Answers:
[tex](f+g)(\text{x}) = \boldsymbol{2\text{x}^2+2\text{x}-12}[/tex]
Domain = set of all real numbers
========================================================
Work Shown:
[tex](f+g)(\text{x}) = f(\text{x})+g(\text{x})\\\\(f+g)(\text{x}) = (2\text{x}^2+\text{x}-11)+(\text{x}-1)\\\\(f+g)(\text{x}) = 2\text{x}^2+\text{x}-11+\text{x}-1\\\\(f+g)(\text{x}) = 2\text{x}^2+(\text{x}+\text{x})+(-11-1)\\\\(f+g)(\text{x}) = 2\text{x}^2+2\text{x}-12\\\\[/tex]
The domain of each f(x) and g(x) is "set of all real numbers" since we can replace x with any real number to get some output.
By extension, this means the domain of (f+g)(x) is also "set of all real numbers".
It turns out any polynomial will have this domain. We don't have to worry about things like applying square roots to negatives, or dividing by zero. This is why there isn't a restriction on x.
To write "set of all real numbers" in interval notation, we would say [tex](-\infty, \infty)[/tex] to indicate x is anything between negative infinity and positive infinity.
What is the remainder when f(x) = x3 + 5x2 –32x – 7 is divided by x – 4? Show your work.
The remainder of f(x) is 385.
What are the 5 steps of long division?
The five steps of long division are given by:
Step 1: Divide
Step 2: Multiply
Step 3: Subtract
Step 4: Bring down
Step 5: Repeat
Given,
f(x) = x3 + 5x2 –32x – 7 is divided by x – 4
To find the Remainder
Now, The solution is:
[tex]x^{2} -9x+98[/tex]
[tex]x-4\sqrt{x^3+5x^2-32x-7}\\[/tex]
[tex]x^{3} - 4x^2[/tex]
- +
-----------------------------
[tex]9x^{2} -32x[/tex]
[tex]9x^{2} +36x[/tex]
- -
-------------------------------
98x -7
98x - 392
- +
----------------------------------
Remainder 385
Hence, The remainder of f(x) is 385.
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The ordered pair (a,b) satisfies the inequality y
A. If you subtract 6 from b, it will be less than or equal to a.
B. If you add 6 to a, it will be greater than b.
C. a is greater than b.
D. If you add 6 to a, it will be less than b.
The false statement about the statement is (a) If you subtract 6 from b, it will be less than or equal to a.
How to determine the true statement?From the question, the inequality is given as
y > x - 6
The ordered pair is given as
(a, b)
The above ordered pair implies that
(x, y) = (a, b)
So, we have
x = a and y = b
This means that
b > a - 6
Subtract 6 from both sides
b - 6 > a - 6 - 6
Evaluate
b - 6 > a - 12
Using the above as a guide, we cannot determine the direct relationship between variables a and b.
However, it is false that b is less than a
Hence, the false statement is (a)
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Complete question
The ordered pair (a,b) satisfies the inequality y > x - 6
Which statement is NOT true?
A. If you subtract 6 from b, it will be less than or equal to a.
B. If you add 6 to a, it will be greater than b.
C. a is greater than b.
D. If you add 6 to a, it will be less than b.
Quadrilateral EFGH is inscribed inside a circle as shown below. Write a proof showing that angles H and F are supplementary.
Given
Find
showing that angles H and F are supplementary.
Explanation
Let angle F , which is subtended by minor arc GHE.
so , angle F = half of angle GHE by subtended angle theorem.
similarly , angle H is the angle subtended by major arc GFE.
so , angle H = half of the angle subtended by major arc.
since , total angle around J is 360 degree.
as we know , the sum of angle subtended by minor arc and major arc is 360 degree.
so , angle F + angle H = 1/2(360) = 180 degree.
Final Answer'
Hence , H and F are supplementary angles.
The angle a lies between 0° and 90° and is such that
2 tan²a + sec²a = 5-4 tana
Show that
3 tan²a +4 tana -4 = 0
and hence find the exact value of tan a
11-(15g-13)=-6
what does G stand for
Answer:
g = 2
Step-by-step explanation:
11- (15g - 13) = - 6 ( subtract 11 from both sides )
- (15g - 13) = - 17 ( multiply both sides by - 1 )
15g - 13 = 17 ( add 13 to both sides )
15g = 30 ( divide both sides by 15 )
g = 2
Tea that sells for $2.00 a pound is mixed with a different tea that sells for
$5.00 a pound to produce 40 pounds of a custom blended tea that will
sell for $4.25 a pound. How many pounds of the less expensive tea
should be used in the mixture?
