For this problem, we need to use our integral knowledge to set up the problem:
The bounds will be from 2 to 6, cutting tiny horizontal bars into the graph, to approximate the area
Now for the function inside the integral:
⇒ it is the top function minus the bottom function
top function: y= x²bottom function: x-axis ⇒ y =0⇒ function within integral = x² - 0
Let's put it all together and solve:
[tex]Area=\int\limits^6_2 {x^2-0} \, dx =\int\limits^6_2 {x^2} \, dx=\frac{6^3}{3} -\frac{2^3}{3} \\Area=\frac{6^3-2^3}{3} =\frac{216-8}{3} =\frac{208}{3}[/tex]
Answer: 208/3 ≈ 69.333
Hope that helps!
Find the area of the circle formed when a plane passes 7 cm from the center of a sphere with radius 8 cm. give your answer in terms of pi.
The area of the circle formed when the plane passes through the center of the given sphere is: 15π cm².
What is the Area of a Circle?Area of a circle = πr² (radius of the circle = r).
Given the following:
Radius of sphere = 8 cmDistance of the plane from the center of the sphere = 7 cmRadius of the circle = √((radius of sphere)² - (distance of the plane from the center of sphere²)) = √(8² - 7²)
Radius of the circle = 3.87 cm
Area of the circle = π(3.87²) ≈ 15π cm².
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David Saw three ducks in a pond then he saw two more ducks on the path how many decks did David see all together
Answer:
5
Step-by-step explanation:
A rectangle has a length 10 more than its width. If the width is increased by 8
and the length by 4, the resulting rectangle has an area of 135 square units.
Part A
Write an equation to model the above scenario. Use the model to find the length
of the original rectangle?
powered by
esmos
Part B
What is the perimeter of the expanded rectangle?
Step-by-step explanation:
length = the original length
width = the original width
length = width + 10 or
width = length - 10
(length + 4) × (width + 8) = 135
A
now we are using the first equation in the second to solve then for length :
(length + 4) × (length - 10 + 8) = 135
(length + 4) × (length - 2) = 135
length² - 2×length + 4×length - 8 = 135
length² + 2×length = 143 or
length² + 2×length - 143 = 0
this is the equation to model the scenario.
solving in general such a quadratic equation :
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = length
a = 1
b = 2
c = -143
length = (-2 ± sqrt(2² - 4×1×-143))/(2×1) =
= (-2 ± sqrt(4 + 572))/2 =
= (-2 ± sqrt(576))/2 =
= (-2 ± 24)/2 = (-1 ± 12)
length1 = -1 + 12 = 11
length2 = -1 - 12 = -13
a negative solution for a length is not applicable, so,
length = 11
width = length - 10 = 11 - 10 = 1
B
the expanded length = 11 + 4 = 15
the expanded width = 1 + 8 = 9
the expanded perimeter is then
2×15 + 2×9 = 30 + 18 = 48
Solve the inequality: 10+5≥25
A:≥2
B: ≥30
C: ≥3
D: ≥20
Answer:
no c is write
Step-by-step explanation:
10+5≥ 25
10-10+5≥ 25-10
0+5≥ 15
≥3 ans…
Answer: The correct answer choice A: ≥2
Step-by-step explanation:
10+5>25 is false
Let's solve your inequality step-by-step.
10x+5 ≥ 25
Subtract:
[tex]10x+5-5[/tex] ≥ [tex]25-5[/tex]
[tex]10x[/tex] ≥ [tex]20[/tex]
Divide:
[tex]\frac{10x}{10}[/tex] ≥ [tex]\frac{20}{10}[/tex]
[tex]x[/tex]≥[tex]2[/tex]
10+5≥25 is False: The left side 15 is less than the right side 25, which means that the given statement is false.
you may mean 10x+5≥25, if so your answer is A.
When graphing f(x)=a sin(bx) you would determine the functions period using which of the following?
A. The period is 2pi/b
B. The period is a
C. The period is pi/b
Explanation:
The value of 'a' out front in y = a sin(bx) determines the amplitude.
