Answer:
The values of F will be "16.58 i + 11.18 j".
Step-by-step explanation:
The given values are:
Force, F = 20 N
Angle, Ф = 33°
The formula use in the given scenario will be:
⇒ [tex]x=a \ Cos\theta[/tex]
⇒ [tex]y=a \ Sin\theta[/tex]
Now,
For Force, [tex]F=ai+bj[/tex]
⇒ [tex]a=F \ Cos\theta[/tex]
⇒ [tex]=20 \ Cos(34^{\circ})[/tex]
⇒ [tex]=20\times .829[/tex]
⇒ [tex]=16.58[/tex]
and,
⇒ [tex]b=F \ Sin\theta[/tex]
⇒ [tex]=20 \ Sin(34^{\circ})[/tex]
⇒ [tex]=20\times .55[/tex]
⇒ [tex]=11.18[/tex]
So that,
⇒ [tex]F=16.58 \ i+11.18 \ j[/tex]
A classroom will be assembled so that the desks fit within an area that is 8 m by 12 m. The desks will be surrounded by a border that will be the same width on all sides of the rectangular room, to
allow for walking space. The area of the border will equal 20% of the area of the space that the desks
occupy. What is the width of the border, to the nearest hundredth of a meter?
Answer:
0.46 m
Step-by-step explanation:
area of desks: 8 m by 12 m = 8 m * 12 m = 96 m^2
20% of this area is 20% * 96 m^2 = 19.2 m^2
The area of the border is 19.2 m^2.
Let the path around the desks have width x.
The area of desks plus path is a rectangle 2x + 8 by 2x + 12.
area of desks plus path = (2x + 8)(2x + 12)
= 4x^2 + 24x + 16x + 96 = 4x^2 + 40x + 96
The area of the border is the area of the rectangle that includes the border minus the rectangle that has just the desks.
area of border = (4x^2 + 40x + 96) - (96) =
= 4x^2 + 40x
Above, we have the area of border = 19.2, so we get this equation:
4x^2 + 40x = 19.2
4x^2 + 40x - 19.2 = 0
x^2 + 10x - 4.8 = 0
We now use the quadratic formula to solve the equation for x.
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x = \dfrac{-10 \pm \sqrt{10^2 - 4(1)(-4.8)}{2(1)} [/tex]
[tex] x = \dfrac{-10 \pm \sqrt{100 + 19.2 )}{2} [/tex]
[tex] x = \dfrac{-10 \pm \sqrt{119.2 )}{2} [/tex]
[tex] x = 0.46 [/tex] or [tex] x = -10.46 [/tex]
We discard the negative solution.
Answer: the border is 0.46 m wide.
∠A and \angle B∠B are complementary angles. If m\angle A=(2x+18)^{\circ}∠A=(2x+18) ∘ and m\angle B=(6x-8)^{\circ}∠B=(6x−8) ∘ , then find the measure of \angle B∠B?
Answer:
[tex]m\angle B=52^{\circ}[/tex]
Step-by-step explanation:
Two or more angles are said to be complementary if they sum up to 90 degrees.
Given that angles A and B are complementary, then:
[tex]\angle A+\angle B=90^\circ\\m\angle A=(2x+18)^{\circ}\\m\angle B=(6x-8)^{\circ}\\$Therefore:\\(2x+18)^{\circ}+(6x-8)^{\circ}=90^\circ\\2x+6x+18-8=90^\circ\\8x+10^\circ=90^\circ\\8x=90^\circ-10^\circ\\8x=80^\circ\\$Divide both sides by 8\\x=10^\circ\\$Therefore:\\m\angle B=(6x-8)^{\circ}\\m\angle B=(6(10)-8)^{\circ}\\=60-8\\m\angle B=52^{\circ}[/tex]
Answer:
56 :)
Step-by-step explanation:
Simplify the Expression : -20 - (-5) * (-2^2)
Answer:
-40
Step-by-step explanation:
-20-(-5)*(-2^2)
- and a - = positive
-2^2 = -4 but if it was (-2)^2 then it would be 4
-20+5*(-4)
order of operations
-20-20
-40
hope this helps
1. Using the scale 1 in.: 4 ft, find the dimensions in a blueprint of an 8 ft-by-12 ft
room
Answer:
2 in by 3 in
Step-by-step explanation:
1 in = 4 ft Divide both sides with 4
0.25 in = 1 ft
0.25 * 8 = 2 in
0.25 * 12 = 3 in
2 in by 3 in
Answer: 2 in by 3 in
Step-by-step explanation:
1 in = 4 ft Divide both sides with 4 0.25 in = 1 ft 0.25 * 8 = 2 in 0.25 * 12 = 3 in 2 in by 3 in
What is the inverse of the function f(x) = one-quarterx – 12? h(x) = 48x – 4 h(x) = 48x + 4 h(x) = 4x – 48 h(x) = 4x + 48
Answer:
h(x) = 4x+48Step-by-step explanation:
Given the function f(x) = 1/4x -12. To get the inverse of the function, first we will let y = f(x) to have y = 1/4x - 12.
Then we will make x the subject of the formula as shown:
y = 1/4x - 12
adding 12 to both sides we have;
y + 12= 1/4x - 12 + 12
y + 12 = 1/4x
Multiplying both sides by 4 we have;
4(y+12) = x
x = 4y + 48
Substituting y for x
y = 4x+48
f^-1(x) = 4x+48
h(x) = 4x+48
Thee final expression will give the inverse of the function
Answer:
h(x) = 4x+48
Step-by-step explanation:
Given the function f(x) = 1/4x -12. To get the inverse of the function, first we will let y = f(x) to have y = 1/4x - 12.
Then we will make x the subject of the formula as shown:
y = 1/4x - 12
adding 12 to both sides we have;
y + 12= 1/4x - 12 + 12
y + 12 = 1/4x
Multiplying both sides by 4 we have;
4(y+12) = x
x = 4y + 48
Substituting y for x
y = 4x+48
f^-1(x) = 4x+48
h(x) = 4x+48
Thee final expression will give the inverse of the function
climate scientists use computer models to predict the likely change in global average temperature under various assumptions about CO2 production. What type of data source is this?
Answer:
[tex]\fbox{\begin{minipage}{10em}Option A: Simulation \end{minipage}}[/tex]
Step-by-step explanation:
The data is not collected from the world outside, but a computer.
=> The data can be generated under assumption from simulation only.
=> Option A is correct.
Hope this helps!
:)
Answer:
a. Simulation
Step-by-step explanation:
A computer model is generally a simulation of the real world. Certainly, a model of Earth's climate is a simulation.
__
In some cases, the data of interest is the performance of the computer itself (as opposed to some system outside the computer). In those cases, the running of the computer under different scenarios might be considered an experiment.
There are 350 Families lives in the small town of America. A poll of 50 families revealed the mean annual church contribution is $550 with the standard deviation of $ 75.Construct the 95% confidence interval for the mean annual contribution
Answer:
$550+/-$20.79
= ( $529.21, $570.79)
Therefore, the 95% confidence interval (a,b) = ( $529.21, $570.79)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = $550
Standard deviation r = $75
Number of samples n = 50
Confidence interval = 95%
z(at 95% confidence) = 1.96
Substituting the values we have;
$550+/-1.96($75/√50)
$550+/-1.96($10.60660171779)
$550+/-$20.7889393668
$550+/-$20.79
= ( $529.21, $570.79)
Therefore, the 95% confidence interval (a,b) = ( $529.21, $570.79)
a rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. The equation(x+5) x=104 represents the situation, where x represents the width of the rectangle. (x+5) x=104 x2+5x-104=0. Determine the solutions of the equation. What solution makes sense for the situation?
Answer:
x=8
Step-by-step explanation:
Area of a rectangle=length×width
Area=104
Width=x
Length=5+x
104=x*(5+x)
104=5x+x^2
104-5x-x^2=0
x^2+5x-104=0
Can also be written as
-x^2-5x+104=0
Solve the quadratic equation using formula
−x2−5x+104=0
using the Quadratic Formula where
a = -1, b = -5, and c = 104
x=−b±√b2−4ac/2a
x=−(−5)±√(−5)2−4(−1)(104)/2(−1)
x=5±√25−(−416)/−2
x=5±√441/−2
The discriminant b^2−4ac>0
so, there are two real roots.
Simplify the Radical:
x=5±21/−2
x=-26/2 or 16/2
x=-13 or 8
The value of x can't be negative
So, x=8 is the answer
what is 240:180 in its simplest form thanks
Answer:
4:3
Step-by-step explanation:
240:180=
60(4):60(3)=
4:3
Hope this helps!
Answer:
4:3
Step-by-step explanation:
24:18
4:3
what’s the answers ?
B and D
Step-by-step explanation:
I'm pretty sure its B because an acute angel measure less than 90°
PLLLSSSSSS HURRRYYYY To convert Celsius temperatures to Fahrenheit, you can use the expression 9/5 (C + 32). Tom says that another way to write this expression is 9/5 C + 32. What error did Tom make?
A. Tom did not make an error.
B. Tom should have simplified the fraction .
C. Tom did not distribute to both terms in parentheses.
D. Tom should have added inside the parentheses before multiplying.
Answer:
C.
Step-by-step explanation:
If you are distributing, you must distribute the outside to both terms in the inside.
Let f(x) = ............
Answer:
So first lets find g(-1)
so we plug in the answers:
-2 * -1 ^2 -4
-2*1-4 = -2-4 =
-6
Now lets solve for f(-2)
-2^2-3
4-3=1
-6+1 = 5
3*5 = 15
Im getting answer of 15 but it shows -15 or something, so I dont know if I got it wrong or if its like a dash then the answer.
Solve the following system. x squared / 25 + y squared / 100 = 1 x squared + y squared = 25
Answer :
[tex] \frac{1}{100} (4 {x}^{2} + {y}^{2} )[/tex] [tex] \frac{dy}{dx} = \frac{ - x}{y} [/tex]Ayuuuudeeeeen :')
t.t
Answer: a=4
Step-by-step explanation:
Es facil. La diagonales de un rectangulo se cortan en su punto medio por tanto la diagonal es 10 (el doble de 5).
Por pitagoras entonces:
[tex]a=\sqrt{10^2-8^2}=\sqrt{100-64}=\sqrt{36}=4[/tex]
A cubical block of side 14 cm is surmounted by a hemisphere . what is the greatest radius that the hemisphere can have?
Answer:
9.9cmStep-by-step explanation:
The hemisphere will have its greatest radius along the diagonal of the cube it was surmounted on. The base of the cubical block will be square in nature. Since a cube has all its sides equal, we can find the length of its diagonal using pythagoras theorem as shown.
[tex]hyp^{2} = adj^{2} +opp^{2}[/tex]
Note that the diagonal will be the hypotenuse of the square face which is the longest sides.
Given adjacent = 14cm and opposite = 14cm
[tex]hyp^{2} = 14^{2} +14^{2}\\hyp = \sqrt{196+196} \\hyp = \sqrt{392} \\hyp = 19.8cm[/tex]
The diagonal of the base of the cube is 19.8cm which is equivalent to the greatest diameter of the sphere.
The greatest radius that the hemisphere can have = 19.8/2 = 9.9cm
Drawing diagrams
Circles
Radius rDiameter dRelationship between r and d:Cubes
Length lWidth wHeight hApplication:Let's draw a figure to supplement a visual image to further understand what we need to find. Please refer to the attached image for reference. Please excuse the poor handwriting/drawing. It is also not to scale.
We know that there is a cubical block w/ side measurements of 14 cm. "Surrmounted" means on top. So a hemisphere (half of a sphere) is on top of our block.
If we take a look at our geometrical shape from the top-down angle, we can see that the top would just look like a circle within a square, as depicted in blue.
Labeling our measurements, we can see that the length, width, and height of our cubical block are equal to 14 cm due to the definition of a cube. This extends to the definition of a square as well, so the length and width of our square are also equal to 14 cm.
With the side of the square equal to 14 cm, we know that this is equal to the circle's diameter. So d = 14 cm. We can solve for the radius of the circle/hemisphere by substituting it into the radius formula:
[tex]\begin{aligned}r & = \frac{d}{2} \\& = \frac{14 \ \text{cm}}{2} \\& = \boxed{ 7 \ \text{cm}} \\\end{aligned}[/tex]
Answer:∴ the greatest radius that the hemisphere can have is equal to 7 cm. Any r > 7 cm would result in the hemisphere being over the edge of the cube.
___
Learn more about Geometry: https://brainly.com/question/27732359
___
Topic: Geometry
Unit: Composition of Geometrical Shapes
If you want to increase the length of the side of a square by 30%, what fraction can be used as the
multiplier to find the length of the new side?
The fraction (13/10) can be used as the multiplier to find the length of the new side.
Suppose the length of the side of a square is x.
The new length of the side of the square after an increment of 30%
= x+ (30% of x).
What is the percentage?The percentage is the value per hundred.
So, 30% of x = 30*x/100 =0.3x
So, new length of the side = x+0.3x =1.3x
We can represent 1.3x as (13/10)x
This means we have multiplied the previous length by the fraction 13/10 in order to get an increment of 30%.
Thus, The fraction (13/10) can be used as the multiplier to find the length of the new side.
To get more about the percentage visit:
https://brainly.com/question/24304697
Solve for x. 2x = 15 + x
A.) x = -15
B.) x = 15/2
C.) x = -15/2
D.) x = 15
Option D( X=15)
Solution,
2x=15+x
or, 2x-x=15
X=15
hope it helps...
Good luck on your assignment...
Answer:
[tex]x = 15[/tex]
Step-by-step explanation:
[tex]2x = 15 + x \\ 2x - x = 15 \\ x = 15[/tex]
Answer D is correct
Can someone please help with this answer
Answer:
16x9= 144 cm2
Step-by-step explanation:
$36/4oz is what and , 24/3oz is what , $20/2oz is what plz help
Answer:
see below
Step-by-step explanation:
$36/4oz = $9 per oz
24/3oz = $ 8 per oz
$20/2oz = # 10 per oz
What is the surface area of the right cone below?
slanted height of 13 and radius of 4
A. 5277 units
B. 5477 units2
C. 687 units2
D. 104 units2
Answer:
213.69 units
Step-by-step explanation:
We have to first find the height of the cone.
We can use Pythagoras rule because the slant height, height and radius of a cone all form a right angled triangle:
[tex]h^2 = a^2 + b^2[/tex]
where h = hypotenuse
a and b = the other two sides of the triangle
The radius is 4 units and the slant height is 13 units:
[tex]13^2 = a^2 + 4^2\\\\169 = a^2 + 16\\\\a^2 = 169 - 16 = 153\\\\a = \sqrt{153}\\\\a = 12.37units[/tex]
The height of the cone is 12.37 units.
The surface area of a cone is given as:
SA = [tex]\pi r (r + \sqrt{h^2 + r^2} )[/tex]
[tex]SA = \pi * 4(4 + \sqrt{12.37^2 + 4^2} )\\\\SA = 12.57(4 + \sqrt{13^2} )\\SA = 12.57 (4 + 13)\\\\SA = 12.57(17)\\\\SA = 213.69 units[/tex]
The surface area of the cone is 213.69 units.
solve the equation
7h-5(3h-8) = 72
Answer:
h = -4
Step-by-step explanation:
7h-5(3h-8) = 72
Distribute
7h - 15h +40 = 72
Combine like terms
-8h +40 = 72
Subtract 40 from each side
-8h+40-40 = 72-40
-8h = 32
Divide each side by -8
-8h/-8 = -32/-8
h = -4
Steps:
Step 1: Simplify both sides of the equation.
