Answer:
2±√13
Step-by-step explanation:
9/x=x-4
x² -4x - 9=0
x² -4x +4- 13=0
(x -2)²=13
x-2= ±√13
x= 2±√13
if f(x)=ln(sin(2x)), f''(π/4) is equal to
Use the chain rule to compute the second derivative:
[tex]f(x)=\ln(\sin(2x))[/tex]
The first derivative is
[tex]f'(x)=(\ln(\sin(2x)))'=\dfrac{(\sin(2x))'}{\sin(2x)}=\dfrac{\cos(2x)(2x)'}{\sin(2x)}=\dfrac{2\cos(2x)}{\sin(2x)}[/tex]
[tex]f'(x)=2\cot(2x)[/tex]
Then the second derivative is
[tex]f''(x)=(2\cot(2x))'=-2\csc^2(2x)(2x)'[/tex]
[tex]f''(x)=-4\csc^2(2x)[/tex]
Then plug in π/4 for x :
[tex]f''\left(\dfrac\pi4\right)=-4\csc^2\left(\dfrac{2\pi}4\right)=-4[/tex]
TIMED PLEASE HELP When f = 2 and g = 8, n = 4. If n varies jointly with f and g, what is the constant of variation?
1/4
1/2
4
64
The Answer is 1/4
Step-by-step explanation:
The required constant of variation for given data is k = 1/4
The correct option is (a)
What is constant of variation?In a direct variation, the product of two variables; in an inverse variation, the ratio of two variables, is called constant of variation
Formula:
k = [tex]\frac{n}{fg}[/tex]
How calculate constant of variation?Here we have given that n = 4, f = 2 and g = 8
Substitute the given values into above formula
k = [tex]\frac{4}{2(8)} =\frac{1}{4}[/tex]
The required constant of variation is 1/4
Therefore the correct option is (a)
This is the conclusion to the answer.
Learn more about constant of variation here-
https://brainly.com/question/6499629
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work out the weekly mean number of 50 kg bags of flour used in these 5 weeks
Kim is a baker, she buys flour in 50kg bags.
weeks 1 2 3 4
NO of bags of flour 7 14 8 13
Kim will make 2400 loaves in week 5
Each of these loaves will need 250g of lour
Kim works out weekly mean number of 50kg bags of flour used in these 5 weeks.
she will use the figure for future orders.
Answer:
Weekly Mean Number of 50-kg bags =10.8 bags
Step-by-step explanation:
In Week 1, Kim uses 7 50kg bags of flour
In Week 2, Kim uses 14 50kg bags of flour
In Week 3, Kim uses 8 X 50kg bags of flour
In Week 4, Kim uses 13 X 50kg bags of flour
In Week 5, Kim will make 2400 loaves.
Each of these loaves will need 250g of flour.
Total Mass of flour that will be used =2400 X 250=600,000 grams
[tex]600,000$ grams=600,000 \div 1000$ kg =600kg\\Number of 50-kg bags =600 \div$ 50 =12 bags[/tex]
In Week 5, Kim will use 12 bags.
Therefore:
Weekly Mean number of 50kg bags of flour used in these 5 weeks.
[tex]=\dfrac{7+14+8+13+12}{5}\\\\ =\dfrac{54}{5}\\\\=10.8 \\ \approx 11$ bags[/tex]
The cost of 4kg of Apple and 6kg of orange is Rs620.If the cost of orange is the same as the cost of 5 kg Apple find the cost of per kg of Apple and orange?
Answer:
The apple cost RS 18.24 per kg, while
the orange cost RS 91.18 per kg.
Step-by-step explanation:
Let the cost of 1kg if apple and orange be RS A and RS O respectively.
From the first line:
4A +6O= 620
2A +3O= 310 -----(1) (÷2 throughout)
From the information given in second line:
O= 5A -----(2)
subst. (2) into (1):
2A +3(5A)= 310
2A +15A= 310 (expand)
17A= 310 (simplify)
A= 310 ÷17 (÷17 on both sides)
A= 18.235 (5 s.f.)
A= 18.24 (2 d.p.)
Subst. into (2):
O= 5(18.235)
O= 91.18 (2 d.p.)
Determine the number of ways three trumpet players out of 6 are chosen for 1st chair, 2nd chair, and 3rd chair.
Answer:
120 ways
Step-by-step explanation:
There are 3 spots and 6 options
_ _ _
1 2 3
6 ways for 1st chair to be chosen
5 ways for 2nd chair to be chosen (1st chair is chosen already, so there are 5 players left)
4 ways for 3rd chair to be chosen (1st and 2nd are already chosen, only 4 players left)
Multiply 6*5*4 to find the total number of ways (120)
Simplify
20x over 70x
Answer:
The answer is 2/7.
Step-by-step explanation:
You have to cut out the common terms :
[tex] \frac{20x}{70x} [/tex]
[tex] \frac{20}{70} [/tex]
[tex] \frac{2}{7} [/tex]
Each roll of tape is 30.5 feet long. A box contains 454 rolls of tape. How many yards are there in total
Answer:
Answer: 4615.66667
Steps: 1 foot=0.33333
total feets=30.5×454=13847
13847 feets=46.1566667 yards
What is the slope of a line that is parallel to the line y =3/4 x + 2?
a. -4/3
b. -3/4
c. 3/4
d. 4/3
Answer:
The answer is C, 3/4.
Since it is parallel to y=3/4 x+2, 3/4 is the slope for both equations.
A 120-gallons (gal)tank initially contains 90 lb of a salt dissolved in 90 gal of water. Brine containing 2 lb/gal of salt flows into the tank at the rate of 4gal/min. The mixture is kept uniform by stirring, and the stirred mixture flows out at the rate of 3gal/min. How much salt does the tank contain when it is full
Answer:
The tank will contain 202 Ib of salt when it's full.
Step-by-step explanation
To find the amount of salt in the tank at time t= x(t)
If x(0)= 90Ib
To find the volume of the tank at time t
V(t)= 90+(4-3)t=90+t gal
Other solutions are found attached
For a hyperbolic mirror the two foci are 42 cm apart. The distance of the vertex from one focus is 6 cm and from the other focus is 36 cm. Position a coordinate system with the origin at the center of the hyperbola and with the foci on the y-axis. Find the equation of the hyperbola.
Answer:
[tex]\dfrac{y^2}{225} -\dfrac{x^2}{216}=1[/tex]
Step-by-step explanation:
For a hyperbolic mirror the two foci are 42 cm apart.
The distance between the foci = 2c.
Therefore:
2c=42c=21The distance of the vertex from one focus = 6 cm
The distance of the vertex from the other focus = 36 cm
2a=36-6=30
a=15Now:
[tex]c^2=a^2+b^2\\21^2=15^2+b^2\\b^2=21^2-15^2\\b^2=216\\b=6\sqrt{6}[/tex]
If the transverse axis lies on the y-axis, and the hyperbola is centered at the origin. Then the hyperbola has an equation of the form:
[tex]\dfrac{y^2}{a^2} -\dfrac{x^2}{b^2}=1[/tex]
Therefore, the equation of the hyperbola is:
[tex]\dfrac{y^2}{225} -\dfrac{x^2}{216}=1[/tex]
need answers to 34 35 and 36
Answer:
34) 75
35) 60
36) 210
Step-by-step explanation:
34) Area of a rectangle:
L x B
= 15 x 5
= 75
35) Area of a trapezium :
½ h (sum of || sides)
= ½ x 6 x (12+8)
= 3 x 20
= 60
36) Area of a regular hexagon:
3BH
= 3 x 7 x 10
210
Hope it helps....
Answer:
Step-by-step explanation:
35. 75
area of rectangle : A = b x h
= 15 X 5
= 75
36. 60
area of trapezoid : A = (b1 + b2) x h
2
= (8+12) x 6
2
= 60
37. 210
area of regular polygon : A = P x a (P no. of sides) (a is apothem)
2
= (6 x 10) x 7
2
= 210
Draw a model of square root of 12 using perfect squares
Answer:
The answer is "[tex]\sqrt{12}[/tex] is not a perfect square".
Step-by-step explanation:
12 is not a perfect square because it is the natural number, and no other natural number would square the number 12, that's why it is not a perfect square.
