Answer:
the equation of the circle is
[tex](x-2)^2+(y+4)^2 = 34[/tex]
Step-by-step explanation:
Recall that the equation of a circle is given by [tex](x-h)^2+(y-k)^2 = r^2[/tex] where r is the radius, and (h,k) is the center. Recall that given two points that are the endpoints of a diameter, the center of the circle is their correspondent midpoint. Also, recall that given points (a,b), (c,d) their midpoint is obtained by [tex](\frac{a+c}{2},\frac{b+d}{2})[/tex]
In this case we are given the endpoints (-1,-9), (5,1). So the center of the circle is the midpoint obtained by [tex](\frac{-1+5}{2},\frac{-9+1}{2}) = (2, -4)[/tex]. Recall that the radius of a circle is the distance from the radius to any of the points of the circle. So, the radius is the distance between the center and the point (-1,-9). We will calculate r^2, by using the distance formula. REcall that the distance between points (a,b), (c,d) is given by
[tex]\sqrt[]{(a-c)^2+(b-d)^2}[/tex]. So, its square is
[tex](a-c)^2+(b-d)^2[/tex].
In our case,
[tex]r^2 = (2-(-1))^2+(-4-(-9))^2 = 3^2+5^2 = 34[/tex]
So, the equation of the circle is
[tex](x-2)^2+(y+4)^2 = 34[/tex]
Amy filled bags with mixed nuts. The weights of the bags are 1/8 lb, 1/4 lb, 1/8 lb, 1/2 lb, 1/8 lb, 1/4 lb, 1/8lb, 1/2 lb, 1/8 lb, 1/4 lb, 1/8 lb, 1/2 lb, 1/8 lb, 1/8 lb, 1/4 lb, and 1/2 lb.
Part A: Organize the information in a line plot. (on your own paper)
Part B: What is the average weight of the bags? ________ lb
Answer:
(a)See attached
(b)[tex]\text{Average Weight =}\dfrac{1}{4}$ lb[/tex]
Step-by-step explanation:
The weights of the bag are given below:
[tex]1/8 lb, 1/4 lb, 1/8 lb, 1/2 lb, 1/8 lb, 1/4 lb, 1/8lb, 1/2 lb \\1/8 lb, 1/4 lb, 1/8 lb, 1/2 lb, 1/8 lb, 1/8 lb, 1/4 lb, 1/2 lb.[/tex]
When sorted, we have:
[tex]1/8 lb, 1/8 lb, 1/8lb, 1/8 lb, 1/8 lb, 1/8 lb, 1/8 lb, 1/8 lb\\ 1/4 lb,1/4 lb, 1/4 lb, 1/4 lb\\ 1/2 lb, 1/2 lb, 1/2 lb,1/2 lb,[/tex]
8 bags weigh [tex]\frac{1}{8}lb[/tex]4 bags weigh [tex]\frac{1}{4}lb[/tex]4 bags weigh [tex]\frac{1}{2}lb[/tex]Part A
See attached for the Line plot
Part B
Average Weight of the bags
[tex]=\dfrac{(8X\dfrac{1}{8})+ (4X\dfrac{1}{4})+(4X\dfrac{1}{2})}{16} \\=\dfrac{1+1+2}{16}\\=\dfrac{4}{16}\\$Average Weight =\dfrac{1}{4}$ lb[/tex]
Determine whether the given limit leads to a determinate or indeterminate form. HINT [See Example 2.]
lim
x→−[infinity] 2/−x + 3
determinate form
indeterminate form
Evaluate the limit if it exists. (If you need to use or –, enter INFINITY or –INFINITY, respectively. If an answer does not exist, enter DNE.)
If the limit does not exist, say why. (If the limit does exist, so state.)
Answer:
The limit leads to a determinate form.
[tex]\lim_{x \to \infty} \frac{2}{-x+3} = 0[/tex]
Step-by-step explanation:
The following are indeterminate forms.
