The derivative of tan(cos(t) with respect to t at t= (π/2) is 1.
What is differentiation?The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The given expression is tan(cos(t)). The derivation will be done as below,
[tex]\dfrac{d}{dx}tan(cos(t))=sec^2(cos(t)\dfrac{d}{dx}(cos(t)\\\dfrac{d}{dx}tan(cos(t))=-sin(t)sec^2(cos(t)\\\dfrac{d}{dx}tan(cos(t))=-sin(\dfrac{\pi}{2} )sec^2(cos\dfrac{\pi}{2})\\\\\dfrac{d}{dx}tan(cos(t))=sec^2(0)\\\dfrac{d}{dx}tan(cos(t))=1[/tex]
Therefore, the derivative of tan(cos(t) with respect to t at t= (π/2) is 1.
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A dog breeder is planning to buy more dog food. He makes a table showing how
many pounds of food he will have after shopping. The table is based on how much he
spends and how much food he already has. Which equation generates the table?
Money Spent (x) $0 $20 $40 $60
Pounds of Food (v) 4 12 20 28
O
x=y-4
y=8x-4
x = 8y +4
Oy=x+4
The equation that generate the table in slope intercept form is y = 2 / 5 x + 4
How to generate equation of a table?The equation of a linear table can be represented in different form such as slope intercept form, point slope form, standard form and general form.
Therefore, let's represent the equation of the table of money spent and pounds of food.
using slope intercept form,
y = mx + b
where
m = slopeb = y-interceptTherefore, let's find the slope using (0, 4) and (20, 12)
m = slope = 12 - 4 / 20 - 0
slope = 8 / 20
slope = 2 / 5
Therefore, let's find the y-intercept using (0, 4)
4 = 2 / 5(0) + b
b = 4
Therefore, the equation is y = 2 /5 x + 4
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pls help me asap i dont know the answer
Answer:
96
Step-by-step explanation:
Area of a triangle
A = (1/2) × base × height
A = (1/2) × 12 × 16
A = (1/2) × 192
A = 96 units²
I hope this helps!
Which point is located on the line represented by the equation y + 4 = –5(x – 7)?
(-4, 7)
(-7, 4)
(7, -4)
(4, -7)
Answer:
(7,-4)
Step-by-step explanation:
y + 4 = -5(x-7) Substitute in 7 for x and -4 for y
-4 + 4 = -5 (7-7)
0 = 5(0)
0 = 0 This is a true statement.
29. Write the equation of the line that passes
through the point (-6, 1) and has a slope
of ½.
Answer:
Step-by-step explanation:
M is slope
B is y intercept
X and y are given
using the equation for the y intercept
b=y1-mx1
B=1−(1/2)⋅(−6)=4
Write in y=Mx+b
=12+4
The general equation of the line is −2+8=0
Given the equation F=95C+32 where C is the temperature in degrees Celsius and F is the corresponding temperature in degrees Fahrenheit, and the following ordered pairs:
(−25,F1), (−5,F2)
The values of F1 and F2 are 77 and -22 degrees Fahrenheit respectively.
How to use the equation to convert from degrees Celsius to degrees Fahrenheit?Given that; the equation F=9/5C+32 and ordered pairs are (25, F1), (−30, F2)
To convert the values to degrees Fahrenheit, we have to substitute the given values into the equation to get F1 and F2 respectively:
For (25, F1);
F = 9/5 C+32
Now put C= 25 in the equation;
F1 = 9/5(25) + 32
F1 = 45 +22
F1 = 77 degrees Fahrenheit
For (−30, F2);
F = 9/5 C+32
Now put C= -30 in the equation;
F2 = 9/5(-30) + 32
F2 = -54 + 32
F2 = -22 degrees Fahrenheit
Hence, the values of F1 and F2 are 77 and -22 degrees Fahrenheit respectively.
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121x
10
6
4
909
-6-5-4-3-2-12- 2 3 4 5 6 x
J
-8-
-10
B
h
Which statement is true regarding the functions on the
graph?
Of(6) = g(3)
Of(3) = g(3)
Of(3) = g(6)
Of(6) = g(6)
Answer:
The Question is not Correct but answer is f 3 and g 3
A rectangle has an area of 120 square meters and a width of 8 meters. What is the length?
Answer:
Step-by-step explanation:
Ok:
Area's formula is width* length
1. 120 square meters and width of 8 meters. Reversing the formula, divide area by width to get length!
120/8=15 meters
2. Answer: 15 meters
In a garden club, 90% is ladies. The number of ladies is 12 more than 3 times the number of gentlemen.
How many ladies and how many gentlemen are in the club?
(Note: set up a rational equation and solve)
The number of ladies in the club = 18
and the number of gentlemen in the club = 2
Let x be the number of gentlemen.
So, the number of ladies would be 3x + 12
Total number of people in garden = x + (3x + 12)
= 4x + 12
In a garden club, 90% is ladies.
This means, (3x + 12) is 90 percent of (4x + 12)
We get an equation,
(3x + 12) = 90/100 * (4x + 12)
We solve above equation to find the value of x.
30x + 120 = 36x + 108
6x = 12
x = 2 (number of gentlemen)
So, the number of lades would be:
3x + 12 = 3(2) + 12
= 18
Therefore, the number of ladies in the club = 18 and the number of gentlemen in the club = 2
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If angle A is (2x) and angle B is (3x+11)° and the sum of angle A and angle B is 66°, find the measure of angle B.
11
22
44
25
The angle B is 66°
Given,
In the question:
If angle A is (2x) and angle B is (3x+11)°
and, the sum of angle A and angle B is 66°
To find the angle of B.
Now, According to the question:
Based on the given condition:
Angle A = 2x
Angle B = (3x + 11)°
The sum of angle A and B is 66°
2x + (3x + 11)° = 66°
5x + 11 = 66°
Calculate the sum or difference
5x = 66 - 11
3x = 55
x = 55/3
The angle B is = 3x + 11
Plug the value of x in angle B
3 × 55/3 + 11
= 66
Hence, The angle B is 66°
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1. Analyze When a fraction with a numerator of 30 and a denominator of 8
is converted to a mixed number and reduced, what is the result?
A group of people are asked how many hours of television they watch each day to the nearest hour. Here are the results:
3 1 2 0 0 1 0 3 2 4
Which of the following is true about this data set?
Answer:
2 people watch tv 3 hours a day, 3 people watch tv 0 hours a day, 2 people watch tv 1 hour a day, 2 people watch tv 2 hours a day, and 1 person watches tv 4 hours a day
Step-by-step explanation:
hope it helped :)
The function f(x) is graphed below. What is true about the graph on the interval from x = c to x = ∞?
Answer:
It is positive and increasing
Step-by-step explanation:
After the graph, it becomes positive as it passes the y-axis, the line which is where y=0. Also, the graph is headed up and to the right(after c), so as the value of x increase, the value of the function does as well. This would mean the answers is "It is positive and increasing"
What are the values of x, y, and z?
I need help with this please help me
Answer:
X - 111
Y - 104
Z - 76
Step-by-step explanation:
X - Just add 45 and 66
Y - 180 minus 76
Z - 119 minus 43
Need help please tough question
The value of the investment at the end of 5 years be $ 15,281.012.
Given, 10400 dollars are invested at an interest rate of 8%.
We have to find the value of the investment at the end of 5 years.
Now, on using the compound interest formula, we get
Amount = P(1 + r/100)^t
Amount = 10400(1 + 8/100)^5
Amount = 10400(1.08)^5
Amount = 10400(1.469)
Amount = 15,281.012
Hence, the value of the investment at the end of 5 years be $ 15,281.012.
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Write the equation of the line that perpendicular to y=5/2x + 9/2 that passes through the point (-5,3)
Answer:
y = -2/5 x + 1
Step-by-step explanation:
slope = -2/5
y-3 = -2/5 (x -(-5)
y-3 = -2/5 (x+5)
y - 3 = -2/5 x - 2
y = -2/5 x - 2 + 3
y = -2/5 x + 1
On average, a banana will last 6 days from the time it is purchased in the store to the time it is too rotten to eat. Is the mean time to spoil less if the banana is hung from the ceiling? The data show results of an experiment with 15 bananas that are hung from the ceiling. Assume that that distribution of the population is normal.
6.3, 3.5, 5.6, 4.2, 4.4, 3.9, 4.5, 5.5, 7.1, 5.6, 6.6, 6.1, 6.3, 7.2, 4
What can be concluded at the the
α
= 0.01 level of significance level of significance?
For this study, we should use
t-test for a population mean
The null and alternative hypotheses would be:
H
0
:
?
Select an answer
H
1
:
?
Select an answer
The test statistic
?
=
(please show your answer to 3 decimal places.)
The p-value =
(Please show your answer to 4 decimal places.)
The p-value is
?
α
Based on this, we should
Select an answer
the null hypothesis.
Thus, the final conclusion is that ...
The data suggest that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is not significantly less than 6 at
α
= 0.01, so there is statistically insignificant evidence to conclude that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is less than 6.
The data suggest the population mean is not significantly less than 6 at
α
= 0.01, so there is statistically insignificant evidence to conclude that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is equal to 6.
The data suggest the populaton mean is significantly less than 6 at
α
= 0.01, so there is statistically significant evidence to conclude that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is less than 6.
Considering the situation described, it is found that:
A t-test for a population mean should be used.The null hypothesis is: [tex]H_0: \mu = 6[/tex]The alternative hypothesis is: [tex]H_1: \mu < 6[/tex]The test statistic is of: t = -1.94.The p-value is of: 0.0364.The conclusion is of: The data suggest the population mean is not significantly less than 6 at α = 0.01, so there is statistically insignificant evidence to conclude that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is equal to 6.What are the hypothesis tested?At the null hypothesis, it is tested if the mean is of 6 minutes, that is:
[tex]H_0: \mu = 6[/tex]
At the alternative hypothesis, it is tested if the mean is less than 6, hence:
[tex]H_1: \mu < 6[/tex]
What is the test statistic?The test statistic is obtained as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters of the equation are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.Using a calculator from the sample, the values of the parameters are:
[tex]\overline{x} = 5.39, \mu = 6, s = 1.22, n = 15[/tex]
Hence the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{5.39 - 6}{\frac{1.22}{\sqrt{15}}}[/tex]
t = -1.94.
What is the p-value and the conclusion?The p-value is obtained with a t-distribution calculator, with a left-tailed test, as we are testing if the mean is less than a value, with t = -1.94 and 15 - 1 = 14 df, hence it is of 0.0364.
Since the p-value is greater than the significance level of 0.01, the null hypothesis is not rejected and there is not enough evidence that the mean is less than 6 days.
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how many different rectangles are there
Nine less than twice the difference between a number and seven
Step-by-step explanation:
9 < 2(x - 7)
hope this helpful
Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.
slope: −3, ordered pair: (−4,−2)
Answer:
y = - 3x - 14
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 3 , then
y = - 3x + c ← is the partial equation
to find c substitute (- 4, - 2 ) into the partial equation
- 2 = 12 + c ⇒ c = - 2 - 12 = - 14
y = - 3x - 14 ← equation of line
Answer to each expression
(3 + 9) x 2 dived 4
Answer: [tex]6\\[/tex]
Step-by-step explanation:
[tex]\frac{(3+9) * 2}{4}[/tex]
Add 3 and 9 to get 12.
[tex]\frac{12 * 2}{4}[/tex]
Multiply 12 and 2 to get 24.
[tex]\frac{24}{4}[/tex]
Divide 24 by 4 to get 6.
[tex]6[/tex]
5. Jen and Kevin and their children: Jon
(age 14), Beth (age 8), and Joshua
(age 4) are visiting a science museum.
Admission prices are shown below.
Museum Admission
Adult (18-64)
Youth (12-17)
Child (5-11)
Under 5
$22.50
$16.25
$9.75
Free
What will be the total cost of admission
for the family?
?
Answer:
$48.5
Step-by-step explanation:
From the question, we know that Jen and Kevin are definitely adults and the fee for adults
= $22.50
Jon is 14, and any number from 12 to 17 is classified as a youth, so his fee is
= $16.25
Beth is 8, classified as a child, her fee is
= $9.25
Joshua's age which is below 5 is granted free entry without a fee
Hence, the total cost of admission for the family is
$22.50 + $16.25 + $9.75
= $48.5
Given the image of the two triangle, which method can you use to show △LHJ≅△KIE
Answer:
ASA
Step-by-step explanation:
As you can see in the picture it is giving us 2 angles, in between those 2 angles are aside. Therefore it is ASA.
We can also eliminate SSS because 2 angles and shown and SAS can also be eliminated because there are 2 angles, not sides.
An aircraft (at Z) is spotted by two observers (at X and Y) who are L = 1050 feet apart..
airplane passes over the line joining them, each observer takes a sighting of the angle
elevation to the plane, as indicated in the figure. If A = 40 degrees and B = 30°, how high is th
airplane?
The airplane is 359.12 feet high.
Given,
The distance between the observers = 1050 feet
When an aero plane crosses the line connecting them, each observer measures the plane's elevation angle.
Angle A = 40 degrees
Angle B = 30 degrees
We have to find the height of the airplane.
Here,
C = 180 - (40 + 30) = 110°
According to the sine rule :
Sin110 / 1050 = Sin40 / b = Sin 30 / a
1050 sin40 / sin 110 = b = 718.24 ft
1050 sin 30 / sin 110 = a = 558.69 ft
Sin 40 = h / 558.69
h = 558.69 × sin 40
h = 359.12 feet
That is,
The airplane is 359.12 feet high.
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A certain element has a half-life of approximately 15 hours. How long would it take for 500 grams of the element to decay to 299 grams? Leave your answer as an integer or simplified expression.
It would take 11.1 hours to decay from 500 grams to 299 grams.
How long takes to decay?We know that for an element with an half-life T has a decay equation that can be written as:
f(t) = A*e^(-t*ln(2)/T)
Where A is the initial amount, and f(t) is the amount of the element t hours after.
