Answers
Given:
a)
[tex]\int ^1_0g(x)dx[/tex]Consider the shape included in the region from 0 to 1 of g(x).
The area is,
[tex]\int ^1_0g(x)dx=\frac{1}{2}\times1\times4=2[/tex]b) From x = to x = 6 includes the semi-circle. Its area is calculated as,
[tex]\int ^6_2g(x)dx=-\frac{1}{2}(\pi\times r^2)=-\frac{1}{2}(\pi\times2^2)=-2\pi=-6.28[/tex]
Related Questions
AB = 18.5, AX = 8.1 and BC = 18.5. Whatis the length of AC?
Answers
We can see that the value for the segment AC is AX + XC ---> AC = 8.1 + 8.1 ---> AC = 16.2.
We can obtain this result if we use the Angle bisector theorem. It says that an angle bisector of a triangle will divide the opposite side of the angle into two segments that will be proportional to the other sides of the triangle.
In this case, we have that both sides, AB and CB are congruent, therefore, we have:
[tex]\frac{AX}{AB}=\frac{XC}{CB}\Rightarrow\frac{8.1}{18.5}=\frac{XC}{18.5}\Rightarrow XC=8.1[/tex]Brenda received a gift card for an internet cafe. The cost,y, of renting a computer and using it for x hours at the cafe is shown in the graph below. Which equation represents the same relationship as the graph?
Answers
In order to find the equation of the graph, we need to get two points on the graph.
Two points on the graph are points (2, 24) and (4, 33)
The next step is to find the slope of the graph, using the two points above
[tex]\begin{gathered} \text{ slope, m = }\frac{y_2-y_1}{x_2-x_1} \\ \text{ (x}_1,y_1)=(2,24)_{} \\ (x_2,y_{2_{}})=(4,\text{ 33)} \\ m=\frac{33-24}{4-2} \\ m=\frac{9}{2} \\ m=4.5 \end{gathered}[/tex]Then, using slope and one point formula, find the equation of the line
[tex]\begin{gathered} \text{ y-y}_1=m(x-x_1) \\ m=\text{ 4.5, (x}_1,y_1)=(2,24) \\ y-24=4.5(x-2) \\ y-24=4.5x-9 \\ y=4.5x-9+24 \\ y=4.5x+15 \end{gathered}[/tex]The correct answer is y= 4.5x + 15
You are helping with some repairs at home. You drop a hammer and it hits the floor at a speed of 12 feet per second. If the acceleration due to gravity (g) is 32 feet/second2, how far above the ground (h) was the hammer when you dropped it? Use the formula:A.8.5 feetB.1.0 footC.2.25 feetD.18.0 feet
Answers
Solution
Step 1:
Given data:
[tex]\begin{gathered} v\text{ = 12} \\ \text{g = 32} \\ h\text{ = ?} \end{gathered}[/tex]Step 2:
[tex]\begin{gathered} v\text{ = }\sqrt{2gh} \\ \\ 12\text{ = }\sqrt{2\times32\times h} \\ \\ 12\text{ = }\sqrt{64h} \\ \\ Take\text{ square of both sides} \\ \\ 12^2\text{ = \lparen}\sqrt{64h})^2 \\ \\ 144\text{ = 64h} \\ \\ h\text{ = }\frac{144}{64}\text{ = 2.25 feet} \end{gathered}[/tex]Final answer
C. 2.25 feet
Try, check and revise, or write an equation to solve each problem. 1).The volume of a cube is 79.507 cubic inches. -How long is each edge of the cube? 2). What are the two whole numbers whose product is 294 and whose quotient is 6? 3). Tickets for a concert are sold for $ 8 for the stalls and $ 6 for the gallery. For one function, 400 seats were sold for a total of $ 2,888. How many seats of each type were sold? 4). Aaron bought 6 books and 2 notebooks for $ 46.86. Erin bought 2 books and 6 notebooks for $ 27.78. How much does a book cost?
Answers
Answer:
4.3inches
Explanation:
1) Volume of a cube is expressed as;
[tex]V=L^3[/tex]L is the length of each side of the cube
Given
Volume of a cube = 79.507 cubic inches
Substitute into the formula and get L
[tex]\begin{gathered} 79.507=L^3 \\ L^3\text{ = }79.507 \\ L\text{ = }\sqrt[3]{79.507} \\ L\text{ }=4.3\text{inches} \end{gathered}[/tex]hence eahc edge of the cube is 4.3inches
Determine the quotient of (7.7 × 10–2) ÷ (2.2 × 10–2). Write your answer in scientific notation.