The b term helps us compute the period, which is 2pi/b for sine, cosine, secant, and cosecant functions.
For example, y = 2sin(3x) has an amplitude of 2 and period of 2pi/3
For tangent and cotangent functions, the period would be pi/b.
3. a local sports store charges $22.33 for a football and 6% tax. how much
will the total price be to purchase the football? *
Given the charges for a football and the tax rate, the total price to purchase a football is $23.6698.
How much will the total price be to purchase the football?
Given that;
Charges for a football = $22.33Tax rate = 6%Total price to purchase football = ?First, we calculate the tax price on the football.
Tax price = Tax rate × Charges for the football
Tax price = 6% × $22.33
Pax price = 0.06 × $22.33
Tax price = $1.3398
Now, total price to purchase football will be;
Total price = Charges for a football + Tax price
Total price = $22.33 + $1.3398
Total price = $23.6698
Given the charges for a football and the tax rate, the total price to purchase a football is $23.6698.
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for the function f(x) = x^2, what effect will be multiplying f(x) by 1/2 have on the graph?
If y varies inversely with x and y=2 when x=5, what is the value of x when y=3?
Answer:
Step-by-step explanation:
Method
Inversely in this sentence means
y = k/x
So you first step is to find the value of k. You do that by setting up an inverse relationship with y = 2 , x = 5
2 = k/5 Multiply both sides by 5
2*5 = 5*k/5
10 = k
Now you are able to answer the question.
k = 10y = 3x = ?y = 10/x
3= 10/x Multiply both sides by x
3*x = x * 10/x
3x = 10 Divide both sides by 3
3x/3 = 10/3
x = 3.33 or x = 3 1/3
Answer
x = 3.33 or x = 3 1/3
Julia has 15 nails she uses 8 to build a birdhouse she substract to find the number of nails left.wich addition sentence can use to check her work
Answer:
8+7=15
Step-by-step explanation:
15-8=7
so if she adds 8 to 7 and she gets 15 she did it right.
Answer: Julia can use 7 + 8 = 15 to check her work.
Step-by-step explanation: As fifteen minus eight equals seven, Julia can check her work by performing the inverse operation of seven plus eight to check her work. This is true as when c - b = a, a + b = c.
What is the length of line segment AB in the triangle shown below?
Answer:
the lenght of the segment ab is 15 inches
Please help asap!! drag each tile to the correct box.
arrange the steps in the correct order to solve this trigonometric equation.
cos^2x = 3sin^2x
cos²(x) = 3 sin²(x)
1 - sin²(x) = 3 sin²(x)
1 = 4 sin²(x)
1/4 = sin²(x)
± √(1/4) = sin(x)
± 1/2 = sin(x)
sin(x) = 1/2 or sin(x) = -1/2
[x = arcsin(1/2) + 2nπ or x = π - arcsin(1/2) + 2nπ]
… … … or [x = arcsin(-1/2) + 2nπ or x = π - arcsin(-1/2) + 2nπ]
(where n is any integer)
[x = π/6 + 2nπ or x = 5π/6 + 2nπ]
… … … or [x = -π/6 + 2nπ or x = 7π/6 + 2nπ]
Which ratio is equivalent to Sun U?
(IMAGE ABOVE)
SOMEONE PLEASE HELP ME ILL GIVE YOU BRAINLIST ANSWER!!!!!
Answer:
(a) SV/VW
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationship between trig functions and sides in a right triangle. This problem also makes use of the properties of similar triangles:
corresponding sides are proportionalcorresponding angles are congruent__
sine ratioThe sine of angle U is given by ...
Sin = Opposite/Hypotenuse
The side opposite angle U in ΔTUS is ST. The hypotenuse of that right triangle is side TU. This means the desired ratio is ...
sin(U) = Opposite/Hypotenuse = ST/TU
corresponding ratioIn similar ΔVWS, angle W has the same measure as angle U. Its sine will be the ratio of the corresponding sides. The similarity statement ΔTUS~ΔVWS tells you that the side corresponding to ST is SV, and the side corresponding to TU is VW.
sin(U) = sin(W) = SV/VW
What is the value of v? With working out please
Answer:
v = 130
Step-by-step explanation:
substitute the given values for u, a and t into the equation
v = 32 + ( 9.8 × 10) = 32 + 98 = 130
Select the correct answer.