(1) 10
(2) 15
(3) 25
(4) 30
Pls show work pls show work pls show work pls show work
10 pounds of less expensive tea should be used in the mixture.
How to find the less expensive tea price?Inferior tea price = $2.00
Superior tea price = $5.00
Blended tea price = $4.25
Solution:
Price of 40 pounds of a custom blended tea = $4.25 * 40 = $170
Let x be the inferior tea quantity and
(40 - x) be the superior tea quantity.
2x + 5(40 - x) = 4.25 * 40
2x + 200 -5x = 170
-3x = -30
x = 10
Therefore, 10 pounds of less expensive tea should be used in the mixture.
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-26, 174, 374, 574, …
Find the explicit and recursive formula.
The explicit formula and the recursive formula are aₙ₋₁ + 200 and the rest is mentioned below.
What does explicit and recursive formula mean?A formula can be either recursive or explicit. The main difference between Recursive and Explicit is that Recursive formula gives the value of a specific term based on the previous term while Explicit formula gives the value of a specific term based on the position.
Given : a₁ = -26, a₂ = 174, a₃ = 374, a₄= 574
The common difference that is d can be found out by
thus d = a₂ - a₁ = 174 -(- 26 ) = 174 + 26 = 200
And this is same for all the numbers of this particular sequence.
Thus aₙ = aₙ₋₁ + d
= aₙ₋₁ + 200
Recursive formula : aₙ₋₁ + d
That is the following sequence will have a common difference of 200 and the next 5th, 6th, 7th and nth term is going to be .
774 , 974 ... etc
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When driving up a certain hill, you rise 15 feet for every 1000 feet you drive forward. What is the slope of the rode?
slope of the rode is 0.015.
What is slope of line ?
Slope of line is the angle made by the line from positive x-axis in anticlockwise direction, it also denoted the steepness of the line.
The point with coordinate having same slope as with given coordinates can be plotted on the same line.
Here, it is given that :
When driving up a certain hill, we rise 15 feet for every 1000 feet that is :
for 15 feet up = 1000 feet forward
Now,
slope = upward distance / horizontal distance covered
slope = 15/1000
slope = 0.015
slope is a unitless quantity.
Therefore, slope of the rode is 0.015.
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I NEED HELP WITH MY HOMEWORK
Chester made 9 sales and Vickie made 16 sales this week
Base salary of Vickie = $70
Vickie's commission per sale = $24
Base salary of Chester = $142
Chester's commission per sale = $9
Both people earned the same amount this week. Let x represent the number of sales made by Vickie, then sales made by Chester is x+7
Formulating the equation we get:
Base salary of Vickie + Vickie's commission per sale*Number of sales = Base salary of Chester + Chester's commission per sale*Number of sales
= 70 + 24x = 142 + 9(x+7)
70+24x = 142+9x+63
70+24x = 205+9x
15x = 135
x = 9
Chester sales = 9
Vickies sales = 9+7 = 16
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44+400 divided by (4+62)-24
Answer:
185
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
250
244
18
10
are one of the answers
give this 5 stars if correct
Let g(x) = |2x - 10| find g(-3)
Answer:
g(-3) = 16
Step-by-step explanation:
To find g(-3), we need to plus -3 into the given function. So, g(-3) = |2(-3) - 10|. Now we solve using PEMDAS. Two times -3 is -6, then we have g(-3) = |-6-10| which is essentially g(-3) = |-16|. Lastly, we take the absolute value of |-16| which is just 16, therefore g(-3) = 16.
A ball is thrown in the air the function H = 30t-5t^2 can be used to find the height (h) of the ball in meters after t seconds. how long does it take the ball to reach a height of 45 meters?
The most appropriate choice for Distance will be given by:
The ball takes [tex]3s[/tex] to reach a height of [tex]45[/tex] [tex]m[/tex].
What is Distance?
The length of the path an object takes without taking into account the direction of motion of the object is known as distance.