[tex]\frac{0}{0} \ and \ \frac{\infty}{\infty}[/tex]
Given the limit of a function [tex]\lim_{x \to \infty} \frac{2}{-x+3}[/tex], to show if the given limit is determinate or indeterminate form, we will need to substitute the value of -[tex]\infty[/tex] into the function as shown,
[tex]\lim_{x \to \infty} \frac{2}{-x+3}\\= \frac{2}{-(-\infty)+3}\\= \frac{2}{\infty+3}\\= \frac{2}{\infty}\\\\Generally, \ \frac{a}{\infty} =0[/tex]
where a is any constant, therefore [tex]\frac{2}{\infty} = 0[/tex]
Since we are able to get a finite value i.e 0, this shows that the limit does exist and leads to a determinate form
An oblique cone has a height equal to the diameter of the base. The volume of the cone is equal to 18π cubic units. An oblique cone has a diameter of 2 x and a height of 2 x. The volume of the cone is 18 pi cubic units. What is the radius of the cone? 2 units 3 units 6 units 9 units
Answer:
3 units
Step-by-step explanation:
The formula for the volume of the cone is given by
[tex]V=\frac{1}{3} \pi r^{2}h[/tex]
[tex]V=18\pi\ unit^{3} \\\\ r=\frac{2x}{2} =x\ units \\ \\ h=2x\ units[/tex]
Substituting in above formula
[tex]18\pi=\frac{1}{3} \pi*x^{2}*2x\\ \\ 54=2x^{3} \\ \\ x^{3} =27\\ \\ x=\sqrt[3]{27} \\ \\ x=3\ units[/tex]
Thus, the radius of the cone is 3 units.
Does anyone know the answer to this?
Answer:
1.88
Step-by-step explanation:
From Trigonometry Identity;
Cos 20° = AC/ CB
AC = Cos 20° × CB
= Cos 20° × 2
= 1.879
= 1.88 ( to the nearest hundredth)
Consider the following linear programming problem: Max Z = $15x + $20y Subject to: 8x + 5y ≤ 40 0.4x + y ≥ 4 x, y ≥ 0 Determine the values for x and y that will maximize revenue. Given this optimal revenue, what is the amount of slack associated with the first constraint?
Answer:
x=0, y=8
slack is zero
surplus is 4
Step-by-step explanation:
See graph for optimal region
if x=0, y=8
15(0)+20(8)= 160
if x= 0, y=4
15(0) + 20(4)= 80
if x=10/3 , y=8/3
15(10/3) + 20(8/3)= 310/3
Slack
8(0)+ 5(8) ≤ 40
40≤40
slack is zero
0.4(0) + 8 ≥ 4
8 ≥ 4
im awful with dis TwT pls help me it makes me understand better and learn
also:
- surface area
- lateral area
- volume
Answer:
Surface Area: 1,200 units²
Lateral Area: 624 units²
Volume: 960 units³
Step-by-step explanation:
Surface Area is the area of all the faces of the object.
Lateral Area is the area of all the faces of the object NOT INCLUDING the base.
Volume is how much the object can hold.
Using the formula [tex]\frac{1}{2} *b*h[/tex] the area of ONE of the lateral faces of the pyramid is
0.5×24×13=
12×13=
156 units²
156 un² × 4 lateral faces =
624 un²
The lateral surface area is 624 units²
Since the lateral surface area + base is the total surface area:
The base is 24² or 576 units²
624 un²+576 un²=
1,200 units² is the total surface area.
Volume formula for a pyramid is [tex]\frac{1}{3} *b*h[/tex]
We know the base is 576 units².
We don't know the height yet.
We can use the Pythagorean Theorem to find the height of our pyramid.
a²+b²=c²
Half of 24 is 12
12²+b²=13²
144+b²=169
Subtract 144 from both sides.
b²=25
Square root both sides.
b=[tex]\sqrt{25}[/tex]
b=5
The height of our pyramid is 5.
[tex]\frac{1}{3} *576*5=\\\\192*5=\\\\960[/tex]
Our volume for the pyramid is 960 units³
Hope you understand more!
Someone plz help me solved this problem I need help ASAP! Plz help me!!
Answer:
a. $52.20
b. [tex]z=11x+0.09y[/tex]
Step-by-step explanation:
[tex]z=7x+0.11y[/tex]
a.
x = 4
y = 220
[tex]z=(7*4)+(0.11*220)\\z=28+24.2\\z=52.2[/tex]
It costs $52.20 under those conditions.
b.
[tex]z=11x+0.09y[/tex]
If z is still how much it costs in total
If x is how many days rented
If y is how many miles driven
I need help I think I have the but I might be wrong
Answer:
D
Step-by-step explanation:
3 to 7 is about 4.
Two points A and B are on opposite sides of a building. A surveyor selects a third point to place a transit. Point C is 49 feet from point A and 71 feet from point B. The angle ACB is 45°. How far apart are points A and
B? Round your answer to the nearest tenth as needed.
O A 111.2 ft
O B. 99.5 ft
O c. 70.61
OD. 50.2 ft
Answer:
According to the Law of Cosines, the correct answer would be D) 50.2 feet
What’s the correct answer for this?
Answer:
A.
Step-by-step Explanation:
P(A or B) = P(A)+P(B)-P(A and B)
Now
Putting the givens
0.68 = 0.2 + P(B) - 0.12
P(B) = 0.68 - 0.2 +0.12
P(B) = 0.6
Find the distance between the two points rounding to the nearest tenth (if necessary).
(2, -8) and (5, -6)
Answer:
Submit Answer
attempt 1 out of 2
Approximately 3.6
:) Hope this helps
Dilate the point B(-4,5) by a scale factor of 3 with the center at the origin.
Identify the coordinates of the pre-image.
B(-4,5)
Identify the scale factor.
Scale factor: n = 3
Multiply the scale factor by each coordinate
the pre-image to find the coordinates of the image.
B'(3(-4), 3(5))
The image point B' has coordinates B ( , )
Answer:(-12,15)
Step-by-step explanation:
My Instagram: kxng_V2
There are 18 students attending band camp, 4 girls and 14 boys. What is the
ratio of girls to boys at band camp?
Answer:
4:14 or 2:7
Step-by-step explanation:
there are 4 girls and 14 boys
the ratio is 4:14
correct me if this is wrong
Answer:
2/7
Step-by-step explanation:
two find the answer you need to reduce 4 and 14 into the lowest common denominator.
A student's course grade is based on one midterm that counts as 5% of his final grade, one class project that counts as 25% of his final grade, a set of homework assignments that counts as 35% of his final grade, and a final exam that counts as 35% of his final grade. His midterm score is 72, his project score is 83, his homework score is 91, and his final exam score is 74. What is his overall final score? What letter grade did he earn (A, B, C, D, or F)? Assume that a mean of 90 or above is an A, a mean of at least 80 but less than 90 is a B, and so on.His overall final score is nothing.
Answer:
His overal final score is 81.2. His letter grade is a B.
Step-by-step explanation:
Weighed average:
The sum of all values multiplied by it's weight. The weight is a proportion(a value between 0 and 1).
So.
Score of 72 on the midterm, which counts 5%.
Score of 83 on the project score, which counts 25%.
Score of 91 on homework assignments, which counts 35%.
Score of 74 on the final exam, which counts 35%.
His grade is:
G = 72*0.05 + 83*0.25 + 91*0.35 + 74*0.35 = 82.1.
His overal final score is 81.2.
At least 80 but less than 90 is a B
So his letter grade is a B.
nevermind...
what is the domain?
(-infinity,infinity) -answer
(-infinity, 4)
(-4, 4)
(0, 4)
What is the range?
(-infinity, infinity)
(-infinity, 4) -answer
(-4, 4)
(0, 4)
Answer:
its A for the domain and B for the range
domain: (-infinity,infinity) Range: (-infinity,4]
Step-by-step explanation:
Answer:
its 3
Step-by-step explanation:
HELP ILL GIVE YOU BRAINLIEST IF YOUR RIGHT ‼️‼️‼️‼️
Answer:
first question: 36
second question: 5
Step-by-step explanation:
for the first question, the parentheses just mean you are multiplying. so it would be 2 x 3 x 6 which equals 36.
For the second question, you would add d and g together and e and f, then subtract the sum of e and f from the sum of d and g.
(2 + 12) - (3 + 6)
14 - 9 = 5
Step-by-step explanation:
d=2
e=3
f=6
g=12
therefore , (2)×(3)×(6)
=36
2. d=2
e=3
f=6
g=12
(d+g) - (e+f)
(2+12) - (3+6)
(14) -(9)
=5.
This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint.
f(x, y, z) = x2 + y2 + z2; x4 + y4 + z4 = 7
Answer:
The maximum value is +√21 and the minimum value is -√21
Step-by-step explanation:
f(x,y,z) = x² + y² + z². Let g(x,y,z) = x⁴ + y⁴ + z⁴ - 7 = 0
Using Lagrange multipliers,
df/dx = λg/dx, df/dy = λg/dy. and df/dz = λg/dz
df/dx = 2x, df/dy = 2y, df/dz = 2z
dg/dx = 4x³, dg/dy = 4y³, dg/dz = 4z³
So, df/dx = λg/dx ⇒ 2x = 4λx³ (1)
df/dy = λg/dy ⇒ 2y = 4λy³ (2)
df/dz = λg/dz ⇒ 2z = 4λz³ (3)
From (1) 4λx³ - 2x = 0
2λx³ - x = 0
x(2λx² - 1) = 0
solving, x = 0 or (2λx² - 1) = 0 ⇒ 2λx² = 1 ⇒ x = ±1/√(2λ) since x ≠ 0
From (2) 4λy³ - 2y = 0
2λy³ - y = 0
y(2λy² - 1) = 0
solving, y = 0 or (2λy² - 1) = 0 ⇒ 2λy² = 1 ⇒ y = ±1/√(2λ) since y ≠ 0
From (3) 4λz³ - 2z = 0
2λz³ - z = 0
z(2λz² - 1) = 0
solving, z = 0 or (2λz² - 1) = 0 ⇒ 2λz² = 1 ⇒ z = ±1/√(2λ) since z ≠ 0
g(x,y,z) = x⁴ + y⁴ + z⁴ - 7 = 0
(1/√(2λ))⁴ + (1/√(2λ))⁴ + (1/√(2λ))⁴ - 7 = 0
3 (1/√(2λ))⁴ = 7
(1/√(2λ))⁴ = 7/3
1/√(2λ) = ⁴√7/3
√(2λ) = ⁴√3/7
2λ = √3/7
λ = 1/2(√3/7)
Since x = 1/√(2λ) = 1/√(2 [1/2(√3/7)]) = 1/⁴√3/7 = ±⁴√7/3
Also y = 1/√(2λ) = 1/√(2 [1/2(√3/7)]) = 1/⁴√3/7 = ±⁴√7/3
and z = 1/√(2λ) = 1/√(2 [1/2(√3/7)]) = 1/⁴√3/7 = ±⁴√7/3
Substituting x,y and z into f(x,y,z) we have
f(x,y,z) = (⁴√7/3)² + (⁴√7/3)² + (⁴√7/3)² = 3(⁴√7/3)² = 3(√7/3) = √(7 × 3) = ±√21
The maximum value is +√21 and the minimum value is -√21
Please answer this correctly
Answer:
24 cm
Step-by-step explanation:
Assuming that the triangles are similar,
then the ratio of their sides must be the same.
in this case you are dealing with 2 longest sides and the 2 shortest sides.
We are asked to find the y (the length of the shortest side of the blue triangle)
because they are similar, we can form a ratio with their sides:
Purple Long Side / Blue Long Side = Purple Short Side / Purple Long side
100 / 80 = 30 / y
100y = (30)(80)
y = (30)(80) / 100
y = 24 cm
Answer:
y = 24
Step-by-step explanation:
Since these triangles are similar, you can set up a proportion like this:
[tex]\frac{100}{80} =\frac{30}{y}[/tex]
→Cross multiply:
[tex]\frac{100y}{2400}[/tex]
→Divide 2400 by 100:
y = 24
At the Northside assembly plant, 30% of the workers were classied as minority, while at the Southside assembly plant, 60% of the workers were classied as minority. When Northside and Southside were closed, all workers transferred to the new Eastside plant to make up its entire work force. If 40% of the 3750 employees at Eastside are minority, then how many employees did Northside and Southside have originally?A. Northside had 2500 employees, and Southside had 1250 employees. B. Northside had 1250 employees, and Southside had 2500 employees. C. Northside had 1000 employees, and Southside had 1100 employees. D. Northside had 1875 employees, and Southside had 1875 employees.
Answer:
A. Northside had 2500 employees, and Southside had 1250 employees.Step-by-step explanation:
At the Northside assembly plant, 30% of the workers were classied as minority, while at the Southside assembly plant, 60% of the workers were classied as minority. When Northside and Southside were closed, all workers transferred to the new Eastside plant to make up its entire work force. If 40% of the 3750 employees at Eastside are minority, then how many employees did Northside and Southside have originally?
Can someone help me with these two problems?
Answer:
C. 38°
D. 30°
Step-by-step explanation:
The relevant relation in both cases is the inscribed angle measures half the measure of the arc it intercepts.
__
C. Angle TSQ intercepts arc TQ, so the measure of arc TQ is 2(86.5°) = 173°. The measure of arc TR is the difference between the measures of arcs TQ and RQ, so is ...
arc TR = 173° -135° = 38°
__
D. Inscribed angle PQR intercepts arc PR, so is half its measure.
angle PQR = 60°/2 = 30°
How do you do this question
Answer:
the answer for the question is 26√13/12
The average daily volume of a computer stock in 2011 was μ= 35 1 million shares, according to a reliable source. A stock analyst believes that the stock volume in 2014 is different from the 2011 level. Based on a random sample of 40 trading days in 2014, he finds the sample mean to be 25,1 million shares, with a standard deviation of s = 12 4 million shares. Test the hypotheses by constructing a 95% confidence interval. Complete parts (a) through (c) below.
a. State the hypotheses for the test.
b. Construct a 95% confidence interval about the sample mean of stocks traded in 2014
c. Will the researcher reject the null hypothesis?
A. Do not reject the null hypothesis because μ= 35 1 million shares falls in the confidence interval.
B. Reject the null hypothesis because μ= 35 1 million shares falls in the confidence interval.
C. Do not reject the null hypothesis because μ=35 1 million shares does not fall in the confidence interval.
D. Reject the null hypothesis because μ= 35 1 million shares does not fall in the confidence interval.
Answer:
a) The null and alternative hypothesis are:
[tex]H_0: \mu=35.1\\\\H_a:\mu< 35.1[/tex]
b) The 95% confidence interval for the mean stocks traded in 2014 in millions is (21.13, 29.07).
c) D. Reject the null hypothesis because μ= 35 1 million shares does not fall in the confidence interval.
Step-by-step explanation:
The claim is that 2014 stock volumes are significantly different from 2011 stock volumes (35.1 millions).
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=35.1\\\\H_a:\mu< 35.1[/tex]
We can test this by calculating a 95% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=25.1.
The sample size is N=40.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{12.4}{\sqrt{40}}=\dfrac{12.4}{6.32}=1.961[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=40-1=39[/tex]
The t-value for a 95% confidence interval and 39 degrees of freedom is t=2.023.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=2.023 \cdot 1.961=3.966[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 25.1-3.966=21.13\\\\UL=M+t \cdot s_M = 25.1+3.966=29.07[/tex]
The 95% confidence interval for the mean is (21.13, 29.07).
The value 35.1 is not included in the interval, so we can conclude that there is significant difference from the 2011 stock volume.
Line k has an equation of y = -2x - 6. Perpendicular to line k is line I, which passes through
the point (3, 6). What is the equation of line l?
Write the equation in slope-intercept form. Write the numbers in the equation as proper
fractions, improper fractions, or integers.
Answer:
y = x/2 +9/2
Step-by-step explanation:
y = -2x - 6.
The equation of the line perpendicular to the above equation has a slope 1/2
The equation of a slope is
y2-y1/x2-x1 = 1/2
To form an equation of the line we chose a point that lies on the graph which is perpendicular to y = -2x - 6 and an arbitrary point (x,y)
A point is given us already and that point is (3, 6).
Tie all together to compute the slope we have;
y-6/x-3 = 1/2
2(y-6) = x-3
2y-12= x-3
2y = x-3+12
2y= x+9
Dividing through by 2 we have
y = x/2 +9/2
y = x/2 + 4.5
The required equation is 2x-y =0, interception point is (0,0) and the equation is in integers.
What is slope ?Slope is a notation that shows that a surface of which one end or side is at a higher level than another surface.
The equation of a line which passes through point (x₁, y₁) with slope m can be given by,
y - y₁ = m(x - x₁)
The given equation of line k is y= -2x-6 (1).
The slope of line k = -2.
Since, line l is perpendicular to line k,
Slope of line l = 2
Line l passes through the point (3,6), therefore, the equation of line l,
y-6= 2(x-3)
⇒2x-y =0 (2)
To find interception point of slope of line l,
Substitute y=0, in equation (2) ,
x intercept = 0
Substitute x=0, in equation (2),
y intercept = 0
The equation is 2x-y =0, and it is in integer form.
To know more about Slope on :
https://brainly.com/question/16180119
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I keep getting this answer wrong please help!!
Answer:
30 mph50 mphStep-by-step explanation:
They closed the 200 mile distance in 2.5 hours, so the sum of their speeds was ...
(200 mi)/(2.5 h) = 80 mi/h
If s is the speed of the slower one, then ...
s + (s+20) = 80
2s = 60
s = 30
The slower wander's speed was 30 mph; the faster one's was 50 mph.
4. Find the volume of the given solid bounded by the elliptic paraboloid z = 4 - x^2 - 4y^2, the cylinder x^2 + y^2 = 1 and the plane z = 0.
5. Sketch the region of integration and change the order of integration.
Answer:
2.5π units^3
Step-by-step explanation:
Solution:-
- We will evaluate the solid formed by a function defined as an elliptical paraboloid as follows:-
[tex]z = 4 - x^2 -4y^2[/tex]
- To sketch the elliptical paraboloid we need to know the two things first is the intersection point on the z-axis and the orientation of the paraboloid ( upward / downward cup ).
- To determine the intersection point on the z-axis. We will substitute the following x = y = 0 into the given function. We get:
[tex]z = 4 - 0 -4*0 = 4[/tex]
- The intersection point of surface is z = 4. To determine the orientation of the paraboloid we see the linear term in the equation. The independent coordinates ( x^2 and y^2 ) are non-linear while ( z ) is linear. Hence, the paraboloid is directed along the z-axis.
- To determine the cup upward or downwards we will look at the signs of both non-linear terms ( x^2 and y^2 ). Both non-linear terms are accompanied by the negative sign ( - ). Hence, the surface is cup downwards. The sketch is shown in the attachment.
- The boundary conditions are expressed in the form of a cylinder and a plane expressed as:
[tex]x^2 + y^2 = 1\\\\z = 4[/tex]
- To cylinder is basically an extension of the circle that lies in the ( x - y ) plane out to the missing coordinate direction. Hence, the circle ( x^2 + y^2 = 1 ) of radius = 1 unit is extended along the z - axis ( coordinate missing in the equation ).
- The cylinder bounds the paraboloid in the x-y plane and the plane z = 0 and the intersection coordinate z = 4 of the paraboloid bounds the required solid in the z-direction. ( See the complete sketch in the attachment )
- To determine the volume of solid defined by the elliptical paraboloid bounded by a cylinder and plane we will employ the use of tripple integrals.
- We will first integrate the solid in 3-dimension along the z-direction. With limits: ( z = 0 , [tex]z = 4 - x^2 -4y^2[/tex] ). Then we will integrate the projection of the solid on the x-y plane bounded by a circle ( cylinder ) along the y-direction. With limits: ( [tex]y = - \sqrt{1 - x^2}[/tex] , [tex]y = \sqrt{1 - x^2}[/tex] ). Finally evaluate along the x-direction represented by a 1-dimensional line with end points ( -1 , 1 ).
- We set up our integral as follows:
[tex]V_s = \int\int\int {} \, dz.dy.dx[/tex]
- Integrate with respect to ( dz ) with limits: ( z = 0 , [tex]z = 4 - x^2 -4y^2[/tex] ):
[tex]V_s = \int\int [ {4 - x^2 - 4y^2} ] \, dy.dx[/tex]
- Integrate with respect to ( dy ) with limits: ( [tex]y = - \sqrt{1 - x^2}[/tex] , [tex]y = \sqrt{1 - x^2}[/tex] )
[tex]V_s = \int [ {4y - x^2.y - \frac{4}{3} y^3} ] \, | .dx\\\\V_s = \int [ {8\sqrt{( 1 - x^2 )} - 2x^2*\sqrt{( 1 - x^2 )} - \frac{8}{3} ( 1 - x^2 )^\frac{3}{2} } ] . dx[/tex]
- Integrate with respect to ( dx ) with limits: ( -1 , 1 )
[tex]V_s = [ 4. ( arcsin ( x ) + x\sqrt{1 - x^2} ) - \frac{arcsin ( x ) - 2x ( 1 -x^2 )^\frac{3}{2} + x\sqrt{1 - x^2} }{2} - \frac{ 3*arcsin ( x ) + 2x ( 1 -x^2 )^\frac{3}{2} + 3x\sqrt{1 - x^2} }{3} ] | \limits^1_-_1\\\\V_s = [ \frac{5}{2} *arcsin ( x ) + \frac{5}{3}*x ( 1 -x^2 )^\frac{3}{2} + \frac{5}{2} *x\sqrt{1 - x^2} ) ] | \limits^1_-_1\\\\V_s = [ \frac{5\pi }{2} + 0 + 0 ] \\\\V_s = \frac{5\pi }{2}[/tex]
Answer: The volume of the solid bounded by the curves is ( 5π/2 ) units^3.
(4x-4)+(3x-2)+(2x+6)=180
Answer:
x=20
Step-by-step explanation:
Let's solve your equation step-by-step.
4x−4+3x−2+2x+6=180
Step 1: Simplify both sides of the equation.
4x−4+3x−2+2x+6=180
4x+−4+3x+−2+2x+6=180
(4x+3x+2x)+(−4+−2+6)=180(Combine Like Terms)
9x=180
9x=180
Step 2: Divide both sides by 9.
9x
9
=
180
9
x=20
Answer:
x=20
Answer:
x=20
Step-by-step explanation:
im pretty sure this is right. you can't take away 4 from 4 x, so you do it like this: -4+(-2)+6 =0. 4x + 3x + 2x =9x. 180/9 = 20
A cylinder has a diameter of 14 centimeters and a volume of 112π cubic centimeters. What is the height in centimeters of the cylinder?
Step-by-step explanation:
we have diameter and volume
and volume function is : v=(3.14)(r^2)h
so : h = 196/112
R(3,3), S(-6,-6) , indicate in standard form the equation of the line passing through the given points
Answer:
x - y = 0
Step-by-step explanation:
We see that in both cases, y = x. The standard-form version of this equation is ...
x - y = 0
A mixture of gases consists of N2, O2, H2 and F2. The total pressure of the mixture is 511.56 kPa. The pressure of the N2 is 584 mm Hg, the pressure of the O2 is 196 kPa and the pressure of the H2 is standard pressure. What is the pressure of the F2 (in mm Hg)?
Answer:
Step-by-step explanation:
The total pressure of a gas is the sum of the partial pressures of the gases that it consists of. It means that
N2 + O2 + H2 + F2 = pressure of mixture
1 kpa = 7.50061683 mmhg
The total pressure of the mixture is 511.56 kPa. Converting to mmHg, it becomes
511.56 × 7.50061683 = 3837.02 mmhg
The pressure of the O2 is 196 kPa. Converting to mmhg, it becomes
196 × 7.50061683 = 1470.12 mmhg
Since the the pressure of the H2 is standard pressure, it means that the pressure is 760 mmhg
Also, pressure of the N2 is 584 mm Hg
Therefore,
1470.12 + 760 + 584 + F2 = 3837.02
2814.12 + F2 = 3837.02
F2 = 3837.02 - 2814.12
F2 = 1022.9 mm Hg
Which is the best solution that represents the equation x2=196
Answer:
-14, 14
Step-by-step explanation:
[tex] {x}^{2} = 196 \\ x = \pm \sqrt{196} \\ x = \pm \: 14 \\ x = 14 \: \: or \: \: x = - 14 \\ x = \{ - 14, \: \: 14 \}[/tex]
Answer:
[tex]x = 14[/tex]
x= -14
Step-by-step explanation:
[tex] {x}^{2} = 196 \\ x = \sqrt{196} \\ x = 14[/tex]
x= -14
To check whether the answer is correct,
[tex] {x}^{2} = 196 \\ [/tex]
[tex]x = 14[/tex]
[tex] {14}^{2} = 196 \\ 14 \times 14 = 196 \\ 196 = 196[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
