Answer:
34.8 N at 2.5 degrees from the positive x-axis
Step-by-step explanation:
From the given information:
The force F makes an angle A with the positive x axis can be expressed in terms horizontal and vertical components.
[tex]F_x = F cos A\\\\ F_y = Fsin A[/tex]
Given that
[tex]F_1 = 50 \ N[/tex]
[tex]\theta_1 = 30 ^0 \ \ \ (x-axis)[/tex]
[tex]F_{1x} = F_1 \times Cos A_1[/tex]
= 50 × cos 30
= 43.3 N
[tex]F_{1y} = F_1 \times Sin \ A_1[/tex]
= 50 × sin 30
= 25 N
Similarly;
[tex]F_2 = 25 \ N[/tex]
[tex]\theta_2 = 250 ^0 \ \ \ ( x-axis)[/tex]
[tex]F_{2x} = F_2 \times cos \ A_2[/tex]
= 25 × cos 250
= - 8.55 N
[tex]F_{2y} = F_2 \times A_2[/tex]
= 25 × sin 250
= -23.5 N
The total net force;
[tex]F_{net} = F_{(net)}_x + F_{(net)}_y[/tex]
[tex]F_{net} = (F_{1x} + F_{2x} ) i + (F_{1y} + F_{2y} )j[/tex]
[tex]F_{net} = (43.3 - 8.55) i + (25-23.5 ) j[/tex]
[tex]F_{net} =34.75 i + 1.5 j[/tex]
[tex]|F_{net} | = \sqrt{F_{net}_x^2 + F_{net}_y^2}[/tex]
[tex]|F_{net} | = \sqrt{34.75^2 + 1.5^2}[/tex]
[tex]|F_{net} | = 34.8 \ N[/tex]
Finally, the direction of the angle for the net force is:
[tex]tan \theta = \dfrac{F_{net_y}}{F_{net_x}}[/tex]
[tex]\theta = tan^{-1} \Big (\dfrac{F_{net_y}}{F_{net_x}} \Big)[/tex]
[tex]\theta = tan^{-1} \Big (\dfrac{1.5}{34.75}} \Big)[/tex]
[tex]\theta = tan^{-1}( 0.043165)[/tex]
[tex]\theta \simeq 2.5^0\ with \ positive \ x-axis[/tex]
(HELP PLEASE)Patrick Mahomes completed 15 of his 25 passes for the Kansas City Chiefs. What
percent of this throws were completions?
Answer:
60%
Step-by-step explanation:
15/25 = x/100
0.60 = x/100
0.60 * 100 = x
60 = x
25 * 60% = 15
Find the dimensions of the box with volume 8000 cm3 that has minimal surface area. (Let x, y, and z be the dimensions of the box.)
Answer:
[tex]x = y = z = 20[/tex]
Step-by-step explanation:
Given
[tex]Volume = 8000cm^3[/tex]
Required
Determine the dimensions that minimizes the surface area.
