Evaluate the integral by interpreting it in terms of areas. integral -3 to 0(1+(9-x^2)^1/2)dx
Answer:
[tex]\int\limits^0_{-3}(1+\sqrt{9-x^{2}})\, dx=3+\frac{9\pi}{4}=10.068[/tex]
Step-by-step explanation:
We need to evaluate the following integral by interpreting it in terms of areas :
[tex]\int\limits^0_{-3}(1+\sqrt{9-x^{2}})\, dx[/tex]
The first step is to separate the integral into two easier integrals
[tex]\int\limits^0_{-3}(1+\sqrt{9-x^{2}})\, dx=\int\limits^0_{-3} 1 \, dx+\int\limits^0_{-3}\sqrt{9-x^{2}}\, dx[/tex] (Integral of the sum)
Now we can calculate each integral by studying the area below each function.
For the first integral the function is [tex]f(x)=1[/tex]
(I will attach a file with the functions)
The area below this function is the area of a rectangle with sides 1 and 3 ⇒
[tex]\int\limits^0_{-3}1 \, dx=3[/tex]
For the second integral the function is
[tex]f(x)=y=\sqrt{9-x^{2}}[/tex]
If we study this function :
[tex]y=\sqrt{9-x^{2}}[/tex]
[tex]y^{2}=9-x^{2}[/tex] (I)
[tex]x^{2}+y^{2}=9[/tex]
Which is the equation of a circle centered at (0,0) with radius equal to 3
From the equation (I)
[tex]y^{2}=9-x^{2}[/tex]
[tex]|y|=\sqrt{9-x^{2} }[/tex]
The two possible solutions are :
[tex]y=\sqrt{9-x^{2}}[/tex] (II) and [tex]y=-\sqrt{9-x^{2}}[/tex]
We will use (II) to solve the integral (which is the upper part of the circle)
The area of a circle with radius equal to 3 is
[tex]\pi.3^{2}[/tex]
In the integral we only need a quarter of circle ⇒ We divide the total area by 4 ⇒ [tex]\frac{\pi.3^{2}}{4}[/tex] ⇒ [tex]\frac{9\pi }{4}[/tex]
Finally the integral is equal to
[tex]\int\limits^0_{-3}(1+\sqrt{9-x^{2}})\, dx=3+\frac{9\pi}{4}=10.068[/tex]
Subtract. Fill in the missing numbers. 11-4=? 4=3+1 So, 11-4=
Answer:
7
Step-by-step explanation:
drag each statement to show it true,based on the graph.
Answer:
1). Cinnamon costs $7 per one pound
2). Price per pound of the cinnamon equals $[tex]\frac{5.25}{0.75}[/tex].
Step-by-step explanation:
x-values on the graph define the weight of cinnamon and y-values define the price.
Slope of the line drawn from the origin (0, 0) and (0.75, 5.25) will determine the per lb price of the cinnamon.
Slope of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] will be,
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
If the points on the given line re (0,0) and (0.75, 5.25),
Slope = [tex]\frac{5.25-0}{0.75-0}[/tex]
= 7
Therefore, two options are the correct options.
1). Cinnamon costs $7 per one pound
2). Price per pound of the cinnamon equals $[tex]\frac{5.25}{0.75}[/tex].
Which answer describes the type of numbers that are dense? whole numbers and integers whole numbers but not integers rational numbers and irrational numbers rational numbers but not irrational numbers
Answer:
rational numbers and irrational numbers
Step-by-step explanation:
A bakery wants to determine the best placement for day-old goods. What type of data collection source do you think the bakery should use? Choose the correct answer below. A. The bakery should conduct an experiment. B. The bakery should collect information from operational or transactional systems. C. The bakery should conduct an observational study. D. The bakery should obtain information that was distributed by an organization or individual. E. The bakery should conduct a survey
Answer: C. The bakery should conduct an observational study
Step-by-step explanation:
From the question, we are informed that a bakery wants to determine the best placement for day-old goods. The type of data collection source that the bakery should use is an observational study.
An observational study is a form of study whereby the individuals who are to be observed are being studied by the researcher and certain conclusions are derived about them. When the bakery conductd an observational study, the behavior of the customers regarding goods placement can be observed.
Algebra 1A, I need help
Answer:
for the first question at the top, x=10
Step-by-step explanation:
x+3+9x=8x+23
(subtract 8x from both sides)
x+3+x=23
(combine the x terms)
2x+3=23
(subtract 3 from both sides)
2x=20
(divide by 2 from each side)
x=10
Please hurry! Which expression is equivalent to 2 (5) Superscript 4? 2 times 5 times 4, 2 times 5 times 5 times 5 times 5, 2 times 4 times 4 times 4 times 4 times 4 ,10 times 10 times 10 times 10
Answer:
10 x 10 x 10 x 10.
Step-by-step explanation:
2(5)^4
10^4
Expanded form; 10*10*10*10.
Answer:
10 x 10 x 10 x 10
Step-by-step explanation:
A tortoise and a hare are competing in a 2000-meter race. The arrogant hare decides to let the tortoise have a 510-meter head start. When the start gun is fired the hare begins running at a constant speed of 8 meters per second and the tortoise begins crawling at a constant speed of 6 meters per second. -Let t represent the number of seconds that have elapsed since the start gun was fired. 1) Write an expression in terms of t that represents the hare's distance from the starting line (in meters) 2) Write an expression in terms of t that represents the tortoise's distance from the starting line (in meters) 3) Write an expression in terms of t that represents the number of meters the tortoise is ahead of the hare.
Answer:
1. 8t
2. 510 + 6t
3. 510 - 2t
Step-by-step explanation:
1. Since the hare moves at a speed of 8 metres per second, the distance it moves from the starting line is d = speed × time = 8t
2. Since the rabbit moves at a speed of 6 metres per second, and gets a head start of 510 metres, the distance it moves from the starting line is d = 510 m + speed × time = 510 + 6t
3. The distance the tortoise is ahead of the hare is thus, distance moved by rabbit - distance moved by hare in time, t.
d' = 510 + 6t - 8t
= 510 - 2t
Please help 4+(-10)-(-9)
Answer:
-15
Step-by-step explanation:
-10+-9=-19+4=-15
For the points P1(-2,3,2) and P2(1,2,0) , find the direction of P1P2 and the midpoint of line segment P1P2.
Given :
Two points [tex]P_1(-2,3,2)\ and\ P_2(1,2,0)[/tex] .
To Find :
The direction of [tex]P_1P_2[/tex] and midpoint of line segment [tex]P_1P_2[/tex] .
Solution :
Direction of [tex]P_1[/tex] and [tex]P_2[/tex] is given by :
[tex]\vec{D}=\dfrac{P_2-P_1}{|P_2-P_1|}\\\\\vec{D}=\dfrac{(-2i+3j+2k)-(i+2j+0)}{P_2-P_1}\\\\\vec{D}=\dfrac{-3i+j+2k}{\sqrt{3^2+1^2+2^2}}\\\\\vec{D}=\dfrac{-3i+j+2k}{\sqrt{14}}[/tex]
Now , mid point is given by :
[tex]M(\dfrac{-2+1}{2},\dfrac{3+2}{2},\dfrac{2+0}{2})\\\\M(\dfrac{-1}{2},\dfrac{5}{2},1)[/tex]
Hence , this is the required solution .
Thrice the product of two and "Y".
Answer:
6Y
Step-by-step explanation:
We need to solve the statement ' Thrice the product of two and "Y" '.
Thrice means 3 times and product means multiply. It means we have to multiply 3,2 and Y.
Let the result is R. It can be calculated as follows :
[tex]R=3\times 2\times Y[/tex]
We know that, 3×2 = 6
So,
[tex]R=6Y[/tex]
Hence, Thrice the product of two and "Y" is 6Y.
what is 12.3 -(-9.6) =12.3 + 9.6 simplified?
Answer:
Step-by-step explanation:
12.3 + 9.6 = 21.9
The expression 12.3 - (-9.6) is equivalent to 21.9.
Given is an expression 12.3 -(-9.6) = 12.3 + 9.6, we need to simplify it,
To simplify the expression 12.3 - (-9.6), we can rewrite it as 12.3 + 9.6.
When subtracting a negative number, it is equivalent to adding the positive value of that number.
So, -(-9.6) becomes +9.6.
Therefore, 12.3 - (-9.6) simplifies to 12.3 + 9.6.
Adding 12.3 and 9.6 gives us 21.9.
