Answer:
The "formula" for an exponential function is f(x) = a * bˣ where a is the initial value / y-intercept. Therefore, a = 4 so f(x) = 4 * bˣ. To solve for b, we can plug in the values x = 3 and f(x) = 500 which becomes:
500 = 4 * b³
125 = b³
b = 5 so the answer is f(x) = 4 · 5ˣ.
Answer:
f(x)=4(5)x
Step-by-step explanation:
An exponential equation in the form y=a(b)x has initial value a and common ratio b. The initial value is the same as the y-intercept, 4, so the equation is in the form y=4(b)x. Substituting the point (3,500) gives 500=4(b)3. Solve for b to find that the common ratio is 5.
Use the formula A=2πrh to find the area of the curved surface of each of the cylinders below. (Express your answers correct to 1 decimal place.)
Answer:
here,
A=2×22÷7×17/2×21
A=22×17×3
A=1122 sq.cm
PLSS HELP I NEED THIS
Answer:
t = kp, i think
FIND THE EQUATION OF THE ELLIPSE WITH A CENTER AT (2, 2), VERTICES AT (-3,
2) AND (7, 2), AND FOCI AT (-1, 2) AND (5,2),
Answer:
Step-by-step explanation:
The standard equation of an ellipse centered at the point (h,k) is
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2} = 1[/tex]
where a is the distance from the center to one of the vertex. We have the relation [tex]c= \sqrt[]{a^2-b^2}[/tex] where c is the distance from one of the focus to the center.
The distance between one vertex and the center is 5. So a=5. The distance from one focue to the center is 3. Then c =3. So we have that [tex]b^2 = a^2-c^2 = 16[/tex]
so the equation is
[tex]\frac{(x-2)^2}{25}+\frac{(y-2)^2}{16} = 1[/tex]
Find the range of the data set represented by this box plot. 80 76 40 56
Answer:
56
Step-by-step explanation:
The range is the right line value minus the left line value
140 - 84
56
Which of the following situations describes a continuous distribution? A probability distribution showing the number of vaccines given to babies during their first year of life A probability distribution showing the average number of days mothers spent in the hospital A probability distribution showing the weights of newborns A probability distribution showing the amount of births in a hospital in a month
Answer:
Continous distributions:
- A probability distribution showing the average number of days mothers spent in the hospital.
- A probability distribution showing the weights of newborns.
Step-by-step explanation:
A probability distribution showing the number of vaccines given to babies during their first year of life will have a discrete distribution as only a natural number can represent the number of vaccines (0, 1, 2 vaccines and so on).
A probability distribution showing the average number of days mothers spent in the hospital can be described as continous because we are averaging days and this average can be fractional, so it is not discrete.
A probability distribution showing the weights of newborns is continous, as the weights are a continous variable (physical measurement), not discrete.
A probability distribution showing the amount of births in a hospital in a month is a discrete distribution, as the number of births can only be represented by natural numbers.
The option that describes a continuous distribution include:
A probability distribution showing the average number of days mothers spent in the hospital.A probability distribution showing the weights of newborns.A continuous distribution simply means the probabilities of the values of a continuous random variable.
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The graph of a function is shown:
In which interval is the graph decreasing?
Answers:
A - AB
B - BC
C - CD
D - DE
Answer:
Maybe D-DE
Step-by-step explanation:
Because D has been decrease to E
What is the value of the expression below?
(-8)^4/3
Answer:
16
Step-by-step explanation:
(-8)^4/3
-(8^1/3)⁴
-(∛8)⁴
-(2)⁴
-2⁴
= 16
Answer: the ^^^^ right I check it
Step-by-step explanation:
Ellie bought two planks of wood that were each 4ft 3in long, and two planks of wood that were each 6 ft 5in long. What is the total length of the wood she purchased?
Answer:
21 feet 4 inches
Step-by-step explanation:
Ellie bought two planks of wood that were each 4ft 3in long
Total length of these two planks = 4ft 3in + 4ft 3in = 8 feet 6 inches
she also bought two planks of wood that were each 6 ft 5in long
Total length of these two 6 ft 5in planks = 6 ft 5in + 6 ft 5in = 12 feet10 inches
Thus, total length of all the woods purchased = Total length of 4ft 3in two planks + Total length of the two 6 ft 5in planks
= 8 feet 6 inches + 12 feet 10 inches
adding feet with feet and inches with inches term
= 20 feet 16 inches
we know that 12 inches is equal to 1 feet
thus, 16 inches can be written as 1 feet 4 inches
thus,
20 feet 16 inches will be same as 21 feet 4 inches
The total length of the wood Ellie purchased is 21 feet 4 inches.
By the congruent complements theorem, which angle is congruent to Angle4? Angle1 Angle2 Angle3 Angle5
Answer:
Option (1)
Step-by-step explanation:
Congruent complements theorem;
"If two angles are complementary to the same angle, then these angles are congruent to each other."
It's given that ∠4 and ∠5 are the complements and ∠1 and ∠5 are compliments.
Which shows ∠1 and ∠4 are complimentary to the same angle ∠5.
Therefore, ∠1 and ∠4 will be congruent.
Option (1) will be the answer.
Answer:
1
Step-by-step explanation:
The hypotenuse of an isosceles triangles measures 10 inches long. What is the length of one leg of the triangle?
For any isosceles right triangle (aka 45-45-90 triangle), the hypotenuse is always equal to sqrt(2) times the leg. If x is the leg and y is the hypotenuse, then
[tex]y = x*\sqrt{2}[/tex]
which solves to
[tex]x = \frac{y}{\sqrt{2}}[/tex]
from here we plug in the given hypotenuse y = 10 to get the final answer. Optionally we could rationalize the denominator, but your teacher has chosen not to.
Answer:b
On edge
Step-by-step explanation:
Can u guys tell me the answer to question 8 and 9 thank you so much
I would really appreciate it
Thank you
Step-by-step explanation:
Q8.
Step 1.
35.4 - 31 = 4.4
Step 2.
4.4 ÷ 31 = 0.1419....
Step 3.
0.1419.... x 100 = 14.19...
Step 4.
To one decimal place = 14.2% increase
Q9.
Step 1.
£10 ÷ 40 articles = £0.25 = 25p (this is the answer to part a)
Step 2.
32p x 40 articles = £0.32 x 40 articles = £12.80 (this is the answer to part b)
Step 3.
£12.80 - £10 = £2.80 (this is the answer to part c)
Step 4.
£2.80 ÷ £10 = 0.28
Step 5.
0.28 x 100 = 28% (this is the answer to part d)
Hope this was what you were looking for :)
(Also, hi to a fellow Brit - there aren't that many of us around here)
Bluey :)
Karissa buys a bag of cookies that contains 4 chocolate chip cookies, 4 peanut butter cookies, 9 sugar cookies and 6 oatmeal cookies. What is the probability that Karissa reaches in the bag and randomly selects an oatmeal cookie from the bag, eats it, then reaches back in the bag and randomly selects a chocolate chip cookie
Answer:
12 / 253
Step-by-step explanation:
There are a total of 4 + 4 + 9 + 6 = 23 cookies in the bag, therefore, there are 23 * 22 = 506 ways to pick one cookie, eat it, and then pick another cookie. There are 6 ways to choose the first cookie (because there are 6 oatmeal cookies) and 4 ways to choose the second cookie (because there are 4 chocolate chip cookies) so there are 6 * 4 = 24 successful ways. The probability is thus 24 / 506 = 12 / 253.
Betty and Karen have been hired to paint the houses in a new development. Working together, the women can paint a house in two-thirds the time that it takes Karen working alone. Betty takes 14 h to paint a house alone. Betty takes 6 h to paint a house alone.
Required:
How long does it take Karen to paint a house working alone?
Answer: 3 hours
Step-by-step explanation:
Here is the correct question:
Betty and karen have been hired to paint the houses in a new development. Working together the women can paint a house in two thirds the time that it takes karen working alone. Betty takes 6 hours to paint a house alone. How long does it take karen to paint a house working alone?
Since Betty takes 6 hours to paint a house alone, that means she can paint 1/6 of the house in 1 hour.
Karen can also paint 1/x in 1 hour
Both of them will paint the house in 3/2 hours.
We then add them together which gives:
1/6 + 1/x = 3/2x
The lowest common multiple is 6x
1x/6x + 6/6x = 9/6x
We then leave out the denominators
1x + 6 = 9
x = 9 - 6
x = 3
Karen working alone will paint a house in 3 hours.
If 2/3 of a certain number is subtracted from twice the number, the result is 20. Find the number.
Answer:
[tex]\boxed{x = 15}[/tex]
Step-by-step explanation:
Let the number be x
Condition:
[tex]2x - \frac{2}{3} x = 20[/tex]
Multiplying 3 to both sides
=> 3(2x) - 2x = 3(20)
=> 6x - 2x = 60
=> 4x = 60
Dividing both sides by 4
=> x = 15
Answer:
15
Step-by-step explanation:
Let x be that number.
2/3 of x subtracted from twice of x is 20.
2x - 2/3x = 20
Solve for x.
Combine like terms.
4/3x = 20
Multiply both sides by 3/4
x = 60/4
x = 15
The number is 15.
√50 as a mixed radical!
Answer:
5sqrt(2)
Step-by-step explanation:
you can split 50 into sqrt(25×2)
and the sqrt(25) is 5, so than your left with just the 2 in the sqrt.
1. Write the inverse of equation of the function f(x) = x^2 - 4? 2. Sketch the inverse of the function f(x)= x^2 - 4 on graphing paper. Remember that the inverse graph should look identical in shape to the original, only flipped or rotated in some way. You equation should represent the equation you provided in #1. 3. You should notice that your graph in #2 is not a function. Choose part of the graph that would represent a function when graphed on its own. Highlight this portion of your graph . 4. Now that you have a function highlighted in #3, what are the domain and range of this highlighted function? (We are asking you to find the restricted domain and range of the inverse equation from #1 that makes this an inverse function on its own).
Answer: 1) [tex]\pm \sqrt{x+4}[/tex]
2) see graph
3) Choose one color from the graph
4) D: x ≥ -4
R: y ≥ 0 for [tex]\sqrt{x+4}[/tex] or y ≤ 0 for [tex]-\sqrt{x+4}[/tex]
Step-by-step explanation:
1) To find the inverse, swap the x's and y's and solve for y:
Given: y = x² - 4
Swap: x = y² - 4
x + 4 = y²
[tex]\pm \sqrt{x+4}=y[/tex]
2) see attachment. Red and Blue combined creates the graph of the inverse.
3) Choose either the positive (red graph) or the negative (blue graph).
red graph: [tex]y= \sqrt{x+4}[/tex]
blue graph: [tex]y= -\sqrt{x+4}[/tex]
4) Domain reflects the x-values of the function. The x-values for the red graph is the same as the blue graph so the answer will be the same regardless of which equation you choose.
Domain: x ≥ 0
Range reflects the y-values of the function. The y-values differ between the positive and negative inverse functions. Positive is above the x-axis. Negative is below the x-axis.
Range (red graph): y ≥ 0 for [tex]y= \sqrt{x+4}[/tex]
Range (blue graph): y ≤ 0 for [tex]y= -\sqrt{x+4}[/tex]
Enter the range of values for x
Greetings from Brasil...
See the attached figure. The smaller the θ angle, the smaller the AB side will be. If the angle θ = 90º, then AB = 25. As θ < 90, then AB < 25
5X - 10 < 25
5X < 25 + 10
X < 35/5
X < 7
The AB side can be neither zero nor negative. So
5X - 10 > 0
5X > 10
X > 10/5
X > 2
2 < X < 7Based on the dot plot, which statements are correct? Check all that apply
Eleven students answered Mr. Chiu's question.
Twelve students answered Mr. Chiu's question.
Three people studied for two hours.
Three people studied for three hours.
Everyone who responded studied for at least one hour.
Four people studied for four or more hours
Answer: options 2,3and 6
Answer:
option
2-Twelve students answered Mr. Chiu’s question.
3-Three people studied for two hours.
6-Four people studied for four or more hours.
Step-by-step explanation:
hope this helps:)
What is the sum of arithmetic series 19+25+31+37+… Where n=9 ?
Answer:
387
Step-by-step explanation:
The required sum of the arithmetic series 19+25+31+37+… Where n=9 is 387.
An arithmetic series is given,19+25+31+37+… sum of this series is to be determined where n=9.
Arithmetic progression is the series of numbers that have a common difference between adjacent values.
Here,
The Sum of an arithmetic series is given as
[tex]Sn=n/2(2a+(n-1)d)[/tex]
Where n (total terms) =9
a (first term) = 19
d (common difference) = 6
Now,
[tex]S_9=9/2(2*19+(9-8)6)\\ S_9=9/2(38+64)\\S_9=9/2*86\\S_9=387[/tex]
Thus, the required sum of the arithmetic series 19+25+31+37+… Where n=9 is 387.
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My boss has told me that I will need one gallon of paint for every 300 square feet of wall I must paint. Unfortunately, the store only sells cans containing 4 liters of paint, and our client has told me that she needs 400 square meters of wall painted. One liter contains approximately 0.264 gallons, and there are approximately 3.28 feet in a meter. What is the smallest number of cans of paint I can buy to complete the paint job?
Answer: 14 cans
Step-by-step explanation:
Given, Total area to paint = 400 square meters
approximately 3.28 feet in a meter.
So, 400 square meters = 400 x (3.28)² square feet
i.e. Total area to paint = 4303.36 square feet
One gallon of paint requires for every 300 square feet.
One liter contains approximately 0.264 gallons
Then, One gallon = [tex]\dfrac{1}{0.264}\approx3.78\text{ liters}[/tex]
So, 3.78 liters paint requires for every 300 square feet.
Paint requires for each square feet = (3.78)÷(300) liters
Total paint required = (Total area to paint ) x (Paint requires for each square feet)
= (4303.36)x (3.78)÷(300)
≈54.22 liters
Each can contains 4 liters of paint.
Smallest number of cans required = (Total paint required )÷ 4
=(54.22 ) ÷ 4
= 13.55≈ 14
Hence, 14 cans are required .
Simplify.
cot x
CSC X
Use algebra and the fundamental trigonometric identities.
Your answer should be a number or use a single trigonometric
Answer:
Cosx is the answer.
Step-by-step explanation:
We have to simplify the trigonometric fraction given in this question.
[tex]\frac{\text{Cotx}}{\text{Cscx}}[/tex]
Further we can rewrite this ratio in the simplified form.
Since, Cot x = [tex]\frac{\text{Cosx}}{\text{Sinx}}[/tex] and Cosec(x) = [tex]\frac{1}{\text{Sinx}}[/tex]
Now substitute these simplified forms of Cotx and Cscx in the given fraction.
[tex]\frac{\text{Cotx}}{\text{Cscx}}[/tex] = [tex]\frac{\frac{\text{Cosx}}{\text{Sinx}}}{\frac{1}{\text{Sinx}}}[/tex]
= [tex]\frac{\text{Cosx}}{\text{Sinx}}\times \text{Sinx}[/tex]
= Cosx
Therefore, Cosx will be the answer.
A company is evaluating which of two alternatives should be used to produce a product that will sell for $35 per unit. The following cost information describes the two alternatives.
Process A Process B
Fixed Cost $500,000 $750,000
Variable Cost per Unit $25 $23
Requirement:;
i) Calculate the breakeven volume for Process A. (show calculation to receive credit)
ii) Calculate the breakeven volume for Process B. (show calculation to receive credit)
III) Directions: Show calculation below and Circle the letter of the correct answer.
If total demand (volume) is 120,000 units, then the company should
select Process A with a profit of $940,000 to maximize profit
select Process B with a profit of $450,000 to maximize profit
select Process A with a profit of $700,000 to maximize profit
select Process B with a profit of $690,000 to maximize profit
Answer:
A.50,000 units
B.62,500 units
C.Process A with a profit of $700,000 to maximize profit
Step-by-step explanation:
A.Calculation for the breakeven volume for Process A
Using this formula
Breakeven volume for Process A= Fixed cost/(Sales per units-Variable cost per units)
Let plug in the formula
Breakeven volume for Process A=500,000/(35-25)
Breakeven volume for Process A=500,000/10
Breakeven volume for Process A=50,000 units
B.Calculation for the breakeven volume for Process B
Using this formula
Breakeven volume for Process B= Fixed cost/(Sales per units-Variable cost per units)
Let plug in the formula
Breakeven volume for Process B=750,000/(35-23)
Breakeven volume for Process B=750,000/12
Breakeven volume for Process B=62,500 units
C. Calculation for what the company should do if the total demand (volume) is 120,000 units
Using this formula
Profit=(Total demand*(Sales per units-Variable cost per units for Process A)- Process A fixed cost
Let plug in the formula
Profit =120,000*($35-$25)-$500,000
Profit=120,000*10-$500,000
Profit=1,200,000-$500,000
Profit= $700,000
Therefore If total demand (volume) is 120,000 units, then the company should select Process A with a profit of $700,000 to maximize profit.
The population in Smalltown in 2010 was 47,597 people and is growing exponentially at a rate of 1.8 percent. Which of the following equations defines the population t years after 2010?
Given Information:
Starting population = P₀ = 47,597
rate of growth = 1.8%
Required Information:
Equation that defines the population t years = ?
Answer:
The following equation defines the population t years after 2010.
[tex]$ P(t) = 47,597e^{0.018t} $[/tex]
Step-by-step explanation:
The population growth can be modeled as an exponential function,
[tex]$ P(t) = P_0e^{rt} $[/tex]
Where P₀ is the starting population in 2010, r is the rate of growth of the population and t is the time in years after 2010.
We are given that the starting population is 47,597 and rate of growth is 1.8%
So the population function becomes
[tex]$ P(t) = 47,597e^{0.018t} $[/tex]
Therefore, the above function may be used to estimate the population for t years after 2010.
For example:
What is the population after 10 years?
For the given case,
t = 10
[tex]$ P(10) = 47,597e^{0.018(10)} $[/tex]
[tex]$ P(10) = 47,597e^{0.18}$[/tex]
[tex]$ P(10) = 47,597(1.1972)$[/tex]
[tex]$ P(10) = 56,984[/tex]
write an equation to represent the following statement 29 is 6 more than K solve for K
K =
Answer:
23Step-by-step explanation:
29 is 6 more than K
Let's create an equation
[tex]29 = 6 + k[/tex]
Move variable to L.H.S and change its sign
Similarly, move constant to R.H.S and change its sign
[tex] - k = 6 - 29[/tex]
Calculate
[tex] - k = - 23[/tex]
Change the sign on both sides of the equation
[tex]k = 23[/tex]
Hope this helps..
Best regards!!
The equation for the statement 29 is 6 more than K is solved and K = 23
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
In an equation, the expressions on either side of the equals sign are called the left-hand side (LHS) and the right-hand side (RHS), respectively. The equals sign (=) indicates that the two expressions have the same value, and that the equation is true for certain values of the variables involved.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. It typically consists mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation.
Given data ,
Let the equation be represented as A
Now , the value of A is given by the statement below
29 is 6 more than K
On simplifying , we get
29 = 6 + K
Subtracting 6 on both sides , we get
K = 29 - 6
K = 23
Therefore , the value of K is 23
Hence , the equation is K = 23
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A shipment of 627 tons of sugar is separated into containers of equal size. If the shipment fills 4 containers, how much sugar can one container hold? Write your answer as a mixed number in simplest form.
Answer:
156.75 tons
Step-by-step explanation:
627/4 = 156.75
Answer:
156(3/4)
Step-by-step explanation:
with this your divide.
627/4=156.75
as a mixed numer it would 156(3/4). It is 3/4 because the number ends in .75
A new vaccination is being used in a laboratory experiment to investigate whether it is effective. There are 275 subjects in the study. Is there sufficient evidence to determine if vaccination and disease status are related? Vaccination Status Diseased Not Diseased Total Vaccinated 53 17 70 Not Vaccinated 62 143 205 Total 115 160 275
Answer:
Step-by-step explanation:
From the give information: A new vaccination is being used in a laboratory experiment to investigate whether it is effective. There are 275 subjects in the study. Is there sufficient evidence to determine if vaccination and disease status are related?
Vaccination Status Diseased Not Diseased Total
Vaccinated 53 17 70
Not Vaccinated 62 143 205
Total 115 160 275
In this study, we have two variables ( Vaccination and diseases status ) The null and the alternative hypothesis can be stated as follows:
Null hypothesis: The two variables ( Vaccination and diseases status ) are independent
Alternative hypothesis : The two variables ( Vaccination and diseases status ) are dependent
The Chi-square test statistics can be computed as:
The Expected Values for the table can be calculated by using the formula:
[tex]E_i=\dfrac{row \ total \times column \ total}{grand \ total}[/tex]
Vaccination Status Diseased Not Diseased Total
Vaccinated 29.273 40.727 70
Not Vaccinated 85.727 119.273 205
Total 115 160 275
[tex]Chi - Square \ X^2 = \dfrac{(O_i-E_i)^2}{E_i}[/tex]
Vaccination Status Diseased Not Diseased Total
Vaccinated 19.232 13.823 33.055
Not Vaccinated 6.564 45.573 52.137
Total 25.796 59.396 85.192
Therefore;
the Chi-Square Test Statistics = 85.192
For this study; we two rows and two columns
Therefore, the degree of freedom = (rows-1) × (columns-1)
the degree of freedom = (2 - 1) × (2 - 1)
the degree of freedom = 1 × 1
the degree of freedom = 1
Using the level of significance of ∝ = 0.05 and degree of freedom = 1 for the chi-square test
The p-value for the test statistics = 0.00001
Decision rule: Since the P-value is lesser than the level of significance , therefore we reject the null hypothesis at the level of significance of 0.05
Conclusion:
We accept the alternative hypothesis and conclude that the two variables
(Vaccination and diseases status ) are dependent i.e the vaccination and disease status are related
In a survey of 2257 adults, 716 say they believe in UFOs.
Construct a 99% confidence interval for the population proportion of adults who believe in UFOs.
A 99% confidence interval for the population proportion is (0.292.0.3427)
(Round to three decimal places as needed.)
Interpret your results. Choose the correct answer below.
O A. With 99% confidence, it can be said that the sample proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.
OB. The endpoints of the given confidence interval shows that 99% of adults believe in UFOs.
C. With 99% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.
XD. With 99% probability, the population proportion of adults who do not believe in UFOs is between the endpoints of the given confidence interval.
Answer:
C. With 99% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.
Step-by-step explanation:
A confidence interval let us make an inference about a population parameter from a sample statistic. In this case, a sample proportion let us infere aout the population proportion with a certain degree of confidence.
With this confidence interval, we are 99% confident that the polpulation proportion falls within this interval. This means that there is 99% chances of having the population proportion within this interval.
To estimate the population proportion of adults who do not believe in UFO's we should have to construct another confidence interval with the proportion (1-p), but this parameter can not be estimated from the confidence interval for p.
Please help me solve this
Answer:
See below
Step by step explanation
[tex] \tan( \frac{\pi}{4} + A) \tan( \frac{3\pi}{4} + A) = - 1 [/tex]
L.H.S
[tex] \tan( \frac{\pi}{4} + A) \tan( \frac{3\pi}{4} + A ) [/tex]
We know that ,
[tex] \tan(A + B) = \frac{tan \: A + tan \: B}{1 - \tan \: A \: \tan \: B } [/tex]
[tex]( \frac{ \tan( \frac{\pi}{4} + \tan \: A ) }{1 - \tan \frac{\pi}{4} \tan \: A} ) \: (\frac{ \tan \frac{3\pi}{4} + \tan \: A}{1 - \tan \frac{3\pi}{4} \tan( \: A) } )[/tex]
[tex]( \frac{1 + \tan \: A }{1 - \tan\: A} )( \frac{ \tan( x - \frac{x}{4} + \tan \: A ) }{1 - \tan(\pi - \frac{\pi}{4} ) \: \tan \: A }) [/tex] (tan π / 4 = 1 )
[tex]( \frac{1 + \tan \: A}{ -1 - \: \tan \: A } )( \frac{ - \tan( \frac{\pi}{4} + \tan \: A ) }{1 - ( - \tan \: \frac{\pi}{4}) \: \tan \: A } )[/tex] [ tan ( π - B ) = - tan∅ ]
[tex]( \frac{1 + tan \: A}{1 - tan \: B} )( \frac{ - 1 + \tan\: A }{1 + \tan \: A } )[/tex]
[tex] = \frac{ - (1 - \tan\: A)}{(1 - \tan \: A) } [/tex]
[tex] = - 1[/tex]
L.H.S = R.H.S ProvedHope this helps..
Best regards!!
The temperature over a 9-hour period is given by Upper T (t )equalsnegative t squared plus 4 t plus 34. (a) Find the average temperature. (b) Find the minimum temperature. (c) Find the maximum temperature.
Answer:
(a) 25 degrees
(b) -11 degrees
(c) 38 degrees
Step-by-step explanation:
The temperature function is:
[tex]T(t) = -t^2+4t+34[/tex]
(a) The average value for a temperature is:
[tex]M=\frac{1}{b-a}* \int\limits^b_a {f(x)} \, dx[/tex]
In this particular case, the average temperature is:
[tex]M=\frac{1}{9-0}* \int\limits^9_0 {T(t)} \, dt \\M=\frac{1}{9}* \int\limits^9_0 {(-t^2+4t+34)} \, dt \\M=\frac{1}{9}* {(-\frac{t^3}{3}+2t^2+34t)}|_0^9\\M=\frac{1}{9}*( {(-\frac{9^3}{3}+2*(9^2)+34*9)-0)[/tex]
[tex]M=25[/tex]
The average temperature is 25 degrees.
(b) The expression is a parabola that is concave down, therefore there are no local minimums, which means that the minimum temperature will be at one of the extremities of the interval:
[tex]T(0) = -0^2+4*0+34=34\\T(9) = -9^2+9*4+34=-11[/tex]
The minimum temperature is -11 degrees.
(c) The maximum temperature will occur at the point for which the derivate of the temperature function is zero:
[tex]T(t) = -t^2+4t+34\\T'(t)=-2t+4=0\\2t=4\\t=2[/tex]
At t = 2, the temperature is:
[tex]T(2) = -2^2+4*2+34=38[/tex]
The maximum temperature is 38 degrees.
What do the following two equations represent?
• x + 3y = 5
• 4x + 12y = 20
Choose 1 answer:
The same line
Distinct parallel lines
Perpendicular lines
Intersecting, but not perpendicular lines
Answer:
they represent the same line
Step-by-step explanation:
i went to desmos graphing calculator and put x+3y=5 in the first spot then i put 4x+12y=20 below that and it showed me what the lines looked like
Both the equation represent the same line
What is Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
x + 3y = 5
4x + 12y = 20
Now , the equation 4x + 12y = 20 can be simplified as
4x + 12y = 20
Divide by 4 on both sides ,
x + 3y = 5
Therefore , x + 3y = 5 is the same equation
Hence , both the equation represent the same line
To learn more about equations click :
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