Here we know that:
A = 500g
T = 15h
Then the function is:
f(t) = 500g*e^(-t*ln(2)/15h)
And we want to find the value of t such that f(t) = 299g, then:
299g = 500g*e^(-t*ln(2)/15h)
299/500 = e^(-t*ln(2)/15h)
ln(299/500) = -t*ln(2)/15h
-ln(299/500)*15h/ln(2) = t
11.1h = t
It will take 11.1 hours.
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Question 1
Given the demand function D(p) = √/100 - 2p
Find the Elasticity of Demand at a price of $6.
At this price we would say demand is
Inelastic
Unitary
Elastic
Based on this to increase revenue we should
Lower prices
Keep prices unchanged
Raise prices
Answer:
At this price, i would say the demand is: Unitary Inelastic Elastic Based on this, to increase revenue we should: Lower Prices Raise Prices Keep Prices
a. Find the derivative function f' for the function f.
b. Determine an equation of the line tangent to the graph of f at (a,f(a)) for the given value of a.
The derivative function f' for the function f is f'(x) = -10 / (5x+3)^2 and Equation of the line tangent to the graph of f is 5x+2y+7=0.
Given function:
f(x) = 2/5x+3
a.
f'(x) = d/dx(2/5x+3)
According to power rules:
1/u = -1/u^2
= 2(1/(5x+3)^2) d/dx(5x+3)
= 2*5 / (5x+3)^2
= -10/(5x+3)^2
Hence derivative function f' for the function f is f'(x) = -10 / (5x+3)^2.
b.
(a,f(a)) and a = -1
f(-1) = 2/5(-1)+3
= 2/-5+3
= 2/-2
= -1
point (-1,-1)
slope f'(x) = -10/(5x+3)^2
f'(-1) = -10/(5(-1)+3)^2
= -10/(-2)^2
= -10/4
m = -5/2
Equation of the line is y - y1 = m(x-x1)
y - (-1) = -5/2(x-(-1)
2(y + 1) = -5x - 5
5x + 2y + 2 + 5 = 0
5x+2y+7=0.
Equation of the line tangent to the graph of f is 5x+2y+7=0.
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The Jellybean jar has a radius of 6.2 cm and a height of 18.3 cm. What would be a
reasonable upper limit for the number of jellybeans in the jar? Reminder: Cylinder's
Volume = pi'r^2*h.
1
100
10000
100000
Please help
The volume or the upper limit of the jellybean jar is 2,208.83cm³.
What do we mean by Volume?The space occupied within an object's borders in three dimensions is referred to as its volume.
It is sometimes referred to as the object's capacity.
Volume and mass are the two fundamental characteristics of matter.
Volume is only the amount of space that a thing occupies.
There are a few methods for determining an object's volume depending on its physical state.
So, the volume of the Jellybean jar:
Formula: πr²h
Now, insert values and calculate as follows:
πr²h
π(6.2)²18.3
π38.44(18.3)
π703.452
2,208.83
Therefore, the volume or the upper limit of the jellybean jar is 2,208.83cm³.
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Spencer, a professional golfer, had an average score of 80 points last season. This season, however, his average score has been 5% higher. What is Spencer's current average score?
please
Answer:
84
Step-by-step explanation:
80 x 0.05 = 4
80 + 4 =84
ne
Problem 14:
From this diagram, select the
pair of lines that must be
parallel if 45 47. If there
is no pair of lines, select
"none."
Playback
2
7
4
3
(first taught in
lesson 24)
9
8
6
After you pick your answer press GO.
A. l || n
B. oll q
C. l | m
D. pllq
E. None
10
7
GO
l
Contro
Lecture
& Problem
Scratchpa
Wallpaper
From the given pair of parallel lines , the lines which satisfies the condition of two angles to be congruent that is ∠5 ≅ ∠7 are l || m .
As given in the question,
Given pair of lines,
Condition given that two angles are congruent ,
∠5 ≅ ∠7
Angle 5 is congruent to vertical opposite angle and to make a pair of parallel line Opposite angle should be congruent to angle 7.
Opposite angle and Angle 7 are pair of corresponding angles.
Line l should be parallel to the line m to satisfied the condition of
∠5 ≅ ∠7.
Therefore, from the given pair of parallel lines , the lines which satisfies the condition of two angles to be congruent that is ∠5 ≅ ∠7 are l || m .
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A store sells barrettes for $2 each and combs for $1. Shelby buys 3 barrettes and a comb. Kendra buys 2 barrettes and 4 combs. Write an expression for the amount the two girls spent all together. Find the total amount spent.
I need help!
Answer:
19
Step-by-step explanation:
add it all up its easy
Step-by-step explanation:
Shelby buys 3 barrettes...
2*3=6
and 1 comb
1*1=1
she spent $7 in total
6+1=7
Kendra buys 2 barrettes...
2*2=4
and 4 combs
1*4=4
so Kendra spent $8 in total
4+4=8
the amount spent from the to girls was...
8+7=15