Answer:
Step-by-step explanation:
Given the function f(x) = tan (x)
From trigonometry identity, tan (x) = sin(x)/cos(x)
f(x) = sin(x)/cos(x)
Using the quotient rule to find the derivative of the function, we will have;
f'(x) = cos (x)cos (x) - sin (x)[-sin (x)]/ cos²x
f'(x) = cos²x - sin²x/ cos²x
Divide through by cos²x
f'(x) = cos²x/cos²x + sin²x/cos²x / cos²x/cos²x
f'(x) = 1 + sin²x/cos²x / 1
f'(x) = 1 + (sin²x/cos²x)
f'(x) = 1 + tan²x
From trig identity, 1 + tan²x = sec²x
Hence, f'(x) = sec²x
Hence the expression f'(x) in terms of the secant function is sec²x
f'(x) = 1/cos²x
For the function to be defined, it means that cos²x ≠ 0
cos²x ≠ 0
cos x ≠ 0
x ≠ cos⁻¹0
x ≠ 90⁰
Hence the value of x must not be equal to 90 for the function to be defined. x can be defined at when x = 0 since cos 0 = 1, the equation will becomes f'(0) = 1/cos²0 = 1/1 = 1.
Hence the function is defined at 0≤x<90
What is the factored form of this expression?
-9x^3 - 12x^2 - 4x
A. x(3x - 2)(3x + 2)
B. -x(3x + 2)^2
C. x(3x - 2)^2
D. -x(3x - 2)(3x + 2)
Answer:
B
Step-by-step explanation:
Given
- 9x³ - 12x² - 4x ← factor out - x from each term
= - x(9x² + 12x + 4) ← perfect square
= - x(3x + 2)(3x + 2)
= - x(3x + 2)² → B
-9x^3-12x^2-4x
Factor out -x from the expression
-x×(9x^2+12x+4)
Using a^2+2ab+b^2=(a+b)^2 Factor the expression
-x×(3x+2)^2
now we do the same thing only different way ok
9x^2+12x+4
write the number in the exponential form with an exponent of 2
3^2 x^2+12x+4
write the expression as a product with the Factors 3x and 2
3^2 x^2 +2×3x×2+4
write the number in the exponential form with an exponent of 2
3^2 x^2+2×3x×2+2^2
Multiply the terms with equal exponents by multiplying their bases
(3x)^2+2×3x×2+2^2
Using a^2+2ab+b^2=(a+b)^2 Factor the expression
(3x+2)^2
Solution: -x×(3x+2)^2
answer:B
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ASAP PLS Solve this exercise using the fact that the sum of the measures of the three angles of a triangle is 180°.In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of the third angle is 20° more
than the measure of the second angle. What is the measure of each angle?
Answer:
80°, 40° and 60°
Step-by-step explanation:
Name the second angle X and the first angle to 2X (because it is twice the measure of angle number two) and the third angle to 20°+X (because it was 20° more than the second angle)
so we will have an equation of
180°=2x + x + (20°+x)
160°=4x
40°=x
so the second angle is 40° as it is represented by just one X
therefore the first angle which is twice the measure is 80° and the third angle which is 20° more is 60°. hope that helps!
Ribbon candy costs $2.50 per foot. How many feet of ribbon can you buy if you have $11.25
Answer:
$4.50
Step-by-step explanation:
11.25 / 2.50 = 4.50
Answer:$4.50
Step-by-step explanation: nothing important
This table gives a few (x, y) pairs of a line in the coordinate plane. What is the y-intercept of the line?
Answer:
Y-int = (0,2)
Step-by-step explanation:
-28 -54
-21 -40
-14 -26
-7 -12
0 2
Which table shows a proportional relationship between x and y?
need help again please
What is the value of x in the equation -6x = 5x + 22?
Options:
A. ) –22
B. ) –2
C. ) 2
D. )22
Thank you!
Answer:
D
Step-by-step explanation:
collect like terms and divide by -11
Solve for value of B
Answer:
b = 6
Step-by-step explanation:
[tex](6b - 7) \degree + 90 \degree + 61 \degree = 180 \degree \\ \\ (6b - 7) \degree + 151 \degree = 180 \degree \\ \\ (6b - 7) \degree = 180 \degree - 151 \degree\\ \\ (6b - 7) \degree = 29 \degree \\ \\ 6b - 7 = 29 \\ \\ 6b = 29 + 7 \\ \\ 6b = 36 \\ \\ b = \frac{36}{6} \\ \\ \huge \purple{ \boxed{ b = 6}}[/tex]
If a seed is planted, it has a 70% chance of growing into a healthy plant.
If 8 seeds are planted, what is the probability that exactly 4 don't grow?
Answer:
Thus, the probability that exactly 4 don't grow is 0.1361 or 13.61%
Step-by-step explanation:
Binomial Distribution
Consider a random experience that has only two possible outcomes: Success or Failure. Let's call p to the probability that the event has a successful outcome and q to the failure outcome.
It follows that p+q=1, or q=1-p.
Now repeat the random experience n times. We want to calculate the probability of getting x successful outcomes. This can be done with the Binomial Distribution formula:
[tex]\displaystyle P_{x} = {n \choose x}\cdot p^{x}\cdot q^{n-x}[/tex]
Where :
[tex]\displaystyle {n \choose x}[/tex]
Is the number of combinations, calcula ted as follows:
[tex]\displaystyle {n \choose x} =_nC_x=\frac{n !}{x ! (n-x) !}[/tex]
A planted seed has a 70% chance of growing into a healthy plant. The successful outcome has p=0.7 and q=0.3.
The experience is repeated n=8 times. We want to calculate the probability of having 4 failures (not growing seeds) or x=4 successes.
Apply the formula:
[tex]\displaystyle P_{4} = {8 \choose 4}\cdot 0.7^{4}\cdot 0.3^{8-4}[/tex]
[tex]\displaystyle P_{4} = 70\cdot 0.7^{4}\cdot 0.3^{4}[/tex]
[tex]\displaystyle P_{4} = 0.1361[/tex]
Thus, the probability that exactly 4 don't grow is 0.1361 or 13.61%
if there is 99 apples and i take one of them how many apples are there now
what does 6 x 9 equal?
Answer:
54
Step-by-step explanation:
Answer:
54
Step-by-step explanation:
Which One Doesn't Belong:
A. 1 + 1/2
B. 6/4
C.3/4
D.30/20
Answer:
30/20
Step-by-step explanation:
25 is what percent of 30? (don't forget the % sign and round your answer to the nearest hundredth)
Answer:
83.3% (.3 is recurring)
On a map, 1 inch equals 5 miles. Two cities are 10 inches apart on the map. What is the actual distance between the cities?
Answer:
50 i think. Just count by 5 to 10
Write an equation in Standard Form of the line passing through (5, -4) with a slope of -2/5.
Answer:
The answer is
[tex]y = - \frac{2}{5} x - 2 \\ [/tex]Step-by-step explanation:
To find an equation of a line when given the slope and a point we use the formula
[tex]y - y_1 = m(x - x_1)[/tex]
where
m is the slope
( x1 , y1) is the point
From the question the points is (5, -4) and slope - 2/5
The equation is
[tex]y + 4 = - \frac{2}{5} (x - 5) \\ y + 4 = - \frac{2}{5} x + 2 \\ y = - \frac{2}{5} x + 2 - 4[/tex]
We have the final answer as
[tex]y = - \frac{2}{5} x - 2 \\ [/tex]
Hope this helps you
a man spent 58% of his income and the amount of money left was $210. Find his income
Answer:
500 $
Step-by-step explanation:
[tex]\frac{42\%}{210}=\frac{100\%}{x}[/tex]
[tex]\frac{\frac{21}{50}}{210}=\frac{1}{x}[/tex]
[tex]\frac{21}{50}x=210\\[/tex]
[tex]\frac{21}{50}x\cdot \:50=210\cdot \:50\\[/tex]
x=500
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Red
Which ones no long answer just which one
A,C,D
(going top left to bottom right)
(a) b
(c) (d)
e f
Whats (2^–1)^3 with the same base but one exponent??
