Answer:
[tex]\displaystyle \int\limits^0_\infty {cos(x)} \, dx = sin(\infty)[/tex]
General Formulas and Concepts:
Pre-Calculus
Unit CircleTrig GraphsCalculus
LimitsLimit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]IntegralsIntegration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]Trig IntegrationImproper IntegralsStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int\limits^0_\infty {cos(x)} \, dx[/tex]
Step 2: Integrate
[Improper Integral] Rewrite: [tex]\displaystyle \lim_{a \to \infty} \int\limits^0_a {cos(x)} \, dx[/tex][Integral] Trig Integration: [tex]\displaystyle \lim_{a \to \infty} sin(x) \bigg| \limits^0_a[/tex][Integral] Evaluate [Integration Rule - FTC 1]: [tex]\displaystyle \lim_{a \to \infty} sin(0) - sin(a)[/tex]Evaluate trig: [tex]\displaystyle \lim_{a \to \infty} -sin(a)[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle -sin(\infty)[/tex]Since we are dealing with infinity of functions, we can do a numerous amount of things:
Since -sin(x) is a shift from the parent graph sin(x), we can say that -sin(∞) = sin(∞) since sin(x) is an oscillating graph. The values of -sin(x) already have values in sin(x).Since sin(x) is an oscillating graph, we can also say that the integral actually equates to undefined, since it will never reach 1 certain value.∴ [tex]\displaystyle \int\limits^0_\infty {cos(x)} \, dx = sin(\infty) \ or \ \text{unde}\text{fined}[/tex]
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Improper Integrals
Book: College Calculus 10e
how do you find volume of sphere, cylinder, cone ? ... explaining please
Answer:
Step-by-step explanation:
The formula for the volume of a sphere is given by :
[tex]V_s=\dfrac{4}{3}\pi r^3[/tex]
Where
r is the radius of the sphere
The formula for the volume of a cylinder is given by :
[tex]V_c=\pi r^2 h[/tex]
Where
r and h is the radius and height of the cylinder
The formula for the volume of a cone is given by :
[tex]V_C=\dfrac{1}{3}\pi r^2 h[/tex]
Where
r and h is the radius and height of the cone
Wat is the slope of the line that passes through the points 3,1) and (-2,5)
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]m=\boxed{-\frac{4}{5}}[/tex]
»»————- ★ ————-««
Here’s why:
We can use the slope formula to find the slope of the two points given.⸻⸻⸻⸻
[tex]\boxed{\text{Recall that the slope formula is:}}\\\\\frac{y_2-y_1}{x_2-x_1}\\\\(x_1,y_1), (x_2,y_2)-\text{Points}[/tex]
⸻⸻⸻⸻
[tex]\boxed{\text{Finding the Slope:}}\\\\\rightarrow m=\frac{5-1}{-2-3} \\\\\rightarrow m=\frac{4}{-5}\\\\\rightarrow \boxed{m= -\frac{4}{5}}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
510.4 in
Scientific Notation I need an answer please
Answer:
5.104 X 10^2
Step-by-step explanation:
Answer:
510.4 trillion in scientific notation = 5.104 × 1014.
Step-by-step explanation:
This can also be expressed as 5.104 × 10^14, using the caret symbol, or as 5.104e+14, which is called 510.4 trillion in e-notation,
if x=-4 then what is x^2? in an equation for my homework, they have the solution as positive instead of negative and I don’t understand why.
Answer:
see explanation
Step-by-step explanation:
Given
x² , then when x = - 4
x² = - 4 × - 4 = + 16
[ the product of a negative and a negative results in a positive ]
Bryan, Angela, Elan, and Fiona folded some paper flowers for their school fund-raising project. Elan folded one-fifth of the paper flowers and Bryan folded 25% of them. Angela and Fiona folded the remaining ones in the ratio 1:8. Bryan folded 9 more than Elan.a)How many paper flowers did Fiona folded?b)If each bouquet of 10 flowers was sold at $9, how much money did they raise for school?