If [tex]s[/tex] is the speed of the object and [tex]t[/tex] is the time, then
Distance = [tex]s \times t[/tex]
Here,
[tex]H(t) = 30t - 5t^2[/tex], [tex]t[/tex] is the time in seconds
For finding the time taken by the ball to reach a height of [tex]45[/tex][tex]m[/tex], we need to substitute [tex]H(t) = 45[/tex]
Now putting [tex]H(t) = 45[/tex]
[tex]45 = 30t - 5t^2\\5t^2 - 30t+45 = 0\\ 5(t^2 -6t + 9)=0\\t^2 -6t+9=0\\t^2-3t-3t+9=0\\t(t-3)-3(t-3)=0\\(t-3)(t-3)=0\\t-3 = 0\\t = 3s[/tex]
So the ball takes [tex]3s[/tex] to reach a height of [tex]45[/tex] [tex]m[/tex].
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I have missing work may someone help me with my math
2)
[tex]w^2-3,\quad w=4[/tex]When we say that w = 4, it means that we can rewrite the expression and instead of "w", we will put "4", so
[tex]w^2-3\Rightarrow4^2-3[/tex]Now we have a numerical expression to solve, we can easily solve it!
[tex]\begin{gathered} 4^2-3 \\ \\ 4\cdot4-3 \\ \\ 16-3 \\ \\ 13 \end{gathered}[/tex]Therefore, the final answer is
[tex]4^2-3=13[/tex]5)
Here we will do the same thing, the "hard" part is solving the numeric expression, it will be a little bit harder than the 2).
[tex]3(6m-17),\quad m=5[/tex]Again, repeat the same process, rewrite the expression, and instead of "m" you put "5"
[tex]3(6m-17)\Rightarrow3(6\cdot5-17)[/tex]Again, another expression to simplify, remember that we always solve what is inside ( ) first, and we have a multiplication inside ( ) so we must solve it first
[tex]3(6\cdot5-17)=3(30-17)[/tex]Now we solve the multiplication inside ( ) we can do the subctration
[tex]3(30-17)=3\cdot(13)[/tex]The last step is just to solve another multiplication
[tex]3\cdot(13)=39[/tex]Now we simplified everything we can have the final answer:
[tex]3(6\cdot5-17)=39[/tex]6)
Here we have a division, but it's similar with 5) and 2), we have
[tex]\frac{2a}{3}+13,\quad a=15[/tex]No secrets, repeat the process, but here, "a" will turn into "15", then
[tex]\frac{2a}{3}+13\Rightarrow\frac{2\cdot15}{3}+13[/tex]We can do the multiplication at the numerator of the fraction
[tex]\frac{2\cdot15}{3}+13=\frac{30}{3}+13[/tex]Now we can simplify the fraction, 30 divided by 3 is 10, then
[tex]\frac{30}{3}+13=10+13[/tex]Now just do the sum and it's done!
[tex]10+13=23[/tex]Hence the final answer is
[tex]\frac{2\cdot15}{3}+13=23[/tex]ANSWERS:
1) 43
2) 13
3) 67
4) 12
5) 39
6) 23
Rodney is flying on an airplane to puerto rico. his suitcase and the contents inside must weigh less than 50lbs. his suitcase weighs 4 pounds and the contents he wants to pack weigh 49 pounds. if each of his shirts weighs 0.75 pounds, write an inequality to represent the number of shirts he needs to remove to meet the flight requirements.
The inequality that represents, the number of shirts he needs to remove to meet the flight requirements is 0.75p + 50ibs ≤ 49
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.
Let the weight of Rodney suitcase be p
First the contents inside must weigh less than 50lbs.
x < 50
The suitcase weighs 4 pounds and the contents he wants to pack weigh 49 pounds.
0.75p < 49
Therefore, 0.75p + 50ibs ≤ 49
The inequality that represents, the number of shirts he needs to remove to meet the flight requirements is 0.75p + 50ibs ≤ 49
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Write an equation for the intervals of a parabola with x-intercepts at (2,0) and and (-5,0) that passes through the point (1, -18).
Help is always greatly appreciated.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y= 3 {x}^{2} + 9x - 30[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The values of x where a parabola cuts the x - axis (y = 0) are the roots of the quadratic equation.
