Answer:
[tex]\int {7 \sec(\theta) } \, d\theta = 7\ln(\sec(\theta) + \tan(\theta)) + c[/tex]
Step-by-step explanation:
The question is not properly formatted. However, the integral of [tex]\int {7 \sec(\theta) } \, d\theta[/tex] is as follows:
[tex]\int {7 \sec(\theta) } \, d\theta[/tex]
Remove constant 7 out of the integrand
[tex]\int {7 \sec(\theta) } \, d\theta = 7\int {\sec(\theta) } \, d\theta[/tex]
Multiply by 1
[tex]\int {7 \sec(\theta) } \, d\theta = 7\int {\sec(\theta) * 1} \, d\theta[/tex]
Express 1 as: [tex]\frac{\sec(\theta) + \tan(\theta) }{\sec(\theta) + \tan(\theta)}[/tex]
[tex]\int {7 \sec(\theta) } \, d\theta = 7\int {\sec(\theta) * \frac{\sec(\theta) + \tan(\theta) }{\sec(\theta) + \tan(\theta)}} \, d\theta[/tex]
Expand
[tex]\int {7 \sec(\theta) } \, d\theta = 7\int {\frac{\sec^2(\theta) + \sec(\theta)\tan(\theta) }{\sec(\theta) + \tan(\theta)}} \, d\theta[/tex]
Let
[tex]u = \sec(\theta) + \tan(\theta)[/tex]
Differentiate
[tex]\frac{du}{d\theta} = \sec(\theta)\tan(\theta) + sec^2(\theta)[/tex]
Make [tex]d\theta[/tex] the subject
[tex]d\theta = \frac{du}{\sec(\theta)\tan(\theta) + sec^2(\theta)}[/tex]
So, we have:
[tex]\int {7 \sec(\theta) } \, d\theta = 7\int {\frac{\sec^2(\theta) + \sec(\theta)\tan(\theta) }{u}} \,* \frac{du}{\sec(\theta)\tan(\theta) + sec^2(\theta)}[/tex]
Cancel out [tex]\sec(\theta)\tan(\theta) + sec^2(\theta)[/tex]
[tex]\int {7 \sec(\theta) } \, d\theta = 7\int {\frac{1}{u}} \,du}}[/tex]
Integrate
[tex]\int {7 \sec(\theta) } \, d\theta = 7\ln(u) + c[/tex]
Recall that: [tex]u = \sec(\theta) + \tan(\theta)[/tex]
[tex]\int {7 \sec(\theta) } \, d\theta = 7\ln(\sec(\theta) + \tan(\theta)) + c[/tex]
find the value of x easy math question #3 please help
Answer: x =8
Step-by-step explanation:
-12 + 9x = 60 (the other angles are 60, 180 - (60 + 60) = 60)
9x = 72
x = 8
Answer:
x = 8°
Step-by-step explanation:
We know that sum of interior angles of a triangle is 180°, therefore;
(Angle 1) + (Angle 2) + (Angle 3) = 180°
(60)° + (60)° + (-12 + 9x)° = 180°
120° + (-12 + 9x) = 180°
108° + 9x° = 180°
9x = 180 - 108
9x = 72°
x = 72/9
x = 8°
Therefore the value of x is 8°.
Hope this helps!
Am I correct? If not which of the answers is correct?
Given the following function, find h(-4)
h(x) = 8x2 – 5
h(-4) =
Step-by-step explanation:
put the value of x in the given function...
Answer:
h(-4) = 123
Step-by-step explanation:
h(x) = 8x² – 5
h(-4) = 8(-4)² - 5
h(-4) = 8(16) - 5
h(-4) = 128 - 5
h(-4) = 123
Carl worked 15 hours and Derrick worked 20 hours their combined pay is $640
How much an hour did Carl get paid
Answer:
he got payed 5 dollars an hour
help please !!!!!!!!!!!!!!!
9514 1404 393
Answer:
yes
Step-by-step explanation:
The triangles are given as right triangles. Hypotenuses QT and RS are given as congruent.
We also have XS ≅ TP. By the addition property of equality, this means ...
XS +ST ≅ ST +TP
By the segment sum theorem, this means ...
XT ≅ SP
XT and SP are the corresponding legs of the right triangles. So, we have corresponding hypotenuses and corresponding legs congruent. This lets us conclude ΔXQT ≅ ΔPRS by the HL theorem.
please answer a little quiet
IT is urgent
.Factorize: 4(x-y)^2 -9
.Evaluate : 1001×99
Answer:
1. (2x - 2y)² - 9
2. 99099
Step-by-step explanation:
We know the a+b formula :
(a-b)² = a² - 2ab + b²
1. 4(x-y)^2 -9
4(x² - 2xy + y²) - 9
4x² - 8xy + 4y² - 9
(2x - 2y)² - 9
2. 1001 × 99
= 99099
1001
× 99 ----------
9009
9009× ----------- 99099
please help me out on this one
Try this triangle: 3ft, 4ft, and 1 ft
Is the first plus second greater than the third? Is 3+4> 1? ________
Is the second plus third greater than the first ? is 4+1 >3?___________
Is the third plus first greater than the second? Is 3+1 >4_________
Can it make a triangle? Explain why?
