total volume is 792 cubic centimetres.
Answer: The total volume of the cubes is 792 cm^3
Step-by-step explanation:
We have 3 cubes here.
And remember that the volume of a cube is equal to the length of one of the edges at the power of 3.
So for the bottom cube, we have that the edges are 8cm long, so the volume of this cube is:
V1 = 8cm^3 = 512cm^3
The edges of the next cube are 2cm shorter, so the edges are 6cm long.
Then the volume is:
V2 = 6cm^2 = 216cm^3
The top cube's edges are 2 cm shorter than the previous one, so the length of these edges is 4cm, then the volume is:
V3 = 4cm^3 = 64cm^3
Now, the total volume is equal to:
V = V1 + V2 + V3 = 512cm^3 + 216cm^3 + 64cm^3 = 792 cm^3
which set is closed under subtraction?
Answer:
The rational numbers are "closed" under addition, subtraction, and multiplication. Under division, we run into the problem of division by 0, which makes the statement that "the rationals are closed under division" false.
Step-by-step explanation:
The owner of the Rancho Grande has 3,060 yd of fencing with which to enclose a rectangular piece of grazing land situated along the straight portion of a river. If fencing is not required along the river, what are the dimensions (in yd) of the largest area he can enclose?
Answer:
1170450 yd^2
Step-by-step explanation:
The first thing is to calculate the necessary perimeter, which would be like this:
2 * a + b = 3060
if we solve for b, we are left with:
b = 3060-2 * a
Now for the area it would be:
A = a * b = a * (3060-2 * a )
A = 3060 * a -2 * a ^ 2
To maximize the area, we calculate the derivative with respect to "a":
dA / da = d [3060 * a -2 * a ^ 2
]/gives
dA / day = 3060 - 4 * a
If we equal 0:
0 = 3060 - 4 * a
4 * a = 3060
a = 3060/4
a = 765 and d
Therefore b:
b = 3060 - 2 * a = 3060 - 1530 = 1530
A = a * b
A = 765 * 1530
A = 1170450 and d ^ 2
Final answer:
To find the largest area the owner of the Rancho Grande can enclose, we set up an equation using the perimeter of the rectangular land and the available fencing. By solving the equation and finding the maximum point of a quadratic equation, we determine that the dimensions of the largest area are L = 765 yd and W = 1,530 yd.
Explanation:
To find the dimensions of the largest area the owner of the Rancho Grande can enclose, we need to consider that the rectangular grazing land is situated along the straight portion of a river. Since fencing is not required along the river, the owner can use the available fencing to enclose the other three sides of the rectangular piece of land.
Let's assume the length of the rectangular piece of land is L and the width is W.
Since there are three sides that require fencing, the perimeter of the rectangular piece of land is given by:
P = L + W + L = 2L + W
According to the information provided, the owner has 3,060 yd of fencing available. Therefore, we can write the equation:
2L + W = 3,060
To maximize the area, we need to solve this equation for one variable and substitute it back into the area formula, A = L * W. Let's solve for L:
2L = 3,060 - W
L = (3,060 - W)/2
Substituting L in the area formula:
A = ((3,060 - W)/2) * W
Finally, we can maximize the area by finding the maximum point of the quadratic equation:
A = -0.5W^2 + 1,530W
The maximum point of a quadratic equation in the form A = ax^2 + bx + c occurs at x = -b/2a.
Comparing the quadratic equation to A = -0.5W^2 + 1,530W, we have:
a = -0.5
b = 1,530
Substituting these values into x = -b/2a:
W = -1,530 / (2 * -0.5)
Calculating W:
W = 1,530 / 1
W = 1,530
Now, substituting W back into the equation for L:
L = (3,060 - 1,530) / 2
L = 1,530 / 2
L = 765
Therefore, the dimensions of the largest area the owner of the Rancho Grande can enclose are L = 765 yd and W = 1,530 yd.
Rachel deposited $3000 in an account in the Merrick National Bank, earning 1.5% interest, compounded monthly. She made no deposits or withdrawals. Which equation can be used to find A, her account balance after t years?
Answer:
The expression that should be used to find her ballance over the years is "A = 3000*(1.125)^(12*t)".
Step-by-step explanation:
We can use the compounded interest formula to calculate her balance over t years. The formula is shown below:
A = C*(1 + r/n)^(n*t)
Where A is the final value, C is the initial value, r is the interest rate, n is the rate at which the account is compounded over a year and t is the total elapsed time in years. Applying the data from the problem we have:
A = 3000*(1 + 1.5/12)^(12*t)
A = 3000*(1 + 0.125)^(12*t)
A = 3000*(1.125)^(12*t)
m∠QPS=40
m∠RPS=8x+7
m∠QPR=9x+16
find m∠QPR
Answer:
25
Step-by-step explanation:
from the information given, we know that rps + qpr = qps.
so, (8x+7)+(9x+16) = 40.
simplify to get 17x + 23 = 40.
17x = 17.
x = 1.
plug in: 9+16 = 25.
HELP PLZ I DONT GET THIS AGT ALL I SUCK AT MATH :( I REALLY NEED HELP CAN SOMEONE HELP PLZ
Answer:
£94
Step-by-step explanation:
Basically, we want to find the surface area of this cylinder.
The surface area of a cylinder is denoted by: A = 2πr² + 2πrh, where r is the radius and h is the height. However, note that the farmer only wants to paint the curved surface of the cylinder, so we don't want to include the 2πr² part that accounts for the two circular bases. Instead, we actually just want to find the value of 2πrh.
Here, we see that the diameter is 8 metres, so since the radius is half the diameter, we know that r = 8/2 = 4 metres.
We also see that the height is 6 metres, so h = 6.
Plug these numbers in:
2πrh
2π * 4 * 6 = 48π ≈ 150.8 m²
We see that each can of paint will cover 20 m², so divide 150.8 by 20 to find the number of cans we need:
150.8 ÷ 20 = 7.5 ≈ 8 cans
Each can costs £11.75, so multiply 8 by 11.75 to get the total cost:
11.75 * 8 = £94
The answer is £94.
Answer:
94 euros is the answer, plez mark as brainliest ty big brain man
Step-by-step explanation:
Bryan has $60 in a savings account that earns 5% interest per year. The interest is not
compounded. How much will he have in 1 year?
Answer:
$63
Step-by-step explanation:
Take 60 (the money amount in his savings account) and multiply by .05 percent which is 5 percent. This is 3. So 60 + 3 = $63.
Popular culture may include changing trends in all of the following categories except __________. A. clothing styles B. history C. music D. art
Answer:
B. History
Step-by-step explanation:
Because cultures have certain clothing styles on cations, they listen to one or more types of music in certain lands, and they have art that is so pretty.
Popular culture may include changing trends in all of the following categories except history. Then the correct option is B.
What is history?History is the study of an event that is done in the past.
Examples - The British empire, Hitler's torture, world wars, political interference, etc.
Popular culture may include changing trends in all of the following categories except history.
Thus, the correct option is B.
More about the history link is given below.
https://brainly.com/question/3583505
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Consider the following figure and find the value of v
These are the vertical anvles, so v=50°
Anyone know how to go this ?
Answer:
the first one
P= 34
A= 66
----------------------------
the second one
P= 40
A= 120
----------------------------
the third one
P= 40
A= 81
the fourth one
if that's a 4
P= 12
if that's a 9
P=27
A=?
Según la reacción de abajo, ?Cuantos gramos ácido sulfhídrico se desprenden, cuando reaccionan completamente 5 moles de sulfuro niquélico? Los pesos atómicos son: Ni: 58.7 uma, S: 32 uma, O: 16 uma, H: 1 uma
Ni2S3 + 6 H2O ---> 2 Ni(OH)3 + 3 H2S
Answer:
510g H2S
Step-by-step explanation:
En esta pregunta, se nos pide calcular la masa de H2S emitida cuando 5 moles de sulfuro de níquel reaccionan completamente con el agua.
De la ecuación equilibrada, podemos ver que 1 mol de sulfuro de níquel produjo 3 moles de sulfuro de hidrógeno Por lo tanto, 5 moles de sulfuro de níquel producirán = 5 * 3 moles = 15 moles de sulfuro de hidrógeno
Matemáticamente, la masa se puede calcular multiplicando el número de moles por masa molar La masa molar de H2S es 2 (1) + 32 = 34 g / mol La masa en gramos así producida = 15 mol * 34g / mol = 510g
Y varies directly with x , and y is 84 when x is 16 .which equation represents this situation?
A) y=100x
B) y=5.25x
C) y= 1344x
D) y= 4/21x
Answer:
[tex] \frac{y}{x} = \frac{84}{16} \\ = > \frac{y}{x} = \frac{21}{4} [/tex]
[tex]y = \frac{21}{4} x[/tex]
I think option D will be 21x/4
1. Kenneth bought 315 packages of cookies. Each package had 64 cookies. How many cookies
did Kenneth buy?
Answer:
20160
Step-by-step explanation:
315*64 = 20160
To find the total number of cookies Kenneth bought, you multiply the number of packages (315) by the number of cookies in each package (64). This results to 20160 cookies.
Explanation:This question involves a simple multiplication operation. When Kenneth buys 315 packages of cookies and each package contains 64 cookies, to find the total number of cookies Kenneth bought, you need to multiply the number of packages by the number of cookies in each package. So, we have 315 (packages) x 64 (cookies per package).
The equation is: 315 x 64 = 20160.
Therefore, Kenneth bought a total of 20160 cookies.
Learn more about Multiplication here:https://brainly.com/question/35502092
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What is the equation of the linear function represented by the table?
ху
-5 14
-2 11
18
4 5
y=-x+9
y=-X+ 13
y = x+ 13
y=X+9
Which of the following is the coordinate for the image of point M(3, –7) after a 90° clockwise rotation? a.)M’(–7, –3) b.)M’(7, –3) c.)M’(7, 3) d.)M’(–7, 3)
M,(-7, -3)
Step-by-step explanation:
Answer:
M,(-7, -3) i took the quiz liker 5 seconds ago
Benjamin started her walk from the front door of her ground floor apartment. She walked 6 meters to the corner of the building and then turned the corner and walked 10 meters to her friend's apartment.
Answer:
4 meters.
Step-by-step explanation:
Benjamin has walked two legs of a right triangle, so you can connect her two movements with a line if you were sketching the situation.. The displacement is the objects overall change in position in relation to its origin, so in your case, Benjamin's apartment. While the total distance adds up regardless of her position.
So, the total distance Benjamin walked is 10m + 6m = 16m
Her displacement can be found by your best friends, the Pythagorean Theorem: 10m ^2 + 6m ^2 = delta x^2 (or displacement squared).. giving you a displacement of 11.66, or 12 m.
The difference between the distance she walked and her displacement is 4 meters.
I hope this helps. If you have any more questions, please feel free to post them and someone will be able to help you, whether it's myself or others. Please leave a like, rating, and if possible, Brainliest. Have a great day!
Answer the following questions about the problem above. Write in complete sentences to get full credit.
1. What is the slope for section "b" of Mrs. Washington's commute.
2. What is the slope for section "c" of Mrs Washington's commute?
3. Explain the difference in "b" and "c" in context of Mrs. Washing driving home.
4. How far does Mrs. Washington live from her work?
Answer:
1. -1
2. -1/4
3. As the line nears closer to y = 0, Mrs. Washington is getting closer to her house. As such, the line represents miles driven per minute, representing speed. As the slope of the line becomes steeper, as it does during section B of the commute, Mrs. Washington is driving one mile per minute, or 60 miles per hour. As she drives through section C, she only drove 1 mile after 4 minutes, or 15 miles per hour.
4. She lives 20 miles from her office.
Step-by-step explanation:
1. You can find the slope for section B of the commute by taking two points in section B and using them to find the slope.
I will take (10, 13) and (14, 9) as my points.
You can use [tex]\frac{y2-y1}{x2-x1}[/tex] to find the slope:
[tex]\frac{13-9}{10-14} \\\\\frac{4}{-4}[/tex]
The slope for section b is -1.
2. You can find the slope for section C using the same method.
I will use the points (16, 7) and (20, 6):
[tex]\frac{7-6}{16-20} \\\\\frac{1}{-4}[/tex]
The slope for section c is -1/4.
3. As the line nears closer to y = 0, Mrs. Washington is getting closer to her house. As such, the line represents miles driven per minute, representing speed. As the slope of the line becomes steeper, as it does during section B of the commute, Mrs. Washington is driving one mile per minute, or 60 miles per hour. As she drives through section C, she only drove 1 mile after 4 minutes, or 15 miles per hour.