So, 12.3 - (-9.6) = 21.9.
Learn more about expression click;
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Match the vocabulary to the correct operation
Answer:
Step-by-step explanation:
Product—Multiplication
Sum— Addition
Difference—Subtraction
Quotient—Division
Quantity— Parenthesis
please help Spotting Axis Intercepts
Answer:
Coordinate A ins not intercepting any axis.
Step-by-step explanation:
For a coordinate to intercept an axis, it will be in the form [tex](a, b)\ such\ that:\ a=0, b \in \mathbb{R},\ or:a\in \mathbb{R}, b=0.[/tex]
Since in (3, 6), none of the components are 0, it is not intercepting any axes.
which of the following verifies that triangle YXZ is similar to triangle QPR?
Answer:
AA postulate
Step-by-step explanation:
Because both the angle are identical?
ILL GIVE YOU BRAINLIST !!!
Evaluate the expression given the replacement values.
Answer:
24
Step-by-step explanation:
[tex]a^{2}[/tex]= 49 because any number squared is positive.
Since b=2,
2(-4)= -8.
Then this is 49-8-17, which equals 24.
Answer:
24
Step-by-step explanation:
what five parts make up a data table
Answer:
Step-by-step explanation:
Check boxes.
Sorting (on columns)
Icons that communicate alerts.
Pagination.
Headers Row.
-4.5 x (-2)???????????????????????
Answer:
9
Step-by-step explanation:
-4.5 x (-2) is equal to 9
Find an equation of a plane through the point (3, 0, 2) which is orthogonal to the linex=?2+3t,y=2+4t,z=?1?3tin which the coefficient of x is 3.
Answer: 3x + 4y - 3z - 3 = 0
Step-by-step explanation:
with the given point (3, 0, 2), the plane is orthogonal to this line so it
has directional ratios (3, 4, -3)
therefore the given equation can be written as;
(x+2)/3 = (y-2)/4 = (z+1)/-3
so equation of the plane passing through point x1, y1 and z1 in the one point form is given as;
a(x-x1) + b(y - y1) + c(z -z1) = 0
abc represent the direction ratio
so we substitute
3(x-3) + 4(y-0) + (-3(z-2)) = 0
3x - 9 + 4y - 0 - 3z + 6 = 0
3x + 4y - 3z - 3 = 0
therefore the equation of the plane through the point is 3x + 4y - 3z - 3 = 0
the question can been seen in the picture
Answer:
(2)
Step-by-step explanation:
Find an equation of the sphere with center (-3, 2 , 5) and radius 4. What is the intersection of this sphere with the yz-plane.
Answer:
The equation of the sphere with center (-3, 2 , 5) and radius 4 is [tex](x+3)^{2} +(y-2)^{2} + (z-5)^{2} = 16[/tex]
The intersection of the sphere with the yz- plane gave the equation [tex](y-2)^{2} + (z-5)^{2} = 7[/tex] which is a 2D- circle with center (0,2,5) and radius [tex]\sqrt{7}[/tex].
Step-by-step explanation:
The equation of a sphere of radius r, with center (a,b,c) is given by
[tex](x-a)^{2} +(y-b)^{2} + (z-c)^{2} = r^{2}[/tex]
where, [tex]x,[/tex] [tex]y,[/tex] and [tex]z[/tex] are the coordinates of the points on the surface of the sphere.
Hence, the equation of the sphere with center, (-3, 2 , 5) and radius 4 becomes
[tex](x-a)^{2} +(y-b)^{2} + (z-c)^{2} = r^{2}[/tex]
[tex](x-(-3))^{2} +(y-(2))^{2} + (z-(5))^{2} = 4^{2}[/tex]
Then,
[tex](x+3)^{2} +(y-2)^{2} + (z-5)^{2} = 16[/tex]
This is the equation of the sphere with center (-3, 2 , 5) and radius 4,
Now, for the intersection of this sphere with the yz- plane,
The [tex]yz -[/tex]plane is where [tex]x = 0[/tex], then we set [tex]x = 0[/tex]
Them the equation [tex](x+3)^{2} +(y-2)^{2} + (z-5)^{2} = 16[/tex] becomes
[tex](0+3)^{2} +(y-2)^{2} + (z-5)^{2} = 16[/tex]
[tex](3)^{2} +(y-2)^{2} + (z-5)^{2} = 16\\9 +(y-2)^{2} + (z-5)^{2} = 16\\(y-2)^{2} + (z-5)^{2} = 16 - 9\\(y-2)^{2} + (z-5)^{2} = 7[/tex]
This equation is the equation of a 2D- circle with center (0,2,5) and radius [tex]\sqrt{7}[/tex]
This is the part of the sphere that intersects with the yz-plane.
salesperson receives 16.7% commission. If her total sales for the month are $4900, what is her commission?