Answer:
a) 88
b) 162 $
Step-by-step explanation:
Given Bryan sold 9 more flowers than Elan
1/4 x - 1/5 x = 9
x/20 = 9
x = 180
Flowers with Bryan = 45
Flowers with Elan = 36
45+36 = 81
Remaining flowers = 99
Flowers with Fiona = 8/9 * 99 = 88
Juan plans to use strategies to find 12x380 shows a strategy he could use
Answer:
3 x 4 x 380
Step-by-step explanation:
The correct strategy that he could use would be
3 x 4 x 380
This is basically splitting up the 12 into two numbers whose product equals 12. This shrinks the numbers and makes it easier to multiply the 380. Since it is easier to multiply 380 by 4 as opposed to 12. This strategy will still give you the same result as 12x380 and both will give you a product of 4,560
7*7*7*7*7 written in exponential form
Answer:
7^5
Step-by-step explanation:
7x7x7x7x7 is equal to 7^5. Depending on how much sevens there are, that is the power number. In this case there are 5 sevens so that means it is 7^5.
If this helps please mark as brainliest
Answer:
7^5
Step-by-step explanation:
see image below:)
PLS HELP ASAP, THANK YOU
PS. WILL MARK BRAINLIEST
i am so sorry me dont know
Answer:
Answer: Composite figure: 360 ft3
Explanation:
The volume of the triangular prism:
The base area of the prism = 1/2 x 4 x 6 = 12 ft2
Height = 6 ft
The volume of the triangular prism = 12 x 6 = 72 ft3
The volume of the rectangular prism:
The base area of the prism = 4 x 6 = 24 ft2
Height = 12 ft
The volume of the triangular prism = 12 x 24 = 288 ft3
Volume of the composite figure = (288 + 72)ft3 = 360 ft3
Step-by-step explanation:
Please anyone answer me
Let's divide the shaded region into two areas:
area 1: x = 0 ---> x = 2
ares 2: x = 2 ---> x = 4
In area 1, we need to find the area under g(x) = x and in area 2, we need to find the area between g(x) = x and f(x) = (x - 2)^2. Now let's set up the integrals needed to find the areas.
Area 1:
[tex]A\frac{}{1} = ∫g(x)dx = ∫xdx = \frac{1}{2} {x}^{2} | \frac{2}{0} = 2[/tex]
Area 2:
[tex]A\frac{}{2} = ∫(g(x) - f(x))dx[/tex]
[tex]= ∫(x - {(x - 2)}^{2} )dx[/tex]
[tex] = ∫( - {x}^{2} + 5x - 4)dx[/tex]
[tex]= ( - \frac{1}{3}{x}^{3} + \frac{5}{2} {x}^{2} - 4x) | \frac{4}{2}[/tex]
[tex] = 2.67 - ( - 0.67) = 3.34[/tex]
Therefore, the area of the shaded portion of the graph is
A = A1 + A2 = 5.34
Which of the following theorems verifies that triangle STU is congruent to triangle XYZ
Answer:
B. HL
Step-by-step explanation:
If f(x) = -x2 + 6x, what is f(-3)?A) -162 B) -27 C) -9 D) 9
Answer:
-27
Step-by-step explanation:
f(x) = -x^2 + 6x
Let x = -3
f(-3) = -(-3)^2 + 6(-3)
= -9 - 18
-27
Answer:
f(3)= -9
Step-by-step explanation:
F(x)=-x2+6x
f(3)=--3^2+6.-3
f(3)=9+-18
f(3)=-9
A bag contains 3 blue marbles and
4 yellow marbles. You pull out one
marble, do not replace it, and then pull
out another one. What is the probability
that the first marble is yellow and the
second one is blue? In simplest form
Answer:
2/7
Step-by-step explanation:
Probabilty 1 = 4/7
Probability 2 = 3/6 = 1/2 (because if you not replace it, there is one less
final probability = 4/7 * 1/2 = 4/14 = 2/7
What is the image of (-4, -5) after a reflection over the y-axis?
Answer:
(4,-5)
Explanation:
Jeremy needs to buy three pieces of wood to make a triangular frame. If the wood is cut in 1 l- foot increments, which set of wood length will form a triangle?
What is the length of side x? If necessary, round your answer to two decimal places. 19 12
Answer:
D. 14.73
Step-by-step explanation:
According to Pythagoras,
19^2 = 12^2 + x^2
x^2 = 19^2 - 12^2
x^2 = 361 - 144
x^2 = 217
x = [tex]\sqrt{217}[/tex]
x = 14.73
Simplify the expression:
7r–3r+9r
Answer:
13r
Step-by-step explanation:
-First, collect like terms by calculating the sum or difference of their coefficients.
(7-3+9)r
-Then, calculate the sum or difference and you get..
13r.
Hope this helps! :)
Answer:
13r
I think it is correct but just try making sure oater sorr if I a wrong though
12th grade stat and prob !!!!
Answer:
The 1st one .
Step-by-step explanation:
Find The size of angle XYZ Give your answer to 1 decimal place
Angle XY 6cm
Angle ZY 15cm
Answer: [tex]3\sqrt{21}[/tex]
Step-by-step explanation:
[tex](xy)^{2}+(xz)^2=(yz)^2\\so, (6)^{2}+(xz)^2=15^2 \\(xz)^2=225-36\\xy=3\sqrt{21}[/tex]
Find the equation of the line that contains the point
P(−4, −1)
and is perpendicular to the graph of
y = − 4/5x − 4.
Answer:
Step-by-step explanation:
y = − 4/5x − 4.
y = 5/4 x - 4
-1 = 5/4(-4) + b
-1 = -5 + b
b = 4
y = 5/4 x + 4
Staples, a chain of large office supply stores, sells a line of desktop and laptop computers. Company executives want to know whether the demands for these two types of computers are dependent on one another. Each day's demand for each type of computers is categorized as Low, Medium-Low, Medium-High, or High. The data shown in the table below is based on 205 days of operation. Based on these data, can ? Test at the 5% level of significance.
low med-low med-high high
low 4 15 14 3 36
laptops med-low 6 18 18 23 65
med-high 13 17 10 17 57
high 7 15 15 10 47
30 65 57 53 205
Required:
a. What is the test value for this hypothesis test?
b. What is the conclusion for this hypothesis test?
Answer:
As the calculated χ² = 1.23 is less than the critical region χ²≥ χ²(0.05,9)= 16.92 ,Staples can conclude that demands for these two types of computers are independent at the 0.05 level of significance.
Step-by-step explanation:
As we have to test the independence of the two categories the chi square of independence test is applied.
Let the null and alternate hypotheses be
H0 :The demand for each type of computers is independent
against the claim
Ha: The demand for each type of computers is not independent i.e they are associated.
The significance level alpha is chosen to be 0.05
The critical region for alpha =0.05 and (4-1)(4-1) = 3*3 =9 d.f is
χ²≥ χ²(0.05,9)= 16.92
Actual Data
low med-low med-high high Total
low 4 15 14 3 36
med-low 6 18 18 23 65
med-high 13 17 10 17 57
high 7 15 15 10 47
Total 30 65 57 53 205
Expected Frequencies
low- low = 30*36/205= 5.27
low- med.low = 65*36/205 = 11.41
low- medium high = 57*36/205= 10.009
low- high = 53*36/205 =9.31
medium low- low = 30*65/205 = 9.51
medium low- med.low = 65*65/205= 20.61
medium low- medium high = 57*65/205= 18.073
medium low- high = 53*65/205= 16.80
medium high- low = 30*57/205= 8.34
medium high- med.low = 65*57/205= 18.07
medium high- medium high = 57*57/205= 15.85
medium high- high = 53*57/205= 14.74
high- low = 30*53/205= 7.76
high- med.low = 65*53/205= 16.80
high- medium high = 57*53/205= 14.74
high- high = 53*53/205= 13.70
Summarizing in a table
Expected Frequencies
low med-low med-high high Total
low 5.27 11.41 10.009 9.31 35.999
med-low 9.51 20.61 18.073 16.8 64.993
med-high 8.34 18.07 15.85 14.74 57
high 7.76 16.8 14.74 13.7 53
Total 30.88 66.89 58.672 54.55 210.992
Using Excel
The Chi Square Values are
0.062823
0.270857
0.159572
0.735995791
1.229247532
As the calculated χ² = 1.23 is less than the critical region χ²≥ χ²(0.05,9)= 16.92 ,Staples can conclude that demands for these two types of computers are independent at the 0.05 level of significance,
A third-grade class is using plaster of Paris to make impressions of their hands. Each student needs 12 ounces of plaster to make an impression. There are a total of 20 students in the class. How many pounds of plaster will the teacher need for the activity?
Answer:
15 pounds of plaster
Step-by-step explanation:
First, convert ounces to pounds.
In 1 pound, there are 16 ounces. Create a proportion to convert 12 ounces to pounds.
[tex]\frac{1}{16}[/tex] = [tex]\frac{x}{12}[/tex]
Cross multiply and solve for x:
16x = 12
x = 0.75
So, each student will need 0.75 pounds of plaster. Multiply this by 20 to find the total amount the teacher will need:
20(0.75)
= 15
So, the teacher will need 15 pounds of plaster
Answer:
15 pounds
Step-by-step explanation:
Unit 5 Geometry
i Betty's bedroom is 10; feet by 12 feet,
How much carpet does she need to buy
to cover the entire floor with no carpet
left over?
Answer:
B) 126 square feet
Step-by-step explanation:
10.5 x 12 = 126
(area)
The length of a rectangle is 7.5 inches and the width is 2.75 inches. What is the ratio, using whole numbers, of the length to the width
30:11
30:22
11:15
15:11
Answer:
30 : 11
Step-by-step explanation:
Length : Width
7.50 : 2. 75
750 : 275
30 x 25 : 11 x 25
30 : 11
A prescription requires 10 mg of tablet. A nurse read the incorrect unit of measurement and gave a patient .1 g of the tablet. Is the patient at risk and she should inform the doctor immediately?
A nurse read the incorrect unit of measurement and gave a patient 100 mg of the tablet.
The patient at risk and she should inform the doctor immediately.
What is a unitary method?Unitary method is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
Given
Prescription requires 10 mg of tablet.
A nurse read the incorrect unit of measurement and gave a patient .1 g of the tablet.
We know
1 g = 1000 mg
0.1 g = [tex]x[/tex]
⇒ [tex]x[/tex] × 1 = 0.1 × 1000
⇒ [tex]x[/tex] = 100 mg
10 mg < 100 mg
By using unitary method we can say that
A nurse read the incorrect unit of measurement and gave a patient 100 mg of the tablet.
The patient at risk and she should inform the doctor immediately.
Learn more about unitary method here
https://brainly.com/question/22056199
#SPJ2
2x - 5y + 3 = 6x - 3y + 7. If x = 4, what is the value of y?
Answer:
y = - 10
Step-by-step explanation:
2x - 5y + 3 = 6x - 3y + 7
2(4) - 5y + 3 = 6(4) - 3y + 7
8 - 5y + 3 = 24 - 3y + 7
11 - 5y = 31 - 3y
11 - 11 - 5y = 31 - 11 - 3y
- 5y = 20 - 3y
- 5y + 3y = 20 - 3y + 3y
- 2y = 20
- 2y ÷ - 2 = 20 ÷ - 2
y = - 10
how do you find volume of sphere, cylinder, cone ? ... explaining please
Answer:
hmmmm
Step-by-step explanation:
Cone
The volume of a cone is linked to the volume of a cylinder. A cone is one third of the volume of a cylinder. The volume of a cone is ¹/₃ × π × r² × l. To calculate the volume we multiply these values together. The answer will be written in units³.
Sphere
The volume of a sphere is ⁴/₃ × π × r³. To calculate the volume we multiply these values together. The answer will be written in units³.
Cylinder
The volume of a cylinder is π × r² × l (r is the radius of the circle and l is the length of the cylinder). To calculate the volume we multiply these values together. The answer will be written in units³. It is more accurate to use π = 3.142 or the π button on a calculator.
A cone is a 3D shape with 2 faces and one edge
A sphere is a 3D shape. It has one continuous face and no edges
A cylinder is a type of prism. It has 3 faces and 2 edges
website I used: https://www.bbc.co.uk/bitesize/topics/zrf3cdm/articles/ztqsdxs
I hope this helped!
Solve the inequality:
4 +5t < 19
Answer:
t < 3 is the answer
Step-by-step explanation:
source: https://www.tiger-algebra.com/drill/4_5t%3C19/
^ (it has an explanation too)
Find the missing length indicated
Answer:
The missing length is 80 degrees.
Step-by-step explanation:
Every triangle is equal to 180 degrees. If you add 64 and 36, you get 100. 180-100 is equal to 80, therefor x is equal to 80.
Find the measure of angle 5 if the measure of angle 7 is 115 degrees
Answer:
115 degrees (vertically opposite angles are equal)
Step-by-step explanation:
1. Angles measuring 8x – 3 and 7x + 18 are supplementary. Find the measure of each angle. (5 points)
Answer:
85º and 95º
Step-by-step explanation:
supplementary angle total 180
(8x – 3) + (7x + 18) = 180
Combine like terms
15x + 15 = 180
15x = 165
x = 11
---------------------
8x – 3
8(11) - 3
88 - 3
85º
7x + 18
7(11) + 18
77 + 18
95º