I.e -5 and 2 for the given problem.
and the equation can be represented as :
[tex]\qquad\displaystyle \tt \rightarrow \: y = a(x - x1)(x- x2)[/tex]
where, x1 and x2 are the roots of the quadratic equation, a is a constant value (depicting strech in curve)
Now, plug in the values :
[tex]\qquad\displaystyle \tt \rightarrow \: y= a(x- 2)(x - ( - 5))[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = a(x- 2)(x+ 5)[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = a( {x}^{2} + 5x - 2x - 10)[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y= a( {x}^{2} + 3x - 10)[/tex]
Now, we need to find the value of a, for that let's use the coordinates of a point lying on the curve (1 , -18)
[tex]\qquad\displaystyle \tt \rightarrow \: - 18 = a( {1}^{2} + 3(1) - 10)[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: - 18 = a(1 + 3 - 10)[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: - 18 = a( - 6)[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: a = ( - 18) \div ( - 6)[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: a = 3[/tex]
Now, we got all required values. let's plug the value of a in equation, and we will get the required equation of parabola.
[tex]\qquad\displaystyle \tt \rightarrow \: y= 3( {x}^{2} + 3x - 10)[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y= 3 {x}^{2} + 9x - 30[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
[tex]\textsf{Factored form}: \quad f(x)=3(x-2)(x+5)[/tex]
[tex]\textsf{Standard form}: \quad f(x)=3x^2+9x-30[/tex]
Step-by-step explanation:
Factored form of a quadratic function
[tex]f(x)=a(x-p)(x-q)[/tex]
where:
p and q are the x-intercepts.a is some constant.Given x-intercepts:
(2, 0)(-5, 0)Substitute the given x-intercepts into the formula:
[tex]\implies f(x)=a(x-2)(x+5)[/tex]
To find a, substitute the given point (1, -18) into the equation and solve for a:
[tex]\implies -18=a(1-2)(1+5)[/tex]
[tex]\implies -18=a(-1)(6)[/tex]
[tex]\implies -6a=-18[/tex]
[tex]\implies a=3[/tex]
Therefore, the equation of the function in factored form is:
[tex]\boxed{ f(x)=3(x-2)(x+5)}[/tex]
Expand the brackets:
[tex]\implies f(x)=3(x^2+3x-10)[/tex]
[tex]\implies f(x)=3x^2+9x-30[/tex]
Therefore, the equation of the function in standard form is:
[tex]\boxed{f(x)=3x^2+9x-30}[/tex]
Which represents the inverse of the function f(x) = 4x?
Oh(x)=x+4
Oh(x)=x-4
Oh(x) = 3/4x
○ h(x) = 1/4x
Answer:
(d) h(x) = 1/4x
Step-by-step explanation:
You want to know the inverse of the function f(x) = 4x.
Inverse functionThe inverse of y = f(x) will be the solution to x = f(y).
x = f(y)
x = 4y . . . . . . substitute the argument in the function definition
x/4 = y . . . . . divide by 4 to solve for y
The inverse function is ...
h(x) = (1/4)x
The point B divides AC in the ratio 2:3.
Work out vector OC in terms of a and b.
Simplify your answer.
It is said that the ratio of point B to point AC is 2: 3.
This implies;
BC/AB = 3/2
BC = 3(b - a)/2
Thus;
AB + BC Equals AC
AC equals b-a plus 3(b-a)/2.
b-a - 3b/2 - 3a/2 = AC
AC = 5b/2 - 5a/2
AC = ⁵/₂(b - a) (b - a)
Using the same vector addition law, we can state that;
OC = AC – AO
OC = ⁵/₂(b - a) - (-a) (-a)
Given that giving OA is the inverse of -a, I used -a for AO.
Thus;
OC = 5b/2 - 5a/2 + a
OC = (⁵/₂)b - (³/₂)a
OC = ¹/₂(5b - 3a) (5b - 3a)
What is vector addition law?
Objects with both direction and magnitude are referred to be vectors. When two vectors have the same magnitude and direction, they are deemed to be one and the same. A line and an arrow are used to symbolize these geometrical objects. This arrow points in the direction of the vector, and the line's length indicates the vector's magnitude. These arrows, therefore, have a starting point and an ending point. Physical quantities like velocity, displacement, and acceleration are represented by vectors.
