For a particle moving uniformly along the x axis is located at 16.5 m at 1.82 s and at 4.97 m at 3.81 s, the displacement is -11.53 m
For given question,
A particle moving uniformly along the x axis is located at 16.5 m at 1.82 s and at 4.97 m at 3.81 s.
We can observe that, for t1 = 1.82 s and t2 = 3.81 s
object is moving from right to left along the x axis.
We know that, the displacement of a particle moving in a straight line is the change in its position.
so, d = 4.97 - 16.5
d = -11.53
The negative sign indicates that the object is moving from right to left along the x axis for t1 = 1.82 s and t2 = 3.81 s
Therefore, for a particle moving uniformly along the x axis is located at 16.5 m at 1.82 s and at 4.97 m at 3.81 s, the displacement is -11.53m.
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use this to find the equation of the tangent line to the curve at the point and write your answer in the form: , where is the slope and is the y-intercept.
The equation can be simplified and written in a slope-intercept form as: [tex]y=18 \sqrt{3} x-6(\sqrt{3} \pi-1)[/tex]
What do we mean by equations?An equation is a mathematical declaration composed of two expressions joined by an equal sign. An equation is 3x - 5 = 16. By solving this equation, we obtain the value of the variable x as x = 7.To find the equation:
When we differentiate the function [tex]y=6 \sec (x)-12 \cos (x)[/tex], we get:
[tex]\begin{aligned}y^{\prime} &=\frac{d}{d x}(6 \sec (x)-12 \cos (x)) \\&=6 \frac{d}{d x}(\sec (x))-12 \frac{d}{d x}(\cos (x)) \\&=6 \sec (x) \tan (x)+12 \sin (x)\end{aligned}[/tex]
The slope of the tangent line is given by this derivative at the point [tex]x=\frac{\pi}{3}[/tex]:
[tex]y^{\prime}\left(\frac{\pi}{3}\right)=6 \sec \left(\frac{\pi}{3}\right) \tan \left(\frac{\pi}{3}\right)+12 \sin \left(\frac{\pi}{3}\right)=18 \sqrt{3}[/tex]The general equation y applies to the tangent line passing through the point [tex](a, y(a))[/tex] on the curve [tex]y(x)-y(a)=y^{\prime}(a)(x-a)[/tex].The tangent line in this case passes through the point [tex]\left(\frac{\pi}{3}, y\left(\frac{\pi}{3}\right)\right)=\left(\frac{\pi}{3}, 6\right)[/tex] and has the slope [tex]y^{\prime}\left(\frac{\pi}{3}\right)=18 \sqrt{3}[/tex].As a result, this tangent line has the equation: [tex]y-6=18 \sqrt{3}\left(x-\frac{\pi}{3}\right)[/tex]
Therefore, the equation can be simplified and written in a slope-intercept form as: [tex]y=18 \sqrt{3} x-6(\sqrt{3} \pi-1)[/tex]
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The correct question is given below:
Find the equation of the tangent line to the curve y = 6 sec (x) at the point ([tex]\pi[/tex]/3, 6). Give your answer in the form y = mx + b where m is the slope and b is the y--intercept.
ok, help me out with this one
4 less than a number n is −15 in eqation form
Answer:
n - 4 = - 15
Step-by-step explanation:
Hope this helps :)
B ABCD is a parallelogram and angle A< 90°. The height through the vertex D intersects the diagonal AC at point M. The height through vertex B intersects the diagonal AC at point N. Prove that MBND is a parallelogram.
MBND is a parallelogram as BN=MD and BN║MD.
A parallelogram is a quadrilateral whose both pair of opposite side are equal and parallel. Few examples of parallelograms are square, Rhombus and rectangle.
Given ABCD is a parallelogram and ∠A=90°
Now we have to prove that MBND is a parallelogram
Given BN⊥AC and DM⊥AC
Since BN and DM are both perpendicular to the same straight line AC then we cam say that BN║DM.
Again we know from the properties of parallelogram that the diagonal divides a parallelogram into two equal triangles.
Therefore the diagonal AC divides the parallelogram into two equal triangles ΔABC and ΔADC.
Now we know that the area of a triangle is given by [tex]\frac{1}{2}[/tex] ×base ×height .
Area of ΔABC =Area of ΔADC
Since BN⊥AC and DM⊥AC
∴[tex]\frac{1}{2}[/tex]×BN×AC=[tex]\frac{1}{2}[/tex]×DM×AC
This above equation can be simplified as
BN=MD
Hence BMND is a parallelogram as we know from the properties of parallelogram that when a pair of opposite sides are equal and parallel in a quadrilateral it is a parallelogram.
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A cylindrical tube 14.5 cm high and 4.5 cm in diameter is used to collect blood samples. how many cubic decimeters (dm3) of blood can it hold (v of a cylinder = r2h)?
The amount of blood that a cylindrical tube hold will be 0.23 cubic dm.
What is the volume of a right circular cylinder?Let r be the radius and h be the height of the cylinder. Then the volume of the cylinder will be
V = π r²h cubic units
A cylindrical tube 14.5 cm high and 4.5 cm in diameter is used to collect blood samples. Then the radius of the cylinder will be
r = d / 2
r = 4.5 / 2
Then the volume of the cylinder will be
V = π r²h
V = 3.14 (4.5 / 2)² × 14.5
V = 3.14 × 20.25 × 14.5 / 4
V = 921.98 / 4
V = 230.5 cubic cm
V = 0.23 cubic dm
The amount of blood that a cylindrical tube hold will be 0.23 cubic dm.
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Suppose that A and B are points on the number line.
If =AB11 and B lies at 9, where could A be located?
Answer: A=-2
Step-by-step explanation:
AB=11
B=9
B-11=A
9-11=A
A=-2
Which probability value indicates that there is statistical significance? 0.9756 0.015 0.9078 0.2356
The probability value indicates that there is statistical significance in 0.015 option (b) is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that:
The p-values are:
0.9756 0.015 0.9078 0.2356As we know,
Statistical significance is commonly defined as a probability value of 0.05 or even less. P-value can be used in replacement of or in additional to preset levels of confidence when testing the claim.
Thus, the probability value indicates that there is statistical significance in 0.015 option (b) is correct.
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Find the slope of the line passing through the points (7, -2) and (7,5).
slope:
Answer: the slope=0
Step-by-step explanation:
[tex]\displaystyle\\(7,-2)\ and\ (7,5)\\[/tex]
[tex]\displaystyle\\\boxed {the \ slope=\frac{y_2-y_1}{x_2-x_1} }[/tex]
[tex]x_1=7\ \ \ \ \ x_2=7\ \ \ \ y_1=-2\ \ \ \ \ y_2=5\\Hence,\\\displaystyle\\the slope=\frac{7-7}{5-(-2)} \\\\the\ slope=\frac{0}{5+2} \\\\the\ slope=\frac{0}{7}\\\\ the\ slope=0[/tex]
b) The angle of elevation of a tower at a distance of 27 meter from the foot of the tower is 60°, find the height of the tower. Speedy Additional Mathematics - Book VIII 98
The height of the tower is approximately 46.765 feet
Step-by-step explanation:
The given parameters are;
The distance from the foot of the tower where the angle of elevation is
measured = 27 feet
The angle of elevation to the top of the tower from a point 27 feet from the foot of the tower, θ = 60°
Therefore, by trigonometric ratio, we have;
tan 60= the height of tower / distance from foot of tower
[tex]\sqrt{3}[/tex]= height of tower /27
1.73205 *27 = height of tower
46.765 feet is the height of tower
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Use technology to c ompute the standard deviation for the following sample data. 32, 41, 36, 24, 29, 30, 40, 22, 25, 37
The standard deviation is provided by this. = 6.7528
What role does standard deviation play?Because it aids in comprehending measurements whenever the data is distributed, the standard deviation is significant. The standard deviation of the data will be higher the more evenly distributed the data is.
According to the given data:sample data = ( 32, 41, 36, 24, 29, 30, 40, 22, 25, 37)
To find mean of the given data:
Mean = Sum of items/ Count items
Mean = (32 + 41 + 36 + 24 + 29 + 30 + 40 + 22 + 25 + 37 / 10)
= 31.6
now finding the variance:
First we Add All the sample:
32 + 41 + 36 + 24 + 29 + 30 + 40 + 22 + 25 + 37 = 316
make Square of the solution:
316*316 =99856
and multiply by how many items there are. We have 10 items.
=99856/10
= 9985.6
For the time being, put this number aside.
Take your original set of numbers from Step 1 and square each one this time on its own.
32² + 41² + 36² + 24² + 29² + 30² + 40² + 22² + 25² + 37² = 10396
Subtract the sum from Step 2 from of the sum from Step 3.
10396 - 9985.6 = 410.4
The items in someone data set is reduced by 1 by.10 - 1 = 9
Divide the result of Step 4 even by result of Step 5. You get the variation from this.
410.4 / 9 = 45.6
Your response from Step 6 should be squared. The standard deviation is provided by this.
6.7528
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I understand that the question you are looming for is:
For the following sample data, compute the variance and the standard deviation. 32, 41, 36, 24, 29, 30, 40, 22, 25, 37
evaulate 5m+7 if m=5
Answer:
32
Step-by-step explanation:
[tex]5\cdot \:5+7[/tex]
Helpppppppppppppppppppppppppppp
please help me with this i will mark as brainliest
Answer:
SHOWN BELOW!!!!
Step-by-step explanation:
KEEP IN MIND ----> *Square root of a number is a value, which on multiplication by itself gives the original number. The square root is an inverse method of squaring a number.*
Alright so the first equation C^2 - 49 = 0
Step 1 : Add 49 to both sides
C^2 - 49 + 49 = 0 + 49
C^2 = 49
Step 2 : Take the square root
(squ root) C^2 = (squ root)49
C = +/- (squ root) 49
Final answer ---> C = 7 OR C = -7
2.) 4S^2 - 100 = 0
Step 1 : Add 100 to both sides
4S^2 - 100 + 100 = 0 + 100
4S^2 = 100
Step 2 : Divide both sides by 4
4S^2/4 = 100/4
S^2 = 25
Step 3 : Take the square root
(squ root) S^2 = (squ root) 25
S = +/- (squ root) 25
Final answer ---> S = 5 OR S = -5
3.) 9x^2 = 324
Step 1: Divide both sides by 9.
9x^2/9 = 324/9
x^2 = 36
Step 2: Take the square root
squ root) x^2 = (squ root) 36
x = +/- (squ root) 36
Final answer ---> x = 6 OR x = -6
10. Determine whether the inequality is always, sometimes, or never true. (1 point)
4x-8>1 + 4(x+3)
always
sometimes
Onever
Answer: onever
Step-by-step explanation:
4x-8>1+4(x+3)
4x-8>1+4(x)+4(3)
4x-8>1+4x+12
4x-8>4x+13
4x-8-4x>4x+13-4x
-8>13
Hence, inequality is never true
Draw the graph of y = x² – 4x + 3. Identify the intercepts (x and y), the vertex, and the axis of symmetry.
Answer:
y-intercept : 3
x-intercepts are 1 and 2
Vertex is at (2,-1)
Axis of symmetry is at x = 2
Step-by-step explanation:
See attached graph.
The equation y = x² – 4x + 3 represents a parabola
y-intercept at is at B(0,3); y-intercept is 3
x-intercept points at C(1,0) and D(3,0) so x-intercepts are 1 and 3
The vertex is the lowest point on this parabola (2-1)
Axis of symmetry is a line passing through the vertex and dividing the parabola into two equal halves. This is the vertical line x = 2
An isosceles triangle has a base of 14cm and sides of 50cm. calculate its height
A triangle is a 2-dimensional shape that has 3sides and 3 interior angles. The height of the isosceles triangle is approximately 49.5cm
Pythagoras theoremThe theorem states that the square of the hypotenuse is equal to the sum of the square of other two sides.
From the given question, the hypotenuse is 50cm and the base of the triangle is 14cm
Determine the height using the expression
h² = 50² - (14/2)²
h² = 2500 - 7²
h² = 2500 - 49
h = √2451
h = 49.5cm
Hence the height of the triangle is approximately 49.5cm
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HEEYYY PLEASE ANSWER THIS I GOT COVID SO I DONT UNDERSTAND IT SINCE I CANT BE IN CLASS
You can just try out all the answers but I'll give you a solution.
We will expand out the middle term to 5x^2 - 30x - 6x + 36, then we group the first 2 terms together, and the last 2 terms together.
= 5x (x - 6) - 6(x - 6)
And we put x-6 out : (x-6)(5x-6) = 0
Now, we can just set the value of one bracket to 0 and find out the value of x, and do the same for the other one
x - 6 = 0 -> x = 6
5x - 6 = 0 -> x = 6/5
Because 6 is not a possible option, the answer is x = 1.2
f (3/10)= -5 (3/10) -14
Answer: -15.5 or -31/2
Step-by-step explanation:
it may look weird but if that's what the equations says then your gonna do it.
-5(3/10) -> (5/1)(3/10) = 15/10 = -3/2 or -1.5
-1.5 - 14 = -15.5
:
() =-5-14 (=3/10)
(3/10)= -5 (3/10) -14
f(3/10) = -15/10 -14
= -15-140
----------
10
= -195/10
=- 19.5
Factorise C^2 - ( d + 2 )^2
Answer:
Step-by-step explanation:
[tex]\boxed{x^2-y^2=(x+y)(x-y)}[/tex]
[tex]c^2-(d+2)^2=\\(c+(d+2))(c-(d+2))=\\(c+d+2)(c-d-2)[/tex]
Find the equation of the line shown.
The equation of the line shown in the diagram is y = 0.5x+0.5.
What is a line?A line is a mark connecting two points.
To calculate the equation of the line, we use the formula below
Formula:
y = mx+c.............. Equation 1Where:
m = Slope of the graphc = Intercept on the vertical axis.From the diagram,
Given:
m = 1/2 = 0.5c = 0.5Substitute these values into equation 1
y = 0.5x+0.5Hence, the equation of the line shown in the diagram is y = 0.5x+0.5.
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If I spend 35 every week for a year how much do I spend?
Answer:
$1,820
Step-by-step explanation:
The math problem is $35 times 52 weeks
Which of the following numbers is divisible by 3?
a) 539
b) 85
c) 9,285
d) 640
Answer:
C
Step-by-step explanation:
539/3 = 179.666
85/3 =28.3333
9285/ 3 = 3095
640/3=213.3333
Answer:
C
Hope this helps :)
Step-by-step explanation:
All the others numbers equal a decimal when divided by 3. However, C equals a whole number so it's C.
9,285 ÷ 3 = 3,095
a phrase that describes a set of real numbers is given. express the phrase as an inequality involving an absolute value. all real numbers x more than 2 units from 0
All real numbers x more than 2 units from 0 will be |x - 2| ≤ 0.
What does "real number" mean?
In mathematics, a real number is a quantity that may be represented by an endless number of decimal expansions. In contrast to the natural numbers 1, 2, 3,... that result from counting, real numbers are utilized in measurements of continuously altering quantities such as size and time.All real numbers x at most 2 units from 0
This means if x is centered at 2 then it can move at the max 2 units on either side (i.e. 4 units after 2 and 0 units before 2)
This will be |x - 2| ≤ 0
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please help!
there’s a picture, to see the question
Answer:
it's x+3
Step-by-step explanation:
it seems to go up by one so if you go down by you the input of 1 would be the output of 4 also known as (1,4)
and go again down by 1 and get (0,3)
so we know we have to add 3 each time so it is x+3
-5/6+ 2/6
i really need help
Answer:
1 and 1/6 or 7/6
Step-by-step explanation:
Answer:
7/6
Step-by-step explanation:
=5/6+2/6
=5/6+1/3
7/6
Volume of cone if height is 18 and diameter is 10,
Answer:
150pi
Step-by-step explanation:
The formula for the volume of a cone is one-third the volume of a cylinder.
It is [tex]V=\frac{1}{3} Bh[/tex] where B is the area of the circle base and h is the height of the cone.
To find the base of the cone, use the formula for the area of a circle. So, the radius is 5. So, the area of the base is pi × radius².
[tex]5^{2} =25[/tex]
[tex]\frac{1}{3}[/tex] × 25pi × 18 = 150pi
1/19 7/4 -4/7 in order from least to greatest
Answer:
-4/7, 1/19, 7/4
Step-by-step explanation:
-4/7 is less then zero, and the only negative number so it is first
1/19 is the second lowest
7/4 is the highest because it is the only one that is greater then 1. (simplified, 7/4= 1 3/4)
Solve the quadratic equation by completing the square.
2
x² - 10x+10=0
Answer: x=5+[tex]\sqrt{15}[/tex]
Step-by-step explanation:
x² - 10x+10=0
x² - 5x - 5x+10=0
x² - 5x - 5x+25-15=0
(x-5)^2 -15=0
(x-5)^2=15
x-5=[tex]\sqrt{15}[/tex]
x=5+[tex]\sqrt{15}[/tex]
At a cross-country track meet, Alicia ran 8 mph for the first part of the race, then increased her speed to 12 mph for the second part. If the race was 21 miles long and Alicia finished in 2 hours, how far did she run at the faster pace?
She ran 15 miles at a quicker speed based on the information supplied. See explanation below. This is a distance time problem.
What is the justification for the above result?The distances between the two "half" of the race are our unknowns here. We must assign them to variables - Alicia ran x miles in the first half of the race and y miles in the second.
Since the race is 21 miles in total, x and y together must add up to 21.
Hence,
x + y = 21
The speeds at which she raced and the total time involved are then given; we can link this to the distances using the speed and distance equation
d = st, or t = d/s.
Because she completed in two hours, the hours spent running the first and second parts must sum up to two hours, or:
x/8 + y/12 = 2
Two equations are sufficient to solve for two unknowns. We can approach this by multiplying the second equation by the LCM, 24
3x + 2y = 48
And rearrange the first to get y = 21 - x, which we can plug into the above. This gives us:
3x + 2(21 - x) = 48
3x + 42 - 2x = 48
x = 6
Use y = 21 - x again:
y = 21 - (6) = 15.
Recall that the question asks how long she ran at the faster speed - this would be the second half of the race, which we've labeled y, so 15 miles. But first, let's make sure our solution works.
Obviously, 15 + 6 = 21, thus the overall distance is correct.
In terms of time, 6 miles at 8 mph takes
6/8 =.75 hours = 45 minutes, whereas
15 miles at 12 mph takes 15/12 = 1.25 hours = 75 minutes.
As stated in the question, the total time to complete would be.
75 + 1.25 = 2 hours.
As a result, this solution is correct, as Alicia ran 15 miles at a quicker rate.
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Lamar goes for a bike ride every day. For the last two weeks, he tracked the distance he rode and his time. He made a scatter plot to show the relationship between the distance and time for each of his bike rides.
Which of the following is the best estimate for how long it would take Lamar to ride 15 miles?
Answer:
Where exactly is the "the following" you are talkibg about.
Answer:40 miles
Step-by-step explanation:
