Answer:
Kendra should have multiplied the x-values by 75 to get the y-values
Step-by-step explanation:
Given
Table
X|| Y
1 || 75
2 || 150
3 || 225
4 || 300
5 || 375
Given that Kendra multiply x by 7.5 to get y
The relationship of x and y can be calculated as thus;
y = rx
Where y and x are the values at the y and x column respectively and r is the constant of proportionality
When y = 75, x = 1.
Plug in these values in the above formula
y = rx becomes
75 = r * 1
75 = r
r = 75
When y = 150, x = 2
150 = r * 2
Multiply both sides by ½
150 * ½ = r * 2 * ½
75 = r
r = 75
When y = 225, x = 3
225 = r * 3
Multiply both sides by ⅓
225 * ⅓ = r * 3 * ⅓
75 = r
r = 75
Notice that r remains 75 and the difference between y values is 75
If you apply these formula on when y = 300 or 375 and when x = 4 or 5, the constant of proportionality will remain The value of 75.
Hence, Kendra mistake is that; Kendra should have multiplied the x-values by 75 to get the y-values
g/5 - 3 > 37. Solve for g. PLEASE HELPPP TYSM
Answer:
g = 200
Step-by-step explanation:
trust me.
I big brain.
Given that circle Q has a radius of 5 and a center of (1,4), which point lies on the perimeter of circle Q?
Answer:
(x-1)^2 + (y-4)^2 = 5^2
Step-by-step explanation:
In order to find the points that lie on the perimeter of the circle, you find the algebraic equation of the circle.
The general equation for a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex] (1)
The last is a circle centered at the point (h,k) and with radius r.
In this case you have a circle with a radius of r = 5, and the circle is centered at (1,4). Then, you have:
h = 1
k = 4
r = 5
You replace the values of h, k and r in the equation (1):
[tex](x-1)^2+(y-4)^2=5^2[/tex]
All point that lies on the curve of the last equation, are point that lie on the perimeter of the circle
A manufacturing machine has two processes. One of them is repeated 4 times and the second only once. The entire cycle
can take no longer than 3 minutes. Which graph represents the overall equation represented by this scenario (all points
may not apply to the scenario)?
Answer:
The inequality representing the time taken by the entire cycle is:
[tex]4x+y\leq 3[/tex]
Step-by-step explanation:
The time taken to complete one cycle of a manufacturing machine is no longer than 3 minutes.
It is provided that the manufacturing machine has two processes.
One of them is repeated 4 times and the second only once.
Assume that the variable x represents the time taken to complete the first process once.
Then the time taken to complete the first process 4 times would be, 4x.
Also assume that the variable y represents the time taken to complete the second process.
Then the inequality representing the time taken by the entire cycle is:
[tex]4x+y\leq 3[/tex]
Consider the graph below representing the above equation.
Answer: D
Step-by-step explanation:
Choose the function whose graph is given by:
The function whose graph is given is y = sin (x - 2).
Option B is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The graph of y = sin(x - 2) is a sinusoidal function that is shifted 2 units to the right from the standard sine function y = sin(x).
The sine function oscillates between -1 and 1 as x increases, and the value of x at which the function reaches its minimum or maximum value is a multiple of π.
When we subtract 2 from x in the equation y = sin(x - 2), the entire graph is shifted to the right by 2 units, which means that the minimum and maximum points occur at x-values that are 2 units greater than they would be for the standard sine function.
The graph of y = sin(x - a) is a sinusoidal function that is shifted a units to the right from the standard sine function.
So, in this case, the graph of y = sin(x-2) looks like the standard sine function shifted 2 units to the right.
The amplitude and period of the function remain the same as the standard sine function, but the phase shift changes.
Thus,
The function whose graph is given is y = sin (x - 2).
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√15(√6+6) A. √21+6√15 B. 3√10+6√15 C. √90+6 D. √90+6√15
Answer:
Before A. 32.7247330577, A. 27.8204757722, B. 32.7247330577, C. 15.4868329805, and D. 32.7247330577
Step-by-step explanation:
Used a calculator. Not that Hard.
You have received an order of 100 robotic resistance spot welders which contains 5 defective welders. You randomly select 15 welders from the order without replacement to inspect to check whether they are defective.
(a) Determine the PMF of the number of defective welders in your sample? Remember to list all possible values of the random variable.
(b) Determine the probability that there are at least 4 defective welders in the sample? Hint: No need to calculate the final numerical results. Appropriately plugging in numbers in the mathematical expression is sufficient
Answer:
a)
[tex]P(X = 0) = h(0,100,15,5) = \frac{C_{5,0}*C_{95,15}}{C_{100,15}} = 0.4357[/tex]
[tex]P(X = 1) = h(1,100,15,5) = \frac{C_{5,1}*C_{95,14}}{C_{100,15}} = 0.4034[/tex]
[tex]P(X = 2) = h(2,100,15,5) = \frac{C_{5,2}*C_{95,13}}{C_{100,15}} = 0.1377[/tex]
[tex]P(X = 3) = h(3,100,15,5) = \frac{C_{5,3}*C_{95,12}}{C_{100,15}} = 0.0216[/tex]
[tex]P(X = 4) = h(4,100,15,5) = \frac{C_{5,4}*C_{95,11}}{C_{100,15}} = 0.0015[/tex]
[tex]P(X = 5) = h(5,100,15,5) = \frac{C_{5,5}*C_{95,10}}{C_{100,15}} = 0.00004[/tex]
b) 0.154% probability that there are at least 4 defective welders in the sample
Step-by-step explanation:
The welders are chosen without replacement, so the hypergeometric distribution is used.
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
100 welders, so [tex]N = 100[/tex]
Sample of 15, so [tex]n = 15[/tex]
In total, 5 defective, so [tex]k = 5[/tex]
(a) Determine the PMF of the number of defective welders in your sample?
There are 5 defective, so this is P(X = 0) to P(X = 5). Then
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,100,15,5) = \frac{C_{5,0}*C_{95,15}}{C_{100,15}} = 0.4357[/tex]
[tex]P(X = 1) = h(1,100,15,5) = \frac{C_{5,1}*C_{95,14}}{C_{100,15}} = 0.4034[/tex]
[tex]P(X = 2) = h(2,100,15,5) = \frac{C_{5,2}*C_{95,13}}{C_{100,15}} = 0.1377[/tex]
[tex]P(X = 3) = h(3,100,15,5) = \frac{C_{5,3}*C_{95,12}}{C_{100,15}} = 0.0216[/tex]
[tex]P(X = 4) = h(4,100,15,5) = \frac{C_{5,4}*C_{95,11}}{C_{100,15}} = 0.0015[/tex]
[tex]P(X = 5) = h(5,100,15,5) = \frac{C_{5,5}*C_{95,10}}{C_{100,15}} = 0.00004[/tex]
(b) Determine the probability that there are at least 4 defective welders in the sample?
[tex]P(X \geq 4) = P(X = 4) + P(X = 5) = 0.0015 + 0.00004 = 0.00154[/tex]
0.154% probability that there are at least 4 defective welders in the sample
Answers? can someone help me please
Use trigonometric substitution to evaluate the integral 13 + 12x − x2 dx . First, write the expression under the radical in an appropriate form so that a trigonometric substitution can be performed. 13 + 12x − x2
I don't see a square root sign anywhere, so I'll assume the integral is
[tex]\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx[/tex]
First complete the square:
[tex]13+12x-x^2=49-(6-x)^2=7^2-(6-x)^2[/tex]
Now in the integral, substitute
[tex]6-x=7\sin t\implies\mathrm dx=-7\cos t\,\mathrm dt[/tex]
so that
[tex]t=\sin^{-1}\left(\dfrac{6-x}7\right)[/tex]
Under this change of variables, we have
[tex]7^2-(6-x)^2=7^2-7^2\sin^2t=7^2(1-\sin^2t)=7^2\cos^2t[/tex]
so that
[tex]\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx=-7\int\sqrt{7^2\cos^2t}\,\cos t\,\mathrm dt=-49\int|\cos t|\cos t\,\mathrm dt[/tex]
Under the right conditions, namely that cos(t) > 0, we can further reduce the integrand to
[tex]|\cos t|\cos t=\cos^2t=\dfrac{1+\cos(2t)}2[/tex]
[tex]\displaystyle-49\int|\cos t|\cos t\,\mathrm dt=-\frac{49}2\int(1+\cos(2t))\,\mathrm dt=-\frac{49}2\left(t+\frac12\sin(2t)\right)+C[/tex]
Expand the sine term as
[tex]\dfrac12\sin(2t)}=\sin t\cos t[/tex]
Then
[tex]t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \sin t=\dfrac{6-x}7[/tex]
[tex]t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \cos t=\sqrt{7^2-(6-x)^2}=\sqrt{13+12x-x^2}[/tex]
So the integral is
[tex]\displaystyle-\frac{49}2\left(\sin^{-1}\left(\dfrac{6-x}7\right)+\dfrac{6-x}7\sqrt{13+12x-x^2}\right)+C[/tex]
The length of a rectangular patio is 7 feet and the width is 6 feet. The patio is surrounded by a sidewalk that is x feet wide. Find the expression that represents the area of the patio, including the sidewalk
Answer: A = (7ft + x)*(6ft + x)
Step-by-step explanation:
The area of a rectangle is equal to A = L*W
where W is width and L is lenght.
Here we have that the width is 6 feet + x feet and the lenght is 7 feet + x feet
(because we also are counting the area of the sidewalk)
Then the total area is:
A = (7ft + x)*(6ft + x)
Nia and Trey both had sore throats, so their mom told them to gargle with warm salt water. Nia mixed 1 teaspoon salt with 3 cups warm water. Trey mixes 1 /2 teaspoon salt with one and 1/2 cups warm water. Nia tasted Trey’s water and said, “I added more salt, so I expected that mine would be more salty, but they taste the same! Explain why both salt water mixtures taste the same.
Answer:
Each mixture has the same amount of salt for every 1 cup of water.
Step-by-step explanation:
It is provided that:
Nia mixed 1 teaspoon salt with 3 cups warm water. Trey mixes 1 /2 teaspoon salt with one and 1/2 cups warm water.The ratio of the number of teaspoons of salt to the number of cups of water is 1 : 3 in Nia's solution.
On dividing the amount of salt and the amount of water by 3, the ratio will be the same.
[tex]\text{Salt}: 1\div3=\frac{1}{3}\\\\\text{Water}:3\div3=1\\[/tex]
Thus 1 : 3 is equivalent to the ratio [tex]\frac{1}{3}:1[/tex], which means that Nia's solution has [tex]\frac{1}{3}[/tex]teaspoon of salt for every cup of water.
The ratio of the number of teaspoons of salt to the number of cups of water is [tex]\frac{1}{2}:1\frac{1}{2}[/tex] in Trey’s solution.
On dividing the amount of salt and the amount of water by [tex]1\frac{1}{2}[/tex], the ratio will be the same.
[tex]\text{salt}:\frac{1}{2}\div 1\frac{1}{2}=\frac{1}{3}\\\\\text{Water}:1\frac{1}{2}\div1\frac{1}{2}=1[/tex]
So Trey’s ratio is also equal to the ratio [tex]\frac{1}{3}:1[/tex].
Since each mixture has the same amount of salt for every 1 cup of water, they are equally salty and taste the same.
Between what two consecutive integers does the square root of 24 lie
4 and 5!
4 squared is 16, which is less than 24, and 5 squared is 25, which is more than 24!
[tex]\sqrt{24}[/tex] lies between two consecutive numbers 4 and 5
Given :
Given square root of 24
Lets write all the perfect square numbers
[tex]\sqrt{4}=2\\\sqrt{9}=3\\\sqrt{16} =4\\\sqrt{25} =5\\\sqrt{36} =6\\\sqrt{49}=7[/tex]
From the above perfect square root numbers, we can see that square root (24) lies between [tex]\sqrt{16} \; and\; \sqrt{25}[/tex]
So we can say that [tex]\sqrt{24}[/tex] lies between 4 and 5
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Classify the triangle shown below. Check all that apply.
100°
40°
40°
A. Obtuse
B. Right
C. Isosceles
D. Equilateral
O E. Acute
F. Scalene
Answer:
obtuse
isosceles
Step-by-step explanation:
It has one angle bigger than 90 so it is obtuse
It has two angles that measure the same so it has two sides that measure the same so it is isosceles
The given triangle is an Obtuse triangle.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
We have to given that;
All the angles are,
100°
40°
40°
Here, It has one angle bigger than 90 so it is obtuse.
And, It has two angles that measure the same so it has two sides that measure the same so it is isosceles.
Thus, The given triangle is an Obtuse triangle.
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An athlete eats 85 grams of protein per day while training. How much is this in milligrams (mg)? plz hurry I have a test soon
After four years in college, Josie owes $9500 in student loans. The interest rate on the federal loans is 11% and the rate on the private bank loans is 7%. The total interest she owed for one year was $901.00. What is the amount of each loan?
Step-by-step explanation:
federal= $4180
(9500*0.11*4)
private=$2660
(9500*0.07*4)
Please answer this correctly
Answer:
20% is the correct answer
Answer:
50%
Step-by-step explanation:
40 is the median.
From median to upper quartile is 25% & form from upper quartile to maximum is 25%
So, 25 + 25 = 50 %
plz answer the question below
Answer:123456
Step-by-step explanation:
Apply the distributive property to create an equivalent expression.
1/2 (2a−6b+8) = ?
Answer:
a-3b+4
Step-by-step explanation:
1/2 (2a−6b+8) =
=1/2*2a-1/2*6b+1/2*8
=a-3b+4
Answer:
a - 3b + 4
Explanation:
According to the instructions, we must apply the distributive property to create an equivalent expression.
* reminder
distributive property formula: a (b + c) = ab + ac
Let's start by applying the distributive property to the expression.
[tex]\displaystyle\frac{1}{2} (2a - 6b + 8)\\\\\displaystyle\frac{1}{2} (2a) + \displaystyle\frac{1}{2} (-6b) + \displaystyle\frac{1}{2} (8)[/tex]
Simplify by multiplying.
[tex]\displaystyle\frac{1}{2}(2a)+\displaystyle\frac{1}{2}(-6b)+\displaystyle\frac{1}{2}(8)\\\\a+\displaystyle\frac{1}{2}(-6b)+\displaystyle\frac{1}{2}(8)\\\\a-3b+\displaystyle\frac{1}{2}(8)\\\\a-3b + 4[/tex]
Therefore, an equivalent expression to the given expression is a - 3b + 4.
QUALITY CONTROL1)Specifications for a part for a DVD player state that the part should weigh between 24.6 and 25.6 ounces. The process that produces the parts has a mean of 25.1 ounces and a standard deviation of .26 ounce. The distribution of output is normal. a)What control chart will you use and why?b)With a 2-sigma confidence, what are the upper and lower control limitsif sample of n = 11are taken and the process is in control (random)?c)Is the process in control
Answer:
Step-by-step explanation:
Given that,
μ = 25.1
σ = 0.26
a) since standard deviation is ideal measure of dispersion , a combination of control chart for mean x and standard deviation known as
[tex]\bar x \\\text {and}\\\mu[/tex]
Chart is more appropriate than [tex]\bar x[/tex] and R - chart for controlling process average and variability
so we use
[tex]\bar x \\\text {and}\\\mu[/tex]charts
b)
n = 11
we have use 2 σ confidence
so, control unit for [tex]\bar x[/tex] chart are
upper control limit = [tex]\mu +2\times\frac{ \sigma}{\sqrt{n} }[/tex]
lower control limit = [tex]\mu -2\times\frac{ \sigma}{\sqrt{n} }[/tex]
control limit = μ
μ = 25.1
upper control limit =
[tex]25.1+2\times \frac{0.26}{\sqrt{11} } \\\\=25.2567[/tex]
lower control limit =
[tex]25.1-2\times \frac{0.26}{\sqrt{11} } \\\\=24.9432[/tex]
Upper control limit and lower control limit are in between the specification limits , that is in between 24.9 and 25.6
so, process is in control
c) if we use 3 sigma limit with n = 11
then
upper control limit = [tex]\mu +3\times\frac{ \sigma}{\sqrt{n} }[/tex]
[tex]25.1+3\times\frac{0.26}{\sqrt{11} } \\\\=25.3351[/tex]
lower control limit = [tex]\mu -2\times\frac{ \sigma}{\sqrt{n} }[/tex]
[tex]25.1-3\times\frac{0.26}{\sqrt{11} } \\\\=24.8648[/tex]
control limit is 25.1
Then, process is in control since upper control limit and lower control limit lies between specification limit
So, process is in control
The result of rounding the whole number 2,746,052 to the nearest hundred thousands place is:
Answer:
2700000
Step-by-step explanation:
Because it is not at 750000 it gets rounded down
2.Sketch the region whose area is given by the integral and evaluate the integral.
3.Evaluate the given integral by changing to polar coordinates.....
2. The integration region,
[tex]\left\{(r,\theta)\mid\dfrac\pi6\le\theta\le\dfrac\pi2\land2\le r\le3\right\}[/tex]
corresponds to what you might call an "annular sector" (i.e. the analog of circular sector for the annulus or ring). In other words, it's the region between the two circles of radii [tex]r=2[/tex] and [tex]r=3[/tex], taken between the rays [tex]\theta=\frac\pi6[/tex] and [tex]\theta=\frac\pi2[/tex]. (The previous question of yours that I just posted an answer to has a similar region with slightly different parameters.)
You can separate the variables to compute the integral:
[tex]\displaystyle\int_{\pi/6}^{\pi/2}\int_2^3r^2\sin^2\theta\,\mathrm dr\,\mathrm d\theta=\left(\int_{\pi/6}^{\pi/2}\sin^2\theta\,\mathrm d\theta\right)\left(\int_2^3r^2\,\mathrm dr\right)[/tex]
which should be doable for you. You would find it has a value of 19/72*(3√3 + 4π).
3. Without knowing the definition of the region D, the best we can do is convert what we can to polar coordinates. Namely,
[tex]r^2=x^2+y^2[/tex]
so that
[tex]\displaystyle\iint_De^{x^2+y^2}\,\mathrm dA=\iint_Dre^{r^2}\,\mathrm dr\,\mathrm d\theta[/tex]
How can I trust your guys
Answer:
Step-by-step explanation:
you just do, everyone in here needs help so i dont think theres people in here just messing arround, you can trust.
Answer:
because we are amazing as always.
Step-by-step explanation:
Please dont do this or i will report u.
bye
Gracie went to Home Depot to buy wall-to-wall carpeting for her house. She needs 104.8 square yards for downstairs, 17.4 square yards for halls, and 165.8 square yards for the upstairs bedrooms. Gracie chose a shag carpet that costs $13.95 per square yard. She ordered foam padding at $2.75 per square yard. The installers quoted Gracie a labor cost of $5.75 per square yard in installation.Whatb will the total job cost Gracy?
Add the rooms together to find total square yards:
104.8 + 17.4 + 165.8 = 288 square yards
Add the costs together: 13.95 + 2.75 + 5.75 = $22.45 per square yard
For total cost, multiply total square yards by total cost per square yard
288 x 22.45 = 6,465.60
Total cost: $6,465.60
The total job cost Gracie is $6,465.60.
To find the total job cost Gracie doneStep 1:
Add the rooms together to find total square yards
=104.8 + 17.4 + 165.8
= 288 square yards
Step 2:
Add the costs together
= 13.95 + 2.75 + 5.75
= $22.45 per square yard
Step 3:
For total cost, multiply total square yards by total cost per square yard
=288 x 22.45
= 6,465.60
Therefore, the total cost: $6,465.60
To calculate the total cost of work done, refer,
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A curved graph could be a example of
Answer:On a graph, these values form a curved, U-shaped line called a parabola. All quadratic functions form a parabola on a graph. ... Quadratic functions are used to describe things with smooth symmetrical curves, like the path of a bouncing ball or the arch of a bridge.
Step-by-step explanation:
A circle's radius that has an initial radius of 0 cm is increasing at a constant rate of 5 cm per second.
a. Write a formula to expresses the radius of the circle, r (in cm), in terms of the number of seconds, t since the circle started growing.r=
b. Write a formula to express the area of the circle, A (in square cm), in terms of the circle's radius, r (in cm). A =
c. Write a formula to expresses the circle's area, A (in square cm), in terms of the number of seconds, t, since the circle started growing. A =
d. Write your answer to part (c) in expanded form - so that your answer does not contain parentheses. A =
Answer:
a) [tex]r(t)=5t[/tex]
b) [tex]A=\pi\cdot r^2[/tex]
c) [tex]A=\pi\cdot (5t)^2[/tex]
d) [tex]A=25\pi t^2[/tex]
Step-by-step explanation:
We know that the circle is increasing its radio from an initial state of r=0 cm, at a rate of 5 cm/s.
This can be expressed as:
[tex]r(0)=0\\\\dr/dt=5\\\\r(t)=r(0)+dr/dt\cdot t=0+5t\\\\r(t)=5t[/tex]
a) Radius of the circle, r (in cm), in terms of the number of seconds, t since the circle started growing:
[tex]r(t)=5t[/tex]
b) Area of the circle, A (in square cm), in terms of the circle's radius, r (in cm):
[tex]A=\pi\cdot r^2[/tex]
c) Circle's area, A (in square cm), in terms of the number of seconds, t, since the circle started growing:
[tex]A=\pi\cdot r^2\\\\A=\pi\cdot (5t)^2[/tex]
d) Expanded form for the area A:
[tex]A=\pi\cdot (5t)^2=25\pi\cdot t^2[/tex]
Persia make a flower arrangement using the eight longest flowers which is the combined height of flowers Persia uses
Answer:
Persia should measure the length of each flower that she used in creating this flower arrangement and add up all the values to get the total height (i.e., the combined height) of the eight flowers used. Make sure to keep the units consistent all throughout the calculation to avoid any errors. For example, if centimetres are used to measure height of one flower, use centimetres all throughout and not switch to using inches at any point.
Hope that answers the question, have a great day!
Answer:
61 1/2
Step-by-step explanation:
math is ez
Solve for x in the following 4/2.6=5/x
The value of X is 3.25
Look at the attached picture
Hope it will help you
Good luck on your assignment
7x + 3 = 5 and y - 1= 6
Answer:
first answer is x= -5 second answer is y=7.
Step-by-step explanation:
7-5=2. 2+3=5.
7-1=6.
Find T, N, and kappa for the plane curve Bold r left parenthesis t right parenthesis equalsleft parenthesis 7 Bold cos t plus 7 t Bold font size decreased by 1 sin t right parenthesis Bold i plus left parenthesis 7 Bold sin t minus 7 t Bold font size decreased by 1 cos t right parenthesis Bold j, t greater than 0 .
Find T, N, and for the plane curve r(t) = (7 cost + 7t sin t)i + (7 sin t - 7t cos t)j, t> 0.
Answer:
Step-by-step explanation:
r(t) = (7 cost + 7t sin t)i + (7 sin t - 7t cos t)j
[tex]\frac{d \bar r t}{dt} =(7\frac{d}{dt}\cos t + 7\frac{d}{dt} (t \sin t)i+(7\frac{d}{dt} \sin t-7\frac{d}{dt} t \cos t)j[/tex]
[tex]=(7(-\sin t)+7(1* \sin t+t \cos t))i+(7 \cost -7(1*\cos t - t \sin t))j\\\\=7((-\sin t+\sin t+t \cos t)i+(\cos t-\cos t+t \sin t)j)\\\\=7((t\cos t)i+(t\sin t)j)[/tex]
[tex]\bar r'(t)=\frac{d \bar r t}{dt} =(7t\cos t)i+(7t\sin t)j---(1)\\\\11\bar r(t)=\sqrt{(7t\cos t)^2+(7t\sin t)^2}\\\\=\sqrt{49t^2(\cos^2t+\sin^2 t)} \\\\=7t[/tex]
[tex]\bar T (t)=\frac{\bar r'(t)}{11\bar r(t)11} =\frac{(7t\cos t)i+(7t\sin t)j}{7t} \\\\\barT(t)=(\cos t)i+(\sin t)j[/tex]
[tex]\bar T'(t)=\frac{d}{dt} (\cos t)i+\frac{d}{dt} (\sin t) j\\\\\bar T'(t)=(-\sin t)i+(\cos t)j---(2)\\\\11\bar T'(t)=\sqrt{(-\sin t)^2+(\cos t)^2} \\\\=\sqrt{\sin^2t+\cos^2t} \\\\=1[/tex]
[tex]\bar N(t)=\bar T'(t)=\frac{(-\sin t)i+(\cos t)j}{(1)} \\\\ \large \boxed {\bar N(t)=(-\sin t)i+(\cos t)j}[/tex]
[tex]K(t)=\frac{|\b\r T'(t)|}{\bar r (t)|} \\\\=\frac{|-\sin t i+\cos t j|}{|7t\cos t +7t \sin t j|}[/tex]
Using eq (1) and (2)
[tex]K(t)=\frac{\sqrt{(-\sin t)^2+(\cos t)^2} }{\sqrt{(7t\cos t)^2+(7t\sin t)^2} }\\\\=\frac{\sqrt{\sin^2 t+\cos^2t} }{\sqrt{49t^2(\cos^2 t+\sin^2t)} }\\\\=\frac{\sqrt{1} }{\sqrt{49t^2\times 1} } \\\\ \large \boxed {K(t)=\frac{1}{7t} }[/tex]
What value of x will make the equation true?
( 15 )( V5) = x
Answer:
[tex]x=15\sqrt{5}[/tex]
Step-by-step explanation:
[tex]15 \times \sqrt{5} = x[/tex]
[tex]33.54102 \approx x[/tex]
Find the volume of the cone.
Either enter an exact answer in terms of T or use 3.14 for and round your final answer to the nearest
hundredth.