Answers
Given:
[tex](7.7\ast10^{-2})\div(2.2\ast10^{-2})[/tex]The quotient is the result of the division of both numbers.
To find the quotient, let's perform the division.
We have:
[tex]\frac{7.7\ast10^{-2}^{}^{}_{}}{2.2\ast10^{-2}}=3.5[/tex]The quotient is 3.5
The answer in scientific notation is:
[tex]3.5\ast10^0[/tex]ANSWER:
[tex]3.5\ast10^0[/tex]Find the domain of the function using interval notation. f(x)=−2x(x−1)(x−8)
Answers
Solution:
Given:
The function,
[tex]f(x)=-2x(x-1)(x-8)[/tex]The domain of a function is the set of all possible inputs for the function's output to become real and defined.
From the function given, the function has no main constraint or undefined point when we input all real values of x. This means the function is defined for all real values of x.
Therefore, since there is no constraint to make the function undefined, the domain is all real values of x.
Thus,
[tex]\begin{gathered} \text{The solution is;} \\ -\inftyIn interval notation, the domain of the function is;
[tex](-\infty,\infty)[/tex]how to solve this one k(k-9)
Answers
Simplify the expression by multipliaction of terms.
[tex]\begin{gathered} k(k-9)=k\cdot k-9\cdot k \\ =k^2-9k \end{gathered}[/tex]So answer is
[tex]k^2-9k[/tex]A student takes a 10 question multiple choice quiz- each question having 4 choices. Suppose a student randomly picks an answer for each question. Find the following.
Answers
Assume that an A is a 90% (getting at least 9 questions out of 10 right).
The probability that exactly 9 questions are right is 10 (choose one question to get wrong) * (1/4)^9 (1/4 chance of getting each question right) * (3/4) (chance of getting the wrong question wrong) = 10∗3∗(1/4)10 .
The probability that all 10 questions are right is (1/4)10 (1/4 chance of getting each question right).
The total probability of getting an A is (10∗3+1)(1/4)10=31410, or about 0.002956%.
I hope I helped! If I misinterpreted your question, please let me know and I'll try my best to help.
A small toy rocket is launched from a 12-foot pad. The height (h, in feet) of the rocket t seconds after taking off is given by the formulah=−2tcubed2−2+12How long will it take the rocket to hit the ground?t= (Separate answers by a comma if applicable. Write answers as integers or reduced fractions.)
Answers
Solution
Gievn:
[tex]h=-2t^2-2t+12[/tex]When the rocket hits the ground. The distance is zero
Set h = 0 and solve for t
[tex]\begin{gathered} -2t^2-2t+12=0 \\ 2t^2+2t-12=0 \\ 2t^2+6t-4t-12=0 \\ 2t(t+3)-4(t+3)=0 \\ (t+3)(2t-4)=0 \end{gathered}[/tex][tex]\begin{gathered} t+3=0\text{ or 2t-4=0} \\ t=-3\text{ or 2t=4} \\ t=-3\text{ or t=}\frac{4}{2}=2 \end{gathered}[/tex]But, time can not be in negative, hence the answer t = 2
Consider the line y=x+3.Find the equation of the line that is parallel to this line and passes through thepoint (-6, -3).Find the equation of the line that is perpendicular to this line and passes throughthe point (-6, -3).
Answers
Given:
Consider the line y=x+3.
Required:
We want to Find the equation of the line that is parallel to this line and passes through the point (-6, -3).
Find the equation of the line that is perpendicular to this line and passes through the point (-6, -3)
Explanation:
To find parallel to this line and passes through the point (-6, -3)
The slope is same for parallel line is 1
[tex]\begin{gathered} y-(-3)=1(x-(-6)) \\ y+3=x+6 \\ y=x+3 \end{gathered}[/tex]Which is same so there is no parallel line of given line which is passes through point (-6, -3)
Now to find the perpendicular to the given line
for this the slope of this line is -1
[tex]\begin{gathered} y+3=-x-6 \\ y=-x-9 \end{gathered}[/tex]Final answer:
y=x+3
y=-x-9
Can you helpMe with this Equation:y = - 2x-+ 3
Answers
EXPLANATION
Since we have the equation y= -2x + 3
The appropriate y-intercept is +3, thus the second and third options are the only possible.
Finally, we can plug the value 4 in order to obtain the y-intercept:
y= -2*4 + 3
Multiplying and adding numbers:
y = -8 + 3
Adding numbers:
y = -5
In conclusion, the solution is the following graph:
First blank options are 2416872800Second options are 1681880247third blanks are 2428801687fourth blanks are No its to long No its to small yes
Answers
We have to find the expression for the volume of the box in terms of its height (x).
Then, the height is h = x
The length is l = 24 in.
The width is w = x - 7 in, as it is 7 inches less than the height.
The volume is 2880 cubic inches.
We then can express the volume as:
[tex]\begin{gathered} V=2880 \\ l\cdot w\cdot h=2880 \\ 24\cdot(x-7)\cdot x=2880 \\ 24(x^2-7x)=2880 \\ 24x^2-168x=2880 \end{gathered}[/tex]Then, the blancks are filled with 24, 168 and 2880.
We now have to check if the height of the box can be 15 inches.
We can replace x with 15 and see if the equation is still valid:
[tex]\begin{gathered} 24(15)^2-168(15)=2880 \\ 24\cdot225-2520=2880 \\ 5400-2520=2880 \\ 2880=2880\longrightarrow\text{True} \end{gathered}[/tex]It is possible that the height is 15 in.
Answer:
The volume of the box is 24x² - 168x = 2880.
Yes, it is possible that the height is 15 inches.
BACKGROUND INFORMATION:The familiar diagram from our lesson is shown below. The county'sDepartment of Transportation is planning the construction of another road,to be called Oak Street. Oak Street will begin at North Street, 30 milesnorth of Wilson Street. Note: North Street continues north, beyond itsintersection with Main Street. Oak Street will be parallel to Main Street.DIAGRAM:New Street20 miaNorth StreetMain Street3 miWilson Street14 mi
Answers
The distance between Oak Street and Main Street is 5.7 miles.
The oak street begins at North Street, 30 miles north of Wilson Street. The oak street is parallel to the main street. We need to find the distance between Oak Street and Main Street. The slope of the main street is (20-0)/(0-14) = -10/7. The coordinates of the passing point of the main street are (0, 20). The equation of the main street can be written as (y - 20) = (-10/7)(x - 0). Thus, the equation of the main street is y = (-10/7)x + 20. The slope of Oak Street is -10/7. The coordinates of the passing point of the main street are (0, 30). The equation of the oak street can be written as (y - 30) = (-10/7)(x - 0). Thus, the equation of the oak street is y = (-10/7)x + 30. Let the distance between the streets be "D".
D = (c2 - c1)/√(1 + m²) = (30 - 20)/√(1 + (10/7)²) = 10*7/√(10² + 7²) = 5.7
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Can someone verify and corrrect me if I did it wrong please
Answers
Solution:
Given the triangle
Let h represent the hypotenuse
[tex]\begin{gathered} h^2=8^2+15^2\text{ \lparen pythagoras theorem\rparen} \\ h^2=64+225 \\ h^2=289 \\ h=\sqrt{289} \\ h=17 \end{gathered}[/tex][tex](a)\text{ }sin\theta=\frac{opposite}{hypotenuse\text{ }}\text{ = }\frac{15}{17}[/tex][tex](b)\text{ cos}\theta=\frac{adjacent}{hypotenuse}=\frac{8}{17}[/tex][tex](c)\text{ Tan}\theta=\frac{opposite\text{ }}{adjacent}=\frac{15}{8}[/tex][tex](d)\text{ Csc}\theta=\frac{1}{sin\theta}=\frac{1}{\frac{15}{17}}\text{ = }\frac{17}{15}[/tex][tex](e)\text{ Sec}\theta=\frac{1}{cos\theta}=\frac{1}{\frac{8}{17}}=\frac{17}{8}[/tex][tex](f)\text{ Cot}\theta=\frac{1}{tan\theta}=\frac{1}{\frac{15}{8}}=\frac{8}{15}[/tex]If ∆ABC = ∆EDF where the coordinates of A(0,2), B(2,4), and C(2,-1), what is the measure of DF?A-3B-3.1C-5D-5.9Please respond quickly
Answers
The triangles ABC and EDF are congruent, meaning they have the same side lengths and angles measures.
The measure of DF, as both triangles are congruent, is equal to the measure of BC.
We can calculate the length of BC using the distance formula:
[tex]\begin{gathered} D=\sqrt[]{(x_c-x_b)^2+(y_c-y_b_{})^2} \\ D=\sqrt[]{(2-2)^2+(-1-4)^2} \\ D=\sqrt[]{0^2+(-5)^2} \\ D=\sqrt[]{(-5)^2} \\ D=|-5| \\ D=5 \end{gathered}[/tex]As BC is congruent with DF and BC=5, the length of DF is 5 units.