Surface area of a box is;
[tex]S = 2(xy + xz + yz)[/tex]
Volume of a box is:
[tex]V = xyz[/tex]
Make z the subject
[tex]z = \frac{V}{xy}[/tex]
Substitute 8000 for V
[tex]z = \frac{8000}{xy}[/tex]
Substitute 1000/xy for z in [tex]S = 2(xy + xz + yz)[/tex]
[tex]S = 2(xy + x\frac{8000}{xy}+y\frac{8000}{xy})[/tex]
[tex]S = 2(xy + \frac{8000}{y}+\frac{8000}{x})[/tex]
Expand:
[tex]S = 2xy + \frac{16000}{y}+\frac{16000}{x}[/tex]
[tex]S = 2xy + 16000(\frac{1}{y}+\frac{1}{x})[/tex]
Differentiate S w.r.t x
[tex]\frac{dS}{dx} = 2y - \frac{16000}{x^2}[/tex]
Differentiate S w.r.t y
[tex]\frac{dS}{dy} = 2x - \frac{16000}{y^2}[/tex]
Equate both differentiation to 0
[tex]2x - \frac{16000}{y^2} = 0[/tex]
Multiply through by [tex]y^2[/tex]
[tex]2xy^2 - 16000 = 0[/tex]
[tex]2xy^2 = 16000[/tex]
Divide through by 2
[tex]xy^2 = 8000[/tex] -- (1)
[tex]2y - \frac{16000}{x^2} = 0[/tex]
Multiply through by x^2
[tex]2x^2y - 16000 = 0[/tex]
[tex]2x^2y = 16000[/tex]
Divide through by 2
[tex]x^2y = 8000[/tex] --- (2)
Divide (1) by (2)
[tex]\frac{x^2y = 8000}{xy^2 = 8000}[/tex]
[tex]\frac{x}{y} = 1[/tex]
[tex]x = y[/tex]
Substitute y for x in (1)
[tex]x^2y = 8000[/tex]
[tex]x^2 * x = 8000[/tex]
[tex]x^3 = 8000[/tex]
Take cube roots
[tex]x =20[/tex]
Hence;
[tex]x = y = 20[/tex]
Recall that:
[tex]z = \frac{8000}{xy}[/tex]
[tex]z = \frac{8000}{20 * 20}[/tex]
[tex]z = 20[/tex]
Hence, the dimension of the box that minimizes the surface area of the box is:
[tex]x = y = z = 20[/tex]
A rectangle measures 54 feet by 72 feet. What is the length, in feet, of
the diagonal of the rectangle?
a. 48 ft
b. 90 ft
c. 110 ft
d. 2268 ft
e. 8100 ft
length (l) =54
breath (b) =72
l²+b²= diagonal²..........(Pythagoras theorem) and (all sides of rectangle are 90degree)
(54)²+(72)²=diagonal²
2916+5184=diagonal²
8100=diagonal²
90= diagonal.............(taking square root)
length of diagonal is 90ft
i hope it helps
have a nice day and thanks for asking this question
HELP QUICKLY PLEASE Which of these is used to find the estimated age range of a fossil?
Absolute dating
Half-life
Index fossils
Radioactive dating
Answer:
Step-by-step explanation:
Radioactive dating becouse they look how long the fossils were there
[6TH GRADE] Kidneys are components of the urinary system, a subsystem that filters waste from the blood. A kidney is made up of millions of smaller units, called nephrons. Based on this information, which of the statements could be true? Select ALL that apply.
A. A nephron is a subsystem.
B. A kidney is a subsystem.
C. A kidney is an organ system.
D. A kidney is an organ.
help please:/ 11 points :D
im going to put this in mathematics because mathematics is most viewed.
Answer:
D. A kidney is an organ is correct.
Step-by-step explanation:
A kidney is a part of our body that cleans our blood, ridding it of all uncleanliness, similar to a water filter.
A kidney is an organ because it's one of the essential parts of our body that we need to survive. Our body couldn't live with too much/ too little salt and other substances in our blood.
Therefore, the correct answer is D. A kidney is an organ.
Hope this helps! :D
Find the scale factor of trapezoid QRST if it’s dilated to Q’R’S’T’. Type your result in the empty box provided below. HELPP PLEASE!!!!!!
Answer:
5 units
Step-by-step explanation:
its hard to tell but i think it dilated 5 units
We want to find the scale factor at which QRST is dilated to form Q'R'S'T'
We will find that the scale factor is 2.
In a general dilation, we will see that all the measures change in the same way, by the scale factor.
This means that:
QR*k = Q'R'
RS*k = R'S'
And so on, where k is the scale factor.
Then we can just find one of the equivalent measures in both trapezoids and find the value of k.
For example, we have:
Q'R' = 8
QR = 4
Replacing these on the above equation we get:
4*k = 8
k = 8/4 = 2
k = 2
The scale factor of dilation is 2.
If you want to learn more, you can read:
https://brainly.com/question/14793702
Which shape is similar to shape x?