What is the general form of the equation for the given circle centered at O(0, 0)?
A.
x2 + y2 + 41 = 0
B.
x2 + y2 − 41 = 0
C.
x2 + y2 + x + y − 41 = 0
D.
x2 + y2 + x − y − 41 = 0
The general form of the equation for the given circle centered at O(0, 0) is x² +y² - 41=0.
The correct option is (B).
What is equation of circle?The general equation for a circle is ( x - h )² + ( y - k )² = r², where ( h, k ) is the center and r is the radius.
as, general equation for a circle is ( x - h )² + ( y - k )² = r²
Here, centered at O(0, 0).
So,
a =0 and b = 0
now, r² = (BO)²
r² = (4-0)² +(5-0)²
r² = 16+25
r² = 41
Hence, Center at the origin passing through B(4, 5) is x² +y² = 41.
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The value of the surface area of the rectangular prism is equal to the value of the volume of the rectangular prism. Write and solve an equation to find the value of x.
Answer:
Equation: 24x + 2(36) = 6(6x) or 24x + 72 = 36x Answer: x = 6
Step-by-step explanation:
24x + 72 = 36x
-24x -24x
72 = 12x
/12 /12
6 = x
URGENT
Christian installed an electric pump to pump water from a borehole into a 30 000 litre cement dam. If the water is pumped at a rate of 75 litres per minute. How long does it take to fill the dam? A 4 h
B. 6 h 40 min
C 6 h 20 min
D 3 h 40 min
Jennifer needs to use a ladder to clean a second floor window on a building. If the window is 13 ft above the ground and the base of the ladder is 4 ft from the building, which equation below can be
used to determine the length (x) of the ladder needed to reach the window? Draw a picture
By using the Pythagoras theorem, the length of the ladder will be 13.6 feet.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
Jennifer needs to use a ladder to clean a second-floor window on a building.
If the window is 13 ft above the ground and the base of the ladder is 4 ft from the building.
Then the length of the ladder will be
H² = 13² + 4²
H² = 169 + 16
H² = 185
H = 13.6 ft
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Answer: 4^2+13^2=x^2
Step-by-step explanation:
trust
help please I really need help and thank you :))))
Answer:
14) x = 30°
15) x = 50°
Step-by-step explanation:
14) 60 + x = 90
x = 90 - 60
x = 30°
15) 130 + x = 180
x = 180 - 130
x = 50°
Hope this helps
Step-by-step explanation:
Is first image we are given a right angle and we know that right angle = 90°
So,
60 + x = 90
x = 90 - 60 = 30°
x = 30°
In the second image we are given a straight line and we know that on the 180° angle is a straight line.
so,
130 + x = 180
x = 180 - 130
x = 50°
Could you help me find X,
when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one. Check the picture below.
[tex]\cfrac{4}{x}~~ = ~~\cfrac{x}{9}\implies 36=x^2\implies \sqrt{36}=x\implies 6=x[/tex]
Please help mee I'm gonna have a mental break downnn
Answer:
y[tex]\leq[/tex]-2/5x + 2
Step-by-step explanation:
-2/5x + 2 would be the slope and y intercept of the line
The line is solid, so it has to be either less than or equal to or greater than or equal to
It is shaded below the line, which means it has to be less than. you can tell this by looking at the closed end of the inequality sign. If it points left, you shade below, if it points right, you shade above.
[tex]\sqrt{8+2\sqrt{15}[/tex] Simplify this equation! Please help ASAP
[tex] \sqrt{8 \: + \: 2 \sqrt{15} } [/tex]
Factor the indicated expression:[tex] \sqrt{( \sqrt{3 } \: + \: \sqrt{5} ) ^{2} } [/tex]
Simplified the index, the root and also the exponent using the number 2.[tex] \boxed{ \bold{\sqrt{3} \: + \: \sqrt{5} }}[/tex]
MissSpanishThe height of lava fountains spewed from volcanoes cannot be measured directly. Instead, their height in meters can be found using the equation y=1/2 gt^2
where y represents the height, g is 9.8, and t represents the falling time of the lava rocks. Find the height in meters of a lava rock that falls for 5 seconds.
The height in meters of a lava rock that falls for 5 seconds is; 122.5 m.
How to calculate height from quadratic equations?
We are told that the height is modelled by the equation;
y = ¹/₂gt²
where;
y represents the height.
g is 9.8 m/s²
t represents the falling time of the lava rocks.
Thus, at t = 5, we have;
y(5) = ¹/₂(9.8)(5)²
y(5) = 122.5 m
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12. The mean number of boxes of cookies sold by
each girl scout in Emma's troop was 28 with a
standard deviation of 8. If Emma's z-score
was -1.5, how many boxes of cookies did she
sell?
Answer:
Answer:
16
Step-by-step explanation:
i hope this help you
simplify 9+ (-2)^3 HELP PLEASE
Answer:
1
Step-by-step explanation:
Raise -2 to the power of 3 = -8
9-8= 1
Answer:
1
Step-by-step explanation:
A number raised to the 3rd power is equal to that number multiplied by itself twice. Below I have expanded the expression to visualize this process. If this makes it more confusing, the main way is just to go from line 1 to line 4.
9 + (-2)³ <---- Original expression
9 + (-2 x -2 x -2) <---- (-2)³ expanded
9 + (4 x -2) <---- -2 times -2
9 + (-8) <---- 4 x -2
1 <---- 9 - 8
Daniel was offered a job after college earning a salary of $60,000. He will get a raise
of $4,000 after each year working for the company. Answer the questions below.
regarding the relationship between salary and the number of years working at the
company.
The independent variable, x, represents the
and the
dependent variable is the
because the
depends on the
A function relating these variables is M(x) =
So M (5) =
meaning 5
The independent variable represents the number of years that Daniel has worked.
The dependent variable is the total salary of Daniel. This is because it depends on the number of years worked.
M(5) is $80,000.
What is independent and dependent variable?
The independent variable is that is given. The dependent variable is the variable that is being determined. It is usually affected by the independent variable.
M(5) = $60,000 + (4000 X 5) = $80,000
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The measure of the base angle of an isosceles triangle is 52.
What is the measure of the vertex angle?
Answer:
76°
Step-by-step explanation:
The 2 base angles are equal so
52+52+vertex angle=180° (Angle Sum Property)
104+ vertex angle=180°
vertex angle= 180-104
vertex angle=76°
Lawyer Fees:
A lawyer charges a base (one time) fee of
$200 and $75 each hour for consulting with
her. What would be the equation to model the situation?
Abby has 159 bonus coupons. She wants to staple them in groups of 30. How many complete groups of 30 can Abby make?
5 complete groups
6 complete groups
14 complete groups
59 complete groups
Abby can make 5 complete groups with 9 extra bonus coupons.
What is Division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Here, Abby has total number of coupons = 159
Number of coupons in a group = 30
Total number of groups = Total Coupons / coupons in a group
= 159 / 30
= 5.3
Thus, Abby can make 5 complete groups with 9 extra bonus coupons.
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Two angles are supplementary.
measures (4x + 9)° and the other angle measures
(x + 1)°. What is the measure of the smaller
angle?
Answer:
35°
Step-by-step explanation:
If 2 angles are supplementary, that means they add up to 180 :
Now we make an equation and solve for x :
(4x+9) + (x+1) = 180
5x+10 = 180
5x = 170
x = 34
Now we find the measure of the smaller angle using our value of x :
x+1 = 34 +1
x+1 = 35
Hope this helped and have a good day
Can y’all help with this?
Answer:
Quadrilateral: shape with 4 sides
Perpendicular means at right angles. Therefore, draw two sides at a right angles to each other. Mark this with a right angle symbol.
Draw 2 sides that are parallel. Mark these with arrows.
Please see attached diagrams.