May I please get help with finding the stammers and reasonings
Answers
Answer:
Explanation:
Here, we want to get the reason why the two triangles are congruent
We start with the 3rd statement
We can see that the line AC is present in both and thus will be equal
So, what is the reason for this?
The reason for this is the reflexive property of congruence
Lastly, why are the two triangles congruent?
They share a similar side, have one angle equal and with equal base line lengths
The angle ie between the two equal sides so we call this kind of congruence SAS (side-angle-side)
What ratio is equivalent to the scale 3 in: 1ft?
Answers
Help me please I got the second can’t figure the 1 one out
Answers
The area of a rectangular field is given by:
[tex]\text{Area}=W\cdot L[/tex]if this area has a width of 59m we can solve the length:
[tex]\begin{gathered} L=\frac{Area}{W} \\ L=\frac{5428m^2}{59m} \\ L=92m \end{gathered}[/tex]So the length of this rectangular field is 92m.
I have a question about area of an arc and i have a picture of it
Answers
step 1
Find out the area of the complete rectangle
[tex]A=b*h[/tex]where
b=(13-1)=12 ft
h=9 ft
substitute
[tex]undefined[/tex]Hello! I’m having trouble on this prep guide problem in calc Need help,
Answers
Answer:
The point of intersection would be (3,-2)
Step-by-step explanation:
To determine the intersection of the conics we can use a system of equations since they intersect when they are both equal.
Then, we have these equations:
[tex]\begin{gathered} (x+1)^2+(y+2)^2=16\text{ (1)} \\ (y+2)^2=16-(x+1)^2\text{ (1)} \\ (y+2)^2=4(x-3)\text{ (2)} \end{gathered}[/tex]Equalize equations (1) and (2).
[tex]\begin{gathered} 4(x-3)=16-(x+1)^2 \\ \end{gathered}[/tex]Solve for the x-coordinate.
[tex]\begin{gathered} 4x-12=16-(x^2+2x+1) \\ 4x-12=16-x^2-2x-1 \\ x^2+6x-27=0 \\ (x-3)(x+9)=0 \\ \text{Possible x-intersections:} \\ x=3 \\ x=-9 \end{gathered}[/tex]Since the circle has a radius of 4, we know that the intersection cannot be x=-9. Then, the x-coordinate to use is x=3.
Substitute x=3 into one of the equations to determine the y-coordinate:
[tex]\begin{gathered} (y+2)^2=4(3-3) \\ (y+2)^2=0 \\ y^2+4y+4=0 \\ (y+2)(y+2)=0 \\ y-\text{coordinate:} \\ y=-2 \end{gathered}[/tex]Hence, the point of intersection would be (3,-2)
estimates by first rounding each number to the place value 1.8×3.62
Answers
By estimation you have:
3.62 ≈ 4.0
1.8 ≈ 2.0
2.0 x 4.0 = 8.0
He has only hundreds, tens, and ones blocks. Part A How can Asher model the number 1,414?
Answers
ANSWER:
14 blocks of hundreds
1 blocks of tens
4 blocks of ones
STEP-BY-STEP EXPLANATION:
The first thing is to decompose the number 1414, like this:
[tex]1414=1000+400+10+4[/tex]Since we have only hundreds, tens, and ones blocks.
[tex]1414=1400+10+4[/tex]Therefore, would be:
14 blocks of hundreds
1 blocks of tens
4 blocks of ones
Answer:
use ten 100 blocks,four 10 blocks,and fourteen 1s blocks.
Step-by-step explanation:
hope that helps.
Amy's doctor increased the dose of her medication from 2.5 to 7.5. what the percent increase?
Answers
Amy's doctor increased the dose of her medication from 2.5 to 7.5.
Initial dose = 2.5
New dose = 7.5
Chan
Consider triangle DEF , where d = 17 , e = 19 and f = 30 Determine the measure of the largest angle.
Answers
The Solution.
