Answer:
Exact answer = 10.41666666666666666666666666666pi
Estimated answer = 32.70938
Step-by-step explanation:
Semi circle formula: 1/2 * 4/3 * pi * r^3
r = 2.5
1/2 * 4/3 * pi * 2.5^3
2/3 * pi * 2.5^3
2/3 * pi * 15.625
10.416..... * pi
Exact answer = 10.417pi
We can estimate pi as 3.14
So, 10.417 * 3.14 = 32.70938
Exact answer = 10.41666666666666666666666666666pi
Estimated answer = 32.70938
1. Determine the set of each of the following equations for 0° ≤ x 360° or 0° ≤ t ≤ 360°
a) sin 2 x°= 1/2√2
2. find all the solution in the interval 0° ≤ z ≤ 360° of the following equation
sin 3 z = - 0,42
Please help Me
SOS
Answer:
a).
[tex] \sin(2x) = \frac{1}{2 \sqrt{2} } \\ \\ 2x = { \sin }^{ - 1} ( \frac{1}{2 \sqrt{2} } ) \\ \\ 2x = 45 \degree[/tex]
since sine is in the 2nd quadrant, other angle = 180° - x:
[tex]2x = 45 \degree, \: 135 \degree[/tex]
we must make two rotations since it's a double angle:
[tex]2x = 45 \degree, \: 135\degree, \: 225\degree, \: 315\degree, \: 495\degree, \: 675\degree \\ [/tex]
divide each angle by 2:
[tex]x = 22.5\degree, \: 67.5\degree, \: 112.5\degree, \: 157.5\degree, \: 247.5\degree, \: 337.5\degree \\ [/tex]
Answer = {x: x = 22.5°, 67.5°, 112.5°, 157.5°, 247.5, 337.5°}
b).
[tex] \sin(3z) = - 0.42 \\ 3z = { \sin }^{ - 1} ( - 0.42) [/tex]
since ans is negative, we take the quadrants of cosine and tangent:
[tex]3z = 204.8\degree, \: 335.2\degree [/tex]
we make three rotations:
[tex]3z = 384.8\degree, \: 515.2\degree, \: 695.2\degree, \: 875.2\degree, \: 1055.2\degree, \\ [/tex]
answer is {z : z = 128.3°, 171.7°, 231.7°, 291.7°, 351.7°}
PLZ HELP ME ASAP PLZZ
Answer:
helloo thereeee
we do such construction from a making bc arc then from b and c making x just when we need to make
Angle bisector
hope that helps ig :)
Function f is graphed. According to the graph, is f even, odd, or neither?
Answer:
C
Step-by-step explanation:
f is neither even nor odd
Last night, the two dinner specials at Will's favourite restaurant were salmon fillet and steak. The restaurant served 15 salmon fillets and 5 steaks. What percentage of the specials served were salmon fillets?
Answer:
75% of the specials served were salmon fillets
Step-by-step explanation:
We have that:
15 + 5 = 20 specials were served.
Of those, 5 were salmon fillets.
What percentage of the specials served were salmon fillets?
15*100%/20 = 75%
75% of the specials served were salmon fillets
show that's ABE = EBC
Answer:
abe = ebc
Step-by-step explanation:
bcos both the seperate angels have the same degree
find the probability of picking a red marble and a green marble when 2 marbles are picked (without replacement)from a bag containing 6 red and 6 green marbles.}
p = 6/11.
So we have a bag that contains 6 red marbles and 6 green marbles.
Then the total number of marbles that are in that bag is:
6 + 6 = 12
There are 12 marbles in the bag, and we assume that all marbles have the same probability of being randomly drawn.
Now we draw two marbles, we want to find the probability that one is red and the other is green.
The first marble that we draw does not matter, as we just want the second marble to be of the other color.
So, suppose we draw a green one in the first attempt.
Then in the second draw, we need to get a red one.
The probability of drawing a red one will be equal to the quotient between the red marbles in the bag (6) and the total number of marbles in the bag (12 - 1 = 11, because one green marble was drawn already)
Then the probability is:
p = 6/11.
Notice that would be the exact same case if the first marble was red.
Then we can conclude that the probability of getting two marbles of different colors is:
p = 6/11.
Write down all the prime numbers between 20 and 70
Answer:
23,29,31,37,41,43,47,53,59,61 and 67.
