Answer:
[tex]\displaystyle x=\left \{\frac{2\pi}{3}+2\pi k,\frac{4\pi}{3}+2\pi k, \frac{8\pi}{3}+2\pi k, \frac{10\pi}{3}+2\pi k\right \}k\in \mathbb{Z}[/tex]
Step-by-step explanation:
Hi there!
We want to solve for [tex]x[/tex] in:
[tex]4\sin^2(\frac{x}{2})=3[/tex]
Since [tex]x[/tex] is in the argument of [tex]\sin^2[/tex], let's first isolate [tex]\sin^2[/tex] by dividing both sides by 4:
[tex]\displaystyle \sin^2\left(\frac{x}{2}\right)=\frac{3}{4}[/tex]
Next, recall that [tex]\sin^2x[/tex] is just shorthand notation for [tex](\sin x)^2[/tex]. Therefore, take the square root of both sides:
[tex]\displaystyle \sqrt{\sin^2\left(\frac{x}{2}\right)}=\sqrt{\frac{3}{4}},\\\sin\left(\frac{x}{2}\right)=\pm \sqrt{\frac{3}{4}}[/tex]
Simplify using [tex]\displaystyle \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}[/tex]:
[tex]\displaystyle \sin\left(\frac{x}{2}\right)=\pm \sqrt{\frac{3}{4}},\\\sin\left(\frac{x}{2}\right)=\pm \frac{\sqrt{3}}{\sqrt{4}}=\pm \frac{\sqrt{3}}{2}[/tex]
Let [tex]\phi = \frac{x}{2}[/tex].
Case 1 (positive root):[tex]\displaystyle \sin(\phi)=\frac{\sqrt{3}}{2},\\\phi = \frac{\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\phi =\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z}[/tex]
Therefore, we have:
[tex]\displaystyle \frac{x}{2}=\phi = \frac{\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\frac{x}{2}=\phi =\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z},\\\\\begin{cases}x=\boxed{\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z}},\\x=\boxed{\frac{4\pi}{3}+2\pi k , k \in \mathbb{Z}}\end{cases}[/tex]
Case 2 (negative root):[tex]\displaystyle \sin(\phi)=-\frac{\sqrt{3}}{2},\\\phi = \frac{4\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\phi =\frac{5\pi}{3}+2\pi k, k\in \mathbb{Z},\\\begin{cases}x=\boxed{\frac{8\pi}{3}+2\pi k, k\in \mathbb{Z}},\\x=\boxed{\frac{10\pi}{3}+2\pi k , k \in \mathbb{Z}}\end{cases}[/tex]
please solve this equation using quadratic formula
Step-by-step explanation:
x+3/x-2-1-x/x=17/4find the LCM of the denominators (x-2)x=x^2-2x
(x^2-2x)4=4x^2-8x divide the denominator by the LCM and then multiply x to the numerator
(x+3)4=4×+3
(1-x)(4x-8)
1(4x-8)-x(4x-8)
4x-8-4x^2-8x=4x
Shannon is planning to tile a rectangular kitchen countertop that is 24 inches wide and 64 inches long. She determined that 1 tile will be needed for each 4-inch-by-4-inch region. What is the minimum number of tiles that will be needed to completely cover the countertop to its edges
Answer:
96
Step-by-step explanation:
[tex]\frac{24*64}{4*4}=96\\[/tex]
or
[tex]\frac{24}{4}=6, \frac{64}{4}=16\\6*16=96[/tex]
The minimum number of tiles that will be needed to completely cover the countertop to its edges is 96.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.
The number of tiles will be calculated by calculating the area of the rectangular kitchen and the area of a tile then dividing the whole area by the area of a tile.
Area of kitchen,
A(k) = 64 x 24 = 1536 Square inches
Area of a tile,
A(T) = 4 x 4 = 16 square inches.
Divide the area of the kitchen by the area of a tile.
N = 1536 / 16 = 96 tiles
Therefore, the minimum number of tiles that will be needed to completely cover the countertop to its edges is 96.
To know more about an area follow
https://brainly.com/question/25292087
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A tank initially has 300 gallons of a solution that contains 50 lb. of dissolved salt. A brine solution with a concentration of 2lb of salt/gallon is admitted into the tank at a rate of 6 gallons per minute. The well-stirred solution is drained at the same rate. How long will it take for the tank to have 100 lb. of dissolved salt
Let s(t) be the amount of salt in the tank at time t. Then s(0) = 50 lb.
Salt flows into the tank at a rate of
(2 gal/min) (6 lb/gal) = 12 lb/min
and flows out at a rate of
(2 gal/min) (s(t)/300 lb/gal) = s(t)/150 lb/min
so that the net rate at which salt is exchanged through the tank is
ds(t)/dt = 12 - s(t)/150 … (lb/min)
Solve for s(t). The DE is separable, so we have
ds/dt = 12 - s/150
150 ds/dt = 1800 - s
150/(1800 - s) ds = dt
Integrate both sides to get
-150 ln|1800 - s| = t + C
Solve for s :
ln|1800 - s| = -t/150 + C
1800 - s = exp(-t/150 + C )
1800 - s = C exp(-t/150)
s = 1800 - C exp(-t/150)
Now given that s(0) = 50, we solve for C :
50 = 1800 - C exp(-0/150)
50 = 1800 - C
C = 1750
Then the amount of salt in the tank at any time t ≥ 0 is
s(t) = 1800 - 1750 exp(-t/150)
To find the time it takes for the tank to hold 100 lb of salt, solve for t in
100 = 1800 - 1750 exp(-t/150)
1700 = 1750 exp(-t/150)
34/35 = exp(-t/150)
ln(34/35) = -t/150
t = -150 ln(34/35) ≈ 4.348
So it would take approximately 4.348 minutes.
By the way, we didn't have to solve for s(t), we could have instead stopped with
-150 ln|1800 - s| = t + C
Solve for C - this C is not the same as the one we found using the other method. s(0) = 50, so
-150 ln|1800 - 50| = 0 + C
C = -150 ln|1750|
==> t = 150 ln(1750) - 150 ln|1800 - s|
Then s(t) = 100 lb when
t = 150 ln(1750) - 150 ln(1700)
t = 150 ln(1750/1700)
t = 150 ln(35/34)
t ≈ 4.348
Please answer this question now
Answer:
30.9 cm²
Step-by-step explanation:
To find the surface area of this figure, we find the area of the base and the 3 identical sides.
The base is split into two identical right triangles. Let's find the area of one and multiply by two.
Half of 3: 1.5
[tex]1.5\cdot2.6=3.9\\3.9\div2=1.95[/tex]
There are two right triangles:
[tex]1.95\cdot2=3.9[/tex]
The area of one of the sides will be the same thing, except the height is 6.
[tex]1.5\cdot6=9\\9\div2=4.5\\4.5\cdot2=9[/tex]
There are 3 sides identical to this one:
[tex]9\cdot3=27[/tex].
Add 27 and 3.9:
[tex]27+3.9=30.9[/tex]
Hope this helped!
Answer:
30.9 square centimeters
Step-by-step explanation:
3 * 1/2(3)(6) + 1/2(3)(2.6) = 30.9
ASAP!!! PLEASE help me solve this question! No nonsense answers, and solve with full solutions.
Answer:
When two inscribed angles in one circle both equal 75°, the two angles must intercept the same arc that measures 75°
Step-by-step explanation:
Based on the Inscribed Angles Theorem, the measure of an intercepted arc is twice the measure of the inscribed angle that intercepts it in a circle.
Consequently, the theorem also Holds that the measure of two inscribed angles intercepting the same arc, are congruent. In other words, both angles together are the same, and their sum would give you the measure of the arc they both intercept.
In the diagram shown in the attachment below, we have 2 inscribed angles, angle A and B. They both intercept the same arc of 75°.
Therefore, we can conclude that the measure of both angles equal 75°, which is the same as the measure of the arc they intercept.
Angle A = Angle B
m<A + m<B = measure of intercepted arc = 75°
What is the slope of the line shown below?
A.
[tex] \frac{1}{2} [/tex]
B.
[tex] - \frac{1}{2} [/tex]
C.
[tex]2[/tex]
D.
[tex] - 2[/tex]
Answer:
The choose C. 2
Step-by-step explanation:
[tex]slope = \frac{y2 - y1}{x2 - x1} \\ = \frac{ - 2 + 4}{3 - 2} = \frac{2}{1} = 2[/tex]
Answer:
option C is correct
Step-by-step explanation:
slope = [tex] \frac{ - 2 + 4}{3 - 2} [/tex][tex] = \frac{2}{1} [/tex][tex] = 2[/tex]Hope it is helpful....
x2 +15-8x entre 3-x ayuda pliz
help me please
[tex] \frac{ \cos(80) }{ \sin(10) } + \frac{ \sin(20) }{ \cos(70) } = 2 \\ \\ \frac{ \cot(40) }{ \tan(50) } + \frac{ \cos(65) }{ \sin(115) } = 2[/tex]
Answer:
[tex] \frac{ \cos(80) }{ \sin(10) } + \frac{ \sin(20) }{ \cos(70) } = 2 \\ \frac{ \cos(90 - 10) }{ \sin(10) } + \frac{ \sin(20) }{ \cos(9 0 - 20) } = 2 \\ \frac{ \sin(10) }{ \sin(10) } + \frac{ \sin(20) }{ \sin(20) } = 2 \\ 1 + 1 = 2 \\ 2 = 2 \\ \\ \frac{ \cot(40) }{ \tan(50) } + \frac{ \cos(65) }{ \sin(115) } = 2 \\ \frac{ \cot(90 - 50) }{ \tan(50) } + \frac{ \cos(65) }{ \sin(90 + 65) } = 2 \\ \frac{ \tan(50) }{ \tan(50) } + \frac{ \cos(65) }{ \cos(65) } = 2 \\ 1 + 1 \\ = 2[/tex]
What is 73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73=
Answer:
1533
Step-by-step explanation:
73x21= 1533
Answer:
73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73
=73x21=1533
Step-by-step explanation:
Help please! will give brainiest
Answer:
cd a gimem ?
Step-by-step explanation:
Directions: Simplify each expression by combining like
Terms (pls help if u can )
Answer:
1. -y
3. 9a-7
5. 14x-2
7. 7d-6
Step-by-step explanation:
1. 8y-9y=-y
3. 8a-6+a-1
=(8a+a)-(6+1)
=9a-7
5. -x-2+15x
=(-x+15x)-2
=14x-2
7. 8d-4-d-2
=(8d-d)-(4+2)
=7d-6
Answer:
1. -x
3. 9a-7
5. 14x-2
7. 7d-6
Step-by-step explanation:
To do the first one you would just subtract 8 by 9 which is -1 so you would get -x as 1.
To do the third one would would just move the numbers around so you get 8a+a-6-1 and when you simplify you get 9a-7.
To do the fifth one you just have to move the numbers so you get -x+15x-2 and when you simplify you get 14x-2
To do the seventh one you just have to move the numbers so you get 8d-d-4-2 and when you simplify you get 7d-6.
how do you solve division easly
Answer:
division involves 5 steps:
D Divide
M Multiply
S Subtract
B Bring down
R Repeat or Remainder
Step-by-step explanation: i hope it helped
PLEASE HELP ME ANSWER THESE !!!
1 There are 63 students marching in a band, and they’re marching in 7 rows. How many students are in each row?
2 A candy factory made 54 boxes of chocolates. Each box weighs 2 pounds. They packed the boxes in 6 cases with the same number of boxes in each case. How many pounds of chocolates were there in each case?
3 Max bought tools costing $75. He made a $30 down payment and plans to pay off the rest of the money in 5 monthly installments. How much will Max’s monthly payments be?
4 Harry has decided to give his collection of 24 old coins to his four grandsons. John, the oldest, gets half the collection. Walt, Matt, and Richie will divide the remaining coins evenly among themselves. How many coins will each boy receive?
5 Mr. and Mrs. Pierotti are remodeling their kitchen. They need 9 square yards of covering for the floor. Jackson Interiors quoted them a price of $81 for 9 square yards of linoleum. Carpet Master told them that carpeting would cost $6 per square yard. Which is cheaper—the linoleum or the carpeting
Answer:
1)9 2)18 3)9. 4)4. 5)carpeting
Step-by-step explanation:
1) divide 63 by 7 = 9
2)multiply 54 by 2 = 108 total weight of the boxes then divide 108 by 6 to get 18
3) 75 -30 to get remaining amount which is 45 then divide by 5 to get how much he will pay each month which is 9
4 24- 12= 12 the remaining for the 3 and divide by 3 to get 4
5) multiply 6 * 9 which is $54 which is cheaper than the $81
Wait times at a dentist's office are typically 21 minutes, with a standard deviation of 2 minutes. What percentage of people should be seen by the doctor between 17 and 25 minutes for this to be considered a normal distribution?
Answer:
95%
Step by step explanation:
z = 17-21 / 2 and z = 25-21/2
z=-2 (2.28%) z=2 (97.72%)
97.72 - 2.28 = 5.44
100% - 5.44% is about equal to 95%
Please answer this question now
Answer:
65.94 square inches
Step-by-step explanation:
Surface area of a cone=πr(r+√h^2+r^2)
π=3.14
r=diameter/2
=14/2
=7 in
h=?
h=a
To find h using Pythagoras theorem
c^2 = a^2 + b^2
14^2 = a^2 + 7^2
14^2 - 7^2= a^2
196-49=a^2
147=a^2
Square root both sides
√147=√a^2
12.12=a
a=12.12 in
Surface area of a cone=πr(r+√h^2+r^2)
=3.14(7+√12.12^2+7^2)
=3.14(7+√147+49)
=3.14(7+√196)
=3.14(7+14)
=3.14(21)
=65.94 square inches
Simple Algebra problem. Includes the x and y axis. Also need help finding the perimeter.
Answer:
31.5cm²
Step-by-step explanation:
area of a triangle =1/2 b h
b= 7cm
h=9cm
1/2×7×9
= 1/2×63
= 31.5cm²
hypotenuse is unknown so,
c²=a²+b²
c²= 7² + 9²
= 49 + 81
c²= 130
c= 11.4cm
perimeter= 7 +9+11.4
=27.4cm
pls note that no unit was stated
Write an equation for a parabola with a focus of (1,-2) and a directrix of y=6
Answer:
y = - [tex]\frac{1}{16}[/tex](x - 1)² + 2
Step-by-step explanation:
Any point (x, y) on the parabola is equidistant from the focus and the directrix.
Using the distance formula
[tex]\sqrt{(x-1)^2+(y+2)^2^}[/tex] = | y - 6 |
Square both sides
(x - 1)² + (y + 2)² = (y - 6)² ( expand the factors in y )
(x - 1)² + y² + 4y + 4 = y² - 12y + 36 ( subtract y² - 12y from both sides )
(x - 1)² + 16y + 4 = 36 ( subtract 4 from both sides )
(x - 1)² + 16y = 32 ← subtract (x - 1)² from both sides )
16y = - (x - 1)² + 32 ( divide all terms by 16 )
y = - [tex]\frac{1}{16}[/tex] (x - 1)² + 2
Please give me the correct answer
Answer:
Area= 452.23 ft²
Step-by-step explanation:
Angle at U = 180-48-20
Angle at U = 112°
UT/sin 112=46/sin 48
UT= 0.9272*46/0.7431
UT=57.4 ft
UV= sin 20*46/sin48
UV= 0.3420*46/0.7431
UV= 21.2 ft
S=( 21.2+57.4+46)/2
S=124.6/2
S= 62.3
Area= √((62.3)(62.3-21.2)(62.3-57.4)(62.3-46))
Area= √((62.3)(41.1)(4.9)(16.3))
Area= √204509.5311
Area= 452.23 ft²
1) 4+8r-6r=6+2r
2) 1-3x=-6+7-2x-x
1:-
[tex]\\ \sf \longmapsto 4+8r-6r=6+2r[/tex]
[tex]\\ \sf \longmapsto 4+2r=6+2r[/tex]
[tex]\\ \sf \longmapsto 2r-2r=6-4[/tex]
[tex]\\ \sf \longmapsto 0=2[/tex]
[tex]\\ \sf \longmapsto r=\infty[/tex]
2:-
[tex]\\ \sf \longmapsto 1-3x=-6+7-2x-x[/tex]
[tex]\\ \sf \longmapsto 1-3x=1-3x[/tex]
[tex]\\ \sf \longmapsto 0=0[/tex]
[tex]\\ \sf \longmapsto x=\infty[/tex]
What is the sum of the three solutions (find the values for x, y, and z, then add the answers)? 2x + 3y − z = 5 x − 3y + 2z = −6 3x + y − 4z = −8 Show All Work !!
