What is the change of base property?
Answers
The change of base property is a formula that makes it possible to express a logarithm in terms of logs expressed in a different base.
It is possible to express a logarithm in terms of logs stated in a different base using the change of base property formula. This is especially useful when evaluating a log to a base other than 10 or e using a calculator. X, a, and b are all taken to be positive. The base change property can be used to simplify equations with different bases for the logarithmic terms. All the logarithmic terms of an equation with logarithmic functions should have the same base in order to be solved.
Examples given below:
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Related Questions
A chemist has three different acid solutions. the first acid solution contains 20 % acid, the second contains 30 % and the third contains 60 % . he wants to use all three solutions to obtain a mixture of 54 liters containing 45 % acid, using 2 times as much of the 60 % solution as the 30 % solution. how many liters of each solution should be used? the chemist should use liters of 20 % solution, liters of 30 % solution, and liters of 60 % solution.
Answers
Let [tex]a,b,c[/tex] denote the amounts (in liters) of the 20%, 30%, and 60% acid solutions, respectively. These quantities then contain [tex]0.20a[/tex], [tex]0.30b[/tex], and [tex]0.60c[/tex] liters of acid.
The chemist wants to end up with a total volume of 54 liters, so
[tex]a + b + c = 54[/tex]
and a concentration of 45% acid. This comes out to 0.45×54 = 24.3 total liters of acid, so
[tex]0.20a + 0.30b + 0.60c = 24.3[/tex]
He will also use twice as much of the 60% solution as the 30% solution, so
[tex]c = 2b[/tex]
Substitute this into the first two equations and solve for [tex]a,b[/tex].
[tex]\begin{cases} a + 3b = 54 \\ 0.20a + 1.50b = 24.3 \end{cases}[/tex]
Eliminating [tex]b[/tex], we have
[tex](a + 3b) - 2 (0.20a + 1.50b) = 54 - 2(24.3) \implies 0.60a = 5.4 \implies \boxed{a = 9}[/tex]
Solve for [tex]b[/tex].
[tex]9+3b=54 \implies 3b=45 \implies \boxed{b=15}[/tex]
Solve for [tex]c[/tex].
[tex]c = 2(15) \implies \boxed{c=30}[/tex]
a = 9, b = 15 and c = 30 liters of each solution should be used.
What liter means?According to the metric system, a liter is a unit for measuring volume. A bottle of Coke that holds 33.76 ounces, or 1.0567 quarters, is an example of a liter. 2. The fundamental metric unit of liquid volume or capacity, which is equivalent to 1.06 quarts or 2.12 pints.What is a liter of water?Let's examine this with the help of the following justification. Despite the fact that there is no established standard size for glasses, their capacity varies. In contrast, we estimate that a glass of water holds 8 ounces, and a liter holds 32 ounces.According to the question:
Let a, b, and c stand for the relative volumes (in liters) of the 20 percent, 30 percent, and 60 percent acid solutions. The amount of acid in these amounts is 0.20a, 0.30b, and 0.60c liters.
a+b+c = 54 because the chemist wishes to have a final volume of 54 liters.
and a concentration of 45% acid. This comes out to 0.45×54 = 24.3 total liters of acid, so
0.20a + 0.30b + 0.60c = 24.3
Additionally, he will consume twice as much of the 60% solution as the 30% solution, thus c = 2b.
Substitute this into the first two equations and solve for a,b
a + 3b = 54
0.20a + 1.50b = 24.3
Eliminating b, we have[tex](a+3 b)-2(0.20 a+1.50 b)=54-2(24.3) \\0.60 a=5.4[/tex]
a = 9.
Solve for b.9+3b = 54
3b = 45
b = 15.
Solve for c.c = 2(15)
c = 30.
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Wayne is holding a can of juice that has a diameter of 4 inches. there is a price tag stuck to the side of the can. wayne places the can on its with side with the sticker on the bottom and rolls it across a table top at a constant speed. the can reaches wayne's friend at the other end of the table in 5 seconds and completes 4 full rotations. which function could represent the price tag's height relative to the table top, , after it has been rolling for t seconds?
Answers
The function that could represent the price tag's height relative to the table top is h(t) = 4sin (22) +4
Disclaimer!!The question is incomplete because the options are not given and hence the correct option is shown below
Which function could represent the price tag's height relative to the table top, h(t), after it has been rolling for e seconds?
A n(t) = 2008(832) +2
B. h(t) =-2005(522) +2
C h(t) = –2sin(572) +2
D. h(t) = 4sin (22) +4
Given diameter is 4 inches and the time given is 5 seconds and
the number of rotations given is 4
We need to find the function that could represent the price tag's height relative to the table top .
Diameter = 4
So, Radius will be D/2 = 4/2
Radius=2
time given is 5 seconds and
the number of rotations given is 4
So , 5/4 = 2π/w
Therefore ,
W = 8π / 5
Therefore
h(t) = h(t) = 4sin (22) +4
Hence The function that could represent the price tag's height relative to the table top is h(t) = 4sin (22) +4
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Which expression is equivalent to (x^6y^8)^3/x^2y^2
Answers
Answer:
x^7y^9
Step-by-step explanation:
Remembering the laws of indices and applying BODMAS
(x^6y^8)^3/x^2y^2
(x^6 * y^8)^3/x^2 * y^2
opening bracket
we get;
x^6+3 * y^8+3/x^2 * y^2
x^9 * y^11/x^2 * y^2
Applying law of indices at which when the values are the same during division we pick one coefficient and minus the power
therefore;
x^9-2 * y^11-2
x^7 * y^9
=x^7y^9
Computer geometric modeling is used regularly to help design solid figures we see and use every day. Software programs use techniques such as scaling and rotation to create solid figures that model objects. Research computer geometric modeling and then answer these questions. What basic shapes are used in modeling real-world objects? How are some of the concepts you learned in this unit related to computer geometric modeling? Why is creating a geometric model of something before producing it important?
Answers
The geometric modeling is analyzed below.
How to illustrate the information?Basic shapes are generally created using points, lines, circles, and triangles. Some basic shapes are rectangles, ellipses, triangles, and curves.
In geometric modeling, we make a cad model of parts for virtual analysis. By geometric modeling, one can model, and perform CAE analysis to optimize the product.
The best part is the period of doing all this is very small compared to practical manufacturing and looking at the product. In CAD one can very quickly alter the design and come up with new concepts in a very small span of time.
Here chances of error can be shorted easily and there is no wastage of material hence cost saving is there compared to practically manufacturing the part and altering it.
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Which function in vertex form is equivalent to f(x) = x² + x +1?
○ f(x) = (x + 1/ 1³² + 1 ²1/0
3
4
○ f(x) = (x + 1)² + 2/1/2
○ f(x) = (x + ²/2 1²³ + ²/
4
5
f(x) = (x + 1/2-1² + ²/1/2
4
Answers
Answer:
[tex]\left( x+\frac{1}{2} \right)^{2} + \frac{3}{4}[/tex]
Step-by-step explanation:
NOTE :
[tex]x^2+ax=\left( x+\frac{a}{2} \right)^{2} -\left( \frac{a}{2} \right)^{2}[/tex]
………………………………………
f(x) = x² + x +1
[tex]=x^{2}+2\times \frac{x}{2} +1[/tex]
[tex]=\left( x+\frac{1}{2} \right)^{2} -\left( \frac{1}{2} \right)^{2} +1[/tex]
[tex]=\left( x+\frac{1}{2} \right)^{2} - \frac{1}{4}+1[/tex]
[tex]=\left( x+\frac{1}{2} \right)^{2} + \frac{3}{4}[/tex]
Six pyramids are shown inside of a cube. The height of the cube is h units. Six identical square pyramids can fill the same volume as a cube with the same base. If the height of the cube is h units, what is true about the height of each pyramid
Answers
The height of squared pyramid is [tex]\frac{1}{3}h[/tex] unit.
What is the volume of a cube?A cube is a solid three-dimensional object with six square faces or sides, three of which meet at each vertex. One of the five Platonic solids, the cube is the only regular hexahedron. It contains 8 vertices, 6 faces, and 12 edges.
Volume of cube [tex]= (side)^3 \ unit^3[/tex]
Given the height of cube is [tex]h[/tex] unit.
Volume of cube is [tex]h^3 \ unit^3[/tex]
Let the height of squared pyramid is [tex]x[/tex] unit
Volume of squared pyramid is [tex]\frac{1}{3} h^{2} \times x \ unit^3[/tex]
According to the question, we have
Volume of cube = [tex]6 \times[/tex] volume of squared pyramid
[tex]\Rightarrow h^3=6 \times \frac{1}{3}h^2 \times x\\\Rightarrow h^3=2 \ h^2 \times x\\\Rightarrow h=2x\\\Rightarrow x= \frac{1}{2}h[/tex]
Therefore, the height of squared pyramid is [tex]\frac{1}{3}h[/tex] unit.
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Write the equation of the circle whose center is at the origin and whose diameter is 12.5
Answers
The equation of the circle whose center is at the origin and whose diameter is 12.5 is x²+y²=39.0625
Equation of a circleThe formula for finding the equation of a circle is expressed as:
(x-a)² + (y - b)² = r²
where
(a, b) is the centre
r is the radius
Given the following
(a, b) = (0, 0)
r = 12.5/2 = 6.25
Substitute
(x-0)² + (y - 0)² = 6.25²
x²+y²=39.0625
Hence the equation of the circle whose center is at the origin and whose diameter is 12.5 is x²+y²=39.0625
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The nth term of a sequence is 3nsquared/2 1 find the second term of this sequence
Answers
Answer:
6
Step-by-step explanation:
Substituting in n = 2,
[tex]\frac{3(2)^{2}}{2}=6[/tex]
(x 2 + 3) (x 3 + 4x)(x 2 + x - i - xi) = 0
Answers
The possible values of x according to the give. equation are; 0, ±√3i, ±2i, i, -1.
What are the possible values of x?The possible values of x in the equation given in the task content represent the zeroes of the equation and can be determined as follows;
(x²+3) (x³+4x) (x²+x-i-xi) = 0.
Hence, by further factorisation; we have;
x(x²+3) (x²+4) (x-i) (x+1) = 0.
The possible values of x are therefore;
x = 0;
x²+3 = 0; x = ±√3i
x² +4 = 0; x = ±2i
x -i = 0; x = i.
x +1 = 0; x = -1
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A 393939-meter ladder is sliding down a vertical wall so the distance between the bottom of the ladder and the wall is increasing at 101010 meters per minute. At a certain instant, the bottom of the ladder is 363636 meters from the wall. What is the rate of change of the distance between the top of the ladder and the ground at that instant (in meters per minute)
Answers
The rate at which the distance between the top of the ladder and the ground at that instant is decreasing at 42 meters per minute.
Given length of ladder 39 m and the rate at which the wall is increasing is 101, the bottom of the ladder is 36 m from the wall.
Let bottom is x and the length of wall be y.
We have to find the rate at which the distance between the top of the ladder and the ground at that instant.
we have to find dy/dt.
We have to apply pythagoras theorem first.
[tex]x^{2} +y^{2} =39^{2}[/tex]---------------1
[tex]x^{2} +y^{2} =1521[/tex]
put the value of x=36 in the above equation
[tex]36^{2} +y^{2} =1521[/tex]
[tex]y^{2} =225[/tex]
y=15 m
We have to find the derivative of equation 1 with respect to t.
2x*dx/dt+2y*dy/dt=0
Because it is given that bottom is increasing at 101 meters per minute so dx/dt=101
2x*101+2y*dy/dt=0
put the value of y=15
2x*101+2*15*dy/dt=0
2x*101+2*15*dy/dt=0
dy/dt=-3030/2*36
dy/dt=-42.08
Hence the rate at which the rate at which the top of the ladder and the ground at that instant is decreasing at 42 meters per minute.
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Question is wrong so it includes ladder length be 39 meters and the rate of increasing of bottom of ladder from bottom of wall is 101 meters per minute and the bottomis 36 m from the wall.
The price of a new television is $423. This price includes VAT in 17 1/2%.
a) Work out the cost of the television before VAT was added.
By the end of the year, the value of a television has fallen by 12% of its value at the start of that year. The value of a television was $423 at the start of the year.
b) Work out the value of the television at the end of the third year. Give your answer to the nearest penny.
Answers
The cost of the television before VAT was added is $360 and the value of the television at the end of the third year is $288.3
What is the meaning of VAT ?VAT is an acronym for Value Added Tax. This is a tax attach to goods and products.
Given that the price of a new television is $423. This price includes VAT in 17 1/2%.
a) The cost of the television before VAT was added is calculated below.
Let the initial cost = C
(17.5 + 100)/100 x C = 423
117.5/100 x C = 423
1.175C = 423
C = 423/1.175
C = $360
b. By the end of the year, the value of a television has fallen by 12% of its value at the start of that year. If the value of a television was $423 at the start of the year, the value of the television at the end of the third year will be calculated by using the formula
A = P(1 - R%)^3
Substitute all the parameters
A = 423(1 - 12/100)^3
A = 423 x [tex]0.88^{3}[/tex]
A = 288.3 dollars
Therefore, cost of the television before VAT was added is $360 and the value of the television at the end of the third year is $288.3
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One-eight of 32 students in the class went abroad for fall break. how many students went aboard
Answers
Answer:4
Step-by-step explanation: 32\8 = 4
Phan fills the tank of her car with gasoline before starting her road trip. The table below shows the amount of gas left in her tank as she drives.
Number of Hours vs. Amount Left in Tank
Number of Hours Spent Driving (h)
3
5
7
9
Amount of Gas Left in Tank, in gallons (g)
12
8
4
0
Which equation models the amount of gas left in the car as Phan drives, and how many gallons of gasoline does it take to fill her tank?
g = 18 – 2h; 18 gallons
g = 18 – 2h; 16 gallons
g = 3h + 3; 30 gallons
g = 3h + 3; 12 gallon
Answers
The equation models the amount of gas left in the car as Phan drives, and how many gallons of gasoline does it take to fill her tank is g = 3h + 3; 12 gallon
EquationNumber of hours = 3 hoursAmount of gas left = 12 gallonsCheck all equation
g = 18 – 2h; 18 gallons
= 18 - 2(3)
= 18 - 6
= 12
g = 18 – 2h; 16 gallons
= 18 - 2(3)
= 18 - 6
= 12
g = 3h + 3; 30 gallons
= 3(3) + 3
= 9 + 3
= 12
g = 3h + 3; 12 gallon
= 3(3) + 3
= 9 + 3
= 12
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Solve for x please anyone?
Answers
Answer: x=11
Step-by-step explanation:
The lines are parallel, which you can tell by the two arrows. 4x-8 is a corresponding angle to 3x+3, meaning they are congruent.
4x-8 = 3x+3
x=11
Answer:
x = 11
Step-by-step explanation:
these angles are corresponding angles so they are equal to each other.
4x - 8 = 3x + 3 Subtract 2x from both sides
x - 8 = 3 Add 8 to both sides
x = 11
Plug 11 back into the equations find the angle measurements
4(11) -8 = 36 degrees
3(11) + 3 = 36degrees
A bicycle race follows a triangular course. The 3 legs of the race are, in order, 2.3 km, 5.9 km, 6.2 km. Find the angle between the starting leg and the finishing leg, to the nearest degree.
How did you get the answer?
Answers
Answer:
About 71.77 degrees
Step-by-step explanation:
The starting leg is 2.3 km and the finishing leg is 6.2 km.
Using the law of cosines C^2 = A^2 + B^2 -2AB*cos(c) where A = 2.3 km, B = 6.2 km, C = 5.9 km, and angle c is the opposite angle to side C, we get:
5.9^2 = 2.3^2 + 6.2^2 -2(2.3)(6.2)*cos(c)
cos(c) = -(5.9^2 - 2.3^2 - 6.2^2)/(2*2.3*6.2)
c = 71.77 degrees
Answer:
72°
Step-by-step explanation:
when we have all the sides and need an angle, we use the law of cosine (the extended Pythagoras) :
c² = a² + b² - 2ab×cos(C)
where c is the side opposite of the angle C.
so, since the starting leg is 2.3 km, and the finishing leg is 6.2 km, we know that 5.9 km is the side opposite of the angle between the starting and finishing legs.
so, we have
5.9² = 2.3² + 6.2² - 2×2.3×6.2×cos(C)
34.81 = 5.29 + 38.44 - 28.52×cos(C)
-8.92 = -28.52×cos(C)
cos(C) = -8.92/-28.52 = 0.312762973...
C = 71.77418076...° ≈ 72°
The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equations can be used to model the height as a function of time, t, in hours
Answers
The correct option is (b) h=0.5cos([tex]\pi[/tex]/6t)+9.5.
The equations can be used to model the height as a function of time, t, in hours is h=0.5cos([tex]\pi[/tex]/6t)+9.5.
Equation of cosine function:The following is a presentation of the cosine function's generic form;
y = a + cos(bx - c) + d
amplitude = a
b = cycle speed
Calculation for the model height;
The height, h (feet) of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet.