7h−5(3h−8)=72
7h+(−5)(3h)+(−5)(−8)=72(Distribute)
7h+−15h+40=72
(7h+−15h)+(40)=72(Combine Like Terms)
−8h+40=72 −8h+40=72
Step 2: Subtract 40 from both sides.
−8h+40−40=72−40
−8h=32
Step 3: Divide both sides by -8
Answer: h=−4
The answer for this question is h=-4
Please mark me brainliest
Hope this helps.
Simplify to create an equivalent expression
8k-5(-5k+3)
Answer:
33k - 15
Step-by-step explanation:
8k-5(-5k+3)
Distribute
8k +25k -15
Combine like terms
33k - 15
_______________________________
Solution,
8k-5(-5k+3)
= 8k+25k-15
=33k-15
hope it helps..
Good luck on your assignment
_____________________________
Evaluate 10x^2y^–2 for x = –1 and y = –2.
Answer:
10
Step-by-step explanation:
10x^2y^-2
10(-1)^2(-2)^2=10
An inspector checks 98 cell phones and finds 2 of them not working. If a company
has 850 of the phones, how many are likely to not be working?
Answer:
17
Step-by-step explanation:
Use ratio method
98:2
850:x
so, x = (850 x 2) divided by 98 = 17.3469388
Round it to nearest whole number = 17
Arturo, Pedro y Jorge son hermanos y duermen en la misma habitación. Su papá les compró una pintura para que entre los tres pinten su cuarto. Arturo como es el más grande tiene que pintar 1/2 del total de la habitación, Pedro 3/8 y Jorge como es el más pequeño pintará la última parte.
¿Que fracción de la habitación pintará Jorge?
Porfís ayudenme es para mañana
Answer:
1/8
Step-by-step explanation:
1/2= 4(1/2) = 4/8
4/8+3/8= 7/8
7/8 + 1/8 = 1
The price of a train ticket consists of an initial fee plus a constant fee per stop. The table compares the number of stops and the price of a ticket (in dollars). What is the initial fee?
Answer:
Initial Fee is $2.
Step-by-step explanation:
HOW CAN YOU USE SUBTRACTION TO DESCRIBE DIVISION? GIMME AN EXAMPLE PLS :(
Answer:
By repeated subtraction.
Step-by-step explanation:
It is pretty much the same thing as division, but in subtraction. Since, Dividing and Subtraction are a like, repeated subtraction is a great example to use for this example
Hope this helps. :)
Answer:
kk so like, division is just repeated subtraction. like idk say you have 36 and you divide it by 9 so I think you just keep subtracting 9 until you reach 0? so you end up subtracting 9 four times which happens to be the quotient for 36/9. yeah. it's almost like how multiplication is just repeated addition.
What is the sum of the measures of the interior angles of a 12-gon?
1620°
O 1800°
O 1980°
O 2160°
Answer:
The answer is 1800!
Step-by-step explanation:
Answer:
B. 1800 degrees.
Step-by-step explanation:
Just took the quiz on Edg (2020-2021)!
3(a-2/3)= 3/4a+2 1/4
Steps:
Step 1: Simplify both sides of the equation.
3(a−2/3)=3/4a+21/4
(3)(a)+(3)(−2/3)=3/4a+21/4(Distribute)
3a+−2=34a+2143a−2=3/4a+21/4
3a+−2=34a+2143a−2=3/4a+21/4
Step 2: Subtract 3/4a from both sides.
3a−2−3/4a=3/4a+21/4−3/4a
9/4a−2=21/4
Step 3: Add 2 to both sides.
9/4a−2+2=21/4+2
9/4a=29/4
Step 4: Multiply both sides by 4/9.
(4/9)*(9/4a)=(4/9)*(29/4)
Answer:
A=29/9
Please mark me brainliest
Hope this helps.
PLEASE HELP!!!the pattern follows the rule, starting with a value of 4, every consecutive row has a value that is 2 less than twice the value of the previous row. What is the value of the fifth row
Answer:
34
Step-by-step explanation
1- 4
2- 4(2) - 2 = 6
3- 6(2) - 2 = 10
4- 10(2) - 2 = 18
5- 18(2) -2 = 34