Answer:
x + y + z = 4
Step-by-step explanation:
Give equations are,
2x + 3y - z = 5 --------(1)
x - 3y + 2z = -6 --------(2)
3x + y - 4z = -8 --------(3)
By adding equations (1) and (2),
(2x + 3y - z) + (x - 3y + 2z) = 5 - 6
3x + z = -1 -------(4)
By multiplying equation (3) by 3, then by adding to equation (2)
(9x + 3y - 12z) + (x - 3y + 2z) = -24 - 6
10x - 10z = -30
x - z = -3 --------- (5)
By adding equation (4) and (5),
(3x + z) + (x - z) = -1 - 3
4x = -4
x = -1
From equation (5),
-1 - z = -3
z = 2
From equation (1),
2(-1) + 3y - 2 = 5
-2 + 3y - 2 = 5
3y = 5 + 4
y = 3
Therefore, x + y + z = -1 + 3 + 2
x + y + z = 4
PLEASE HELP ME WITH THIS QUESTION
Answer:
answer is 90°
Step-by-step explanation:
it's simple , these both angles are complementary so sum of both is 90°
I hope it helped:)
Answer:
see below
Step-by-step explanation:
58+32 = 90
The angles add to 90 degrees, so the angles are complementary
PLEASE HELP!!!
Find an equation for the straight line that passes through the point (2.3) and is parallel to
the line x = 4.
Answer:
Answer is x=1 inthe sentences
2 square5 + 5 square5
Answer:
=2^5+5^5
=32+3125
=3157
Look at this cube:
If the side lengths are doubled, then which of the following statements about its surface area will be true?
Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of wood, and accommodates 300 sailors. She receives a delivery of 4 tons of wood each day. The deliveries can continue for 100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?
-Khan Academy
Answer:Astrid needs 280 tons of wood
Step-by-step explanation:
Because:
1 ship requires 40 tons of wood=accomodates 300 sailors
We must:
2100, sailors needed to be accomodated
÷
300, sailors that can be accomodated by 1 ship that requires 40 tons of wood
=7 groups of 300 sailors that can be accomodated by 1 ship that requires 40 tons of wood.
So:
I ship that requires 40 tons of wood × the 7, groups = 280 tons of wood.
I hope this helps! Im sorry its too complicated.
Simplier:
2100 ÷ 300= 7
40 × 7= 280
Answer:
280 tons of wood or 10 ships
Step-by-step
khan academy
If SP = Rs 100 and CP = Rs 800 find profit %.
Answer:
c
Step-by-step explanation:
The graph of f(x)=sin(x) is transformed into a new function, g(x) , by stretching it vertically by a factor of 4 and shifting it 3 units down. What is the equation of the new function g(x) ?
Answer:
f(x) = 4sin(x) - 3
Step-by-step explanation:
- X, what is the value of (f - g)(2)?
Answer:
2
Step-by-step explanation:
because ther is in the picture
For a sample of eight bears, researchers measured the distances around the bears' chests and weighed the bears. Minitab was used to find that the value of the linear correlation coefficient is r=0.989. Using alph=0.05, determine if there is a linear correlation between chest size and weight. What proportion of the variation in weight can be explained by the linear relationship between weight and chest size?
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
Correlation Coefficient (r) = 0.989
alph=0.05
Number of observations (n) = 8
determine if there is a linear correlation between chest size and weight.
Yes, there exists a linear relationship between chest size and weight as the value of the correlation Coefficient exceeds the critical value.
What proportion of the variation in weight can be explained by the linear relationship between weight and chest size?
To determine the the proportion of variation in weight that can be explained by the linear regression line between weight and chest size, we need to obtain the Coefficient of determination(r^2) of the model.
r^2 = square of the correlation Coefficient
r^2 = 0.989^2 = 0.978121
Hence, about 0.978 (97.8%) of the variation in weight can be explained by the linear relationship between weight and chest size.
A. A polynomial of the 5th degree with a leading coefficient of 3 and a constant of 2.