Answer:
-4.5ft per sec
Step-by-step explanation:
Assume that vertical wall has a distance of y and the horizontal floor is x (6 ft).
This forms a triangle with the ladder as the hypothenus of length 10ft
We have dy/dt = 6ft per sec
According to Pythagoras law the relationship between x and y is
(x^2) + (y^2) = (hypothenus ^2) = 10^2
When we differentiate both sides of the equation
2x(dx/dt) + 2y(dy/dt) = 0
dy/dt = (x/y) * (dx/dt)
y= √(10^2) - (6^2) = 8ft
So dy/dt = (6/8)* (6/1)= -4.5 ft per sec
It is a negative rate
The dot plot represents a sampling of ACT scores: dot plot titled ACT Scores with Score on the x axis and Number of Students on the y axis with 1 dot over 24, 3 dots over 26, 3 dots over 27, 5 dots over 28, 3 dots over 30, 3 dots over 32, 1 dot over 35 Which box plot represents the dot plot data? box plot titled ACT Score with a minimum of 24, quartile 1 of 25, median of 26, quartile 3 of 29, and maximum of 35 box plot titled ACT Score with a minimum of 23, quartile 1 of 25, median of 26, quartile 3 of 29, and maximum of 36 box plot titled ACT Score with a minimum of 23, quartile 1 of 27, median of 30, quartile 3 of 34, and maximum of 36 box plot titled ACT Score with a minimum of 24, quartile 1 of 27, median of 28, quartile 3 of 30, and maximum of 35
Answer:
box plot titled ACT Score with a minimum of 24, quartile 1 of 27, median of 28, quartile 3 of 30, and maximum of 35
Step-by-step explanation:
The scores of the students represented on the dot plot are:
1 dot => 24
3 dots => 26, 26, 26
3 dots => 27, 27, 27
5 dots => 28, 28, 28, 28, 28
3 dots => 30, 30, 30
3 dots => 32, 32, 32
1 dot => 35
Quickly, we can ascertain 3 values from these data points of which we can use to find out which box plot represents the dot plot data.
The minimum score = 24
The maximum score = 35
The median score is the 10th value, which is the middle value of the data point = 28
Therefore, we can conclude that: "box plot titled ACT Score with a minimum of 24, quartile 1 of 27, median of 28, quartile 3 of 30, and maximum of 35".
The lines shown below are parallel. If the green line has a slope of -1/2, what is the slope of the red line?
A.
2
B.
-
C.
-2
D.
Explanation: Parallel lines have the same slopes, but different y intercepts.
Answer:
the slope of the red line is also -1/2
Step-by-step explanation:
How many solutions does the system have? x+2y=2 2x+4y=−8
Answer:
Step-by-step explanation:
x + 2y = 2
2x + 4y = -8
-2x - 4y = -4
2x + 4y = -8
0 not equal to -12
no solution
The red blood cell counts (in millions of cells per microliter) for a population of adult males can be approximated by a normal distribution, with a mean of million cells per microliter and a standard deviation of million cells per microliter. (a) What is the minimum red blood cell count that can be in the top % of counts? (b) What is the maximum red blood cell count that can be in the bottom % of counts?
Answer:
(a) Minimum red blood cells 5.744 million cells per micro liter
(b) Maximum red blood cells 5.068 million cells per micro liter.
Step-by-step explanation:
Z-score formula is = [tex]\frac{x-u}{Standard deviation}[/tex]
Z-score = [tex]\frac{x-5.5}{0.4}[/tex]
The value of z-score is 0.61 so then x will be;
x = 5.744
The minimum red blood cells count that can in top is 27% of count which is 5.744 million cells per micro liter.
Z-score = [tex]\frac{x-5.5}{0.4}[/tex]
The value of z-score is 0.14 so then x will be;
x = 5.068
The maximum red blood cells count that can be in top is 14% of count which is 5.068 million cells per micro liter.
the amount of gas in sarahs car is uniformly distributed between 1 and 16 gallons. Calculate the probability that the amount of gas is exactly 7 gallons
Answer:
The probability that the amount of gas in Sarah's car is exactly 7 gallons is 0.067.
