Answer:
[tex]t=\frac{10345-10460}{\frac{1540}{\sqrt{900}}}=-2.24[/tex]
The degrees of freedom are given by:
[tex]df=n-1=900-1=899[/tex]
The p value for this case would be given by:
[tex]p_v =2*P(t_{(899)}<-2.24)=0.0127[/tex]
The p value is low and if we use a significance level of 0.05 we can reject the null hypothesis and we can conclude tha the true mean is different from 10460
Step-by-step explanation:
Information given
[tex]\bar X=10345[/tex] represent the mean height for the sample
[tex]s=1540[/tex] represent the sample standard deviation for the sample
[tex]n=900[/tex] sample size
[tex]\mu_o =10460[/tex] represent the value to verify
t would represent the statistic
[tex]p_v[/tex] represent the p value for the test
Hypothesis to test
We want to verify if the true mean is equal to 10460, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 10460[/tex]
Alternative hypothesis:[tex]\mu \neq 10460[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{10345-10460}{\frac{1540}{\sqrt{900}}}=-2.24[/tex]
The degrees of freedom are given by:
[tex]df=n-1=900-1=899[/tex]
The p value for this case would be given by:
[tex]p_v =2*P(t_{(899)}<-2.24)=0.0127[/tex]
The p value is low and if we use a significance level of 0.05 we can reject the null hypothesis and we can conclude tha the true mean is different from 10460
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)
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]
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
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
plz answer the question below
Answer:123456
Step-by-step explanation:
√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.
Someone let me know this answer
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]
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 %
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,
https://brainly.com/question/23043352#SPJ2
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.
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
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.
Answers? can someone help me please
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:
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]
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
Learn more : brainly.com/question/19028403
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.
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).
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ7
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.
Learn more about the triangle visit;
brainly.com/question/1058720
#SPJ7
Suppose a large shipment of stereos contained 18% defectives. If a sample of size 306 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 6%
Answer:
99.36% probability that the sample proportion will differ from the population proportion by less than 6%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a sample proportion p in a sample of size n, we have that the sampling distribution of the sample proportions has [tex]\mu = p, s = \sqrt{\frac{p(1-p)}{n}}[/tex].
In this question:
[tex]n = 306, p = 0.18, \mu = 0.18, s = \sqrt{\frac{0.18*0.82}{306}} = 0.0220[/tex].
What is the probability that the sample proportion will differ from the population proportion by less than 6%
This is the pvalue of Z when X = 0.18 + 0.06 = 0.24 subtracted by the pvalue of Z when X = 0.18 - 0.06 = 0.12. So
X = 0.24
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.24 - 0.18}{0.022}[/tex]
[tex]Z = 2.73[/tex]
[tex]Z = 2.73[/tex] has a pvalue of 0.9968
X = 0.12
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.12 - 0.18}{0.022}[/tex]
[tex]Z = -2.73[/tex]
[tex]Z = -2.73[/tex] has a pvalue of 0.0032
0.9968 - 0.0032 = 0.9936
99.36% probability that the sample proportion will differ from the population proportion by less than 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]
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:
What is the solution of StartRoot x minus 4 EndRoot + 5 = 2? x = –17 x = 13 x = 53 no solution
The solution to the given function is determined as 13.
Solution of the function
The solution of the function is calculated as follows;
[tex]\sqrt{x - 4} \ +\ 5 = 2[/tex]
collect similar terms together
[tex]\sqrt{x - 4} \ = 2-5\\\\\sqrt{x - 4} \ = -3[/tex]
square both sides of the equation
[tex](\sqrt{x - 4} )^2 = (-3)^2\\\\x - 4 = 9\\\\x = 9 + 4\\\\x = 13[/tex]
Thus, the solution to the given function is determined as 13.
Learn more about solution of functions here: https://brainly.com/question/10439235
#SPJ9
Answer:
No solution
Step-by-step explanation:
Edge.
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.
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
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)
