Answer:
229.18 degrees
Step-by-step explanation:
The circumference of a circle with radius r is 2×pi×r.
So if it has a radius of 1 mile, then the circumference is 2×pi×1=2pi miles.
So if we travel 4 miles, then the percentage of this circle we traveled is 4/(2pi)=63.66% approximately.
There are 360 degrees in a circle and we want to how much of that rotation belongs to traveling 4 miles of the circumference of a circle that measures 2pi miles. So 63.66%×360 degrees =229.18 degrees.
Which value is equivalent to
(7•5•2)^2 X ( 5^0 ) X 2-^9?
( 7•3 ) ( 2-^3)
Answer:
[tex]\frac{25}{144}[/tex]
Step-by-step explanation:
[tex](\frac{7 * 5 * 2}{7 * 3} )^2 * (\frac{5^0}{2^-3})^3 * 2^{-9}[/tex]
Simplified becomes;
[tex](\frac{10}{3})^2 * 2^3 * \frac{1}{2^9}[/tex]
Simplifying further gives; [tex]\frac{25}{144}[/tex]
the sides of this right triangle are 18 inches and 24 inches in length.
how long would the hypotenuse of this triangle be?
Answer:
30
Step-by-step explanation:
[tex]c^{2} = b^{2} + a^{2} \\[/tex] = formula
a = 24
b = 18
576+324 = 900
do [tex]\sqrt{900} \\[/tex]
= 30
Solve for x in the equation 2/5x = 12
A: -30
B: -4 4/5
C: 4 4/5
D: 30
Find the reciprocal of 4/5
Answer:
its 5/4! haha i used to be good at this when i was in 6th grade:)
A chef mix his salt and pepper. If he put 2/3 cup of salt and 1/2 cup of pepper in his shaker, what is the ratio of salt to pepper ?
Answer:
salt: pepper
4 : 3
Step-by-step explanation:
salt: pepper
2/3 : 1/2
Multiply each by 6
2/3 *6 : 1/2 *6
4 : 3
Identify the glide reflection rule in the given figure.
Question 8 options:
Translation: (x,y) → (x – 5,y); Reflection across y-axis
Translation: (x,y) → (x,y – 5); Reflection across y-axis
Translation: (x,y) → (x,y + 5); Reflection across y-axis
Translation: (x,y) → (x,y + 5); Reflection across x-axis
Answer:
B
Step-by-step explanation:
The shape clearly is reflected across y axis and the x coordinates remain the same. We can see a change in the y coordinates and the shape has shifted 5 units down. Hence (x, y) -> (x, y-5) and then reflection across y axis is the answer
Answer:
B
Step-by-step explanation:
Yet another calculus question :)
Given [tex]y = x^3 - 2x[/tex] for [tex]x \geq 0[/tex], find the equation of the tangent line to y where the absolute value of the slope is minimized.
I have tried taking both the first and second derivatives and setting them equal to 0 and using that as the answer, but they're incorrect. Could somebody please explain how to complete the question correctly? Thank you so much!
Answer: y = (-4/3)*sqrt(2/3)
This is the same as writing [tex]y = -\frac{4}{3}\sqrt{\frac{2}{3}}[/tex]
============================================================
Explanation:
The phrasing "where the absolute value of the slope is minimized" is an interesting way of saying "the tangent slope is 0". This is because absolute values are never negative, so the smallest it can get is 0.
Your teacher has given you
y = x^3 - 2x
which differentiates into
dy/dx = 3x^2 - 2
after using the power rule
The derivative function lets us determine the slope of the tangent. The slope is the dy/dx value. Since we want a slope of 0, we'll set 3x^2-2 equal to zero and solve for x. So you have the correct idea, but you won't involve the second derivative.
dy/dx = 0
3x^2 - 2 = 0
3x^2 = 2
x^2 = 2/3
x = sqrt(2/3)
Notice how I'm ignoring the negative version of this root. This is due to the fact that [tex]x \ge 0[/tex]
-------------------------
Now plug this x value back into the original equation to find its corresponding y coordinate.
y = x^3 - 2x
y = x(x^2 - 2)
y = sqrt(2/3)*( 2/3 - 2 )
y = sqrt(2/3)*( -4/3 )
y = (-4/3)*sqrt(2/3)
Note that x = sqrt(2/3) leads to x^2 = 2/3 after squaring both sides.
-------------------------
Therefore, the equation of this tangent line is y = (-4/3)*sqrt(2/3)
All horizontal lines are of the form y = k, for some constant k. This constant value is basically what number you want the horizontal line to go through on the y axis. That number would be (-4/3)*sqrt(2/3).
find the last common denominator for these two rational expressions
Answer:
Least common denominator = (x - 1)²(x - 2)
Step-by-step explanation:
Least common denominator of two rational expressions = LCM of the denominator of the expressions.
[tex]\frac{x^3}{x^2-2x+1}[/tex] and [tex]\frac{-3}{x^{2}-3x+2}[/tex]
Factorize the denominators of these rational expressions,
Since, [tex]x^{2}-2x+1[/tex] = x² - 2x + 1
= (x - 1)²
And x² - 3x + 2 = x² - 2x - x + 2
= x(x - 2) -1(x - 2)
= (x - 1)(x - 2)
Now LCM of the denominators = (x - 1)²(x - 2)
Therefore, Least common denominator will be (x - 1)²(x - 2).
What the answer question
Answer:
P = 44Step-by-step explanation:
JK = JO = 4
MN = NO = 6 ⇒ LM = 18 - 6 = 12
KL = LM = 12
NJ = NO + OJ = 6 + 4 = 10
JL = JK + KL = 4 + 12 = 16
LN = 18
P = NJ + JL + LN = 10 + 16 + 18 = 44
Topic: Simultaneous equations Class 9 ICSE
Denote the number by 10a + b, where both a and b are integers picked from {1, 2, 3, …, 9}.
"the difference of whose digits is 3" ==> |a - b| = 3
"4 times the number is equal to 7 times the number obtained by reversing the digits" ==> 4 (10a + b) = 7 (10b + a)
Simplifying the second equation, you get
40a + 4b = 70b + 7a
33a - 66b = 0
a - 2b = 0
Assume a > b, in which case we would have |a - b| = a - b, so
a - b = 3
Eliminate a to solve for b, then for a :
(a - b) - (a - 2b) = 3 - 0
b = 3 ==> a = 6
Then the original number is 63.
If instead we had assumed a < b, we would have had |a - b| = b - a = 3. Then
2 (b - a) + (a - 2b) = 2×3 + 0
-a = 6
But neither a nor b can be negative, so this case is moot.
[tex]15 \times 94 - 89 \div 5[/tex]
Can I name my Angle VTS as STV? And use it interchangeably in proving?
Answer:
both angles are the same, so you can use it interchangeably in proving.
But i suggest you to mantain only one, because it's easier to understand and it looks better.
The graph below shows Roy's distance from his office (y), in miles, after a certain amount of time (x), in minutes: Graph titled Roys Distance Vs Time shows 0 to 10 on x and y axes at increments of 1.The label on x axis is time in minutes and that on y axis is Distance from Office in miles. Lines are joined at the ordered pairs 0, 0 and 1, 1 and 2, 2 and 3, 3 and 4, 4 and 5, 4 and 6, 4 and 7, 4.5 and 7.5, 5 and 8, 6. Four students described Roy's motion, as shown in the table below: Student Description Peter He drives a car at a constant speed for 4 minutes, then stops at a crossing for 6 minutes, and finally drives at a variable speed for the next 2 minutes. Shane He drives a car at a constant speed for 4 minutes, then stops at a crossing for 2 minutes, and finally drives at a variable speed for the next 8 minutes. Jamie He drives a car at a constant speed for 4 minutes, then stops at a crossing for 6 minutes, and finally drives at a variable speed for the next 8 minutes. Felix He drives a car at a constant speed for 4 minutes, then stops at a crossing for 2 minutes, and finally drives at a variable speed for the next 2 minutes. Which student most accurately described Roy's motion? Peter Shane Jamie Felix
Answer:
Felix
Step-by-step explanation:
The graph contains 3 segments,
first one is for the first 4minutes,
second one is for the next 2 minutes (standing still)
third one is for the last 2 minutes.
Only Felix has it right, the other students use absolute time in their statements, in stead of the difference between start and end. (e.g., from 4 to 6 is 2 minutes).
The student that most accurately described Roy's motion is Felix.
How to find the function which was used to make graph?There are many tools we can use to find the information of the relation which was used to form the graph.
A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
We need to find the student that most accurately described Roy's motion.
Here we can see that the graph contains 3 segments, first one is for the first 4 minutes, Second one is for the next 2 minutes (standing still) and the third one is for the last 2 minutes.
Now, Only Felix has it right, the other students use absolute time in their statements, in stead of the difference between start and end.
Therefore, the student that most accurately described Roy's motion is Felix.
Learn more about finding the graphed function here:
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10.
Define an operation ★ on the set of real numbers as follows:
a ★ b = 0.5ab
If 0.1 ★ b = 10, then evaluate bb.
a. 500
b. 200
c. 20
d. 50
Please explain how you got your answer.
If a ★ b = 0.5ab, then
0.1 ★ b = 0.5 (0.1) b = 0.05b = 10
==> b = 10/0.05 = 200
©
Christine went shopping and bought each of her ten nephews a gift, either a video costing $14.95 or a CD costing $16.88. She spent $164.94 on the
gifts. How many videos and how many CDs did she buy
Answer:
She bought 2 videos and 8 CDs.
How do you simplify 3 times the square root 13?
Answer:
3√13
Step-by-step explanation:
3√13
This expression cannot be simplified because you cannot take any common factor outside the root.
What is the sign of y = £?
y
Choose 1 answer:
A
Positive
B
Negative
Zero
Answer:
I'm pretty sure is
Positive b
If(a-b) =4 and ab=2,find the value of a^2+b^2
Answer:
a² + b² = 20
Step-by-step explanation:
Given
(a - b) = 4 ← square both sides
(a - b)² = 4²
a² - 2ab + b² = 16 ← substitute ab = 2
a² - 2(2) + b² = 16
a² - 4 + b² = 16 ( add 4 to both sides )
a² + b² = 20
The area of a trapezium is 31.5 cm². If the parallel sides are of length 7.5 cm and 5.3 cm, calculate the perpendicular distance between them
Answer:
The answer is 4.9cmStep-by-step explanation:
To find the perpendicular distance between them that's the height we use the formula
[tex]Area \: \: of \: \: a \: \: trapezium = \frac{1}{2} (a + b) \times h[/tex]
where
a and b are the parallel sides of the trapezium
h is the perpendicular distance
From the question
Area = 31.5cm²
a = 7.5 cm
b = 5.3 cm
Substituting the values into the above formula we have
[tex]31 .5 = \frac{1}{2} (7.5 + 5.3) \times h[/tex]
[tex]31.5 = \frac{1}{2} \times 12.8h[/tex]
[tex]31.5 = 6.4h[/tex]
Divide both sides by 6.4
[tex]h = \frac{31.5}{6.4} [/tex]
h = 4.921875
We have the final answer
h = 4.9cmHope this helps you
What is the slope of the line containing (-2, 5) and (4,-4)?
O A. 3/2
O B. -2
O C -3/2
O D. 2
Answer:
Option C is correct.
Step-by-step explanation:
[tex]slope \: = \: \frac{y2 - y1}{x2 - x1} [/tex][tex] = \frac{ - 4 - (5)}{4 - (2)} [/tex][tex] = \frac{ - 9}{4 + 2} [/tex][tex] = \frac{ - 9}{6} [/tex][tex] = \frac{3( - 3)}{3 - 2} [/tex][tex] = - \frac{3}{2} [/tex]Hope it is helpful....True or false? If false give counterexample The product of a rational number and an integer is not an integer
Answer:
False
Step-by-step explanation:
Required
State if the product of rational numbers and integer is an integer
The statement is false and the proof is as follows
Literally, rational numbers are decimal numbers that can be represented as a fraction of two integers;
Take for instance: 0.2, 0.5, 2.25, etc.
When any of these numbers is multiplied by an integer, the resulting number can take any of two forms;
1. It can result to an integer:
For instance;
[tex]0.2 * 5 = 1[/tex]
[tex]0.5 * 4 = 2[/tex]
[tex]2.25 * 8 = 18[/tex]
2. It can result in a decimal number
For instance;
[tex]0.2 * 3 = 0.6[/tex]
[tex]0.5 * 5 = 2.5[/tex]
[tex]2.25 * 7 = 15.75[/tex]
From (1) above, we understand that the product can result in an integer.
Hence, the statement is false
A theme park ride carriage with a mass off 1000kg when empty needs to be accelerated at 0.5m/s2 along a horizontal track. What force is required to accelertae the empty ride carriage
Answer:
Required force (F) = 500 N
Step-by-step explanation:
Given:
Mass of carriage (m) = 1,000 kg
Acceleration (a) = 0.5 m/s²
Find:
Required force (F)
Computation:
Required force (F) = Mass × Acceleration
Required force (F) = 1,000 kg × 0.5 m/s²
Required force (F) = 500 kg-m/s²
Required force (F) = 500 N
Answer:
Answer:
Required force (F) = 500 N
Step-by-step explanation:
Given:
Mass of carriage (m) = 1,000 kg
Acceleration (a) = 0.5 m/s²
Find:
Required force (F)
Computation:
Required force (F) = Mass × Acceleration
Required force (F) = 1,000 kg × 0.5 m/s²
Required force (F) = 500 kg-m/s²
Required force (F) = 500 N
THANKS
1
3.0
(2 votes)
Step-by-step explanation:
Given:
Mass of carriage (m) = 1,000 kg
Acceleration (a) = 0.5 m/s²Find:Required force (F)Computation:Required force (F) = Mass × AccelerationRequired force (F) = 1,000 kg × 0.5 m/s²Required force (F) = 500 kg-m/s²
Required force (F) = 500 N
Two solid spheres have surface areas of 1441 cm? and 2567 cm² respectively. They are melted and recast to form a larger sphere. Find the surface area of the larger sphere in square centimetres.
Surface area of small sphere = 1441cm^2
Surface area of bigger sphere = 2567cm^2
Surface area of largest sphere = 1441 + 2567
= 4008cm²
Must click thanks and mark brainliest
Write the equation for the line that passes through the points (4, 5) and
(6,9). *
Answer:
y = 2x + 1
Step-by-step explanation:
first find slops
(9-5)/(6-4) = 4/2 = 2 = m
y = mx + b
5 = 2(2) + b
1 = b
y = 2x + 1
Answer:
y = 2x - 3
Step-by-step explanation:
gradient of the line is
[tex] \frac{9 - 5}{6 - 4 } = 2[/tex]
equation will be:
[tex] \frac{y - 5}{ x - 4} = 2[/tex]
y - 5 = 2x - 8
y = 2x - 3
I forgot how to do this. I will give brainliest!
Answer:
A = 2, B = 3 and C = 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
2x + 3y = 2 ( subtract 2x from both sides )
3y = - 2x + 2 ( divide all terms by 3 )
y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{2}{3}[/tex] ← in slope- intercept form
with slope m = - [tex]\frac{2}{3}[/tex]
Parallel lines have equal slopes, thus
y = - [tex]\frac{2}{3}[/tex] x + c ← is the partial equation
To find c substitute (2, 0) into the partial equation
0 = - [tex]\frac{4}{3}[/tex] + c ⇒ c = [tex]\frac{4}{3}[/tex]
y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{4}{3}[/tex] ← in slope- intercept form
Multiply through by 3
3y = - 2x + 4 ( add 2x to both sides )
2x + 3y = 4 ← in standard form
with A = 2, B = 3 and C = 4
question : 4(3x + 2) -6 x 6
Answer:
x= 24
Step-by-step explanation:
open the bracket
4×3x =12x + 4 × 2 =8
12×+ 8-6×6
12×+ 12
x= 24
Answer:
12x - 28
Step-by-step explanation:
Because of PEMDAS you start with the parentheses and distribute the 4.
So,
(12x + 8) -6 x 6
Then, solve for the 6's
(12x + 8) -36
Remove the parentheses
12x + 8 - 36
Lastly, you get
12x - 28.
This is as far as you can go because there is no equals sign so you cannot actually solve for x.
In ΔABC, m∠A=a, m∠B=β, m∠C=y. AB = c, AC = b, BC = a. Find the remaining parts of each triangle if the following parts are given.
a=6.00, b=7.56, y = 54°
Answer:
c=6.31, a=50.28 degrees, B=75.72 degrees
Step-by-step explanation:
The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. The remaining parts of the triangle can be found as shown.
What is Sine rule?The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,
[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ B}{\beta} =\dfrac{Sin\ C}{\gamma}[/tex]
where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,
Sin B is the angle and β is the length of the side of the triangle opposite to angle B,
Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.
Given that the length of side a and b is 6 and 7.56, also, the measure of the angle γ is 54°.
Now, Using the law of cosine, we can write,
[tex]c =\sqrt{a^2 + b^2 -2ab\cdot \cos\gamma}[/tex]
[tex]c =\sqrt{(6)^2 + (7.56)^2 -2(6)(7.56)\cdot \cos(54^o)}[/tex]
c = √39.8297
c = 6.311
Now, using the sine law the ratio of the sides and angles can be written as,
[tex]\dfrac{\sin\alpha}{a} =\dfrac{\sin\beta}{b} =\dfrac{\sin\gamma}{c}[/tex]
[tex]\dfrac{\sin\alpha}{6} =\dfrac{\sin\beta}{7.56} =\dfrac{\sin (54^o)}{6.311}[/tex]
[tex]\dfrac{\sin\alpha}{6}=\dfrac{\sin (54^o)}{6.311}[/tex]
α = 50.2775°
[tex]\dfrac{\sin\beta}{7.56} =\dfrac{\sin (54^o)}{6.311}[/tex]
β = 75.726°
Hence, the remaining parts of the triangle can be found as shown.
Learn more about Sine Rule here:
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N. Alicia has $192 in her checking
account. She writes checks for $32, $27
and $51. What is the balance of her
account now?
Answer:
Step-by-step explanation:
82 hope this helps
Factorize: 4m^2-y^2+4m+1
Answer:
(2m + 1 + y) (2m + 1 - y)
Step-by-step explanation:
steps are done in the above photo and i have also written the identifies
Solve two-step equations. -5/2 a + 5 = 25
Answer:
a = -8
Step-by-step explanation:
-5/2 a + 5 = 25
Subtract 5 from each side
-5/2 a + 5-5 = 25-5
-5/2 a = 20
Multiply each side by -2/5
-2/5 *-5/2 a = 20*-2/5
a = -8