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Answer:
23, 29, 31, 37, 41, 43, 47, 53, 61, 67
Step-by-step explanation:
Im not entirely sure but I believe I'm correct here.
Please answer this!!
Answer:
BC = 6.8
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta =opp /adj
tan C = AB / BC
tan 45 = 6.8/ BC
BC = 6.8 / tan 45
BC = 6.8 / 1
BC = 6.8
Answer: Choice D. 6.8
Step-by-step explanation:
45,45,90 triangles, memorize that the short sides are equal to each other in length and are [tex]\frac{1}{\sqrt{2} }[/tex] the length of the long side.
If a ray bisects a right angle, then each newly formed angle measures 45 degrees.
A) Sometimes
B) Always
C) Never
Answer:
Always
Step-by-step explanation:
Bisects means to divide in half
90/2 = 45
So the angles are each 45 degrees
GH bisects LM at K. LK = 5x+2 and LM = 64 Find x
Answer:
x = 6
Step-by-step explanation:
Since GH bisects LM at K , then
LK = [tex]\frac{1}{2}[/tex] LM , that is
5x + 2 = [tex]\frac{1}{2}[/tex] × 64 = 32 ( subtract 2 from both sides )
5x = 30 ( divide both sides by 5 )
x = 6
The value of x is 6.
Here,
GH bisects LM at K.
LK = 5x+2 and LM = 64
We have to find the value of x.
What is Bisection in line?
Bisecting a line is cutting a line exactly in half. It may also be referred to as constructing a perpendicular bisector as the line you are drawing will be at a right angle to the original line.
Now,
GH bisects LM at K.
LK + KM = LM
2 LK = LM
2 ( 5x + 2 ) = 64
5x + 2 = 32
5x = 30
x = 6
Hence, The value of x is 6.
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Find the missing probability of 3
v2 = u? + 2as
u = 12
a = -3
S =
= 18
(a) Work out a value of v.
Answer:
6√7 m/s
Step-by-step explanation:
Given,
u = 12
a = - 3
s = 18
v^2 = u^2 - 2as
= 12^2 - 2 ( - 3 ) ( 18 )
= 144 + 108
v^2 = 252
v = √252
v = 6√7 m/s
Step-by-step explanation:
hope it helps you...:)....
What is the area of the triangle in the diagram?
Answer:
l think the answer is =C for this area of triangle
If all the books on a shelf with fewer than 45 books were put into piles of five books each, no books would remain. If the same book were put into piles of seven books each, two books would remain. What is the greatest number of books that could be on the shelf?
Answer:
Hence the greatest number of books that could be on the shelf is 30.
Step-by-step explanation:
Step 1:-
Here the given number of books is m,
m < 45.
If they are arranged into piles of five books, each no books would remain.
m is divisible by 5.
The last digit of m would be 5 or 0.
The same number of books, when arranged with piles of 7 books each, two books remain.
m-2 is divisible by 7.
Step 2:-
The last digit of m is 5 or 0.
m-2 will have the last digit 3 or 8.
Multiples of 7 are 7,14,21,28,35, 42;
among which only number 28 has the last digit 8 or 3.
m - 2 = 28
m = 30
The greatest number of books that could be on the shelf is 30.
Geometry - Triangle d) In the given figure, BE = EC and CE is the bisector of ZACB. Prove that ZBEC = ZACD. E B D С
Answer:
Let m∠BCE = x
Then m∠ACE = x as well since CE is bisecting ∠ACB.
m∠ACD + x + x = 180° ⇒ m∠ACD = 180° - 2xConsider ΔBEC
Since BE = EC, the opposite angles are congruent:
∠BCE ≅ ∠CBEThen:
m∠CBE = m∠BCE = xFind the angle BEC:
m∠BEC = 180° - (x + x) = 180° - 2xComparing the above we see that:
m∠BEC = m∠ACDprovedAt one sitting, a typical doughnut eater consumes 4 doughnuts containing a total of 680 calories and 40 grams of fat. The typical bagel eater consumes exactly one bagel, at 500 calories and one or two grams of fat per sitting, though the addition of spreads can raise calorie and fat content to the four-doughnut range. Thus, as far as total calorie content is concerned, there is very little difference between what a typical doughnut eater and a typical bagel eater each consumes at one sitting.