Step-by-step explanation:
[tex] ({2}^{ - 1} )^{3} [/tex]
[tex] {2}^{ - 3} [/tex]
........
Answer:
2^-3
Step-by-step explanation:
When multiplying two exponents with the same base, we basically add the exponents.
One bag of grapefruit weighs 5 3/4 pounds. How many pounds of grapefruit are in 2 1/3 bags?
A) 8 1/12
B) 11 1/2
C) 11 2/3
D) 13 5/12
Answer:D is the answer :)
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
I need help plzz I need the answer
Factor the following expression completely. 4b^8-61b^4+225
If f(x) = -3x + 4 and g(x) = 2, solve for the value of x for
which f(x) = g(x) is true.
x=
y = f(x)
3
y = g(c)
2
1
1
х
-2 -1
2
3
Answer:
Examine the chart and graph.
On the left is a 5-column table with 10 rows titled Religion in North America. The first column is titled Religion with entries Christianity, Unaffiliated, Judaism, Buddhism, Islam, Hinduism, Other Religions, Folk Regions, and Total. The second column is titled 2010 population with entries 266,630,000; 59,040,000; 6,040,000; 3,860,000; 3,480,000; 2,250,000; 2,200,000, 1,020,000; and 344,530,000. The third column is titled percent in 2010 with entries 77.4, 17.1, 1.8, 1.1, 1.0, 0.7, 0.6, 0.3, and 100.0. The fourth column is titled 2050 Projected Population with entries 286,710,000; 111,340,000; 5,920,000; 6,080,000; 10,350,000; 5,850,000; 6,540,000; 2,630,000; and 435,420,000. The fifth column is titled percent in 2050 with entries 65.8, 25.6, 1.4, 1.4, 2.4, 1.3, 1.5, 0.6, and 100.0. On the right is a pie chart titled Religions Practiced in Central America. Christianity is 95.86 percent, Agnostic 2.42 percent, Native Religions 0.99 percent, Atheism 0.15 percent, Spiritism 0.13 percent, and Other is 0.44 percent.
Which is the
Step-by-step explanation:
If Khalid uses 3 liters of paint to cover 8 square meters of wall. How much paint does Khalid need to paint 40 square meters of the wall.
Answer:
15l
Step-by-step explanation:
There are 5 8sq m in 40sq m
total paint is 5*3=15
To eliminate 6X you would Transform 2x by multiplying what number ?
Answer:
-3
Step-by-step explanation:
to eliminate 6x we need the same no. 6x but that should be negative. so
2X × -3 = -6X
and
6X+(-6X)=0
Write thirty eight thousandths as a decimal
Answer:
0.0038
Step-by-step explanation:
The thousands spot is four away from the decimal so you would put the eight right there, the three in front of it, and fill in the other spots with zeros.
Is 0.040040004... a rational number? Explain your reasoning.
Choose the correct answer below.
Answer:
The quick answer: No.
Step-by-step explanation:
(pinquancaro)
Given : Number 0.040040004.....
To find : Is the number is rational or irrational ?
Solution :
Rational number is defined as number written in form of p/q where p and q are integers and q is non-zero.
Rational number is terminating and repeating.
Irrational number is defined as number which cannot be written in form of p/q.
Irrational number is non-terminating and non-repeating.
The number given is 0.040040004..... is non-terminating and non-repeating.
Therefore, The number 0.040040004..... is an irrational number.
The quotient of a number and 3 is less than 24
Answer:
6 is the answer
Step-by-step explanation:
average cost,average
revenue, average profit
Solve.
(6a + 4)(5a + 3)
If I have 5 candy bars in a bowl and I take 2 out and set it on the table. How many candy bars do I have?
Answer:
5
Step-by-step explanation: