The equation for a horizontal plane through the point (0,−2,−3) is z= -3.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Let's assume n is the normal vector for the horizontal plane < 0, 0, 1 > .
The co-ordinate of the point is (0,−2,−3)
The general equation of a plane is -
[tex]n < x-x_0 , y - y_0, z-z_0 > =0\\\\ < 0,0,1 > \\\\0(x)+0(y+2) +1(z+3)\\\\z = -3[/tex]
Thus, The equation for a horizontal plane through the point (0,−2,−3) is z= -3.
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Write the product using exponents.
Answer:
[tex]\pi ^{3} *x^{4}[/tex]
Step-by-step explanation:
Simplifying using the exponent rule with the same base [tex]a^{n} *a^{m}[/tex]
[tex]=a^{n+m} :\pi ^{1+1+1} *\pi ^{1+1+1+1}[/tex]
Calculate the sum or difference: [tex]\pi^ {3} *x^{4}[/tex]
Answer: [tex]\pi^ {3} *x^{4}[/tex]
In a multiple-choice test, there are 10 questions. Each question has 4 choices, one of which is correct. Tom, who knows nothing about the subject, guesses each answer at random. Let X be the number of questions that Tom has actually guessed correctly. Find the mean and standard deviation of the X-distribution.
Answer:
B
Step-by-step explanation:
what is pi and why do we need it
Answer:
See below
Step-by-step explanation:
π, pronounced as pi is the ratio between 2πr which is circumference to 2r which is diameter.
In word, π is circumference/diameter which has exact value of 3.14159... and it is also an irrational number too.
π is often used to be defined as 3, 3.14 or 22/7 [Keep in mind, these numbers are only approximation.] in some fields. In trigonometry, π is mostly used to refer as π radians or π rad which is equivalent to 180°.
Why do we need it? Because it’s useful in a field that requires rotation. If you notice, figure with circular base will always have π with it, the volume is an example.
In calculus, you need π to do solid of revolution method which is:
[tex]\displaystyle \large{V =\pi \int\limits^a_b {[f(x)]^2} \ dx }\\\\\displaystyle \large{V = \pi \int\limits^a_b {[g(y)]^2} \ dy}[/tex]
In trigonometry, you need it for measurement/angle.
So anything that’s related to revolution, rotation or related to circle must require π at least.
In general life, you do not use it but this is mostly applied in engineering field and anything related to science that involves with circle or revolve.
Let me know if you have any questions!
The nth term of a sequence is represented by [tex]\frac{ 2n^3+25n^2+32n-15}{6n^4+2n^3-11n^2-2n+17}[/tex]
What is the limit of the nth term as x becomes increasingly large?
A. 0
B. 1/3
C. 3
D. Limit does not exist.
Answer:
A) 0
Explanation:
[tex]\sf \lim _{x\to \infty }\left(\dfrac{2n^3+25n^2+32n-15}{6n^4+2n^3-11n^2-2n+17}\right)[/tex]
1) Limit does not exist when the numerator is bigger.
2) Limit is zero when the denominator is bigger.
3) Limit is the ratio of coefficients when both powers are equal.
Here, the denominator have a power of 4, bigger than the numerator.
Hence, the limit of the nth term is 0.
Sheena wants to measure the volume of a ball that is 24 cm across. How should she set up her equation?
O v=-24²(12)
O v=12² (24)
O v=
O V=R24³
O v= 12³
Answer:
V = 4/3 π (12)³
Step-by-step explanation:
The volume of a sphere is:
V = 4/3 π r³
where r is the radius.
Here, the ball has a diameter of 24 cm. Radius is half the diameter, so r = 12.
V = 4/3 π (12)³
solve 11 ≤ w + 3.4 i dont know the answer please help me
Answer:
7.6 ≤w
Step-by-step explanation:
Hey there!
In order to solve this inequality, you need to simplify the inequality like the following:
Subtract 3.4 from both sides
7.6 ≤w
This means that w is greater than or equal to 7.6
The sum of two numbers is twenty-one the larger number is three more than twice the smaller number . What are the two numbers ?
Answer:
6 and 15
Step-by-step explanation:
n1 + n2 = 21
2(n1) + 3 = n2
n1 = 6
n2 = 15
6 + 15 = 21
What makes up the sides of polyhedra?
A. squares
B. rays
C. polygons
D. cubes
C. polygons!!
the polygons it is made of are called faces. the edges of the faces are called the edges of the polyhedron
NEED ASAP: Carlos builds a robot that moves on small wheels. Each wheel has six 5-inch-long metal spokes that meet in the center. What is the area of the sector between these spokes? Express your answer as a simplified fraction in terms of \piπ.
Answer:
27π/8 inches²
Step-by-step explanation:
= πr² × [3π/(4 × 2π)]
= π(3)² × 3π/8π
= 27π/8 inches²
The area of a circle is 9π in². What is the circumference, in inches? Express your answer in terms of \piπ
Answer:
[tex]6\pi[/tex] in
Step-by-step explanation:
The formula to find the area of a circle: [tex]\pi r^{2}[/tex], where [tex]r[/tex] is the radius.
The formula to find the circumference (perimeter) of a circle: [tex]2\pi r[/tex], where [tex]r[/tex] is the radius.
1) To find the circumference of the circle, we need to find the radius ([tex]r[/tex]) first. Since the area of the circle is given to us, we need to equate this to the formula to find the area of a circle.
[tex]9\pi =\pi r^2[/tex]
Cancel the [tex]\pi[/tex] by bringing it to the other side.
[tex]9 =\pi r^2[/tex] ÷ [tex]\pi[/tex]
[tex]9 = r^2\\\sqrt{9} = r\\3 = r[/tex]
2) Find the circumference of the circle by using the formula, [tex]2\pi r[/tex].
= [tex]2*\pi *3[/tex]
= [tex]6\pi[/tex] in
What is the measure of
Answer:
about 54
Step-by-step explanation:
due to the fact that it is just about a reflection but the thing is that it must be around 90, but it really depends on the angle you measure it at.
Apply the distributive property (m−3+4n)⋅(−8)
Answer:
-8m+24-32n
Step-by-step explanation:
-8 times m is -8m
-8 times -3 is 24
-8 times 4 is -32
put it together, you have -8m+24-32n
What is the 83rd term of the sequence 91, 87, 83, 79, ... ( = a1, a2, a3, a4, ...)?
Answer:
Common difference: tₙ = (95x - 4)
Question: How do we find the 83rd term?
Step-by-step explanation:
[tex]t_n = (95x-4)\\83 * 4 = 332\\95x - 332 = -237x\\-237x = -237\\-237[/tex]
Therefore, the answer is -237
helpppppppppppppppppppp
(a) Check the graph given below.
(b) 9 is located to the right of -6
(c) complete the statement: 9 > -6
The graph of the parent function y = x3rd power is horizontally stretched by a factor of 1/5 and reflected over the y-axis. What is the
equation of the transformed function?
('
O y=(5x)3
Oy=(-5x)3
Oy=(1/5x)3
Oy=(-1/5x)3
Step-by-step explanation:
The graph of y = √x is reflected in the y-axis, is horizontally stretched by a factor of 2, shifted 3 units up and 1 unit left. What is the equation of the transformed graph?
Original: y = √(x)
Reflected in the y-axis: y = √(-x)
Horizontally stretched by a factor of 2: y = √(-x/2)
Shifted 3 units up: y = 3 + √(-x/2)
And 1 unit left: y = 3 + √(-(x+1)/2)
The equation of the transformed function is y = (-5x)³.
What is Translation?A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of modifying a shape's size or position.
we have, Function
y = x³
Scale factor = 1/5
Now, stretch the function horizontally by factor 1/5 then
y = (5x)³
Now, reflection of graph about y axis result change x to -x.
y = (-5x)³
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Please help with this question. 100 points!! I know it is a little long but I could really use the help.
The owners of the resort want to expand and build a row of condos at the western base of the mountain. Because of the amount of snow, the area gets most winters, it is important to have the pitch (steepness) of the roof of each condo at least 60°. To make the condos appealing to skiers and boarders, they want to model the condos after their cabins, but on a larger scale. The cabins have an A-line roof that forms an isosceles triangle as shown, with the base angles at 65° . The base length is 6m. Note: the slant height is the length of the side of the roof. (Picture Below)
Required Formula
[tex]\sf cos(x) = \dfrac{adjacent}{hypotenuse}[/tex]
Part A
Given: base length: 6m, half base: 3m, angle: 65°, let hypotenuse: h
Hence solve,
[tex]\rightarrow \sf cos(x) = \dfrac{a}{h}[/tex]
[tex]\rightarrow \sf cos(65) = \dfrac{3}{h}[/tex]
[tex]\rightarrow \sf h = \dfrac{3}{cos(65)}[/tex]
[tex]\rightarrow \sf h =7.0986\ \approx \ 7.1 \ m[/tex]
The slant height is 7.1 meters when base length is 6 meter.
Part B
Given: base length: 9.6m, half base: 4.8m, angle: 65°, let hypotenuse: n
Hence solve,
[tex]\rightarrow \sf cos (x) = \dfrac{a}{n}[/tex]
[tex]\rightarrow \sf cos (65) = \dfrac{4.8}{n}[/tex]
[tex]\rightarrow \sf n = \dfrac{4.8}{cos (65)}[/tex]
[tex]\rightarrow \sf n = 11.357 \ \approx \ 11.4 \ m[/tex]
The slant height is 11.4 meters when base length is 9.6 meter.
Answer:
A) 7.1 m
B) 11.4 m
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)Part AThe slant height of the roof is the hypotenuse of a right triangle.
Considering the information given, use the cos trig ratio to determine the slant height.
A roof's base length is the distance from one corner of the roof to the other. Therefore, the base length of the given right triangle is half the roof base length.
Given:
[tex]\theta[/tex] = 65°A = Half of roof base length = 6 ÷ 2 = 3 mH = Slant heightSubstituting the given values into the formula and solving for H:
[tex]\sf \implies\cos(\theta)=\dfrac{A}{H}[/tex]
[tex]\sf \implies\cos(65^{\circ})=\dfrac{3}{H}[/tex]
[tex]\sf \implies H =\dfrac{3}{\cos(65^{\circ})}[/tex]
[tex]\implies \sf H=7.1 \: m \: (nearest\:tenth)[/tex]
Part BThe slant height of the roof is the hypotenuse of a right triangle.
Considering the information given, use the cos trig ratio to determine the slant height.
A roof's base length is the distance from one corner of the roof to the other. Therefore, the base length of the given right triangle is half the roof base length.
Given:
[tex]\theta[/tex] = 65°A = Half of roof base length = 9.6 ÷ 2 = 4.8 mH = Slant heightSubstituting the given values into the formula and solving for H:
[tex]\sf \implies\cos(\theta)=\dfrac{A}{H}[/tex]
[tex]\sf \implies\cos(65^{\circ})=\dfrac{4.8}{H}[/tex]
[tex]\sf \implies H =\dfrac{4.8}{\cos(65^{\circ})}[/tex]
[tex]\implies \sf H=11.4 \: m \: (nearest\:tenth)[/tex]
Can someone help me with this question please
Answer:
∠A≅∠Y AB≅YZ
∠B≅∠Z AC≅YX
∠C≅∠X BC≅ZX
ΔABC≅ΔYZX
Step-by-step explanation:
congruent is identical in form so if the angle has one dash than look for the identical version on the other triangle
2/7 x 4/9 - 1/4 + 2/7 x 1/3 evaluate using appropriate property
The solution of the given expression will be equal to ( -1 / 36 ).
What is an expression?
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
The solution of the given expression will be:-
[tex]=[\dfrac{2}{7}\times \dfrac{4}{9}]-\dfrac{1}{4}+[\dfrac{2}{7}\times \dfrac{1}{3}][/tex]
[tex]= \dfrac{8}{63}-\dfrac{1}{4}+\dfrac{2}{21}[/tex]
[tex]=\dfrac{32-63+24}{252}[/tex]
[tex]=\dfrac{-1}{36}[/tex]
Therefore the solution of the given expression will be equal to ( -1 / 36 ).
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Which of the points shown below are on the line given by the equation y = 2x? Check all that apply.
Answer:
B
Step-by-step explanation:
g5 ⦁ g2 is equal to g25
- - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - -- - - - - - - - - - - - -- - - - - - - - -
[tex]\blue\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]
Is g⁵•g² equal to g²⁵?
[tex]\blue{\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}[/tex]
No, the expression is not equal to g²⁵.
Reason:-
If we multiply two numbers with the same base, we add their exponents.
So we add 5+2:
g⁽⁵⁺²⁾=g⁷
Good luck.- - - - - - -- - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - -- - - - - - - - - -
Is the following statement true or false?
The intersection of three planes can be a ray.
The statement which says "The intersection of three planes can be a ray." is; True
How to define planes in math's?In terms of line segments, the intersection of a plane and a ray can be a line segment.
Now, for the given question which states that the intersection of three planes can be a ray. This statement is true because it meets the definition of plane intersection.
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Answer:
False
Step-by-step explanation:
Saw a one star rating on the other answer, so I put false as my answer and got it correct.
27.
In a certain statistics class. he
average grade is 83% with a standard deviation of 4.2%. What
the z-score corresponding to
grade of 81.8%?
-5.04
B.O-1.2
c.O-0.29
D.® 1.2
The corresponding z score for a grade of 81.8% for a class with average grade of 83% and standard deviation of 4.2% is -0.29.
What is a z score?The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = (raw score - mean) / standard deviation
Given that mean is 83%, standard deviation = 4.2%, for x = 81.8:
z = (81.8 - 83)/4.2 = -0.29
The corresponding z score for a grade of 81.8% for a class with average grade of 83% and standard deviation of 4.2% is -0.29.
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A pyramid has a height of 17 meters and a base area of 6 square meters. what is the volume of the pyramid.
Answer:
34 m²
Step-by-step explanation:
Given,
Height ( h ) = 17 m
Base Area ( A ) = 6 m²
To find : Volume of Pyramid
Formula : -
Volume of Pyramid = Ah / 3
Volume of Pyramid
= 17 x 6 / 3
= 17 x 2
= 34 m²
Hence,
The Volume of pyramid is 34 m².
Doug is planning to build a model of a sailboat using a scale where 2 inches represents 25 feet. If the sailboat has a sail-height of 210 feet, what is the length in inches that Doug should build sail-height of the model of the airplane.
Answer: 16.8
Step-by-step explanation:
2:25 = X:210
210/25 = 8.4
Multiply 8.4 by 2
Use the Pythagorean Identity and Tangent Identity to find tan theta if sin theta= -1 and 0 ≤ theta <2Pi radians.
By using the Pythagorean identity the value of tan [tex]\theta[/tex] will be ∞.
tan [tex]\theta[/tex] = ∞.
What is Pythagorean identity?
Pythagorean identities are identities in trigonometry that are extensions of the Pythagorean theorem. The fundamental identity states that for any angle [tex]\theta[/tex],
[tex]sin \; ^{2} \theta + cos \; ^{2} \theta =1[/tex]
By Pythagorean Identity we have,
[tex]sin \; ^{2} \theta + cos \; ^{2} \theta =1[/tex]we have, [tex]sin \theta \; = \; -1[/tex]
So, [tex](-1)^{2} \; + \; cos^{2}\; \theta =\; 1[/tex]
[tex]\; cos^{2}\; \theta =\; 1 - \; 1[/tex]
[tex]cos^{2}\; \theta =0[/tex]
[tex]cos\; \theta =0[/tex]
Now, we know that
[tex]tan \; \theta= \frac{sin\; \theta}{cos\; \theta}[/tex]
= [tex]\frac{-1}{0}[/tex]
[tex]tan \; \theta=[/tex] ∞....................... (1)
Again, tan [tex]90^{0}[/tex] = ∞
If we compare from equation (1), we have
[tex]\theta = 90^{0}[/tex]
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To rent a certain meeting room, a college charges a reservation fee of $49 and an additional fee of $5.40 per hour. The chemistry club wants to spend less than $86.80 on renting the meeting room.
Answer:
The maximum amount of money the chemistry club can spend without going over their buget is $81.4 ... With a total of 6 hours their allowed to use the room for.
Step-by-step explanation:
$49 is our constant and will not change. 5.40 however will. Let's use variable h for the amount hours they can rent the room for. Now we can make an inequality;
49+ 5.40h < 86.80
5.40h < 86.80
5.4h< 37.8
h< 7
Now that we know h will have to be less than seven for the chemistry club to spend less than their buget we can find that 6 is the maxium amount of hours they can spend in the room while staying within their budget.
(This answer does not consider decimals or half hours)
Write and solve an addition or subtraction equation to find the missing angle measure
Answer:
90°
Step-by-step explanation:
The three angles : 45°, n°, and 45° will form a line.
A property of a line is that it creates a 180° angle.
⇒ 45 + n + 45 = 180⇒ n + 90 = 180⇒ n = 90°need help with all of these questions you see on the top. there the red squares. please someone smart ( dose not show rn ). this is one of the problems I need to finish this tonight.
Answer:
402.1 in^3
Step-by-step explanation:
To find the area of a cylinder, you multiply the base by the height. Given a base area of [tex]32\pi[/tex] in^2 and a height of 4 in results in the following equation:
V = 32π x 4
This comes out to be 402.123859659 which is 402.1 when rounded to the nearest tenth.
Y is between points J and A. JA=17 and YA=3.
What is JY?
Enter your answer in the box.
JY =
Answer: the answer is 14
Step-by-step explanation: i hope this helps :)
The value of JY is 14
How to calculate the value of JY?According to the problem,
Y is between points J and A.
JA=17 and YA=3∴ JY = ( JA - YA) = (17 - 3) = 14
∴ JY = 14
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Hello! Please answer these questions, it's for a maths assignment, thank you.
1. What is your average daily screen time?
2. How much sleep do you get on a daily basis?
Answer:
bro I'm so confused is this a trick ?