If we calculate the square root of [tex]\sqrt{12}[/tex]. so, it is will give [tex]2\sqrt{3}[/tex] that is not a perfect square root which can be described as follows:
[tex]\Rightarrow \sqrt{12}= \sqrt{2\times 2\times 3}[/tex]
[tex]= \sqrt{2^2\times 3}\\\\= 2\sqrt{3}\\\\[/tex]
[tex]\bold{\sqrt{12}}[/tex] is not a perfect square root.
Answer:
Here's a picture
Step-by-step explanation:
In a random sample survey 75 people at a high school football game 60 people said that they wanted the home team to win there a total of 600 people at the football game how many people would predict do you want the home team to win based on the survey
Answer:
480
Step-by-step explanation:
Which type of symmetry?
Answer:
both rotational and reflectional
Answer: both rotational and reflectional
Step-by-step explanation: a p e x
It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) of an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. The following data were obtained for a collection of archaeological sites in New Mexico. x = 5.22 5.69 6.25 6.75 7.25 y 17 12 33 37 62What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? a. 95.7% b. 0.7% c. 8.4% d. 91.6% e. 4.3%
Answer:
(B) 0.7%
Step-by-step explanation:
X = Land Elevation (in ,000 feet)
Y = Unidentified Artifacts (in %)
The hypothetical theory says that:
The higher the elevation, the higher the percentage of unidentified artifacts in the location.
To find the percentage of variation in Y that can be explained by variations in X, we find the slope of the graph of X on Y.
Transforming X to thousand feets, we have 5220, 5690, 6250, 6750, 7250. This is in the attachment, plotted against 17, 12, 33, 37 and 62 respectively.
Further calculations, along with the graph, are in the attachment below. The answer therein is (B) 0.7%
A = (5,2), B = (2,4), C = (6,7) and D = (9,5) What is the length of the shorter diagonal of parallelogram ABCD?
Answer:
[tex] AC = \sqrt(26) \approx 5.1 [/tex]
Step-by-step explanation:
The diagonals are AC and BD.
Now we find the lengths of the diagonals using the distance formula.
[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
AC:
[tex] AC = \sqrt{(6 - 5)^2 + (7 - 2)^2} [/tex]
[tex] AC = \sqrt{(1)^2 + (5)^2} [/tex]
[tex] AC = \sqrt{1 + 25} [/tex]
[tex] AC = \sqrt{26} [/tex]
BD:
[tex] BD = \sqrt{(9 - 2)^2 + (5 - 4)^2} [/tex]
[tex] BD = \sqrt{(7)^2 + (1)^2} [/tex]
[tex] BD = \sqrt{49 + 1} [/tex]
[tex] BD = \sqrt{50} [/tex]
Since sqrt(26) < sqrt(50), then the shorter diagonal is AC.
Answer: AC = sqrt(26) or approximately 5.1
Answer:
A = (5.2)
Step-by-step explanation:
c2= (6-5)^2 + (7-2)^2
To find AC we calculate within parenthesis (6-5) : 1
c2= 1 + (7-2)^2
calculate within parenthesis (7-2) : 5
c2 = 1^2 + 5^2
then calculate exponents 1^2:1
c^2 = 1+5^2
add and subtract left to right
c^2 = 1+25
c^2 =26
Sr of 26 = 5.09901951359
Which means the closest answer is A = 5.2
To find BD we calculate within parenthesis (9-2):7
c2= (9-2)^2 + (5 - 4)^2
calculate within parenthesis (5-4) : 1
c2 = (7)^2 + (1)^2
calculate exponents 1 ^2 : 1
c2 = 49 +1
add and subtract left to right
c2 = 50
Sr of 50 = 7.07106781187
An item has a listed price of 90$. If the sales tax rate is 6% how much is the sales tax (in dollars)?
Answer:
five dollars and forty cents
5.40$
Step-by-step explanation:
90+6%= 95.40
Write the equation of the line parallel to y+4= 1/4(x+5) and passing through the point (8, 20). Write in the format y = mx + b
Answer:
[tex]y=0.25x+18[/tex]
Step-by-step explanation:
So first we take the equation we are given and write it in slope-intercept form (y = mx + b):
[tex]y+4= \frac{1}{4} (x+5)\\\\y+4=0.25x +1.25\\\\y=0.25x-2.75[/tex]
Now we know parallel lines have the same slope, so the line we are looking for has a slope of 0.25.
so we can start to set up our equation:
[tex]y=0.25x+b[/tex]
and then substitue in the point (8,20) to find the y-intercept.