Answer:
$818,3
Step-by-step explanation:
16.7% in decimal is 0.167
= 0.167 x $4900
= $818,3
The product of -4 and d
Answer:
-4d
Step-by-step explanation:
please help me with this problem
Answer:
A) sin 70 = x/10
Step-by-step explanation:
From the angle 70 degrees, 10 is the hypotenuse and x is the opposite and if we go by SOH-CAH-TOA I have an O and a H so its sin.
so we know it's sin so we need to figure out the equation. since we have a hypotenuse as a factor it is on top. and the other number is on the bottom.
so,
A) sin 70 = x/10
Solve for b: 15 - 2b = -9
pleasee help:(
Answer:
b = 12
Step-by-step explanation:
15 - 2b = -9
Minus 15 to both sides
-2b = -24
Divide both sides by -2
b = 12
Write an equation in slope-intercept form (y = mx + b).
Perpendicular to 7x - 2y = 16 passing through (-7, 5).
Answer:
y = 2/7x + 7
Step-by-step explanation:
We start off by putting the original equation into slope-intercept form. Subtract 7x from both sides, then divide both sides by -2. Your new equation should be y = -7/2x - 8. It's important to know that when two lines are perpendicular, their slopes (m) are opposite reciprocals of each other. So -7/2 becomes 2/7. The first part of your final equation is y = 2/7x + b.
Next, we need to find the y intercept (b). You need to plug the x and y values from the given coordinate point (-7,5) into your final equation. You should end up with: 5 = 2/7(-7) + b. Then, solve for b.
5 = -14/7 + b
5 = -2 + b
7 = b
Finally, plug the b value into your final equation and you will have your answer.
please help me out with this
Answer:
up is equal to 5/ 6
left side is equal to 3/4
Step-by-step explanation:
1/6 + 1/6+ 1/6+ 1/6+ 1/6= 5/6
1/4 + 1/4 + 1/4= 3/4
When three professors are seated in a restaurant, the hostess asks them: "Does everyone want coffee?" The first professor says: "I do not know." The second professor then says: "I do not know." Finally, the third professor says: "No, not everyone wants coffee."
The hostess comes back and gives coffee to the professors who want it. How did she figure out who wanted coffee?
the first two professors did not know if everyone wanted coffee because the third professor had to choose yes or no if he wanted coffee. the first two professors were waiting for the third to say something, and when he said no, they knew he did not want coffee. if one of the first two professors said no, the answer would be no.
Help please if u can
Answer:
Negative infinity
Step-by-step explanation:
The line points down infinitely in the graph.
Israel started to solve a radical equation in this way:
square root of x plus 6 − 4 = x
square root of x plus 6 − 4 + 4 = x + 4
square root of x plus 6 = x + 4
(square root of x plus 6)2 = (x + 4)2
x + 6 = x2 + 8x + 16
x + 6 − 6 = x2 + 8x + 16 − 6
x = x2 + 8x + 10
x − x = x2 + 8x + 10 − x
0 = x2 + 7x + 10
0 = (x + 2)(x + 5)
x + 2 = 0 x + 5 = 0
x + 2 − 2 = 0 − 2 x + 5 − 5 = 0 − 5
x = −2 x = −5
Solutions = −2, −5
What error did Israel make?
He subtracted 6 before subtracting x.
He added 4 before squaring both sides.
He factored x2 + 7x + 10 incorrectly.
He did not check for extraneous solutions.
Answer:
He did not check for extraneous solutions.
Step-by-step explanation:
He solved the equation correctly and obtained solutions -2 and -5, but there is one final step he did not do.
Every time you square both sides of an equation to solve it, you must check for extraneous solutions. If he did, he would have eliminated x = -5.
Answer: He did not check for extraneous solutions.