The argument depends on assuming which one of the following?
(A) The calories and fat in bagels have the same health impact on bagel eaters as the calories and fat in doughnuts have on doughnut eaters.
(B) Most bagel eaters are not fully aware of the calorie and fat content of a bagel.
(C) Eating bagels instead of eating doughnuts provides no real health benefit.
(D) The typical doughnut eater does not add to doughnuts any substances that increase the total caloric intake.
(E) Most typical doughnut eaters are not also bagel eaters.
Answer:
C. Eating bagels instead of eating doughnuts provides no real health benefits.
Step-by-step explanation:
There is no such difference in health benefit due to eating bagels or doughnuts. The bagel eaters are not necessarily doughnut eaters. The calories in bagels is 500 cal per bagel while the calories in doughnuts is 680cal for every 4 doughnuts intake.
3.Find the area of Triangle and Parallelogram having base 13.5cm and height is 18cm.
[tex]\\ \sf\longmapsto Area=\dfrac{1}{2}Base\times Height[/tex]
[tex]\\ \sf\longmapsto Area=\dfrac{1}{2}(18)(13.5)[/tex]
[tex]\\ \sf\longmapsto Area=9(13.5)[/tex]
[tex]\\ \sf\longmapsto Area=121.5cm^2[/tex]
What is the equation of the line that passes through the points (–12, –8) and (–17, –16)?
Answer:
firstly find the gradient given by the equation
m=y2-y1/x2-x1
in this case x1 is -12,x2 is -17, y1 is -8 and y2 is-16
m=-16+8/-17+12
=-8/-5 or1.6
then use the equation
y-y1=m(x-x1)
y+8=1.6(x+12)
y+8=1.6x+19.2
y=1.6x+11.2
I hope this helps and sorry if it's wrong
What is the completely factored form of the expression 16x2 + 8x + 32?
4(4x2 + 2x + 8)
4(12x2 + 4x + 28)
8(2x2 + x + 4)
8x(8x2 + x + 24)
(IM ON EDGE)
A is the answer to your question
To solve this, just distribute the 4 to each of the coefficient and see if it would result in the same coefficients in the original expression
the Marked price of a book is rupees 500 if 30% discount is all over there in a loss of rupees hundred is made what is the cost price of the book
Answer:
cost price of book is Rs. 570
The function f(c)=95c+32 is used to convert temperatures from Celsius, c, to Fahrenheit, f(c). What is the temperature in Fahrenheit when it is 22° Celsius? Round your answer to the nearest integer. A 40° B 54° C 72° D 97°
C 72°
Answer:
we have
f(c)=9/5C+32
now
22°C to °F
°C=22°
we have
f(c)=9/5C+32
f(c)=9/5*22+32=71.6≈72
answer is
22°C=72°F
Answer: [tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd\displaystyle\ \Large \boldsymbol{72^\circ F}[/tex]
Step-by-step explanation:
[tex]\displaystyle\ \Large \boldsymbol{} f(c)=\frac{9}{5} c+32 \ \ in \ \ our \ \ case \\\\\\\\f(22)=\frac{9\cdot 22}{5} +32=39,6+32=7\underline1,6\approx72^\circ F[/tex]
If -10x = 5 what is the value of x
Answer:
x = -1/2
Step-by-step explanation:
-10x = 5
Divide both sides by -10.
x = -1/2
Instructions: Find the value of the trigonometric ratio. Make sure to
simplify the fraction if needed.
С
32
40
B
24
A
Tan C =
Answer:
tanC will be given by the opposite over the adjacent
tanC=24/32
simplified to 6/8
I hope this helps
find the value (2x +3,y-1=5,3)
Answer:
(5,3)
Step-by-step explanation:
Evaluate (2x+3,y-1=5,3)
Then you will get 5,3
So then your answer will be (5,3)
Heres your answer! Enjoy :D
Answer:
x = 1, y = 4
Step-by-step explanation:
Equating the corresponding coordinates
2x + 3 = 5 ( subtract 3 from both sides )
2x = 2 ( divide both sides by 2 )
x = 1
and
y - 1 = 3 ( add 1 to both sides )
y = 4
If m = 8 and n = 5, then m(n + 3) – n + 1 =
a. 60
b. 58
c. 39
d. 32
simplify : 3p+2p+8-3=15
Answer:
3p+2p+8-3=15
5p+5=15
5p=15-5
5p=10
p=10/5
p=2
have a great dayy.
Answer:
p = 2
Step-by-step explanation:
One is given the following equation:
3p + 2p + 8 - 3 = 15
Combine like terms. In essence, if two number have the same variable, then one can perform operations between their coefficients. If two number have no variables, then these two terms are also like terms. After combing like terms, simplify the expression.
3p + 2p + 8 - 3 = 15
5p + 8 - 3 = 15
5p + 5 = 15
Inverse operations,
5p + 5 = 15
5p = 10
p = 2
A shop owner made a loss of 12% when he sold an item for $264. What was the cost price of the item?.
One of the factors of x² + y² + 2xy - z² is ?
Answer:
x + y + z.
Step-by-step explanation:
x² + y² + 2xy - z²
= (x + y)^2 - z^2
This is the difference between 2 squares so the factors are:
(x + y + z) and (a + y - z).
Answer: The factors are (x+y+z) and (x+y-z)
In other words, it factors to (x+y+z)*(x+y-z)
=====================================================
Work Shown:
[tex]x^2 + y^2 + 2xy - z^2\\\\(x^2 + 2xy + y^2) - z^2\\\\(x+y)^2 - z^2\\\\(x+y+z)(x+y-z)\\\\[/tex]
Notes:
In the third step, I used the rule (A+B)^2 = A^2+2AB+B^2. For this, A = x and B = y.In the last step, I used the difference of squares factoring rule A^2-B^2 = (A+B)(A-B). In this case, A = x+y and B = z.Staff
Americans eat 7 billion hot dogs between Memorial Day and Labor Day. If all these hot dogs were laid end to end they
would circle the earth 21.5 times. If the circumference of the Earth is approximately 24,860 miles, and one mile is
5,280 feet, find the length (in inches) of each hot dog. (Round your answer to the nearest tenth)
Answer:
The length of each hot dog is 0.5000 inches.
Step-by-step explanation:
Total number of hot dogs eaten = 7 000 000 000
Circumference of the earth = 24 860 miles
21.5 times the circumference of the Earth = 21.5 x 24 860 miles
= 534490 miles
But,
1 mile = 5280 feet
So that,
534490 miles = X
X = 5280 x 534490
= 287707200 feet
Also,
1 feet = 12 inches
Then,
287707200 feet = Y
Y = 12 x 287707200
= 3452486400 inches
Thus,
the length of each hot dog = [tex]\frac{3452486400}{7000000000}[/tex]
= 0.4932
The length of each hot dog is 0.5000 inches.
The Master Chief collects spiders and starfish. If his spiders have 8 legs and his starfish have 5 legs, how many starfish must he have, given that his spider/starfish collection totals 19 creatures and 116 legs
Answer:
12 starfish
Step-by-step explanation:
Create a system of equations where x is the number of starfish he has and y is the number of spiders he has:
x + y = 19
5x + 8y = 116
Solve by elimination by multiplying the top equation by -8:
-8x - 8y = -152
5x + 8y = 116
Add these together and solve for x:
-3x = -36
x = 12
So, he has 12 starfish.
The total number of starfish is 12 starfishes
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of starfish be = x
Let the number of spiders be = y
The number of legs for spiders = 8
The number of legs for starfish = 5
So , the equation will be
The total number of legs for x starfish = 5x
The total number of legs for y spiders = 8y
The total number of creatures = 19
So , x + y = 19 be equation (1)
And ,
The total number of legs = 116
So , 5x + 8y = 116 be equation (2)
Now , from equation (1) , x = 19 - y
Substituting the value of equation (1) in equation (2) , we get
5x + 8y = 116
5 ( 19 - y ) + 8y = 116
95 - 5y + 8y = 116
95 + 3y = 116
Subtracting 95 on both sides , we get
3y = 21
Divide by 3 on both sides , we get
y = 7
So , the number of spiders is 7 spiders
Substituting the value of y in equation (1) , we get
x + y = 19
x + 7 = 19
Subtract 7 on both sides , we get
x = 12
Therefore , the value of x is 12
Hence , The total number of starfish is 12 starfishes
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