Certainly, the largest angle is angle F ( since it is the angle directly opposite the longest side)
By cosine rule, we have
[tex]\cos F=\frac{d^2+e^2-f^2}{2de}[/tex][tex]S\text{ubstituting 17 for d, 19 for e, and 30 for }f,\text{ we get}[/tex][tex]\cos F=\frac{17^2+19^2-30^2}{2\times17\times19}[/tex][tex]\begin{gathered} \cos F=\frac{289+361-900}{34\times19} \\ \\ \cos F=\frac{650-900}{646} \end{gathered}[/tex][tex]\cos F=\frac{-250}{646}=-0.3870[/tex]Taking the cosine inverse of both sides, we get
[tex]F=\cos ^{-1}(-0.3870)=112.77^o[/tex]Therefore, the correct answer is 112.77 degrees.
help me with this question
Answers
the probability is
P=240/350
simplify
P=24/35I need help with this please If the triangle on the grid is translated three units left and nine units down what are the coordinates of c
Answers
Explanation
From the question
we are simply asked to get the new coordinates of point C if the triangle ABC is translated three units to the left and nine units down
To do so, we will make use of the relationship
If a coordinate is translated left or right, it affects the x-coordinate. Left is negative, Right is positive
If a coordinate is translated up or down, it affects the y-coordinates. Down is negative, Up is positive
Therefore
For point C
The initial coordinate is (-1,2)
After the triangle has been translated, we will have
[tex]\begin{gathered} x-value=-1-3=-4 \\ y-value=2-9=-7 \end{gathered}[/tex]Therefore, we have the new coordinate as (-4,-7)
The answer is
Statistic Questions
All of the following statements, except for one, contains an error.
Which statement does not contain an error?
A) The relationship between height and the ability to reach things is strong and positive. The correlation is 1.15.
B) The relationship between height and weight is strong and positive. The correlation is 0.95.
C) The relationship between height and gender is strong and positive. The correlation is 0.95.
D) The relationship between age and height is negative for the elderly. The correlation is –1.25 .
Answers
The correct statement regarding the correlation coefficient is given as follows:
B) The relationship between height and weight is strong and positive. The correlation is 0.95.
What is a correlation coefficient?The correlation coefficient between two variables is an index that measures correlation between these variables, assuming values between -1 and 1.
As the values have to be between -1 and 1, statements A and D are false, as the coefficients have values greater than 1 or less than -1.
From the image given at the end of the answer, the variables are given as follows:
Height.Weight.The scatter plot is increasing, hence statement B is correct, as there is a positive correlation between the variables.
Missing InformationThe graph is given by the image at the end of the answer.
More can be learned about correlation coefficients at brainly.com/question/16355498
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27 students rode bus 5. If the ratio of elementary students to middle school students is 2:1, how many elementary students rode bus 5?
Answers
Take x as the number of middle school students. According to the statement, the ratio of elementary students to middle school students is 2:1, which means that for every x middle school students there are 2x elementary students.
The sum of elementary and middle school students is 27. Which means that the sum of x and 2x is 27:
[tex]\begin{gathered} 2x+x=27 \\ 3x=27 \\ x=\frac{27}{3} \\ x=9 \end{gathered}[/tex]The number of elementary school students is 2x:
[tex]2x=2(9)=18[/tex]There are 18 elementary students on the bus 5.
Select the expressions that are equivalent to -6(40 - 2) - 5b. 4(-2b-6) - 5b 12b - 29 (46 - 2) -6 -56 -2(4 - 6) - 5b sbmit
Answers
Explanation
to solve this we need to expand the expressions and then compare
Step 1
[tex]undefined[/tex]In five years time job will be four times as old as his son Mark. Two years ago Jon was eleven times as old as mark how old are Jon and mark now
Answers
Given that In five years time job will be four times as old as his son Mark and Two years ago Jon was eleven times as old as mark.
Let the age of job and mark now be x and y years old.
So, in five years the age of job will be x + 5 and the age of his son mark will be y + 5.
According to the question,
[tex]\begin{gathered} x+5=4(y+5) \\ x+5=4y+20 \\ x-4y=15 \end{gathered}[/tex]Two years ago, the age of job was x - 2 and the age of his son mark was y - 2.
So, according to the question.
[tex]\begin{gathered} x-2=11(y-2) \\ x-2=11y-22 \\ x-11y=-20 \end{gathered}[/tex]From the first equation, we have x = 4y + 15. Substitute this value in the second equation and solve:
[tex]\begin{gathered} 4y+15-11y=-20 \\ -7y=-35 \\ y=5 \end{gathered}[/tex]Substitute y = 5 in x = 4y + 15.
[tex]\begin{gathered} x=4(5)+15 \\ x=20+15 \\ x=35 \end{gathered}[/tex]Thus, the present age of job is 35 years and the present age of his son mark is 5 years.