The value of the height function h(-2) is 0.
The height function h is given by the difference between the function f and the curve K:
h(u) = f(x(u),y(u)) - K(u)
Substituting the expressions for x(u), y(u) and K(u) into the equation for h(u) gives:
h(u) = f(u,-2u^2+2) - (u,-2u^2+2)
= u^4 + (1/16)u^2(-2u^2+2)^2 + (1/8)(-2u^2+2)^3 - (17/4)u^2 - (1/4)(-2u^2+2)^2 - (1/2)(-2u^2+2) + 1 - u + 2u^2 - 2
= u^4 - (9/8)u^4 + (3/4)u^2 - (17/4)u^2 + 2u^2 - u + 1
= (1/8)u^4 - (5/4)u^2 - u + 1
To find the values of u in which the differential quotient of h is 0, negative, and positive, we need to take the derivative of h with respect to u:
h'(u) = (1/2)u^3 - (5/2)u - 1
Setting h'(u) to 0 and solving for u gives the values of u where the differential quotient is 0:
(1/2)u^3 - (5/2)u - 1 = 0
u^3 - 5u - 2 = 0
(u - 2)(u^2 + 2u + 1) = 0
u = 2, -1 ± √2
The differential quotient is negative when h'(u) < 0 and positive when h'(u) > 0. Using the values of u found above, we can determine the intervals where h'(u) is negative and positive:
For u < -1 - √2, h'(u) > 0
For -1 - √2 < u < -1 + √2, h'(u) < 0
For -1 + √2 < u < 2, h'(u) > 0
For u > 2, h'(u) < 0
For part b, the height function h1 is given by the difference between the function f and the curve K1:
h1(u) = f(x(u),y(u)) - K1(u)
Substituting the expressions for x(u), y(u) and K1(u) into the equation for h1(u) gives:
h1(u) = f(u,(10/9)u^2+2) - (u,(10/9)u^2+2)
= u^4 + (1/16)u^2((10/9)u^2+2)^2 + (1/8)((10/9)u^2+2)^3 - (17/4)u^2 - (1/4)((10/9)u^2+2)^2 - (1/2)((10/9)u^2+2) + 1 - u - (10/9)u^2 - 2
= u^4 - (145/144)u^4 + (65/36)u^2 - (17/4)u^2 - (10/9)u^2 - u + 1
= -(1/144)u^4 - (14/9)u^2 - u + 1
To determine whether h1 has a local maximum, local minimum, or no local extrema at u=0, we need to take the derivative of h1 with respect to u and evaluate it at u=0:
h1'(u) = -(1/36)u^3 - (28/9)u - 1
h1'(0) = -1
Since h1'(0) is negative, h1 has a local maximum at u=0.
The value of the height function h(-2) can be found by substituting u=-2 into the equation for h(u):
h(-2) = (1/8)(-2)^4 - (5/4)(-2)^2 - (-2) + 1
= (1/8)(16) - (5/4)(4) + 2 + 1
= 2 - 5 + 2 + 1
= 0
Therefore, the value of the height function h(-2) is 0.
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Find the surface area of the square pyramid using the net. Use the
template included if needed. Your response MUST include correct area
labeling.
8 in.
8 in.
5 in...
8 in.
5 in.
8 in.
1 point
Based on the information, we can infer that the surface area of the pyramid is: 105 inches²
How to find the surface area of the pyramids?To find the surface area of the pyramids we must perform the following procedure:
We must find the surface of each of the faces and the base.
height of the triangle faces = 8 inches.Base side length = 5 inches.8 * 5 / 2 = 20 inches²According to this procedure, each face of the pyramid measures 20 inches². Then we must multiply this value by the number of faces of the pyramid (4).
20 inches² * 4 = 80 inches²Base area = b * hBase area = 5 * 5Base area = 25 inches ²We must add the surfaces of the faces and the base.
25 inches² + 80 inches² = 105 inches²According to the above, the surface area of the pyramid would be 105 inches².
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what x-value makes the set of ratios equivalent
The following values of x, makes the set of ratios equivalent:
2: 3 = 6: 9
4: 7 = 24: 42
(6*2)12: 48 = 3: 12
12: 15 = 16: 20
What are ratios?The ratio can be used to determine how much of one item is contained in the other by comparing two sums of the same units. Ratios fall into two different groups.
Whereas the second is a part to whole ratio, the first is a part-to-part ratio. The part-to-part ratio demonstrates the link between two independent entities or organisations.
Now here in the 1st set:
2:3 = 6:x
Now, x = 6×3/2
⇒ x = 9
Similarly,
4:7=x:42
⇒ x = 24
The next ratio we have:
2x:48= 3:12
⇒ x = 6
Now, the last ratio,
12:15 = x:20
⇒ x = 16
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Karina is making a large table in the shape of a trapezoid, as shown. She needs to calculate the area of the table. She is making the longest side of the table twice as long as the table's width. Complete parts a and b below.
The number in the bottom box is 9 yd. The number in the top is 9 yd. The area of the table is 90 yd².
Describe Trapezoid?A trapezoid is a four-sided polygon that has at least one pair of parallel sides. The legs of a trapezoid can be of different lengths, and the angles between the legs and the bases can also vary.
The formula for finding the area of a trapezoid is:
Area = ((Base 1 + Base 2) x Height) / 2
where Base 1 and Base 2 are the lengths of the parallel sides of the trapezoid, and Height is the distance between the parallel sides.
There are several types of trapezoids, including:
Isosceles Trapezoid: An isosceles trapezoid has two parallel sides of equal length and two non-parallel sides of equal length. The angles between the legs and the bases are also equal.
Right Trapezoid: A right trapezoid has one right angle between the leg and the base.
Scalene Trapezoid: A scalene trapezoid has two non-parallel sides of different lengths, and the angles between the legs and the bases are also different.
Let the number in the bottom box=
7.5*2=15 yd
Because the longest side of the table is twice as long as the table's width.
So the number in top box is :
15-3-3=9 yd
Area=( 15 + 9 )* 7.5/2 = 12* 7.5 = 90 yd²
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The complete question is:
Adina makes 53112 per year and is looking to find a new apartment rental in her city. She searched online and found an apartment for 1500 per month. The recommendation is to budget between 25% and 30% of your monthly income for rent. Can Adina afford this apartment based upon the recommended interval? Explain.
( i have to show my work )
Activity Number of Participants Golfing 3(s-2) Snorkeling s Parasailing s+14 Surfing (1)/(2)(s+5)
The total number of participants in all the activities is represented by the expression 5.5s + 11.
The given information about the number of participants in each activity can be represented in the following table:
ActivityNumber of ParticipantsGolfing3(s-2)Snorkeling s Parasailings+14Surfing(1)/(2)(s+5)
To find the total number of participants in all the activities, we can add the number of participants in each activity:
Total number of participants = 3(s-2) + s + (s+14) + (1)/(2)(s+5)
Simplifying the expression gives:
Total number of participants = 5.5s + 11
Therefore, the total number of participants in all the activities is represented by the expression 5.5s + 11.
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The variable a is jointly proportional to b and c. If a=79 when b=6and c=3, what is the value of a when b=3 and c=7? Round your answer to two decimal places if necessary.
The value of a is 92.17 when b=3 and c=7.
What is jointly proportional ?Jointly proportional refers to a relationship between two or more variables in which all of the variables increase or decrease together in the same ratio. For example, if one variable doubles, the other variables double as well.
The variable a is jointly proportional to b and c, which means that a = k*b*c, where k is the constant of proportionality.
We can use the given values of a, b, and c to find the value of k:
79 = k*6*3
79 = 18k
k = 79/18
Now that we know the value of k, we can use it to find the value of a when b=3 and c=7:
a = k*b*c
a = (79/18)*3*7
a = 92.17
Therefore, the value of a when b=3 and c=7 is 92.17.
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Express the following as a linear combination of
u = (3, 1, 7), v = (1, -1, 6)
and w = (7, 5, 5).
(14,10,14)
To express (14, 10, 14) as a linear combination of u = (3, 1, 7), v = (1, -1, 6), and w = (7, 5, 5), we need to find values for a, b, and c such that:
(14, 10, 14) = a(3, 1, 7) + b(1, -1, 6) + c(7, 5, 5)
This can be written as a system of equations:
14 = 3a + b + 7c
10 = a - b + 5c
14 = 7a + 6b + 5c
We can solve this system of equations using any method we prefer, such as substitution or elimination. One possible solution is:
a = 1
b = 2
c = 1
Therefore, the linear combination of u, v, and w that gives us (14, 10, 14) is:
(14, 10, 14) = 1(3, 1, 7) + 2(1, -1, 6) + 1(7, 5, 5)
= (3, 1, 7) + (2, -2, 12) + (7, 5, 5)
= (14, 10, 14)
So, the linear combination is 1u + 2v + 1w.
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Help
Algebra 2 please help answer 17
The natural logarithm function is ln(p) = ln(100) - 0.35t
How to determine the natural logarithm functionFrom the question, we have the following parameters that can be used in our computation:
The table of values
The function can be represented as
p = ae^kt
Using the points on the table, we have
ae^(k * 0) = 100
So, we have
a = 100
This gives
p = 100e^kt
Using another point, we have
70.5y = 100e^(k * 1)
70.5y = 100e^k
So, we have
e^k = 0.705
Take the natural logarithm of both sides
k = ln(0.705)
k = -0.35
The function becomes
p = 100e^(-0.35t)
Take the natural logarithm of both sides
ln(p) = ln(100) - 0.35t
Hence, the function is ln(p) = ln(100) - 0.35t
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System of Equations
y = (x-2)² + 35
y = -2x + 15
been trying to figure this one out for hours, please help
The solution of the system of equations is ([2+9.48i]/2, 17+9.48i).
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
The given system of equations are y=(x-2)²+35 ----(i) and y=-2x+15 ----(ii).
Here, equation (i) = (ii)
(x-2)²+35= -2x+15
x²-4x+4+35= -2x+15
x²-4x+39= -2x+15
x²-4x+39+2x-15=0
x²-2x+24=0
x²-2x+24=0
By using quadratic formula, we get
x = [-b ± √(b² - 4ac)]/2a
x=[2±√((-2)² - 4×1×24)]/2×1
x=[2±√(-90)]/2
x=[2±9.48i]/2
Here, x=[2+9.48i]/2 and x=[2-9.48i]/2
So, y=2+9.48i+15=17+9.48i
Therefore, the solution of the system of equations is ([2+9.48i]/2, 17+9.48i).
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Need help on this question
A quadrilateral is called cyclic if its vertices lie on a circle. Show that opposite interior angles of a quadrilateral are supplementary if and only if the quadrilateral is cyclic. [Hint: Use the preceding problem and facts about circumcircles of triangles]
Opposite interior bof a quadrilateral are supplementary if and only if the quadrilateral is cyclic.
A quadrilateral is called cyclic if its vertices lie on a circle. This means that there is a circumcircle that passes through all four vertices of the quadrilateral. If opposite interior angles of a quadrilateral are supplementary, then the sum of these angles is 180 degrees. This means that the opposite angles of a cyclic quadrilateral are supplementary.
To prove this, let us consider a quadrilateral ABCD that is cyclic. Let O be the center of the circumcircle that passes through all four vertices of the quadrilateral.
Since the quadrilateral is cyclic, angle AOB and angle COD are both subtended by the same arc, and therefore they are equal. Similarly, angle BOC and angle DOA are both subtended by the same arc, and therefore they are equal.
Now, let us consider the sum of the opposite interior angles of the quadrilateral.
Angle A + angle C = angle AOB + angle BOC + angle COD + angle DOA = 2(angle AOB) + 2(angle BOC) = 2(180) = 360
Since the sum of the opposite interior angles of the quadrilateral is 360 degrees, this means that the opposite interior angles of the quadrilateral are supplementary.
Therefore, opposite interior angles of a quadrilateral are supplementary if and only if the quadrilateral is cyclic.
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What is the estimated quotient for 2 1/2 divided by 1 7/9
The estimated quotient of the given dividend 2 1 / 2 divided by the divisor 1 7/9 is equal to 1.41 ( round off up to the two decimals ).
Divisor = 1 7/9
Convert the divisor (mixed fraction ) into improper fraction,
1 7 /9
= [( 9× 1 ) + 7]/ 9
= 16/9
Dividend = 2 1 / 2
Convert the dividend (mixed fraction ) into improper fraction,
2 1 / 2
=[ ( 2 ×2 ) + 1] /2
= 5 /2
Divide the 5 / 2 by 16 /9 to get the estimated quotient ,
( 5 / 2 ) ÷ ( 16 / 9)
= ( 5 / 2 ) × ( 9 / 16 )
= ( 5 × 9 ) / ( 2 × 16 )
= 45 / 32
= 1.40625
= 1.41 ( round off up to the two decimals )
Therefore, the estimated quotient of the division is equal to 1.41( round off up to the two decimals ).
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The diameter of a circle is 32 cm. Find its area to the nearest whole number.
Answer:
804 cm^2
Step-by-step explanation:
The area of a circle is given by the formula:
A = πr^2
where r is the radius of the circle. Since we are given the diameter of the circle, which is 32 cm, we can find the radius by dividing the diameter by 2:
r = d/2 = 32/2 = 16 cm
Substituting this value into the formula for the area of a circle, we get:
A = πr^2 = π(16)^2 = 256π
To find the approximate value of this expression in square centimeters, we can use the approximation π ≈ 3.14. Therefore:
A ≈ 256(3.14) ≈ 804
Rounding this value to the nearest whole number, we get:
A ≈ 804
Therefore, the area of the circle to the nearest whole number is 804 square centimeters.
Find the missing variable and indicated
angle measure.
X =
S
R
(5x – 2)° | 82°
T
m
O
WILL
MARK THE FIRST PERSON WHO ANSWERS BRAINIEST JUST PLEASE ANSWER. ALSO 24 POINTS:)
Answer:
The missing variable "x" = 20
And the Angle measure = 98°
Step-by-step explanation:
Explaination is given in the picture...
Thank you!
Answer:
the angles are 82 degrees and 98 degrees (5(20) -2), and the missing variable (x) is 20.
Step-by-step explanation:
Let us first look at SL. SL is a straight line and has an angle measure of 180 degrees. Angle RTL is 82 degrees and splits SL into 2. The angle right next to RTL is RTS, which is (5x-2) degrees. Since all of SL adds to 180 degrees, this means that RTL and RTS will add up to 180 degrees, since they are in the middle of it.
82 + 5x-2 = 180
80 +5x = 180
5x = 100
x = 20
Therefore, the angles are 82 degrees and 98 degrees (5(20) -2), and the missing variable (x) is 20.
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PLEASE HELP! THIS IS MY LAST QUESTION, BUT I DON'T KNOW HOW TO DO IT!
The mass of a substance, which follows a continuous exponential growth model, is being studied in a lab. A sample increases continuously at a relative rate of 7% per day. Find the mass of the sample after six days if there were 552 grams of the substance present at the beginning of the study.
Do not round any intermediate computations, and round your answer to the nearest tenth.
Also, may you please explain how you got the answer, it would be very helpful because I don't understand how to solve this. Thank you!
Answer:
864.3
Step-by-step explanation:
Since the substance is increasing continuously at a relative rate of 7% per day, we can use the continuous exponential growth formula:
P(t) = P(0) * e^(rt)
where:
P(t) is the mass of the substance after "t" days
P(0) is the initial mass of the substance (552 grams in this case)
e is the mathematical constant e (approximately equal to 2.71828)
r is the relative growth rate (0.07 per day in this case)
Substituting the given values, we get:
P(t) = 552 * e^(0.07t)
To find the mass after 6 days, we can substitute t = 6:
P(6) = 552 * e^(0.07*6)
Using a calculator, we get:
P(6) ≈ 864.3 grams
Therefore, the mass of the substance after 6 days is approximately 864.3 grams rounded to the nearest tenth.
Suppose sin θ = - 3/5, sin ɸ = 20/29 Moreover, suppose θ is in Quadrant IV and ɸ is in Quadrant l. Find the following. sin(θ + ɸ) = ____ cos(θ + ɸ) = ____
sin(θ + ɸ) = 17/145 and cos(θ + ɸ) = 144/145.
Suppose sin θ = -3/5, sin ɸ = 20/29. Moreover, suppose θ is in Quadrant IV and ɸ is in Quadrant l. We can find sin(θ + ɸ) and cos(θ + ɸ) by using the following formulas: sin(θ + ɸ) = sin θ cos ɸ + cos θ sin ɸ and cos(θ + ɸ) = cos θ cos ɸ - sin θ sin ɸ.
First, we need to find cos θ and cos ɸ. Since θ is in Quadrant IV, cos θ is positive. We can use the Pythagorean identity, sin² θ + cos² θ = 1, to find cos θ:
cos² θ = 1 - sin² θ
cos² θ = 1 - (-3/5)²
cos² θ = 1 - 9/25
cos² θ = 16/25
cos θ = √(16/25)
cos θ = 4/5
Similarly, since ɸ is in Quadrant l, cos ɸ is also positive. We can use the Pythagorean identity to find cos ɸ:
cos² ɸ = 1 - sin² ɸ
cos² ɸ = 1 - (20/29)²
cos² ɸ = 1 - 400/841
cos² ɸ = 441/841
cos ɸ = √(441/841)
cos ɸ = 21/29
Now we can plug in the values of sin θ, sin ɸ, cos θ, and cos ɸ into the formulas for sin(θ + ɸ) and cos(θ + ɸ):
sin(θ + ɸ) = sin θ cos ɸ + cos θ sin ɸ
sin(θ + ɸ) = (-3/5)(21/29) + (4/5)(20/29)
sin(θ + ɸ) = -63/145 + 80/145
sin(θ + ɸ) = 17/145
cos(θ + ɸ) = cos θ cos ɸ - sin θ sin ɸ
cos(θ + ɸ) = (4/5)(21/29) - (-3/5)(20/29)
cos(θ + ɸ) = 84/145 + 60/145
cos(θ + ɸ) = 144/145
Therefore, sin(θ + ɸ) = 17/145 and cos(θ + ɸ) = 144/145.
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Use P=PV(i1−(1+i)−n)
to determine the monthly payment for a $60,000 loan compounded monthly for 5 years at a 4.0%.
Answer:
$1,111.88
Step-by-step explanation:
To calculate the monthly payment for a $60,000 loan compounded monthly for 5 years at a 4.0% interest rate, we can use the formula:
P = PV(i / (1 - (1 + i)^(-n)))
where:
P = monthly payment
PV = present value or loan amount
i = interest rate per period
n = total number of periods
In this case, the loan amount is $60,000, the interest rate per period is 4.0% / 12 = 0.00333, and the total number of periods is 5 years x 12 months/year = 60 months.
Substituting these values into the formula, we get:
P = 60000(0.00333 / (1 - (1 + 0.00333)^(-60)))
P = $1,111.88 (rounded to the nearest cent)
Therefore, the monthly payment for a $60,000 loan compounded monthly for 5 years at a 4.0% interest rate is $1,111.88.
A person places $741 in an investment account earning an annual rate of 5.8%, compounded continuously. Using the formula =V=Pe^rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 13 years.
again yea im putting my hw here
Step-by-step explanation:
Using the formula V = Pe^(rt), we have:
P = $741
r = 0.058 (since the interest rate is 5.8%)
t = 13
So, V = 741e^(0.05813) = $1613.87 (rounded to the nearest cent)
Therefore, the amount of money in the account after 13 years is $1613.87.
Answer:
Step-by-step explanation:
Question of the Day: ACT Math Find the mode of the following set of numbers. 2,5,6,8,9,11,15
The mode of the set {2, 5, 6, 8, 9, 11, 15} is the number that appears most frequently in the set. In this case, all of the numbers appear only once, so there is no mode.
The mode of a set of numbers is the value that appears most frequently in the set. To find the mode of the set {2, 5, 6, 8, 9, 11, 15}, we need to count how many times each number appears and then determine which number appears most frequently.
From the set, we can see that no number appears more than once. Therefore, there is no single number that appears most frequently and we cannot determine a mode for this set.
In some cases, a set of numbers may have multiple modes if two or more numbers appear with the same frequency. For example, the set {1, 2, 2, 3, 3, 3, 4, 5, 5} has two modes, 2 and 3, since both of these numbers appear three times in the set.
However, in the case of the set {2, 5, 6, 8, 9, 11, 15}, there are no repeating numbers, so there is no mode.
In conclusion, the mode of the set {2, 5, 6, 8, 9, 11, 15} is undefined as there are no repeating numbers in the set.
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Find the measure of bfg
Answer:
33 degrees
Step-by-step explanation:
Angles BFG + GFC = 90
5r +68 + 8r +113 =90
1
Collect like terms
13r + 181 = 90
Subract 181 from both sides
13r = 90-181
13r = - 91
r = - 7
Now insert the value of r into BFG (5r +68)
5r + 68 = 5(-7) +68
= -35 + 68
=33
Check your answer by inserting the value of r into 8r +113
8r + 113 =8(-7) +113
-56+113= 57
The two angles 33 and 57 must add up to 90, a rt angle
Lucky Duck
What is the probability you will choose each duck described below?
Write the answer as a fraction in lowest terms and place it in the appropriate
box (certain, likely, unlikely, impossible).
The ducks are
numbered from one
through twelve!
Even Unlikely Impossible
The answer response are:
A duck with wings: Likely Duck number 7: Unlikely A duck with a number greater than 3: Certain Duck number 15: Impossible A duck with a number greater than 10: Unlikely A duck with a number: Certain Duck number 4: Likely A duck with sunglasses: Impossible A duck with a hat: Unlikely An even-numbered duck: LikelyHow do you explain the probability?A duck with wings: Likely
There is a high likelihood that all the ducks have wings since it is a natural characteristic of ducks.Duck number 7: Unlikely
There are 12 ducks in total, and only one of them is duck number 7, so the probability of choosing duck number 7 is 1/12, which is unlikely.A duck with a number greater than 3: Certain
There are 9 ducks with numbers greater than 3 (4, 5, 6, 7, 8, 9, 10, 11, 12), so it is certain that you will choose a duck with a number greater than 3.Duck number 15: Impossible
There are only 12 ducks, and none of them are numbered 15, so it is impossible to choose duck number 15.A duck with a number greater than 10: Unlikely
Only two ducks have numbers greater than 10 (11, 12), so the probability of choosing a duck with a number greater than 10 is 2/12 or 1/6, which is unlikely.A duck with a number: Certain
All ducks have numbers from 1 to 12, so it is certain that you will choose a duck with a number.Duck number 4: Unlikely
There is only one duck numbered 4, so the probability of choosing duck number 4 is 1/12, which is unlikely.A duck with sunglasses: Impossible
There is no information given that any of the ducks have sunglasses, so it is impossible to choose a duck with sunglasses.A duck with a hat: Unlikely
There is no information given that any of the ducks have hats, so the probability of choosing a duck with a hat is unlikely.Lastly, An even-numbered duck: Likely
There are six even-numbered ducks (2, 4, 6, 8, 10, 12), so the probability of choosing an even-numbered duck is 6/12 or 1/2, which is likely.Learn more about probability here:
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See transcribed text below
Date:
Period:
What is the probability you will choose each duck described below? Write the answer as a fraction in lowest terms and place it in the appropriate box (certain, likely, unlikely, impossible).
33
1. A duck with wings
2. duck number 7
3. a duck with a number greater than 3
4. duck number 15
5. a duck with a number greater than 10
6. a duck with a number
7. duck number 4
8. a duck with sunglasses
9. a duck with a hat
10. an even-numbered duck
The ducks are numbered From one through twelve!
Kibb
Certain
Likely
Even
Unlikely Impossible
ว
Can someone help please
Answer:
10.39; 6
Step-by-step explanation:
Horizontal component= |v| Cos theta = 12 Cos 60° = 6
Vertical component= |v| Sin theta = 12 Sin 60° = 10.39
Intense trig problem.
The answer is [5sqrt(6)] / (12).
How do I get there?
Using the definition of the tangent function, we will get that:
5√(6)/12 = sin(θ)
How to find the sine of theta?Here you need to remember how the tangent function is defined, we know that:
tan(θ) = sin(θ)/cos(θ)
Here we know that:
tan(θ) = √15/3
cos(θ) = √10/4
Replacing that we can write:
√15/3 = sin(θ)*(4/√10)
Solving for the sine, we will get:
(√15/3)*(√10/4) = sin(θ)
(√15*√10)/(3*4) = sin(θ)
(√150)/(12) = sin(θ)
(√(25*6))/(12) = sin(θ)
5√(6)/12 = sin(θ)
That is the answer.
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¿Cual es la presión total que es perité ya un pez en su superficie si se encuentra a una profundidad de 10 m? La densidad del agua es de 1025kg/m3
So the total pressure experienced by the fish on the surface is 100450 Pa.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.
Here,
When an object is submerged in a fluid, it experiences pressure due to the weight of the fluid above it. This pressure is called hydrostatic pressure, and it increases with depth. The formula to calculate hydrostatic pressure is:
P = ρgh
where P is the hydrostatic pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth of the object below the surface.
In this case, the fish is at a depth of 10m, so h = 10m. The density of water is given as 1025kg/m3, and the acceleration due to gravity is approximately 9.8m/s2. Therefore, the hydrostatic pressure experienced by the fish is:
P = (1025 kg/m3) x (9.8 m/s2) x (10 m)
= 100450 Pa
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Complete question:
"What is the total pressure experienced by a fish on the surface if it is at a depth of 10m? The density of water is 1025kg/m3"
19. A ball is dropped from a height of 30 feet. At the same time, a ball is thrown straight into the air from a height of 5 feet with an initial velocity of 20 feet per second. The polynomials -16t2 + 30 and -16t2 + 20t + 5 represent the heights (in feet) of the balls after t seconds.
a. Write a polynomial that represents the distance between the heights of the balls after t seconds.
b. Interpret any coefficients and constants of the polynomial in part (a.)
A polynomial that represents the distance between the heights of the balls after t seconds. Time t =15/20=0.75 seconds
a. Change of speed versus acceleration and time:
v = u + at
20 = -16t2 + 30 +16t2 + 20t + 5
20= 20t + 35
20t=35-20=15
b. We now interpret this polynomial as follows:Δh(t)=[tex]h_{0} -u_{y} t[/tex]
This shows how far apart the two balls are at time t. The two terms can be interpreted as follows: The initial separation between the two balls at time t=0 is represented by the constant term, h0 (in fact, the first ball is still at the top of the building, while the second ball is on the ground). For this issue[tex]h_{0} =30 feet.[/tex] The second ball's initial velocity, which serves as the coefficient of the linear term, [tex]u_{y}[/tex]tells us that the gap between the two balls closes by [tex]u_{y}[/tex] feet every second.
Time t =15/20=0.75 seconds. Time is the continuous pattern of existence and the events that take place in what appears to be an unbroken progression from the past through the present and into the future. It is a component number of various measurements that are used to compare the lengths of events or the pauses between them, to compare the order in which they occur, and to gauge the rates at which certain quantities in the physical world or in conscious experience change.
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\( \left[\begin{array}{cc}1 & -1 \\ -2 & 2 \\ 2 & -2\end{array}\right] \)
\( \begin{array}{l}\frac{1}{\sqrt{3}}\left[\begin{array}{cc}1 & -1 \\ 1 & 1\end{array}\right] \\ \frac{1}{\sqrt{2}}\left[\beg
The orthonormal basis for this matrix.
To find the orthonormal basis for the given matrix, you will need to begin by taking the right and left singular vectors of the matrix.
The right singular vector for this matrix is 3(1 -1 1 1).
The left singular vector for this matrix is 2(-2 2 2 -2).
Now, divide each vector by its length to make them unit vectors, and you will get the orthonormal basis for the given matrix.
The orthonormal basis for this matrix is 1/3(1 -1 1 1) 1/2(-2 2 2 -2).
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Two weather stations are aware of a thunderstorm located at point c. The weather stations A and B are 34 miles apart. How far is weather station A from the storm?
The distance between weather station A and the storm is [tex]\sqrt{(34^2 + 34^2)}[/tex], which is 48.48 miles, which can be calculated using the Pythagorean theorem.
What is the Pythagorean theorem?The Pythagorean Theorem is an equation in geometry which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In other words, a2 + b2 = c2, where a and b are the two legs of the triangle and c is the hypotenuse.
Weather station A is 34 miles away from the thunderstorm located at point c. To measure the distance between weather station A and the storm, we must calculate the hypotenuse of a right triangle. The right triangle is formed by the two points of the storm and weather station A, with the 34 miles between them forming the base of the triangle. The hypotenuse of the triangle is the distance between the two points, which can be calculated using the Pythagorean theorem. The equation for the Pythagorean theorem is a² + b²= c², where a and b are the sides of the triangle, and c is the hypotenuse.
Therefore, the distance between weather station A and the storm is [tex]\sqrt{(34^2 + 34^2)}[/tex], which is 48.48 miles.
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5(y+25)=−13
y = ??
Please answer this if you can!!
Answer:
y = - 125/18
Step-by-step explanation:
okay so here what i got when i was doing the equation
5 ( y + 25) = - 13y
5 y + 125 = - 13y
then you subtract 125 from both sides
subtract the numbers
and my solution was y = - 125 / 18 trust me!
Hope that helped
a library has fiction and nonfiction books. The ration of the number of fiction books to the total number of books is 5:8. What is the ratio of the fiction to the nonfiction books in the library?
The ratio of fiction books to nonfiction books in the library is 5:3.
What are Ratios?
A ratio is a comparison of two or more quantities that have the same units or are of the same kind. It is expressed as a fraction, using a colon or as a quotient of the two quantities.
Let the number of fiction books in the library be 5x and the total number of books be 8x (since the ratio of fiction books to total books is 5:8).
Then, the number of nonfiction books in the library is 8x - 5x = 3x.
Therefore, the ratio of fiction books to nonfiction books in the library is 5x : 3x, which simplifies to:
5x/3x = 5/3
So, the ratio of fiction books to nonfiction books in the library is 5:3.
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5-6 MathXL for School: Practice and Application Cop Solve the equation by factoring. v^(2)-2v+1=0
The equation v^(2)-2v+1=0 can be solved by factoring. Factoring is a process of breaking down a number or expression into its component parts. In this case, we can factor the equation into (v-1)(v-1), which is equal to zero. Therefore, the solution to the equation is v = 1.
Factoring is a useful tool for solving equations. By factoring, we can break a complex equation into simpler parts, which makes it easier to solve. It can also be used to identify solutions that are not obvious by looking at the equation. It is a valuable skill to have in mathematics, as it can be used to solve many equations quickly and efficiently. It is also an important skill to have when working with polynomials, as it allows us to identify the zeros of a polynomial.
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