Step-by-step explanation:
Let the random variable X represent the amount of gas in Sarah's car.
It is provided that [tex]X\sim Unif(1, 16)[/tex].
The amount of gas in a car is a continuous variable.
So, the random variable X follows a continuous uniform distribution.
Then the probability density function of X is:
[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b[/tex]
For a continuous probability distribution the probability at an exact point is 0.
So, to compute the probability that the amount of gas in Sarah's car is exactly 7 gallons use continuity correction on both sides:
P (X = 7) = P (7 - 0.5 < X < 7 + 0.5)
= P (6.5 < X < 7.5)
[tex]=\int\limits^{7.5}_{6.5} {\frac{1}{16-1}} \, dx \\\\=\frac{1}{15}\times |x|^{7.5}_{6.5}\\\\=\frac{1}{15}\times (7.5-6.5)\\\\=\frac{1}{15}\\\\=0.0666667\\\\\approx 0.067[/tex]
Thus, the probability that the amount of gas in Sarah's car is exactly 7 gallons is 0.067.
Solve for x: x/25 > 5
Answer:
x>125
Step-by-step explanation:
Answer:
x > 125
Step-by-step explanation:
Multiply each side by 25, so it now looks like this: x > 125I hope this helps!
Which is a factor of: 2x2+10x+8 ?
Answer:
2 ( x+4) ( x+1)
Step-by-step explanation:
2x^2+10x+8
Factor out 2
2 ( x^2 +5x+4)
What two numbers multiply to 4 and add to 5
4*1 = 4
4+1 = 5
2 ( x+4) ( x+1)
[tex] \large{ \underline{ \underline{ \bf{ \pink{To \: factorise}}}}}[/tex]
2x² + 10x + 8Factorisation:By middle term factorisation,
⇛ 2x² + 2x + 8x + 8
⇛ 2x(x + 1) + 8(x + 1)
⇛ (2x + 8)(x + 1)
⇛ 2(x + 4)(x + 1)
☃️ Now you can break it down and check which are the factors of the polynomial according to options.
━━━━━━━━━━━━━━━━━━━━
pls give answer
write down the literal coefficient of the monomial
Answer:
-2
Step-by-step explanation:
The coefficient of a term is literally the constant place before a variable. So in this monomial:
-2xy^2z^3
The coefficient would be -2.
Cheers.
Simply this question and get marked branlist
Answer:
13) 16d^8c^8
Other) 72n^-5r^-1
Step-by-step explanation:
13) 2x8=16
d^3*d^5=d^8
c^6*c^2=c^8
16d^8c^8
Other problem: (hard to read, so check my numbers)
8x9=72
n*n^-6=n^-5
r^-4*r^3=r^-1
72n^-5r^-1
Because she has limited shelf space, she can't put out all her copies of the CD at once. On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold. On Tuesday morning, she counted the number of copies left and then added that many more to the shelf. In other words, she doubled the number that was left in the display. At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday. On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday. Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty.
Now, it look like there is some information missing in the answer. The whole problem should look like this:
Alicia Keys's new album As I Am is climbing the charts, and the manager of Tip Top Tunes expects to sell a lot of copies. Because she has limited shelf space, she can't put out all her copies of the CD at once. On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold. On Tuesday morning, she counted the number of copies left and then added that many more to the shelf. In other words, she doubled the number that was left in the display. At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday. On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday. Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty. How many copies of the As I Am CD did she sell each day?
Answer:
She sold 24 copies of the cd each day.
Step-by-step explanation:
In order to solve this problem we must first set our variable up. In this case, since we need to know what the number of sold cd's per day is, that will just be our variable:
x= Number of copies sold.
So we can start setting our equation up. So we take the first part of the problem:
"On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold."