4. She lives 20 miles from her office. This is stated in the question itself.
Answer:
1. Speed = 1 mph
2. ¼ mph
3. She's driving at 4 times faster speed in b than c
4. 20 miles
Step-by-step explanation:
1. Slope of a distance time graph is the speed
(15-7)/(16-8)
8/8
1 mph
2. Speed = (7-6)/(20-16)
1/4 mph
3. Speed in b is greater than c
1 = 4(¼)
4. Distance from 20 to 0, is 20 miles
Help with this problem please. 3x(x-1)
3x (x - 1) = 3x² - 3x
Answer:
3x² - 3x
Step-by-step explanation:
Assuming you require to simplify the expression
Given
3x(x - 1) ← multiply each term in the parenthesis by 3x
= (3x × x) + (3x × - 1)
= 3x² + (- 3x)
= 3x² - 3x
Have trouble with math plz help
Answer:
B. 51
Step-by-step explanation:
Highest number=54
Lowest number=3
Range=Highest-lowest
54-3= 51
Please mark as brainlist and vote my answer.
Answer:
B. 51
Step-by-step explanation:
You have to order the numbers by least to greatest then the biggest number is subtracted by the smallest number
54-3=51
Hope this helps! :)
Examine the diagram. It is not drawn to scale.
A triangle has angles A, C, 57 degrees. The exterior angle to angle A is B and the exterior angle to angle C is 118 degrees.
Use the measurements provided in the diagram to determine the measure of AngleB.
mAngleB =
°
E DGENUITY
Answer: 119
Step-by-step explanation: got it right
In the given figure, measure of angle A is 61°, measure of angle B is 119° and measure of angle C is 62°.
From the given triangle triangle, exterior angle to the angle C is 118°.
We know that, sum of two adjacent angles is 180°.
Here, ∠C+118°=180°
∠C=180°-118°
∠C=62°
By using exterior angle theorem of triangle, we get
∠A+57°=118°
∠A=118°-57°
∠A=61°
So, ∠A+∠B=180° (Adjacent angles)
61°+∠B=180°
∠B=180°-61°
∠B=119°
Therefore, in the given figure, measure of angle A is 61°, measure of angle B is 119° and measure of angle C is 62°.
Learn more about the exterior angle theorem here:
brainly.com/question/2995226.
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What is the size of the angle, below?
To find the size of an angle, one can use the small-angle approximation, which for small angles allows one to estimate the angle based on linear size and distance when measured in radians. The thumb method suggests a thumb at arm's length subtends an angle of 1 degree.
Explanation:To address the question about the size of a given angle, we must consider several mathematical concepts related to angles and their measurement. A key method of estimating angles involves using the small-angle approximation, which relates the linear size of an object to its angular size when viewed from a certain distance.
This approximation states that for small angles, the tangent of the angle is approximately equal to the angle itself when measured in radians. If we know the approximate width of an object, such as a thumb (1 cm) and use a comfortable viewing distance, Lo (\u2248 25 cm), we can estimate the angular size using this relationship.
The size of an angle can be described using different units, primarily degrees, arcminutes, and arcseconds, or radians. As part of learning about angles, students are taught to convert between these units. Given the question's context, if a thumb is estimated to subtend an angle of 1 degree at arm's length, we would have a straightforward method to approximate the angle's size through observation.
Which number is a common factor of 116 and 40
Answer:
4
Step-by-step explanation:
[tex]116 = 2 \times 2 \times 29 \\ 40 = 2 \times 2 \times 2 \times 5 \\ common \: factors = 2 \: \: 2 \\ common \: factors \: of \: 116 \: and \: 40 \\ = 2 \times 2 = 4[/tex]
The numbers 116 and 40 share common factors of 1, 2, and 4, with 4 being their greatest common factor.
The common factor of 116 and 40 can be found by identifying the numbers that divide both without leaving a remainder. To do so, we factorize both numbers:
116 = 2 x 2 x 29 = 2² x 2940 = 2 x 2 x 2 x 5 = 2³ x 5Next, we find the common factors by looking at the prime factors they share. Both numbers have the prime number 2 as a factor. The highest power of 2 that divides both numbers is 2², which is 4. Therefore, the greatest common factor (GCF) is 4. However, since we are looking for a common factor, not necessarily the greatest, 2 and 1 are also common factors of 116 and 40.
A photograph is reduced to 75% of its original size. The photo was originally 12 inches by 16 inches. What are the new dimensions after it has been reduced 75%?
Answer:
9 inches by 12 inches
Step-by-step explanation:
(12)(0.75)=9
(16)(0.75)=12