[tex]20=0.25(8)+b\\20=2+b\\b=18[/tex]
So now we have our equation:
[tex]y=0.25x+18[/tex]
Hope this helps!
Professional basketball coaches may coach at one of three levels: Assistant, Associate, or Head. It is possible to transition from any of these levels (states) to another. Each of these three states is transient because once someone leaves coaching at any level they never return (at least according to our model). On average, annual salary for head coaches is $104,485, for associates is $62,993, and for assistants is $41,389. Using our P matrix, we have solved to find the fundamental matrix (we have called it the (I-Q) inverse matrix): Assist Assoc Head Assist 6 4 2 Assoc 2 6 6 Head 1 2 10 For someone who is a head coach - what is their expected income for the remainder of their professional coaching career?
Answer:
For someone who is a head coach - their expected income for the remainder of their professional coaching career will be
Expected income = 1×$41,389 + 2×$62,993 + 10×$104,485
Expected income = $1,212,225
Step-by-step explanation:
Professional basketball coaches may coach at one of three levels:
AssistantAssociateHeadOn average, the annual salary is given by
Assistant = $41,389Associate = $62,993Head = $104,485Using our P matrix, we have solved to find the fundamental matrix (we have called it the (I-Q) inverse matrix):
Assistant Associate Head
Assistant 6 4 2
Associate 2 6 6
Head 1 2 10
For someone who is a head coach - what is their expected income for the remainder of their professional coaching career?
As per the given P matrix, for someone who is a head coach will be:
Assistant = 1 time
Associate = 2 times
Head = 10 times
Therefore, the expected income will be,
Expected income = 1×$41,389 + 2×$62,993 + 10×$104,485
Expected income = $1,212,225
the sum of three consecutive odd numbers. is 63. ¿what is the smalles of these numbers?
Answer: The answer is 19
Step-by-step explanation:
Tyson’s puppy weighed 8 pounds 3 ounces last year.
In one year the puppy gained 2 pounds 4 ounces.
How much does Tyson’s puppy weigh now in ounces?
Last year- 8 lbs 3 ounces
Add 2 lbs and 4 ounces
Which is 10 lbs 7 ounces
10 lbs in onces is 160 ounces
Then you add the other 7 ounces so the final answer is 167 ounces
Tyson’s puppy weighs 167 ounces!
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A ball is tossed into the air from a height of 6 feet above ground level,
with a velocity of 3.4 feet per second. Which function could be used to
model the height of the ball, after t seconds?
Answer:
I think it would be the first but not 100% sure
Step-by-step explanation:
For all the people that have to do algebra and dont want to do it yourself there is a website or you can download it on your phone its called*** MATH PAPA*** ****IT SHOWS YOU STEP BY STEP AND GIVES YOU THE ANSWER*** Just input the equation
The result of which expression will best estimate the actual product of (-4/5)(3/5)(-6/7)(5/6)
Answer:
[tex]\frac{12}{35}[/tex]
Step-by-step explanation:
[tex]\frac{-4}{5} * \frac{3}{5} * (\frac{-6}{7} ) * \frac{5}{6}[/tex]
[tex]\frac{(-4) * 3}{5 * 1} * \frac{(-1)}{7} \\\\\frac{12}{35}[/tex]
Consider the following numbers Which of these numbers are counting numbers?
{9 ,1, 4/5, √16 , 0.7 , -1, -√2 , π , 0}
The counting number(s) is/are _______(Use a comma to separate answers as needed Do not simplify.)
Answer:
9, 1
Step-by-step explanation:
Counting numbers are numbers that can be used for counting purposes. This group of numbers does not include negative numbers, fractions, zero, decimal numbers etc. They are positively directed whole numbers.
From the question, given the condition not to simplify, then the counting numbers are:
9, 1
others numbers can not be referred to as counting numbers.
Which graph shows exponential growth?
The answer is graph A 7/9/20 edge
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
During your journey, you develop an abscessed tooth and have to visit the dentist. You are prescribed an antibiotic with a dosage of 7.5 mg/kg every six hours. If you weigh 128 pounds and the antibiotic comes in 250 mg tablets, how many tablets should you take each day?
Answer:
I should take 10.44 tablets in a day, approximately 10.5 tablets.
Step-by-step explanation:
In order to solve this problem we need to convert the weight from pounds to kilograms, to do that we need to divide it by 2.205.
[tex]w = \frac{128}{2.205}\\w = 58.05 \text{ kg}[/tex]
Since I need to take 7.5 mg per kg of body weight, then in order to find the dosage we need to multiply the weight in kg by 7.5.
[tex]\text{dosage} = 58*7.5 = 435 \text{ mg}[/tex]
Since I need to take it every six hours and there are 24 hours in a day, we will have to take 4 dosages in a day, therefore we need:
[tex]\text{dosage(day)} = 435*6 = 2,610 \text{ mg}[/tex]
The antibiotic comes in 250 mg in tablets, therefore the number of tablets is:
[tex]tablets = \frac{2610}{250} = 10.44[/tex]
I should take 10.44 tablets in a day, approximately 10.5 tablets.
The tree diagram below shows all of the possible outcomes for flipping three coins.
What is the probability of one of the coins landing on tails and two of them landing on heads?
A) 1/4
B) 3/8
C) 1/2
D) 3/4
Answer:
B
Step-by-step explanation:
In that scenario, you would have one T and two H's, in any order. Looking at the chart, this happens in 3 different scenarios. Since there are a total of 8 possible outcomes, the probability of this happening is 3/8 or answer choice B. Hope this helps!
Answer:B
Step-by-step explanation: the number of event is 3 event={HHT, HTH,THH }
And the number of sample space is 8
By using 2^n formula our n is 3 2^3 = 8
The probability = 3/8
Hope it helps
Brainliest please
The cost of a circular table is directly proportional to the square of the radius. A circular table with a radius of 50cm costs £60. What is the cost of a circular table with a radius of 75cm? Show all your working
Answer:
£135 is the correct answer.
Step-by-step explanation:
Let C be the cost of table.
And let R be the radius of table.
Cost of table is directly proportional to square of radius.
As per question statement:
[tex]C\propto R^{2}[/tex] or
[tex]C=a\times R^2 ....... (1)[/tex]
where [tex]a[/tex] is the constant to remove the [tex]\propto sign[/tex].
It is given that
[tex]C_1 =[/tex] £60 and [tex]R_1 = 50\ cm[/tex]
[tex]C_2 = ?[/tex] when [tex]R_2= 75\ cm[/tex]
Putting the values of [tex]C_1[/tex] and [tex]R_1[/tex] in equation (1):
[tex]60=a \times 50^2 ....... (2)[/tex]
Putting the values of [tex]C_2[/tex] and [tex]R_2[/tex] in equation (1):
[tex]C_2=a \times 75^2 ....... (3)[/tex]
Dividing equation (2) by (3):
[tex]\dfrac{60}{C_2}= \dfrac{a \times 50^2}{a \times 75^2}\\\Rightarrow \dfrac{60}{C_2}= \dfrac{50^2}{75^2}\\\Rightarrow \dfrac{60}{C_2}= \dfrac{2^2}{3^2}\\\Rightarrow \dfrac{60}{C_2}= \dfrac{4}{9}\\\Rightarrow C_2 = 15 \times 9 \\\Rightarrow C_2 = 135[/tex]
So, £135 is the correct answer.
Write an equation of a line that is parallel to the line 3y=-x+6 and passes through the point (6,2).
Answer:
y = x+2
y =-x+2 shows 0
We want to show 1 both sides
2y = x+2 shows 2
y = x+2 shows 0 as explained below.
Step-by-step explanation:
3y−x=6
Solve for y.
y=2+x3
Rewrite in slope-intercept form.
y=13x+2.
Use the slope-intercept form to find the slope and y-intercept.
Slope: 13 y-intercept: 2
Any line can be graphed using two points. Select two
x values, and plug them into the equation to find the corresponding y values.
xy 02, 33
Graph the line using the slope and the y-intercept, or the points.
Slope:
13y-intercept: 2x y (0,2) (3,3)