9514 1404 393
Answer:
yes, yes, no; No
Step-by-step explanation:
We have to assume you have no trouble with single-digit addition and comparison of two numbers.
3+4 > 1 ⇒ 7 > 1 . . . . yes
4+1 > 3 ⇒ 5 > 3 . . . . yes
3+1 > 4 ⇒ 4 > 4 . . . . no
These lengths will not make a triangle because the triangle inequality is not satisfied.
_____
Additional comment
You will notice that we found the result of interest when we added the two smallest numbers (1 and 3) and compared the sum to the largest number (4). This is a shortcut you can use for any "will these make a triangle" question. You don't need to bother comparing larger numbers to smaller ones. You already know they are larger.
Find the value of x.
60° 130°
The value of x is type your answer...
Answer:
x = 170
Step-by-step explanation:
In order to solve this, we need to know that there is 360° in a full circle. Knowing this, we can make the following equation from the diagram provided...
60° + 130° + x° = 360
x° = 360° - 60° - 130°
x° = 170°
x = 170
HELP!!!! Which statement best describes an advantage of indirect democracy over
direct democracy?
A. It can better reflect the democratic principle of majority rule.
B. It can be more responsive to citizens' interests.
C. It can make decision making more efficient.
O D. It can help citizens feel more connected to government.
SUBMIT
Answer:
C. It can make decision making more efficient.
Step-by-step explanation:
I need some help!!! I will try to give brainliest!!!
Answer:
54 ft cubed
Step-by-step explanation:
Area of this rectangular prism is Base, Height, Length all multiplied.
3 * 3 * 6
9 * 6
=54
In which geometry is there more than one line parallel to a given line through a point not on the line?
A. spherical
B. Hyperbolic
C. Euclidean
D.apennine
Answer:
Step-by-step explanation:Its B because Hyperbolic geometry, also called Lobachevskian Geometry, a non-Euclidean geometry that rejects the validity of Euclid's fifth, the “parallel,” postulate. Simply stated, this Euclidean postulate is: through a point not on a given line there is exactly one line parallel to the given line.
Help me pleaseee!! I’ve been stuck on it for a while:(
Answer:
a
Step-by-step explanation:
I did not do the math becals I could not find my pen but based on outher math like this I have a strong feeling it's a if not the maby d
Answer:
its the 3rd one :)
Step-by-step explanation:
An experiment to investigate the survival time in hours of an electronic component consists of placing the parts in a test cell and running them under elevated temperature conditions. Six samples were tested with the following resulting failure times (in hours): 34, 40, 46, 49, 61, 64. (a)Calculate the sample mean and sample standard deviation of the failure time.
Answer:
The sample mean of failure time was of 49 hours.
The standard deviation of the failure time was of 11.7 hours.
Step-by-step explanation:
Sample mean:
Sum of all values divided by the number of values. So
[tex]\overline{x} = \frac{34+40+46+49+61+64}{6} = 49[/tex]
The sample mean of failure time was of 49 hours.
Standard deviation:
Square root of the division between the sum of the differences squared betweene each value and the mean, divided by the sample size subtracted by 1. So
[tex]s = \sqrt{\frac{(34-49)^2+(40-49)^2+(46-49)^2+(49-49)^2+(61-49)^2+(64-49)^2}{5}} = 11.7[/tex]
The standard deviation of the failure time was of 11.7 hours.
Use the distributive property to remove the parenthesis: (m + 2) 3.
Answer:
Step-by-step explanation:
(m+2)3
m*3+2*3
3m+6
distributive property example:
a(b+c)
=a*b+a*c
=ab+ac
[tex]3 \: m + 6[/tex] ✅
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
Using the distributive formula, [tex]\sf\purple{a\: ( \:b + c\: ) = \:a b + a c}[/tex], we have
[tex](m + 2) \: 3 \\ = m \times 3 \: + \: 2 \times 3 \\ = 3 \: m + 6[/tex]
Note:-
[tex]\sf\red{PEMDAS\: rule.}[/tex]
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]
Pls can some help me
9514 1404 393
Answer:
A. 17.5 miles
Step-by-step explanation:
Your knowledge of triangles tells you the hypotenuse is longer than the long leg of the triangle, and is shorter than than the sum of the two legs. This means the difference between Michael's distance and Leah's distance will be strictly less than 25 miles.
The only answer choice in that range is 17.5 miles.
__
If you want to do the math, you can find Michael's distance to be ...
38 +25 = 63 miles.
Leah's distance will be ...
√(38² +25²) = √2069 ≈ 45.5 miles.
Then Michael's excess distance is ...
63 -45.5 = 17.5 miles
Use Newton''s method to find the second and third approximation of a root of x^3 + x + 3= 0 starting with x1 = -1 as the initial approximation.
The second approximation is x2= ?
The third approximation is x3= ?
9514 1404 393
Answer:
see attachment
Step-by-step explanation:
The iterator for Newton's method gives the next approximation (x') as ...
x' = x -g(x)/g'(x) . . . . . where g'(x) is the derivative of g(x)
We have defined g(x) = x^3+x+3, the function we want the zero of. We have defined the iteration function to be f(x).
__
Additional comment
Modern graphing calculators not only make the iteration trivially simple, they also give a first approximation good to 2 or 3 decimal places in many cases.
Let f(x)= -5x+6. Find and simplify f(3b-5).
Answer:
-15b+31
Step-by-step explanation:
f(x)=-5x+6
f(3b-5)=-5(3b-5)+6=-15b+25+6=-15b+31
A little boy stands on a carousel and rotates around the ride 4 times. If the distance between the Little boy and the center of the carousel is 6 feet, then how many feet did the little boy travel?
Solve for x. Show your work.
-1/2x < -12x
Answer: x > 24
Step-by-step explanation: -12x/-1/2x = 24. 24 is the given when dividing. The sign is flipped after dividing negatives.
Answer:
x < 0
Step-by-step explanation:
it's the same thing just with that slash( / ).........
PLEASE HELP ASAP NUMBER 8 AND 9 SHOW WORK AND I WILL GIVE BRAINLIEST
Answer:
question 8
Step-by-step explanation:
y = 4
2x + 3y = 22
put y = 4 into equation 2
2x + 3 ( 4) = 22
2x + 12 = 22
2x = 22 - 12
2x = 10
x = 5
therefore x = 5 and y = 4
Standard form 6,000,000+900,000+80,000+9,000+500+80+2
Answer:
6.989582×10^-6
Step-by-step explanation:
6,000,000+900,000+80,000+9,000+500+80+2
=6989582
=6.989582×10^-6
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y= -2/5x-6
Step-by-step explanation:
y int is at -6
rise/run= -2/5
AABC is similar to ADEF.
Find x.
perimeter of triangle DEF= 60
Work out the surface area of the cylinder. (Image attached)
Answer:
[tex]area = 2\pi {r}h \\ = 2 \times 3.14 \times 10 \times 22 \\ = 1382.3 \: {cm}^{2} [/tex]
Answer:
2010.62cm
Step-by-step explanation:
A =
[tex]2\pi \: rh + 2\pi {r}^{2} [/tex]
[tex] = 2\pi(10)(22) + 2\pi( {10}^{2} )[/tex]
= 1382.30 + 628.32
=2010.62
In a recent survey of 655 working Americans ages 25-34, the average weekly amount spent on lunch was 43.76 with standard deviation 2.67. The weekly amounts are approximately bell-shaped. (c) Between what two values will approximately 95% of the amounts be?
Answer:
Between 38.42 and 49.1.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 43.76, standard deviation of 2.67.
Between what two values will approximately 95% of the amounts be?
By the Empirical Rule, within 2 standard deviations of the mean. So
43.76 - 2*2.67 = 38.42
43.76 + 2*2.67 = 49.1
Between 38.42 and 49.1.
If the area of a circle is 154cm2 what is the radius of that circle
Answer:
7
Step-by-step explanation:
If you use the pi button:
the radius is 7
154cm² ÷ pi = 49
Square root of 49 = 7
formula to find the lateral area of a right cone
Answer:
This is the formula to find a lateral area of a right cone
A=1/2bh
Or A=1/2lw
A 10 meter ladder was placed on an angle. The base of the ladder is 5 meters away from the
building along the ground.
Write an equation to determine the height, h, of the building.
Answer:
5^2 + h^2 = 10^2
Step-by-step explanation:
This is a clear example of the Pythagorean Theorem, a relation of all sides in a right triangle. The equation itself is a^2 + b^2 = c^2. By simply plugging in the given values into the triangle, you would get the answer.
Answer:
To determine the height we will use a² = b²+c²
(10m)²= (5m)²+(h)²
<=> 100m²=25m²+h²
<=> 100m²-25m²=75m²=h²
<=> √ 75m² = h = 8,660m
A grocery store manager notices that this month her store sold a total of 936 gallons of ice cream, which represents a decrease of 20% from last month. On the other hand, her store sold 838 pounds of broccoli this month, which represents an increase of 22% from last month. How much ice cream and broccoli did the store sell last month? Round your answers to the nearest integer.
The store sold _________ gallons of ice cream last month.
The store sold _________ pounds of broccoli last month.
Answer:
the is 30 and 30
Step-by-step explanation:
If the Circumstance of wobble ball is 242cm what is the surface area?
Answer:
1,166 is the SA
correct me if im wrong somehow
Step-by-step explanation:
a wobble ball is a sphere
circumference=8(pi)
242=8(3.14)
so 242 divided by 25.12
this ends up with 9.633757961783439, which is the radius of the circumference
SA of a sphere= 4(pi)r²
SA=4(3.14)9.633757961783439²
SA=4(3.14)92.80929246622581
SA=1,165.684713375796
rounded to the nearest whole # = 1166