Answer:
Step-by-step explanation:
Using chain rule to find the partial deriviative of z with respect to s and t i.e ∂z/∂s and ∂z/∂t, we will use the following formula since it is composite in nature;
∂z/∂s = ∂z/∂x*∂x/∂s + ∂z/∂y*∂y/∂s
Given the following relationships z = x⁸y⁹, x = s cos(t), y = s sin(t)
∂z/∂x = 8x⁷y⁹, ∂x/∂s = cos(t), ∂z/∂y = 9x⁸y⁸ and ∂y/∂s = sin(t)
On substitution;
∂z/∂s = 8x⁷y⁹(cos(t)) + 9x⁸y⁸ sin(t)
∂z/∂s = 8(scost)⁷(s sint)⁹(cos(t)) + 9(s cost)⁸(s sint)⁸ sin(t)
∂z/∂s = (8s⁷cos⁸t)s⁹sin⁹t + (9s⁸cos⁸t)s⁸sin⁹t
∂z/∂s = 8s¹⁶cos⁸tsin⁹t + 9s¹⁶cos⁸tsin⁹t
∂z/∂s = 17s¹⁶cos⁸tsin⁹t
∂z/∂t = ∂z/∂x*∂x/∂t + ∂z/∂y*∂y/∂t
∂x/∂t = -s sin(t) and ∂y/∂t = s cos(t)
∂z/∂t = 8x⁷y⁹*(-s sint) + 9x⁸y⁸* (s cos(t))
∂z/∂t = 8(scost)⁷(s sint)⁹(-s sint) + 9(s cost)⁸(s sint)⁸(s cos(t))
∂z/∂t = -8s¹⁷cos⁷tsin¹⁰t + 9s¹⁷cos⁹tsin⁸t
∂z/∂t = -s¹⁷cos⁷tsin⁸t(8sin²t-9cos²t)
For which positive integer values of $k$ does $kx^2+20x+k=0$ have rational solutions? Express your answers separated by commas and in increasing order.d
When you solve this equation using the quadratic formula, you will get [tex]x = \frac{-20\pm \sqrt{400-4k^2}}{2k}[/tex]. The only way for this number to be irrational is for [tex]\sqrt{400-4k^2}[/tex] to be irrational. The square root of any number that is not a perfect square is irrational*, so the solutions of the quadratic are rational if and only if [tex]400-4k^2[/tex] is a perfect square. We can factor out the 4 (which is already a perfect square), which means that [tex]100-k^2[/tex] must be a perfect square. This occurs exactly when k is equal to one of the following:[tex]\sqrt{100},\sqrt{99},\sqrt{96},\sqrt{91},\sqrt{84},\sqrt{75},\sqrt{64},\sqrt{51},\sqrt{36},\sqrt{19}, \sqrt{0}[/tex].
Of these, the only positive integer values of k are: [tex]\sqrt{100}, \sqrt{64}, \sqrt{36}[/tex], or simply 6, 8, and 10.
* This is quite simple to show: Take any rational number, a/b. Without loss of generality, we can assume that a/b is in reduced form, that is, a and b have no common factors. (a/b)^2 is a^2/b^2, and since a and b have no common factors, neither do a^2 and b^2. Therefore, a^2/b^2 cannot be an integer. In the event that a/b is an integer, b would equal 1, and this proof would not hold.
Global Airlines operates two types of jet planes: jumbo and ordinary. On jumbo jets, 25% of the passengers are on business while on ordinary jets 30% of the passengers are on business. Of Global's air fleet, 40% of its capacity is provided on jumbo jets. (Hint: The 25% and 30% values are conditional probabilities stated as percentages.) What is the probability a randomly chosen business customer flying with Global is on a jumbo jet?
Answer:
Answer:
The probability is [tex]P(J|B) = 0.36[/tex]
Step-by-step explanation:
B =business
J=jumbo
Or =ordinary
From the question we are told that
The proportion of the passenger on business in the ordinary jet is [tex]P(B| Or) = 0.25[/tex]
The proportion of the passenger on business in the jumbo jet is [tex]P(B|J) = 0.30[/tex]
The proportion of the passenger on jumbo jets is [tex]P(j) = 0.40[/tex]
The proportion of the passenger on ordinary jets is evaluated as
[tex]1 - P(J) = 1- 0.40 = 0.60[/tex]
According to Bayer's theorem the probability a randomly chosen business customer flying with Global is on a jumbo jet is mathematically represented as
[tex]P(J|B) = \frac{P(J) * P(B|J)}{P(J ) * P(B|J) + P(Or ) * P(B|Or)}[/tex]
substituting values
[tex]P(J|B) = \frac{ 0.4 * 0.25}{0.4 * 0.25 + 0.6 * 0.3}[/tex]
[tex]P(J|B) = 0.36[/tex]
Step-by-step explanation:
a student showed the steps below while solving the equation 14=log5(2x-3) by graphing. which step did the student make the 1sr error
Answer:
[tex]x= \frac{5^{14}+3}{2}[/tex]
Step-by-step explanation:
The correct steps to solve the equation are:
[tex]14=log_5(2x-5)[/tex]
[tex]5^{14}=5^{log_5(2x-3)}[/tex]
Because [tex]a^{log_am}=m[/tex]
So, solving we get:
[tex]5^{14}=2x-3[/tex]
Sum 3 on every side:
[tex]5^{14}+3=2x-3+3\\5^{14}+3=2x[/tex]
Dividing by 2 into both sides:
[tex]\frac{5^{14}+3}{2}=\frac{2x}{2}\\\frac{5^{14}+3}{2}=x[/tex]
So, the answer is [tex]x= \frac{5^{14}+3}{2}[/tex]
Answer: Step 2
Step-by-step explanation:
This is correct according to Edge 2021
The temperature is 58° F. It gets warmer by h degrees and reaches to 65° F. Find h.
Answer:
h = 7 degrees
Step-by-step explanation:
To find h, we know that it is positive because it increases in value, not decreases:
h = 65 - 58
h = 7
Answer:
h = 7°F
Step-by-step explanation:
58 + h = 65
h = 65 - 58
h = 7
Check:
68 + 7 = 65
The center of a circle is at the origin on a coordinate grid. A line with a positive slope intersects the circle at (0,7).
Which statement must be true?
The circle has a radius greater than 7.
The circle has a radius equal to 7.
The slope of the line is equal to 7.
The slope of the line is not equal to 7.
Save and Exit
Next
Submit
Answer:
the radius of the circle =7
Step-by-step explanation:
the function of a circle:(x – h)^2 + (y – k)^2 = r^2
center(0,0) because the center of a circle is at the origin (h,k)
a line intersect at (0,7)
(0-0)^+7-0)^2=r^2
r^2=49 , r=√49
radius r=7
Can Someone plz help me with the question??
Answer:
[tex]\boxed{x^2+y^2 = 49}[/tex]
Step-by-step explanation:
First, we'll find the length of the radius using distance formula and the coordinates (0,0) and (7,0)
Distance Formula = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
R = [tex]\sqrt{(7-0)^2+(0-0)^2}[/tex]
R = [tex]\sqrt{7^2}[/tex]
Radius = 7 units
Now, Equation of circle:
[tex](x-a)^2+(y-b)^2 = R^2[/tex]
Where (a,b) = (0,0) So, a = 0, b = 0 and R = 7 units
=> [tex](x-0)^2+(y-0)^2 = (7)^2[/tex]
=> [tex]x^2+y^2 = 49[/tex]
This is the required equation of the circle.
Answer:
x^2 + y^2 = 49
Step-by-step explanation:
We can write the equation of a circle as
( x-h) ^2 + ( y-k) ^2 = r^2
where ( h,k) is the center and r is the radius
The radius is the distance from the center to a point on the circle
(0,0) to (7,0) is 7 units
so the the radius is 7
( x-0) ^2 + ( y-0) ^2 = 7^2
x^2 + y^2 = 49
I need help! I don’t understand and need helping
Answer:
125
Step-by-step explanation:
30+25+x=180
55+x=180
x=180-55
x=125
Answer:
x = 64.3Step-by-step explanation:
To find x we use tan
tan ∅ = opposite / adjacent
From the question
x is the adjacent
30 is the hypotenuse
So we have
tan 25 = 30/x
x = 30/tan 25
x = 64.33
x = 64.3 to the nearest tenth
Hope this helps you
Find the number of four-digit numbers which are not divisible by 4?
Answer: without trying each calculation individually, 6750 4-digit numbers are not divisible by 4
Step-by-step explanation: From 1000 to 9999 there are 9000 4-digit numbers 9999 - 999 = 9000.
Eliminate all the odd numbers 9000/2 = 4500
Eliminate the even numbers divisible by 2 but not by 4. 4500/2 = 2250
9000 - 2250 = 6750.
Find the least common multiple of $6!$ and $(4!)^2.$
Answer:
The least common multiple of $6!$ and $(4!)^2.$
is 6×4! or 144
The letters G, E, N, I, D, S are placed in a bag. What is the probability that the letters are randomly pulled from the bag in the order that spells DESIGN?
Answer as a fraction = 1/5040
Answer in decimal form (approximate) = 0.000198
Answer in percentage form (approximate) = 0.0198%
=========================================================
Explanation:
There is only one ordering of the letters to get DESIGN out of 5040 different permutations. The 5040 comes from the fact that 7*6*5*4*3*2*1 = 5040. In shorthand notation, use factorials to say 7! = 5040. Notice how we started with 7 and counted down until reaching 1, multiplying all along the way. You could use the nPr permutation formula to get the same result of 5040 (use n = 7 and r = 7).
So because we have 1 way to order the letters (getting DESIGN) out of 5040 ways total, this means the probability is the fraction 1/5040. Use your calculator to find that 1/5040 = 0.000198 approximately. Move the decimal over 2 spots to the right to convert 0.000198 to 0.0198%
The snowfall from this snowstorm above covered most of IA, northern IL, northern IN, and southern MI. While some locations in that swath saw over a foot of snow, let’s assume the average depth of the snow over this area was 8 inches. If the total area covered by the 8 inch average depth was 72,150 square miles, what percentage of the volume of the Grand Canyon would this amount of snow fill?
Answer:
Percentage volume of the Grand Canyon filled by the snow = 0.911 %
Step-by-step explanation:
This question is incomplete; please find the complete question in the attachment.
Given :
Area of the snow cover = 72150 square miles
Depth of the snow = 8 inches
Volume of the Grand Canyon = 4.166 × 101² m³
Solution:
Area of the snow cover = 72150 square miles
≈ 72150 × 2589988 square meter
≈ 1.868 × 10¹¹ square meter
Depth of the snow = 8 inches ≈ 0.2032 m
Volume of the snow on this area = Area × depth of the snow
= 1.868 × 10¹¹ × 0.2032
= 3.796 × 10¹⁰ m³
Volume of the Grand Canyon = 4.166 × 10¹² m³
Percentage volume of the Grand Canyon filled by the snow
= [tex]\frac{\text{Volume of the snow}}{\text{Volume of the Grand Canyon}}\times 100[/tex]
= [tex]\frac{3.796\times 10^{10} }{4.166\times 10^{12} }\times 100[/tex]
= 0.911%
Help thx!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Answer E
Step-by-step explanation:
If you think about it, the origin is just (0,0). Now, think which one is the closest to that. (0,1/2), or answer E, should be your assumption.
Find the slope of the line passing through the points (3, 4) and (8, -3).
Answer:
-7/5
Step-by-step explanation:
We can find the slope using the slope formula
m = ( y2-y1)/(x2-x1)
= ( -3 -4)/(8-3)
= -7/5
Answer:
-7/5
Step-by-step explanation:
Hey there!
To find the slope of a line with 2 given points we'll use the following formula,
[tex]\frac{y^2-y^1}{x^2-x^2}[/tex]
-3 - 4 = -7
8 - 3 = 5
-7/5
Hope this helps :)
A drawer is filled with 3 black shirts, 8 white shirts, and 4 gray shirts. One shirt is chosen at random from the drawer. Find the probability that it is not a white shirt. Write your answer as a fraction.
The probability that the shirt that is chosen at random from the drawer is not a white shirt, can be found to be 47 %
How to find the probability ?The probability that the shirt picked is not a white shirt can be found by first finding the number of shirts that are not white shorts in the drawer. This number is :
= Number of black shirts + Gray shirts
= 3 + 4
= 7 shirts
Then, find the total number of shirts in the drawer, including the white shirts :
= Number of black shirts + Gray shirts + White shirts
= 3 + 8 + 4
= 15 shirts
The probability that when a shirt is chosen at random, that it is not a white shirt is :
= Number of shirts that are not white / Total number of shirts
= 7 / 15
= 47 %
Find out more on probability at https://brainly.com/question/27831410
#SPJ1
WHat is the answer to this?
Answer:
0.9
Step-by-step explanation:
First, convert them all into fractions:
[tex]2\frac{1}{3}=\frac{7}{3}[/tex]
[tex].5=\frac{1}{2}[/tex]
Now, we have:
[tex]\frac{4x+9}{\frac{7}{3} } =\frac{3x}{\frac{1}{2} }[/tex]
Cross multiply:
[tex]\frac{1}{2} (4x+9)=\frac{7}{3} (3x)[/tex]
On the left, distribute. On the right, notice that the 3 in the denominator and the coefficient 3 cancel:
[tex]2x+4.5=7x[/tex]
[tex]4.5=5x[/tex]
[tex]x=0.9=9/10[/tex]
Answer and step-by-step explanation:
Photo
Transformations of exponential functions
Answer:
It's the last one. We know it's to the right because the -8 is in the exponent and also, it's -8 not +8.
One bag of dog food has 13kg. Vet order dog to eat 683 grams a day. How many bags of dog for will you need to buy for 1yr.
Answer:
20 bags
Step-by-step explanation:
683✖️19=12977
683✖️365=249295
249295/13000=19.17
--> 20 bags
Solve.
1/3-6<24
{s | s<6}
O {S | s < 10}
O {S | s < 54}
O {S | s < 90}
Answer:
The answer is:
The fourth option,
{s | s <90}
Step-by-step explanation:
yes
Answer:
[tex]\boxed{s|s<90}[/tex]
Step-by-step explanation:
1/3s-6<24
Add 6 on both sides.
1/3s<30
Multiply both sides by 3.
s<90
For the following information, determine whether a normal sampling distribution can be used, where p is the population proportion, is the level of significance, p is the sample proportion, and n is the sample size.
Claim: p >=0.28; α:0.08. Sample statistics: p=0.20, n= 180
Required:
If a normal sampling distribution can be used, decide whether to reject or fail to reject the null hypothesis and interpret the decision.
Answer:
The Central Limit Theorem says that if the sample size is more than 30, the data follows a normal sampling distribution. Since the sample size is 180, and that is more than 30, a Normal sampling distribution can be used.
Since a normal sampling distribution can be used, we should FAIL TO REJECT the null hypothesis because p = 0.20, which is more than the significance level of α = 0.08. There is NOT sufficient evidence to suggest that the alternative hypothesis is true.
Hope this helps!
Two ballpoint pens are selected at random from a box that contains3 blue pens, 2 red pensand 3 green pens. If X is the number of blue pens
Answer: 3/(28) ≈ 10.7%
Step-by-step explanation:
3 blue + 2 red + 3 green = 8 total pens
First pick and Second pick
[tex]\dfrac{3\ blue\ pens}{8\ total\ pens}\quad \times \quad \dfrac{2\ remaining\ blue\ pens}{7\ remaining\ total\ pens}\quad =\large\boxed{\dfrac{3}{28}}[/tex]
Find the average rate of change of the function f(x), represented by the graph, over the interval [-4, -1]. Calculate the average rate of change of f(x) over the interval [-4, -1] using the formula . The value of f(-1) is . The value of f(-4) is . The average rate of change of f(x) over the interval [-4, -1] is .
Answer:
2
Step-by-step explanation:
We are given that a graph which represents f(x).
Interval:[-4,-1]
We have to find the average rate of change of the function f(x).
From the graph we can see that
f(-4)=-3
f(-1)=3
We know that the average rate of change of the function
Average rate =[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Using the formula
Average rate of change of f=[tex]\frac{3-(-3)}{-1-(-4)}[/tex]
Average rate of change of f=[tex]\frac{6}{3}=2[/tex]
Please help. I’ll mark you as brainliest if correct
Answer:
1,-1,3,4
1,6,-2,-4
-4,6,-6,6
Step-by-step explanation:
I believe you just put in the values into the box. Watch the video to see how they did it to make sure it looks like how I did it.
A salesperson earns 6% commission on $25.000. How much
commission was earned?
The commission earned was $
Answer: $1500
Step-by-step explanation:
6% commission on $25,000
= 25000 x .06
= 1500
Mike can stitch 7 shirts in 42 hours
He can stitch 1 shirt in hours, and in 1 hour he can stitch of a shirt
Answer:
He stitched 1 shirt in 6 hours.
He can stitch 1/6 of a shirt in one hour
Step-by-step explanation:
Given Mike can stitch 7 shirts in 42 hours
No. of shirt stitch in one hour = total no of shirt stitch/total time taken
No. of shirt stitch in one hour = 7/42 = 1/6
Thus, he can stitch 1/6 of a shirt in one hour
Time taken to stitch 1 shirt = total time taken by him to stitch 7 shirts/ total no. of shirt stitch(i.e 7) = 42/6 = 6 hours.
Thus, he stitched 1 shirt in 6 hours.
Answer:
He can stitch 1/6 of a shirt in one hour
Step-by-step explanation:
Because he stitched 7 shirts in 42 hours
42/7 = 6
so 6 hours per shirt
In one hour:
1/6
For the functions f(x)=2x−5 and g(x)=3x2−x, find (f∘g)(x) and (g∘f)(x).
Hi,
f°g means : apply first g then f . so calculate "g" and then use result as "x" in f.
g°f means : you apply first f then g
so : f°g = 2(3x²-x) -5 = 6x²-2x- 5
To improve in math, you need practice. have a try with g°f :)
give the answer in comments, and I will tell you if you are correct.
good luck.
Of 10 girls in a class, three have blue eyes. Two of the girls are chosen at random. Find the probability that: (a) both have blue eyes; (c) at least one has blue eyes; (b) neither has blue eyes; (d) exactly one has blue eyes.
Answer:
C.
Step-by-step explanation:
It's the most reasonable answer.
Which of the following lines are parallel to 2Y - 3X = 4?
A. Y = 2/3 X + 4
B. Y = 6/4 X
C. 2Y=8-3X
Answer:
B. Y = 6/4 X
Step-by-step explanation:
Well to find its parallel line we need to put,
2y - 3x = 4 into slope-intercept.
+3x to both sides
2y = 3x + 4
Now we divide everything by 2,
y = 3/2x + 2
So a line that is parallel to the given line will have the same slope but different y intercept, meaning we can cross out choices A and C.
To check look at the image below ↓
Thus,
answer choice B. Y = 6/4 X is correct.
Hope this helps :)
According to the World Health Organization (WHO) Child Growth Standards, the head circumference for boys at birth is normally distributed with a mean of 34.5cm and a standard deviation of 1.3cm. What is the probability that a boy has a head circumference greater than 36.32cm at birth
Answer:
0.081
Step-by-step explanation:
To solve this question, we would use the z score formula
z score = (x-μ)/σ, where
x is the raw score = 36.32cm
μ is the population mean = 34.5 cm
σ is the population standard deviation = 1.3cm
z score = (36.32cm - 34.5cm)/1.3cm
z = 1.4
Using the normal distribution to find the z score for 1.4
P(z = 1.4) = 0.91924
Therefore, the probability that a boy has a head circumference greater than 36.32cm at birth is
P(x>36.32) = 1 - P(z = 1.4)
= 1 - 0.91924
= 0.080757
Approximately ≈ 0.081
Simplify the expression:
3+ – 5(4+ – 3v)
Answer:
The answer is
15v - 17Step-by-step explanation:
3+ – 5(4+ – 3v) can be written as
3 - 5( 4 - 3v)
Expand and simplify
That's
3 - 20 + 15v
15v - 17
Hope this helps you
Which inequality has -12 in its solution set?
A
B
С
D
X+6 <-8
X+42-6
X-3 >-10
X+55-4
ОА
B
D
Answer:
D) [tex]x+5\leq -4[/tex]
Step-by-step explanation:
We solve each of the inequalities
Option A
[tex]x+6<-8\\x<-8-6\\x<-14[/tex]
Option B
[tex]x+4\geq -6[/tex]
[tex]x\geq -6-4\\x\geq-10[/tex]
Option C
[tex]x-3>-10\\x>-10+3\\x>-7[/tex]
Option D
[tex]x+5\leq -4[/tex]
[tex]x\leq -4-5\\x\leq -9[/tex]
Therefore, only option D has -12 in its solution set.