Answer:
the c oneStep-by-step explanation:
hope it will helpAnswer:
Step-by-step explanation:
Probably C but I sure wouldn't bet the farm on it. It looks like C is about 1.5 times the size of X
1 and 1/4 - 1/3=
please give the right answer
Answer:
11/12
Step-by-step explanation:
15/12-4/12= 11/12
Answer:
11/12
Step-by-step explanation:
5/4 -1/3 first make the equation easier to look at so take the 1 and add it as 4/4
15/12-4/12 then make the bottom the same with multipulcation and tops are multiples as well
11/12 subtract
Which fraction shoes unit rate that is equal to the ratio 18:2
Answer: 9/1
Step-by-step explanation:
What is |9|?
-18
-9
9
18
Answer:
the true answer is 9
Step-by-step explanation:
Because the product of the absolute value is the same number and positive
Jessica runs 4 miles every 32 minutes. At thisrates, how many miles does she run in 48 minutes
A school carnival is having a dunk tank. The graph shows the temperature, t, in Fahrenheit after h hours.
Tank Temperature
Which linear function does the graph represent?
PLS HELP ASAP
Simplify 8 − (14). (1 point)
Question 5 options:
1)
−22
2)
−6
3)
6
4)
22
A sample of 40 CDs from a student's collection showed a mean length of 52.74 minutes with a standard deviation of 13.21 minutes. Construct a 95% confidence interval for the population standard deviation. (Round your answers to 4 decimal places.) The 95% confidence interval is from to .
Answer:
(48.65, 56.83)
Step-by-step explanation:
Given that :
Sample size (n) = 40
Mean (m) = 52.74
Standard deviation (s) = 13.21
α = 95%
Confidence interval around sample mean can be obtained using the relation :
Mean ± Zstatistic * s/√n
Z score for 95% confidence interval = 1.96 (Z probability calculator)
s / √n = 13.21 / √40 = 2.0886843
Lower limit of confidence interval :
52.74 - (1.96 * 2.0886843) = 48.646178772 = 48.65
Upper limit of confidence interval :
52.74 + (1.96 * 2.0886843) = 56.833821228 = 56.83
The coordinates of the vertices of △JKL are J(1, 4) , K(6, 4) , and L(1, 1) .
The coordinates of the vertices of △J′K′L′ are J′(0, −4) , K′(−5, −4) , and L′(0, −1) .
What is the sequence of transformations that maps △JKL to △J′K′L′ ?
reflection across the x-axis
rotation of 180° about the origin
rotation of 90° counterclockwise about the origin
translation 1 unit left
A sequence of transformations that maps △JKL to △J′K′L′ is a _________ followed by a ___________?
Answer:
The sequence of transformations are;
A translation by 1 unit left, followed by a reflection across the x-axis
Step-by-step explanation:
Here, we want to know the transformation sequence
Let us select one point
J(1,4)
to J’(0,-4)
To translate 1 unit right means that we are subtracting the value of 1 from the x-coordinate
That leaves us with (0,4)
To get the change in the y-coordinate value to negative, it means that we have reflected over the x-axis
x-axis reflection turns (x,y) to (x,-y)
So, the sequence of transformations that maps the two is;
A translation by 1 unit left followed by a reflection across the x-axis
Answer:
translation 1 unit left, then 180 degrees
Step-by-step explanation:
J (1,4)
K (6,4)
L (1,1)
Moving it 1 unit left, x unit - 1
J (0,4)
K (5,4)
L (0,1)
Now, rotate it 180 degrees, (x,y) = (-x,-y)
J' (0,-4)
K' (-5,-4)
L' (0,-1).
Hence, the triangle JKL is transformed into triangle J'K'L' when a triangle JKL translates 1 unit to the left and then rotate 180 degrees about the origin.
Of the following sets, which represents a function?
Situation A = {student's name, all the colors that the student likes}
Situation B = {student's name, names of all of the student's teachers}
Answer:
what
Step-by-step explanation:
Help please due soon
Answer:
1. H=6
2. Y= -1
3. T= 2
4. D= 2.1
5. K= 0
6. -13 1/3
Step-by-step explanation:
Each dairy cow in the U.S. produces an average
of 25 quarts of milk per day. Given that there are
quarts in a gallon, how many gallons of milk does a
cow produce?
find the length of side x in simplest radical denominator
Answer:
324352
Step-by-step explanation:
4x-(12 divided 3) +2x=20
Answer:
4
Step-by-step explanation:
Please help I dont understand..
Answer:
2. A
3. H
4. D
5. C
6. G
7. E
8. F
Subtract. Write the answer in lowest terms.
6 1/6 - 2 5/6
Answer:
61/6_25/6=61_25/6=36/6 we divide =6The answer is 6Step-by-step explanation:
Please mark my answer as a brainliest. Please follow me. ❤❤❤Answer:
3 1/6
Step-by-step explanation:
look on the attachment i sent
4. Mrs. Dion decided to go out to dinner. She
spent $15.40 on her meal. She tipped the waiter
$4.25. How much did she pay all together?
Answer:
$19.65
Step-by-step explanation:
Adding decimals is the same as simple addition just line up the point in the numbers and add.
Use the zero product property to find the solutions to the equation x^2-15x-100=0
Ox=-20 or x = 5
Ox=-20 or x =-5
Ox=-5 or x = 20
Ox= 5 or x=20
Answer:
C. x=-5 or x=20
Step-by-step explanation:
Factor [tex]x^{2}[/tex]-15x−100 using the AC method
(x-20)(x+5)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0
x−20=0
x+5=0
Set x−20 equal to 0and solve for x
x=20
Set x+5 equal to 0 and solve for x
x=−5
The final solution is all the values that make (x−20)(x+5)=0 true. The multiplicity of a root is the number of times the root appears.
x=20(Multiplicity of 1)x=−5 (Multiplicity of 1)
The solutions to the equation x² - 15x - 100 = 0 are:
x = 20 and x = -5.
What is a solution?Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.
We also find the solution in a system of equations using the substitution or elimination method.
Example:
2x + 4 = 8
The solution is x = 2.
We have,
To use the zero product property to solve the equation:
x² - 15x - 100 = 0.
Factor the left-hand side of the equation:
(x - 20)(x + 5) = 0
Apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero:
x - 20 = 0 or x + 5 = 0
Solve for x in each equation:
x - 20 = 0
x = 20
x + 5 = 0
x = -5
Therefore,
The solutions to the equation x² - 15x - 100 = 0 are:
x = 20 and x = -5.
Learn more about solutions of equations here:
https://brainly.com/question/545403
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There are 3 cups of blue paint and 2 cups of red paint. Whats the ratio?
Answer:
3:2
Step-by-step explanation:
can also be written as 3/2 as a fraction!
Answer:
Blue paint to red paint - 3:2
Red paint to blue paint 2:3
Step-by-step explanation:
For every 3 cups of blue paint there is 2 cups of red paint
For every 2 cups of red paint there is 3 cups of blue paint
Fraction Mode: 3/2 or 2/3
Please help me this is 7th grade math all you have to do is find the slope for the graph if it is right i will give you brianliest
Answer:
-10/2 or -5 for the slope
Step-by-step explanation:
rise over run: it's going down 10 and over 2 or
for every 5 down it goes 1 over
Kareem is flying two kites. He has 104 feet of string out to one kite and 120 feet out to the other kite. The angle formed by the two strings is 36° as shown in
the figure below. Find the distance between the kites.
120
104
36 degrees
Carry your intermediate computations to at least four decimal places.
Round your answer to the nearest tenth of a foot.
Submit Assignment
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Answer: Manuel is flying two kites. He has
102
feet of string out to one kite and
111
feet out to the other kite. The angle between the strings is
36°
as shown in the figure below. Find the distance between the kites
Given `∆QRS≅∆TUV,` QS = 5v + 2, and TV = 8v - 7, find the length of QS
Answer:
3
Step-by-step explanation:
You have to equate them so...
5v+2=8v-7
I hope this helps you!
How is 0,2 an answer?
Answer:
it is an answer if you are using a coordinate plane
Step-by-step explanation:
Patrick graphed a square with the area of 50 square units on a coordinate plane. one of the verticles of the square is located at (5,10). which could the other three vertice of the square
Answer:
The other 3 vertices would be (10,5) , (5,0) , and (0,5)
Step-by-step explanation: