Answers
Answer
English translation needed
Related Questions
Which of the following statements best describes the relationship between
any point on an ellipse and each of its two foci?
A. The quotient of the distances to each focus equals a certain
constant.
B. The difference of the distances to each focus equals a certain
constant.
C. The sum of the distances to each focus equals a certain constant.
D. The product of the distances to each focus equals a certain
constant.
Answers
Answer:
C
Step-by-step explanation:
The sum of distances from any point on the ellipse to each foci equals a certain amount, no matter what point on the ellipse it starts from. The foci are on the major radius of the ellipse (the longer length of horizontal/vertical). The foci are of equal distance from the center, with one on each side.
If you wanted to find where the foci are using the major and minor radius, we can find that, representing the distance between the center and any foci as g,
g² = major radius² - minor radius². Then, the distance between the center and the foci is equal to g
Herbert has sold 92, 28, 83 and 75 suits in the last four months, respectively. How many suits will he need to sell this month to maintain an average of at least 71 sales per month?
Answers
Answer: 77 suits
Step-by-step explanation:
Let sales of this month = x
Sales for last 4 months = 92, 28, 83, 75
Average = Sum of Observation ÷ No of Observation
Now, we can form an equation
(92+28 +83+75+x) ÷ 5 =71
(92+28 +83+75+x) = 71 × 5
278 + x = 355
x = 355 - 278
x = 77
Find the average of last 4 month
Find mean
Sum of Numbers divided by the count of numbers
92+ 28+ 28 +75 divided 4
278 divided by 4
69.5
If 4month = 69.5
x. =. 71
Cross multiply
69.5x =71 *4
69.5x.= 284
Divide both side by x
x= 284 / 69.5
x= 4.08 to whole number
x = 4 months
What is the answer for this question
Answers
Answer:
option d. is the correct answer
Finance A bicycle shop hires road bikes for £25 per day and tandems for £40 per day. One day a family pays £155.
a Which type of bicycles did they hire?
b How many people are in the family?
Answers
Answer:
3 road bikes and 2 tandems
7 people
Step-by-step explanation:
25b + 40t = 155
b=3 and t = 2
Check
25*3 + 40*2 = 155
75+80 = 155
Assuming 1 person per road bike and 2 people per tandem
3*1 + 2*2 = 3+4 = 7
m/HCB = 60°, m/DCB = 9x-1, and m/DCH = 2x+ 16. Find x
Answers
Answer:
[tex]x=11[/tex]
Step-by-step explanation:
Note that ∠DCB is the sum of ∠HCB and ∠DCH. Hence:
[tex]m\angle DCB = m\angle HCB + m\angle DCH[/tex]
Substitute in the appropriate values/expressions:
[tex](9x-1) = (60) + (2x+16)[/tex]
Solve for x. Combine like terms:
[tex]9x - 1 = 2x + 76[/tex]
Subtract 2x from both sides:
[tex]7x - 1 = 76[/tex]
Add one to both sides:
[tex]7x = 77[/tex]
And divide. Hence:
[tex]x=11[/tex]
Answer:
x=11
Step-by-step explanation:
<DCB = <DCH + < HCB
9x-1 = 2x+16 + 60
Combine like terms
9x-1 = 2x+76
Subtract 2x from each side
9x-1-2x= 2x+76-2x
7x-1 = 76
Add 1 to each side
7x-1 +1 = 76+1
7x = 77
Divide by 7
7x/7 = 77/7
x=11
Solve for x.
5x – 3 = 2x +12
Answers
Answer:
X = 5
HOPE IT IS HELPFULLY.In an interview for a secretary position at the dealer, a typist claims a tying speed of 45 words per minute. On the basis of 70 trials, she demonstrated an average speed of 43 words per minute with a standard deviation of 15 words per minute. Test at 5% significance level on the typist’s claim.
Answers
According to the typist claim, we build an hypothesis test, find the test statistic and the p-value relative to this test statistic, reaching a conclusion that:
The p-value of the test is 0.1333 > 0.05, which means that there is not enough evidence to reject the typist's claim.
-------------------------------------------------------------
In an interview for a secretary position at the dealer, a typist claims a tying speed of 45 words per minute.
At the null hypothesis, we test if the mean is of at least 45, that is:
[tex]H_0: \mu \geq 45[/tex]
At the alternative hypothesis, we test if the mean is of less than 45, that is:
[tex]H_1: \mu < 45[/tex]
-------------------------------------------------------------
The test statistic is:
We have the standard deviation for the sample, so the t-distribution is used to solve this question
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
-------------------------------------------------------------
45 is tested at the null hypothesis:
This means that [tex]\mu = 45[/tex]
On the basis of 70 trials, she demonstrated an average speed of 43 words per minute with a standard deviation of 15 words per minute.
This means that [tex]n = 70, X = 43, s = 15[/tex]
Value of the test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{43 - 45}{\frac{15}{\sqrt{70}}}[/tex]
[tex]t = -1.12[/tex]
-------------------------------------------------------------
P-value of the test and decision:
The p-value of the test is found using a left-tailed test(test if the mean is less than a value), with 70 - 1 = 69 degrees of freedom and t = -1.12.
Using a t-distribution calculator, the p-value is of 0.1333.
The p-value of the test is 0.1333 > 0.05, which means that there is not enough evidence to reject the typist's claim.
A similar problem can be found at https://brainly.com/question/24241851
The closed form sum of
$$12 \left[ 1^2 \cdot 2 + 2^2 \cdot 3 + \ldots + n^2 (n+1) \right]$$
for $n \geq 1$ is $n(n+1)(n+2)(an+b).$ Find $an + b.$
Answers
Perhaps you know that
[tex]S_2 = \displaystyle\sum_{k=1}^n k^2 = \frac{n(n+1)(2n+1)}6[/tex]
and
[tex]S_3 = \displaystyle\sum_{k=1}^n k^3 = \frac{n^2(n+1)^2}4[/tex]
Then the problem is trivial, since
[tex]\displaystyle\sum_{k=1}^n k^2(k+1) = S_2 + S_3 \\\\ = \frac{2n(n+1)(2n+1)+3n^2(n+1)^2}{12} \\\\ = \frac{n(n+1)\big((2(2n+1)+3n(n+1)\big)}{12} \\\\ = \frac{n(n+1)\big(4n+2+3n^2+3n\big)}{12} \\\\ = \frac{n(n+1)(3n^2+7n+2)}{12} \\\\ = \frac{n(n+1)(3n+1)(n+2)}{12}[/tex]
Then
[tex]12\bigg(1^2\cdot2+2^2\cdot3+3^2\cdot4+\cdots+n^2(n+1)\bigg) = n(n+1)(n+2)(3n+1)[/tex]
so that a = 3 and b = 1.
A candy store owner wants to mix some candy costing $1.25 a pound
with some candy costing $1.45 a pound to make 50 pounds of candy
costing $1.30 a pound. How much of the $1.25 a pound candy should
she use?
Answers
The candy store owner should use 37.5 pounds of the candy costing $1.25 a pound.
Given:
Candy costing $1.25 a pound is to be mixed with candy costing $1.45 a poundThe resulting mixture should be 50 pounds of candyThe resulting mixture should cost $1.30 a poundTo find: The amount of candy costing $1.25 a pound that should be mixed
Let us assume that the resulting mixture should be made by mixing 'x' pounds of candy costing $1.25 a pound.
Since the total weight of the resulting mixture should be 50 pounds, 'x' pounds of candy costing $1.25 a pound should be mixed with '[tex]50-x[/tex]' pounds of candy costing $1.45 a pound.
Then, the resulting mixture contains 'x' pounds of candy costing $1.25 a pound and '[tex]50-x[/tex]' pounds of candy costing $1.45 a pound.
Accordingly, the total cost of the resulting mixture is [tex]1.25x+1.45(50-x)[/tex]
However, the resulting mixture should be 50 pounds and should cost $1.30 a pound. Accordingly, the total cost of the resulting mixture is [tex]1.30 \times 50[/tex]
Equating the total cost of the resulting mixture obtained in two ways, we get,
[tex]1.25x+1.45(50-x)=1.30 \times 50[/tex]
[tex]1.25x+72.5-1.45x=65[/tex]
[tex]0.2x=7.5[/tex]
[tex]x=\frac{7.5}{0.2}[/tex]
[tex]x=37.5[/tex]
This implies that the resulting mixture should be made by mixing 37.5 pounds of candy costing $1.25 a pound.
Learn more about cost of mixtures here:
https://brainly.com/question/17109505
[tex]\to \bold{ 1.25x+1.45(50-x)= 1.30 \times 50}\\\\ \to \bold{ 1.25x+72.5-1.45x= 65}\\\\ \to \bold{ -0.2x= -7.5}\\\\ \to \bold{ x=\frac{7.5}{0.2}}\\\\ \to \bold{ x=37.5}\\\\[/tex]
It implies that [tex]\bold{37.5\ pounds}[/tex] of candy at [tex]\bold{\$1.25}[/tex] a pound must be used to make the final concoction.Learn more:
brainly.com/question/8991725
What is the surface area of the cube, in square inches?
Answers
Answer:
The surface area of the cube is 648.96 sq in.
Step-by-step explanation:
This problem is made a lot easier by the fact that it's a cube.
So we first calculate the area of one of the faces. The length of the side of the side is 10.4 inches, and 10.4 * 10.4 = 100.16.
There are six faces, so we multiply the area of 1 face by 6. 100.16 * 6 = 648.96.
Therefore, the surface area of the cube is 648.96 sq inches.
Hope This Helps!
Warren has money to go see a movie after he pays $8 for the MOVIE he will have $14 left right and solve an equation to show how much money Warren has before paying for the movie
Answers
Answer:
$(8+14)
Step-by-step explanation:
Amount of money Warren has at first=$8+$14=$22
Evaluate the expression for x=-5,y=-7, and z=9
Answers
Answer:
Is 11
Step-by-step explanation:
x+(-y)+z —> -5 +(+7)+9 = -5+7+9 = 11
3x°
30°
x =
degrees dhdjdjdjdjfj
Answers
Answer:
x=10
Step-by-step explanation:
since the angles seem similar they're most likely to be the same but since its 3x and you have to find the value of x then we will do 3 x ?=30, which is 10. if you want to check there is one way, since the angle on a straight line is 180 you can do 180 - 30 =150 which will be the unknown value next to the given angle. Since the unknown angle is on the line with the 150 degree angle we can do 180 - 50 to get the unknown angle (3x) which is 30. So in conclusion x will be 10
Answer: x = 10
Step-by-step explanation:
The angles are voa which means vertically opposite angles which means they are conguerent and also equal
ATQ
⇒3x = 30
⇒x = 30/3
⇒x = 10
Therefore x = 10 degrees
please click thanks and mark brainliest if you like :)
PLEASE HELP ASAP THANK YOU!!! LOVE U
The fish population is decreasing at a rate of 3% per year. In 2002 there were about 1200 fish. Find the fish population in 2010. Round to the nearest whole number.
Answers
Answer:
912 lil fishies
Step-by-step explanation:
since its 3% per year, and 8 years, that's 24%. 1200 x 24% is 288, and 1200-288 is 912 lil fishies :)
hope this helps!!
brainliest is very appreciated!
Find the area and the perimeter of a triangle (shown below)
PLZZZ
Answers
Answer:
A = 120, P = 55
Step-by-step explanation:
Triangle
Area = (bh)/2
A = (20x12)/2
A =240/2
A = 120
Perimeter = a + b + c
to find c, use a^2 +b^2 = c^2
20^2 + 12^2 = c^2
400 + 144 = c^2
544 = c^2
c = about 23
20 + 12 + 23 = 55
looking for the equation, slope, and y-intercept of: (1,-3) and (0,-1)
Answers
Answer:
Equation: y = -2x - 1
Slope: -2
Y intercept: -1
Step-by-step explanation:
First, find the slope using rise over run, (y2 - y1) / (x2 - x1):
(y2 - y1) / (x2 - x1)
(-1 + 3) / (0 - 1)
2 / -1
= -2
So, the slope is -2. Plug this and a point into slope intercept form, y = mx + b, and solve for b:
y = mx + b
-1 = -2(0) + b
-1 = 0 + b
-1 = b
So, the y intercept is -1. Create the equation by plugging in the slope and b into y = mx + b:
y = mx + b
y = -2x - 1
The equation of the line is y = -2x - 1.
Answer: y=-2x-1. Slope is -2 and y int. is -1.
Step-by-step explanation:
First, you need to find the slope by using the slope formula y2-y1/x2-x1. Plug in the x and y coordinates, which simplifies as -1-(-3)/0-1, and furthermore to 2/-1, or -2. The y intercept can be found by the second point, (0,-1). Therefore, the y int. is -1.
Solve for b.
-32 + 10b = -22
Answers
Answer: b = 1
Step-by-step explanation:
= -32 + 10b = -22
-32 + 10 = -22
b = 1
Check: -32 + 10(1) = -22
= -22
Answer:
b=1
Step-by-step explanation:
Hello,
We would like to solve for b in the equation -32+10b=-22.
When we want to solve for a variable, we want to isolate it on one side (have it on one side by itself. No other numbers.)
So to start, add 32 to both sides to remove it from the left side (-32+32=0).
-32+10b=-22
+32 +32
______________
10b=10
Now, there isn't anything with 10b, but we want the value of b by itself (1b), as 10b is 10 times the value of what b is.
So divide both sides by 10
b=1
Hope this helps!
Is this right answer??????………
Answers
Answer:
6 is correct....
actually this problem is quite si,p;e to see that it is correct
notice that the length of the triangle is 4 and the height is 3
thus a rectangle 4*3 area is twelve ...
if you make a copy of the triangle and flip it you will see it makes
a 4x3 rectangle ... the original and copy = 12 thus 1/2 of the 12 is the area of the original triangle
Step-by-step explanation:
prove that the line x-y=0 bisect the line segment joining the point (1,6) and (4, -1)
Answers
Step-by-step explanation:
x-y=0(l.6)-(4.-1)(6-4)-(1--1)2--2=04(x — 8)+10 = -10
What is the solution to this equation?
Answers
Answer:
x = 3
Step-by-step explanation:
We are given the equation 4(x - 8) + 10 = -10 and are asked to find the solution, solution meaning to get x alone.
To do so, first distribute the 4 on the outside of the parenthesis to both values on the inside of the parenthesis :
4(x - 8)
(4 * x - 4 * 8)
4x - 32
4x - 32 + 10 = -10
Now combine like terms :
4x - 22 = -10
Now it's time to get x alone, first get rid of -22 by adding 22 to both sides :
4x = 12
Now get x alone by dividing both sides by 4 :
x = 3
help pls How do you write 0.0000000080 in scientific notation? x 10
Answers
Answer:
0.000000008 written as scientific notation is 8 × 10-9.
Answer:
8x10^-9
0.0000000080 is -9 integers from 0
When x + y = 30 and x < 13, which of the following must be true?
y = 30
y > 17
y = 17
y < 17
y > 30
Answers
Answer:
y>17
Step-by-step explanation:
[tex]x + y = 30 \\ 13 + y = 30 \\ y = 17 \\ for \: x < 13 \\ y > 17[/tex]
Answer:
y>17
Step-by-step explanation:
x+y=30
x<13
What + 13 is 30?
17. So if x+y=30. Because x will be less than 13, y must make up the differnce by being greater than 17.
Ex: x=12
y+12=30
y=18
18 is greater than 17.
This is a great way to check because if your not sure, it elimates the other options!
Hope this helps!
1/6 of a loop around the circle would be a rotation of how many degrees (q)?
A=6
B=60
C=30
D=36
Answers
Answer:
60
Step-by-step explanation:
A circle is 360 degrees
1/6 of 360
1/6 * 360 = 60
simplify the following
Answers
Answer:
1) 11[tex]\sqrt{3}[/tex]
2) 2[tex]\sqrt{2}[/tex]
3) [tex]20\sqrt{3} + 15\sqrt{2}[/tex]
4) [tex]53 + 12\sqrt{10}[/tex]
5) -2
6) [tex]7\sqrt{2} - 5\sqrt{3}[/tex]
Step-by-step explanation:
1) 2[tex]\sqrt{12}[/tex] + 3[tex]\sqrt{48}[/tex] - [tex]\sqrt{75}[/tex]
=(2 × 2[tex]\sqrt{3}[/tex] )+ (3 × 4[tex]\sqrt{3}[/tex]) - 5[tex]\sqrt{3}[/tex]
= 4[tex]\sqrt{3}[/tex] + 12[tex]\sqrt{3}[/tex] - 5[tex]\sqrt{3}[/tex]
= 11[tex]\sqrt{3}[/tex]
2) 4[tex]\sqrt{8}[/tex] -2[tex]\sqrt{98}[/tex] + [tex]\sqrt{128}[/tex]
= (4 × 2[tex]\sqrt{2}[/tex]) - (2 × 7[tex]\sqrt{2}[/tex]) + 8[tex]\sqrt{2}[/tex]
= 8[tex]\sqrt{2}[/tex] - 14[tex]\sqrt{2}[/tex] +8[tex]\sqrt{2}[/tex]
= 2[tex]\sqrt{2}[/tex]
3) 5[tex]\sqrt{12\\}[/tex] - 3[tex]\sqrt{18} + 4 \sqrt{72} +2\sqrt{75}[/tex]
= 5× [tex]2\sqrt{3}[/tex] - 3×[tex]3\sqrt{2}[/tex] + 4×[tex]6\sqrt{2}[/tex] + 2×[tex]5\sqrt{3}[/tex]
= [tex]10\sqrt{3} - 9\sqrt{2} +24\sqrt{2} +10\sqrt{3}[/tex]
= [tex]20\sqrt{3} + 15\sqrt{2}[/tex]
4) [tex](2\sqrt{2} + 3\sqrt{5} )^{2}[/tex]
= [tex]8 + 12\sqrt{10} + 45[/tex]
= [tex]53 + 12\sqrt{10}[/tex]
5) [tex](1+\sqrt{3} ) (1-\sqrt{3} )[/tex]
= [tex]1 - 3[/tex]
= -2
6) [tex](2\sqrt{6} -1) (\sqrt{3} -\sqrt{2} )[/tex]
= [tex]2\sqrt{18}-2\sqrt{12} -\sqrt{3} +\sqrt{2}[/tex]
= 2×[tex]3\sqrt{2}[/tex] - 2×[tex]2\sqrt{3}[/tex] - [tex]\sqrt{3} + \sqrt{2}[/tex]
= [tex]6\sqrt{2} - 4\sqrt{3} -\sqrt{3} +\sqrt{2}[/tex]
= [tex]7\sqrt{2} - 5\sqrt{3}[/tex]
Hope the working out is clear and will help you. :)
Step-by-step explanation:
please I solved the question in the diagram above
which one of the following has a terminating decimal expansion?
a.5/64
b.8/9
c.14/15
d.1/12
Answers
Answer:
b. 8/9
Step-by-step explanation:
step by step explanation
Answer:
A
Step-by-step explanation:
Because if you were to out each fraction into a calculator you see that b,c, and d have a never ending decimal. The only fraction that does end in option A, therefore ur answer is option a
Any help is appreciated (:
Answers
Answer: True
Step-by-step explanation:
The number is going down in a way that cannot be written as a straight line so it is a nonlinear.
Lisa is on the west shore of Mighty River, which is 1 mile wide and has two parallel shorelines running exactly north-to-south. She wishes to get to a point on the opposite shore that is 1 mile south of where she is now as quickly as possible. (So this point is sqrt (2) miles due southeast from her starting position.) Assuming that Lisa can walk twice as fast as she can swim, and that she wants to swim across the river first before walking any necessary distance along the opposite shoreline, at what course (in degrees) should she start swimming?
(The angle is measured from north, so 90 degrees is due east, meaning she swims directly across the river, and 135 degrees is due southeast, meaning she swims directly to her destination point.)
Answers
Lisa should start swimming at an angle of [tex]120^{\circ}[/tex] to reach her destination as quickly as possible.
Given:
The river is 1 mile wideThe end point is 1 mile south of the starting pointLisa's speed of walking is twice that of her speed of swimmingLisa wants to swim across the river first before walking the rest of the distance along the opposite shorelineTo find: The course (in degrees) at which she should start swimming so that she can reach the end point as quickly as possible
To solve this problem, we need to know the following:
Pythagoras theorem states that in a right angled triangle, the square of the length of hypotenuse is the sum of the squares of lengths of perpendicular and baseCosine of an angle is the ratio of base and hypotenuse in the right angled triangleA single variable function is minimized by a value for which, the first derivative of the function is zero and the second derivative of the function is positiveLet us assume that Lisa starts swimming at a course such that she needs to swim for 'x' miles to reach the opposite shore, as shown in the figure.
Labelling the points in the figure, we can say that,
AB = 1 mile (given)
BD = 1 mile (given)
AC = x miles (by our assumption)
It is clear that ABC forms a right angled triangle where,
Perpendicular: BC
Base: AB
Hypotenuse: AC
Using Pythagoras Theorem for triangle ABC, we have,
[tex](Hypotenuse)^{2} =(Perpendicular)^{2} +(Base)^{2}[/tex], which implies,
[tex](AC)^{2} =(BC)^{2} +(AB)^{2}[/tex]
Put AC = x, AB = 1 in the above equation to get,
[tex]x^{2} =(BC)^{2} +1^{2}[/tex]
[tex]x^{2} =(BC)^{2} +1[/tex]
[tex](BC)^{2}=x^{2} -1[/tex]
[tex]BC=\sqrt{x^{2} -1}[/tex]
From the figure, we can say that,
[tex]CD=BD-BC[/tex]
Put [tex]BC=\sqrt{x^{2} -1}[/tex] and [tex]BD=1[/tex] in the above equation to get,
[tex]CD=1-\sqrt{x^{2} -1}[/tex]
According to our assumption, Lisa swims the distance of AC and walks the distance of CD, that is, she swims a distance of [tex]x[/tex] miles and walks a distance of [tex]1-\sqrt{x^{2} -1}[/tex] miles.
Now, let us assume that Lisa's speed of swimming is [tex]k[/tex] miles/hour. It is given that Lisa's speed of walking is twice that of her speed of swimming. Then, accordingly, Lisa's speed of walking must be [tex]2k[/tex] miles/hour. We note that these speeds are constants for Lisa.
We know that,
[tex]Speed=\frac{Distance}{Time}[/tex]
Then,
[tex]Time=\frac{Distance}{Speed}[/tex]
This implies that,
Time spent by Lisa on swimming = [tex]\frac{x}{k}[/tex]
Similarly, time spent by Lisa on walking = [tex]\frac{1-\sqrt{x^{2} -1} }{2k}[/tex]
Then, total time taken by Lisa to travel the whole distance from the starting point to the end point is,
[tex]\frac{1-\sqrt{x^{2} -1} }{2k} +\frac{x}{k}[/tex]
[tex]\frac{1}{2k}( 1-\sqrt{x^{2} -1} +2x )[/tex]
Since Lisa wishes to get to the end point as quickly as possible, we must minimize the total time taken by her to travel the entire distance.
Total time taken: [tex]T=\frac{1}{2k}( 1-\sqrt{x^{2} -1} +2x )[/tex]
Differentiating with respect to 'x', we have,
[tex]T'=\frac{1}{2k}( -\frac{x}{\sqrt{x^{2} -1}} +2 )[/tex]
Differentiating with respect to 'x' again, we have,
[tex]T''=\frac{1}{2k(\sqrt{x^{2} -1})^{3}}[/tex]
Equating the first derivative to 0, we have,
[tex]\frac{1}{2k}( -\frac{x}{\sqrt{x^{2} -1}} +2 )=0[/tex]
[tex]-\frac{x}{\sqrt{x^{2} -1}} +2 =0[/tex]
[tex]\frac{x}{\sqrt{x^{2} -1}} =2[/tex]
[tex]2\sqrt{x^{2} -1}= x[/tex]
Squaring both sides,
[tex]4(x^{2} -1)= x^{2}[/tex]
[tex]4x^{2} -4= x^{2}[/tex]
[tex]3x^{2} =4[/tex]
[tex]x^{2} =\frac{4}{3}[/tex]
[tex]x=\frac{2}{\sqrt{3}}[/tex]
Note that we assumed the positive square root for 'x' because 'x' denotes a distance which cannot be negative.
Put [tex]x=\frac{2}{\sqrt{3}}[/tex] in the expression for second derivative to get,
[tex]T''=\frac{1}{2k(\sqrt{(\frac{2}{\sqrt{3}} )^{2} -1})^{3}}[/tex]
[tex]T''=\frac{1}{2k(\sqrt{\frac{4}{3} -1})^{3}}[/tex]
[tex]T''=\frac{1}{2k(\sqrt{\frac{1}{3}})^{3}}>0[/tex]
The last expression is positive because 'k' denotes a speed which is always positive.
This implies that the obtained value [tex]x=\frac{2}{\sqrt{3}}[/tex] minimizes the quantity of total time taken.
Now, from the figure, we can say that,
[tex]cos(\angle BAC)=\frac{AB}{AC}[/tex]
Put AC = x, AB = 1 in the above equation to get,
[tex]cos(\angle BAC)=\frac{1}{x}[/tex]
Put the obtained minimizing value, [tex]x=\frac{2}{\sqrt{3}}[/tex] in the above equation to get,
[tex]cos(\angle BAC)=\frac{1}{\frac{2}{\sqrt{3}} }[/tex]
[tex]cos(\angle BAC)=\frac{\sqrt{3}}{2 }[/tex]
[tex]cos(\angle BAC)=cos(30^{\circ})[/tex]
Then,
[tex]\angle BAC=30^{\circ}[/tex]
Since the angle is measured from the north, the required angle is, [tex]90^{\circ}+30^{\circ}=120^{\circ}[/tex]
Thus, Lisa should start swimming at an angle of [tex]120^{\circ}[/tex] to reach her destination as quickly as possible.
Learn more about finding optimum course here:
https://brainly.com/question/17587668
Circle the correct term to complete the sentence: When you dilute a solution, the resulting solution has a concentration that is (increased/decreased) and the volume is (increased/decreased).
Answers
Answer:
1st option is decreased 2nd is increased
Step-by-step explanation:
Because you add a liquid to dilute a solution, it makes the solution weaker (less concentrated) you also added more liquid which would increase the volume
Answer:
decreased; increased
Step-by-step explanation:
when you dilute something you make it less concentrated by adding something else (usually water i think). so the concentration decreases while the volume increases
the ratio of boys and girls in a 4:3.If there are 20 boys, find the number of girls.
Answers
Answer:
There are 15 girls.
Step-by-step explanation:
The ratio is 4:3, meaning there are 7 parts.
4 parts= 20 (Boys)
This means 1 part is 20 divided by 4.
1 part= 5
3 parts= Amount of girls.
3 x 5 = 15.
There are 15 girls.
Answer:
15
Step-by-step explanation:
Add:
boys : girls
4 : 3 = 7
20: ? = ?
Divide:
20 / 4 = 5
5 × 3 = 15
20: 15
So, there are 15 girls.
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