This can be translated as:
40-x
where this expression represents the number of copies left on the shelf by the end of monday.
"On Tuesday morning, she counted the number of copies left and then added that many more to the shelf."
so we represent it like this:
(40-x)+(40-x)
"In other words, she doubled the number that was left in the display."
so the previous expression can be simplified like this:
2(40-x)
"At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday."
so the expression now turns to:
2(40-x)-x this is the number of copies left by the end of tuesday.
"On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday."
this translates to:
3[2(40-x)-x]
This is the number of copies on the shelf by the begining of Wednesday.
"Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty."
this piece of information lets us finish writting our equation:
3[2(40-x)-x] -x = 0
since there were no copies left on the shelf, then the equation is equal to zero.
So now we proceed and solve the equation for x:
3[2(40-x)-x] -x = 0
We simplify it from the inside to the outside.
3[80-2x-x]-x=0
3[80-3x]-x = 0
we now distribute the 3 so we get:
240-9x-x=0
we combine like terms so we get:
240-10x=0
we move the 240 to the other side of the equation so we get:
-10x=-240
and divide both sides into -10 so we get:
x=24
so she sold 24 copies each day.
What is (2/3 x 3/5) - (3/4 x 1/6)
Answer:
2/3×3/5=2/3. 3/4×1/6=1/8
2/3-1/8=11/40
Answer:
[tex] \boxed{ \frac{11}{40} }[/tex]Step-by-step explanation:
[tex]( \frac{2}{3} \times \frac{3}{5} ) - ( \frac{3}{4} \times \frac{1}{6} )[/tex]
Reduce the numbers with Greatest common factor 3
⇒[tex] \mathsf{(2 \times \frac{1}{5} ) - ( \frac{1}{4} \times \frac{1}{2} )}[/tex]
Calculate the product
⇒[tex] \mathsf{( \frac{2}{5} )- ( \frac{1}{4} \times \frac{1}{2}) }[/tex]
Subtract the fractions
⇒[tex] \mathsf{ \frac{2 \times 8 - 1 \times 5}{40} }[/tex]
⇒[tex] \mathsf{ \frac{16 - 5}{40} }[/tex]
⇒[tex] \mathsf{ \frac{11}{40} }[/tex]
Hope I helped!
Best regards!
What is the distance between the coordinates (4,2) and (0,2)
Answer: Hi!
The distance between the coordinates (4,2) and (0,2) is 4 units.
The coordinates have the same location on the y axis, but the coordinates have different locations on the x axis. (4,2) is 4 units to the right of the x axis and 2 up on the y axis, while (0,2) goes just straight up to 2 on the y axis. If we graphed these, the two points would be aligned with each other, but a distance of 4 units would separate them horizontally.
Hope this helps!
Find the measure of each angle in Triangle ABC
Answer:
m<A = 133 degrees
m<B = 17 degrees
m<C = 30 degrees
Step-by-step explanation:
In a triangle, all the angles add up to 180 degrees.
So, adding all the angles gets us,
39x + 24
This equals 180 degrees so,
39x + 24 = 180
Subtract 24 from both sides,
39x + 24 - 24 = 180 - 24
39x = 156
Divide both sides by 39
x = 4
Now we have x = 4, we use this to plug in each equation of the angles.
m<A = 40(4) - 27 = 160 - 27 = 133
m<B = 25 - 2(4) = 25 - 8 = 17
m<C = 26 + 4 = 30
Two trains are moving towards each other on the same railroad track. From this track there's an offshoot piece of railroad − the length of which is shorter than the length of the train but longer than the length of one train car. How can the trains pass each other?
Answer:
The train on the course of moving to the side track has to be moving faster so the trains don't hit eachother.
Step-by-step explanation:
Laws of physics....
I dont understand this please help Which expression represents the area of the shaded region
Answer:
I'm gonna say C
The size of a television is the length of the diagonal of its screen in inches. The aspect ratio of the screens of older televisions is 4:3, while the aspect ratio of newer wide-screen televisions is 16:9. Find area of an older 35-inch television whose screen has an aspect ratio of 4:3
Greetings from Brasil...
The TV format is 4:3.
4 ÷ 3 = 1.33...
Let's assign the smallest side of the TV screen as X. Since the ratio between the sides is 4:3 = 1.33, then the other side (the largest) will be 1.33 times larger than the smaller side X, that is
smaller side = X
bigger side = 1.33X
The diagonal expression of the rectangle is:
D = √(base² + height²)
35" = √[(1.33X)² + X²]
35" = √(1.7689X² + X²) squaring both members
(35")² = 1.7689X² + X²
1225" = 2.7689X²
X² = 1225/2.7689
X² = 442.414
X = √442.414
X ≅ 21"
Tthe bigger side:
1.33X
1.33 · 21 ≅ 28"
Rectangle Area = base × height
Rectangle Area = 28 × 21
Rectangle Area = 588PLZ HLEP QUICK!!! Which of the following is an arithmetic sequence? -2, 4, -6, 8, ... -8, -6, -4, -2, ... 2, 4, 8, 16, ...
Answer:
-8, -6, -4, -2, ...
Step-by-step explanation:
-8, -6, -4, -2, ... is an arithmetic sequence: each new term is obtained by adding 2 to the previous term.
Answer:
-8, -6, -4, -2
Step-by-step explanation:
"An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence."
Hector's school is holding a fitness challenge. Student are encouraged to exercise at least 2 1/2 hours per week. Hector exercises about the same number of hours each week. During a 4-week period, he exercises for 11 1/2 hours. Hector wants to compare his exercise rate with the fitness challenge rate. How many hours per week does Hector exercise?
Hector outperformed the challenge rate as he exercised 2.88 hours a week.
It is best to convert the mixed fraction to decimals for easier calculation.
The students are encouraged to exercise 2¹/₂ hours per week. In decimals this is:
= 2 + ¹/₂
= 2 + 0.5
= 2.5 hours per week
In the 4 week period, Hector exercised 11¹/₂ hours which is:
= 11 + ¹/₂
= 11 + 0.5
= 11.5 hours
The number of hours he exercised per week is:
= Number of hours in total / Number of weeks
= 11.5 / 4
= 2.88 hours per week
When compared to the fitness challenge rate, we can conclude that Hector outperformed the challenge rate
Find out more at https://brainly.com/question/17951676.
Answer:
The answer is 2 7/8
5x+4(-x-2)=-5x+2(x-1)+12
Answer:
x=9/2
Step-by-step explanation:
Let's solve your equation step-by-step.
5x+4(−x−2)=−5x+2(x−1)+12
Step 1: Simplify both sides of the equation.
5x+4(−x−2)=−5x+2(x−1)+12
5x+(4)(−x)+(4)(−2)=−5x+(2)(x)+(2)(−1)+12 (Distribute)
5x+−4x+−8=−5x+2x+−2+12
(5x+−4x)+(−8)=(−5x+2x)+(−2+12) (Combine Like Terms)
x+−8=−3x+10
x−8=−3x+10
Step 2: Add 3x to both sides.
x−8+3x=−3x+10+3x
4x−8=10
Step 3: Add 8 to both sides.
4x−8+8=10+8
4x=18
Step 4: Divide both sides by 4.
4x/4=18/4
x=9/2
A research worker gave a scholastic aptitude test to a sample of eighth graders. Then he correlated the aptitude test scores with the chronological ages of the subjects. He found a correlation of - .42. How should this result be interpreted?
Answer: There is an moderate relationship between the aptitude test scores with the chronological ages of the subjects.
Step-by-step explanation:
The correlation coefficient tells about the strength and direction of the relation ship between any 2 variables. When the value of correlation coefficient lies between -0.5 to -0.3 or 0.3 to 0.5, then it indicates that there is moderate association between variables.Here , variables → aptitude test scores and chronological ages of the subjects.
Since correlation coefficient (-0.42) lies between -0.5 and -0.3 .
[-0.5< -0.42< -0.3]
That means there is an moderate relationship between the aptitude test scores with the chronological ages of the subjects.
In an opinion poll, 29% of 100 people sampled said they were strongly opposed to the state lottery. What is the approximate standard error of the sample proportion?
Answer:
The approximate standard error of the sample proportion is [tex]SE = 0.0454[/tex]
Step-by-step explanation:
From the question we are told that
The sample proportion is [tex]\r p = 0.29[/tex]
The sample size is n = 100
Generally the standard error of the sample proportion is mathematically represented as
[tex]SE = \sqrt{ \frac{ \r p (1- \r p )}{n} }[/tex]
substituting values
[tex]SE = \sqrt{ \frac{ 0.29 (1- 0.29 )}{ 100 } }[/tex]
[tex]SE = 0.0454[/tex]
Of 900 people surveyed, 480 were male and 410 had cell phones. Of those with cell phones, 290 were female. What is the probability that a person surveyed was either male or had a cell phone? A. 600/900 = 0.6667 B. 770/900 = 0.8556 C. 360/900 = 0.40 D. 820/900 = 0.9111
Answer:
C. 360/900 = 0.40
Step-by-step explanation:
The number of the males that are using cellphone and the females who are using cell phones are in total 410. The total people surveyed are 900 people. There are total 480 males and rest 420 are females. Among the 420 females there are 290 females who use cellphones. The probability for males can be given by 360/900.
Variable g is 8 more than variable w. Variable g is also 2 less than w. Which pair of equations best models the relationship between g and w? g = 8w g = w + 2 w = g + 8 w = g − 2 w = 8g w = g + 2 g = w + 8 g = w − 2
Answer: g = w + 8 g=w-2
Step-by-step explanation:
We could represent the word phrases by the equations.
g = w + 8
g = w - 2
Answer:
g = w + 8
g = w - 2
Step-by-step explanation:
Assuming that g and w exists, then we can show the relation as described:
"Variable g is 8 more than variable w."
g = w + 8
"Variable g is also 2 less than w."
g = w - 2
These are the two equations of the described relationship between g and w.
Note that g could not actually exist in the real number system:
g = w + 8
g = w - 2
w + 8 = w - 2
w - w = -2 - 8
0 != -10
This is impossible within the real number system.
Cheers.
Circle O has a circumference of approximately 28.3 cm. Circle O with radius r is shown. What is the approximate length of the radius, r? 4.5 cm 9.0 cm 14.2 cm 28.3 cm
Answer:
4.5cm
Step-by-step explanation:
Circumference = 2[tex]\pi[/tex]r
28.3=2[tex]\pi[/tex]r
28.3/2[tex]\pi[/tex]=r
4.456
The radius of the circle O is 4.5 cm.
What is radius?A radius is a measure of distance from the center of any circular object to its outermost edge or boundary.
Given that, a circle having a circumference of approximately 28.3 cm, we need to find its radius,
So, Circumference = 2 π × radius
2 π × radius = 28.3
Radius = 28.3 / 2π
Radius = 28.3 / 6.28
Radius = 4.5
Hence, the radius of the circle O is 4.5 cm.
Learn more about radius, click;
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Fresno County, California is the largest agricultural producing county in the country and almonds are an important crop with more than 99,000 acres harvested. Each acre produces about a ton of almonds and sold at a price of $4300 a ton. The Sagardia Brothers grew 600 acres of almonds . How many tons would the brothers sell if they priced the almonds at $4500 a ton?
Answer:
The brothers would not sell any ton.
Step-by-step explanation:
Facts we are given;
-Fresno coounty is the largest agriculture procuring county.
-It has harvested more than 99000 acres
-Fresno sold at $4300 a ton of almonds
For the Sagardia Brothers;
-Grew 600 acres of almond
- Sold at $4500 a ton of almonds
Now, from the given data, we can see that the price being sold by the brothers is higher than that of fresno county despite the fact that fresno is the biggest county producer in the country and as well has way more products in the market than the brothers.
Thus, the Brothers will likely not sell any product because the industry is price controlled and in addition to that, their prices are higher than the existing benchmark from county.
Also, the brothers don't even have the kind of name or quantity available from Fresno County.
The brothers sold 600 tons at a price of $2,700,000
Let x represent the number of tons of almonds produced by Sagardia Brothers and y represent the amount of money made.
Since 600 acres of almonds were farmed and each acre produces about a ton of almonds. Hence:
Total ton produced = 600 acres * 1 ton per acre = 600 tons
Each ton is priced at $4500 a ton, hence:
y = 600 tons * $4500 per ton
y = $2,700,000
The brothers sold 600 tons at a price of $2,700,000
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An article includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberry drink and another sample filled with cola.Beverage Sample Size Sample Mean Sample SDStrawberry Drink 10 537 22Cola 10 559 17Required:a. Does the data suggest that the extra carbonation of cola results in a higher average compression strength? Base your answer on a P-value.b. State the relevant hypotheses. c. Compute the test statistic value and find the P-value.d. State the conclusion in the problem context.e. What assumptions are necessary for your analysis?1. The distributions of compression strengths are approximately normal.2. The distributions of compression strengths have equal means. 3. The distributions of compression strengths are the same.4. The distributions of compression strengths have equal variances.
Answer:
Explained below.
Step-by-step explanation:
In this case we need to test whether the extra carbonation of cola results in a higher average compression strength.
(a)
The hypothesis for the test can be defined as follows:
H₀: The extra carbonation of cola does not results in a higher average compression strength, i.e. μ₁ - μ₂ = 0.
Hₐ: The extra carbonation of cola results in a higher average compression strength, i.e. μ₁ - μ₂ < 0.
(c)
Since the population standard deviations are not provided, we would use the t-test for difference between means.
The test statistic is:
[tex]t=\frac{\bar x_{1}-\bar x_{2}}{\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}}[/tex]
[tex]=\frac{537-559}{\sqrt{\frac{22^{2}}{10}+\frac{17^{2}}{10}}}\\\\=\frac{-22}{8.792}\\\\=-2.502[/tex]
The test statistic value is -2.502.
(c)
Compute the p-value as follows:
[tex]p-value=P(t_{16}<-2.052)=0.012[/tex]
*Use a t-table.
The p-value of the test is 0.012.
(d)
The significance level of the test is, c
p-value = 0.012 < α = 0.05.
The null hypothesis will be rejected.
Conclusion:
The data suggest that the extra carbonation of cola results in a higher average compression strength.
(e)
The assumption necessary for the analysis is:
The distributions of compression strengths are approximately normal.
The correct option is (A).
A cardboard box without a lid is to be made with a volume of 4 ft 3 . Find the dimensions of the box that requires the least amount of cardboard.
Answer:
2ft by 2ft by 1 ftStep-by-step explanation:
Total surface of the cardboard box is expressed as S = 2LW + 2WH + 2LH where L is the length of the box, W is the width and H is the height of the box. Since the cardboard box is without a lid, then the total surface area will be expressed as;
S = lw+2wh+2lh ... 1
Given the volume V = lwh = 4ft³ ... 2
From equation 2;
h = 4/lw
Substituting into r[equation 1;
S = lw + 2w(4/lw)+ 2l(4/lw)
S = lw+8/l+8/w
Differentiating the resulting equation with respect to w and l will give;
dS/dw = l + (-8w⁻²)
dS/dw = l - 8/w²
Similarly,
dS/dl = w + (-8l⁻²)
dS/dw = w - 8/l²
At turning point, ds/dw = 0 and ds/dl = 0
l - 8/w² = 0 and w - 8/l² = 0
l = 8/w² and w =8/l²
l = 8/(8/l² )²
l = 8/(64/I⁴)
l = 8*l⁴/64
l = l⁴/8
8l = l⁴
l³ = 8
l = ∛8
l = 2
Hence the length of the box is 2 feet
Substituting l = 2 into the function l = 8/w² to get the eidth w
2 = 8/w²
1 = 4/w²
w² = 4
w = 2 ft
width of the cardboard is 2 ft
Since Volume = lwh
4 = 2(2)h
4 = 4h
h = 1 ft
Height of the cardboard is 1 ft
The dimensions of the box that requires the least amount of cardboard is 2ft by 2ft by 1 ft
1.Find the value of x in the equation below
3^(2x+1)÷3^(3x-4)×3^(6-7x)=27x
2.Solve the equation 2^(x+y)=8 and 3^(x-y)=1 simultaneously
Answer:
Step-by-step explanation:
Hello, please consider the following.
Question 1.
[tex]\dfrac{3^{2x+1}}{3^{3x-4}\cdot 3^{6-7x}}=27^x\\\\<=> 3^{2x+1}\cdot 3^{-3x+4}\cdot 3^{-6+7x}=3^{2x+1-3x+4-6+7x}=(3^3)^x=3^{3x}\\\\<=> 2x+1-3x+4-6+7x=3x\\\\<=> 6x-1=3x\\\\<=> 3x=1\\\\<=> \boxed{x=\dfrac{1}{3}}[/tex]
Question2.
[tex]2^{x+y}=8=2^3 <=>x+y=3\\\\3^{x-y}=1=3^0<=>x-y=0[/tex]
So, it gives (by adding the two equations) 2x = 3
[tex]\boxed{x=\dfrac{3}{2} \ \ and \ \ y = x = \dfrac{3}{2} }[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
The diameter of Earth’s moon is on average m. Use the formula to find the approximate surface area. (Use 3.14 for the value of .) (SHOW WORK)
Answer:
Surface Area = 4(3.14)((m/2)^2)
Step-by-step explanation:
The formula of surface area is 4(3.14)(r^2)
where r is the radius
We are given the diameter M which is just the radius times 2. So to find the radius we divide m by 2. So our radius is m/2.
If a cube has an edge of 2 feet. The edge is increasing at the rate of 6 feet per minute. How would i express the volume of the cube as a function of m, the number of minutes elapsed. V(m)= ??
Answer:
v(m) = 8 + 48m+ 180m² +216m³
Step-by-step explanation:
Let's first of all represent the edge of the the cube as a function of minutes.
Initially the egde= 2feet
As times elapsed , it increases at the rate of 6 feet per min, that is, for every minute ,there is a 6 feet increase.
Let the the egde be x
X = 2 + 6(m)
Where m represent the minutes elapsed.
So we Al know that the volume of an edge = edge³
but egde = x
V(m) = x³
but x= 2+6(m)
V(m) = (2+6m)³
v(m) = 8 + 48m+ 180m² +216m³
The volume of cube as function of m is, [tex]V(m)=72m[/tex]
Let us consider that edge of cube is a feet.
Since, The edge is increasing at the rate of 6 feet per minute.
[tex]\frac{da}{dt}=6feet/min.[/tex]
Volume of cube , V = [tex]a^{3}[/tex]
[tex]\frac{dV}{dt} =3a^{2} \frac{da}{dt}[/tex]
Substituting the value of da/dt in above equation.
We get, [tex]\frac{dV}{dt}=3a^{2}*(6) =18a^{2} \\\\dV=18a^{2}dt[/tex]
Integrating on both side.
[tex]V=18a^{2}t[/tex]
Since, number of minutes elapsed is m.
Substitute , t = m and a = 2 feet in above equation.
We get, [tex]V=18(2)^{2}*m=72m[/tex]
Thus, the volume of cube as function of m is, [tex]V(m)=72m[/tex]
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