Obtain amplitude 'a' as
[tex]\begin{aligned}a &=\frac{\text { Maximum value }-\text { Minimum value }}{2} \\a &=\frac{10-9}{2} \\a &=\frac{1}{2} \\a &=0.5\end{aligned}[/tex]
The time 'T' is calculated as-
[tex]\begin{aligned}&\mathrm{T}=\frac{2 \pi}{\mathrm{b}} \\&12=\frac{2 \pi}{\mathrm{b}} \\&\mathrm{b}=\frac{2 \pi}{12} \\&\mathrm{~b}=\frac{\pi}{6}\end{aligned}[/tex]
Now, calculate 'd'
[tex]\begin{aligned}&\mathrm{d}=\frac{\text { Maximum value }+\text { Minimum value }}{2} \\&\mathrm{~d}=\frac{10+9}{2} \\&\mathrm{~d}=\frac{19}{2} \\&\mathrm{~d}=9.5\end{aligned}[/tex]
Therefore, with the height as a function of time, t, expressed in hours, can be modeled by the following equations:
h=0.5cos([tex]\pi[/tex]/6t)+9.5
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The complete question is-
The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equations can be used to model the height as a function of time, t, in hours? Assume that the time at t = 0 is 12:00 a.m.
A. h=0.5cos([tex]\pi[/tex]/12t)+9.5
B. h=0.5cos([tex]\pi[/tex]/6t)+9.5
C. h=cos([tex]\pi[/tex]/12t)+9
D. h=cos([tex]\pi[/tex]/6t)+9
I know this is a supervised data mining task because (choose all that apply) A. Because the target belonged to the same group as some thine else B. We have historical data on the target. C. There a specific quantifiable target that we are interested in or trying to predict. D. We were able to group the target with other variables
Answers
Answer:
The answer to your question is C. There a specific quantifiable target that we are interested in or trying to predict.
Step-by-step explanation:
I hope this helps and have a good day!
-9(z+8)=-9z-72
Llllllll
Answers
Answer:
true
-9(z+8)
-9*z +(-9)*8
-9z-72
Clarice was late paying her credit card bill of $249. She was charged a 5% late fee. What was the amount of the late fee?
Answers
Answer:
You subtract 249 minus 5
If AD BD, which of the following relationships can be proved and why?
B
OA. AACD ABCD, because of AS.
OB. AACD ABCD, because of ASA.
OC. There is not enough information to prove a relationship.
D. AACD ABCD, because of SAS.
Answers
IfIf AD BD, the following relationships that can be proved and why is: D. ΔACD ΔBCD, because of SAS.
Relationship that can be proved if AD=BDThe relationship that can be proved is ΔACD ΔBCD, because of SAS.
The reason is that m<CDA=M<CDB=90°
CD=CD
AD=BD
Hence, ΔACD=ΔBCD because of SAS. SAS congruence can tend to be proved when the length of the two side correspond and when the angle between the two side is equal.
Therefore the correct option is D.
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Instructions:Given the coordinates the translation (x,y)>(x-4,y).
Answers
(-4,-2)
(-2,-2)
(0,-4)
subtract 4 from the x-value
5.5(x+6 1/2)-(x+9 1/3)-(19-x)
Answers
The simplified form of the expression [5.5(x+6 1/2)-(x+9 1/3)-(19-x)] is 11x/2 + 89/12
What is the simplified form of the expressionGiven the expression;
5.5(x+6 1/2) - (x+9 1/3) - (19-x)
First, we convert 6 1/2, 9 1/3 and 5.5 to an improper fraction
6 1/2 = 13/2, 9 1/3 = 28/3 and 5.5 = 11/2
So, we have
(11/2)( x + 13/2 ) - ( x + 28/3 ) - ( 19 - x )
Next, we remove the parentheses
11x/2 + 143/4 - x - 28/3 - 19 + x
11x/2 + 143/4 - 28/3 - 19
11x/2 + 317/12 - 19
11x/2 + 89/12
Therefore, the simplified form of the expression [5.5(x+6 1/2)-(x+9 1/3)-(19-x)] is 11x/2 + 89/12.
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Can someone please explain how [tex](3^{\frac{1}{5} } )^{2}[/tex] can be written as the radical expression [tex]\sqrt[5]{9}[/tex] ???
Answers
We can to convert the expression [tex](3^{\frac{1}{5} } )^{2}[/tex] to the radical expression [tex]\sqrt[5]{9}[/tex]. by using the laws of indices.
What is a radical expression?A radical expression is an expression of the form ⁿ√x where it is called the nth root of x.
Now, to write [tex](3^{\frac{1}{5} } )^{2}[/tex] as the radical expression [tex]\sqrt[5]{9}[/tex], we use following laws of indices
The power law of indices. [tex](x^{\frac{1}{b} } )^{a} = (x^{a} )^{\frac{1}{b} }[/tex] and root law of indices [tex]x^{\frac{1}{a} } = \sqrt[a]{x}[/tex]So, [tex](3^{\frac{1}{5} } )^{2} = (3^{2} )^{\frac{1}{5} }[/tex]
[tex](3^{2} )^{\frac{1}{5} } = 9^{\frac{1}{5} } = \sqrt[5]{9}[/tex]
Thus, we can to convert the expression [tex](3^{\frac{1}{5} } )^{2}[/tex] to the radical expression [tex]\sqrt[5]{9}[/tex]. by using the laws of indices.
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please help will r8 5 + brainliest
Answers
Answer:
Option C more peaked and more widely spread.
Step-by-step explanation:
15 + 35 + 18 + 30 + 25 + 21 + 32 + 16
80 + 78 + 34
192/8 = 24
24 + 22 + 27 + 28
46 + 55 = 101/4 = 25.2
What is the multiplicative inverse of -13/14
Answers
The multiplicative inverse of -13/14 as in the task content is; -14/13.
What is the multiplicative inverse of -13/14?The multiplicative inverse of a number x is given as; 1/x.
On this same note, it follows that since, the number whose multiplicative inverse is to be found is: -13/14, the multiplicative inverse is; -14/13.
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James sleeps for 8 hours in a day. what percentage of the day is james a. asleep b. awake
Answers
Step-by-step explanation:
asleep percentage :- ( 8h /24h ) 100 % = 33.33%
awake percentage :- ( 16h / 24h ) 100 % = 66.67%
Describe the sample variance using words rather than a formula. do the same with the population variance
A. The sample variance is the sum of the deviations from the mean divided by the number of measurements minus one. The population variance is the average of the distances of the measurements on all units in the population from the mean.B. The sample variance is the sum of the squared deviations from the mean divided by the number of measurements. The population variance is the sum of the squared deviations from the mean divided by the number of measurements minus one.C. The sample variance is the sum of the deviations from the mean divided by the number of measurements. The population variance is the sum of the deviations from the mean divided by the number of measurements minus one.D. The sample variance is the sum of the squared deviations from the mean divided by the number of measurements minus one. The population variance is the average of the squared distances of the measurements on all units in the population from the mean.
Answers
The option D is the correct option.
According to the statement
we have to define the sample variance in the words.
So,
The sample variance is the sum of the squared deviations from the mean divided by the number of measurements minus one.
and in the case of the population variance it becomes
The population variance is the average of the squared distances of the measurements on all units in the population from the mean.
This is the method by which we define the sample variance and population variance.
So, The option D is the correct option.
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Charlize accidentally omitted two consecutive integers when adding the elements of the arithmetic sequence, $\{1, 2, 3, \ldots, n\}$. If the sum she obtained is $241$, what is the smallest possible value of $n$
Answers
The smallest possible value of N is 23.
According to the statement
we have given that the sequence {1,2,3.....n}
and the sum is 241. we have to find the smallest value of n.
So, for this purpose we use summation formula of an arithmetic sequence
Sn = n /2 ( a1 +an )
Put the values in it then.
Note that the sum of the first 21 integers is 21 * 22 /2 = 231...this isn't large enough as compare to given value.
And the sum of the first 22 integers = 22 * 23 / 2 = 253
So 253 - 241 = 12 = omitted sum.....
but the sum of two consecutive integers must be odd
And......the sum of the first 23 integers is 23 * 24 / 2 = 276
So.......276 - 241 = 35 = omitted sum
So....the consecutive integers omitted must be 17 and 18
So....... the smallest value of n is 23
So, The smallest possible value of N is 23.
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Simplify this expression.
2√5 (13+√2)
O 2√65+2√10
O 2√5 +2√7
O26√65 +2√10
O 26√5 +2√10
Answers
Answer:
The solution for the expression is choice D 26√5 +2√10
Step-by-step explanation:
Hello!
First, apply distributive law: a(b+c)= ab+ac
2√5(13+√2) ....given expression 2√5.13 +2√5.√2...multiply the numbers2.13=26√5.√2=√1026√5 +2√10Help with this word problem!
Answers
Answer:
2.0 km
Step-by-step explanation:
The Law of Cosines can be used to find the third side of a triangle in which two sides and the angle between them are given.
SetupThe law of cosines tells us ...
c² = a² +b² -2ab·cos(C)
Using the given values, we have ...
c² = 4.2² +4.5² -2(4.2)(4.5)cos(26°)
SolutionSimplifying the equation, we get ...
c² = 37.89 -37.8cos(26°) ≈ 3.91559
c ≈ 1.979 . . . . km
The width of the strait is about 2.0 km.