Notation A vector is frequently written in bold letters, such as an or b.
As seen on the right side, a vector may alternatively be expressed as the letters for its head and tail with an arrow above it.
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Solve for x Correct Answers PLS show work
Answer:
x = 8
Step-by-step explanation:
The angles shown are vertical angles
Vertical angles are congruent (equal to each other)
This means that 8x + 36 = 5x + 60
Using this equation we can solve for x
8x + 36 = 5x + 60
==> subtract 36 from both sides
8x = 5x + 24
==> subtract 5x from both sides
3x = 24
==> divide both sides by 3
x = 8
Answer:
8x + 36 = 5x + 60
8x = 5x + 24
3x = 24
x = 8
What percent of 933 is 391.83?
Answer:
42%
Tell me if you need expalining!
Step-by-step explanation:
Solve the inequality. Graph the solution. |8x−8|≤24
The solution of the given inequality would be x = 4. the graph of the given inequality is attached below.
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
Given the inequality as |8x−8|≤24.
For solving the given expression,
|8x−8|≤24
We can consider the expression as;
8x−8 = 24
8x = 24 + 8
8x = 32
x = 32/8
x = 4
Hence, the solution of the given inequality would be x = 4.
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-15 = -3/4w solve for w and simplify your answer as much as possible
Answer:
w = 20
Step-by-step explanation:
a) Flip the equation.
-3/4 w = -15
b) Multiply both sides by 4/(-3).
(4/-3) * (-3/4 w) = (4/-3) * (-15)
w = 20
On Wednesday, they pick a total of 89 kg of strawberries.
The mean mass of each strawberry is 22 g.
Work out the number of strawberries they picked.
Give your answer correct to the nearest 10
The number of strawberry they picked is about 4050.
What does math division mean?Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.
89 kg = 89000 g conversion
89000=22=4045.45 ≈4045
{unit conversion}
≈4050
The number of strawberry {nearest lo} is about 4050
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your company is producing special battery packs for the most popular toy during the holiday season. the life span of the battery pack is known to be normally distributed with a mean of 250 hours and a standard deviation of 20 hours. what is the probability that a randomly chosen battery pack lasts longer than 260 hours?
The probability that a randomly chosen battery pack lasts longer than 260 hours is 0.69.
What is a normal distribution?
The normal distribution is a probability distribution that is symmetric about the mean and demonstrates that data that are closer to the mean are more likely to occur than data that are farther from the mean.
Since the life span of the battery pack is known to be Normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = life spans of battery packs.
µ = mean life span
σ = standard deviation
From the information given,
µ = 250 hours
σ = 20 hours
The probability that a battery pack lasts longer than 260 hours. It is expressed as
P(x > 260) = 1 - P(x ≤ 260)
For x = 260
z = (260 - 250)/20 = 0.5
Looking at the normal distribution table, the probability corresponding to the z score is 0.69
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The probability that a randomly chosen battery pack lasts longer than 260 hours is 0.69.
What is a normal distribution?
The normal distribution is a probability distribution that is symmetric about the mean and demonstrates that data that are closer to the mean are more likely to occur than data that are farther from the mean.
Since the life span of the battery pack is known to be Normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = life spans of battery packs.
µ = mean life span
σ = standard deviation
From the information given,
µ = 250 hours
σ = 20 hours
The probability that a battery pack lasts longer than 260 hours. It is expressed as
P(x > 260) = 1 - P(x ≤ 260)
For x = 260
z = (260 - 250)/20 = 0.5
Looking at the normal distribution table, the probability corresponding to the z score is 0.69
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A plane (at point P) sees a bridge (at point B) at an angle of depression on 28 degrees. The horizontal distance between the plane and the bridge is 3000 feet. Explain which trigonometric equation can be used to solve for the height of the plane (segment PA). What is the height of the plane? You must show all work and calculations to receive full credit. Round your answer to the nearest foot.
The height of the plane PA is given as; 1591 ft
How to use trigonometric ratios?
There are different trigonometric ratios such as;
cos θ = adjacent/hypotenuse
sin θ = opposite/hypotenuse
tan θ = opposite/adjacent
Now, looking at the given image showing plane and bridge indicated by lines, we can use one of the trigonometric ratios to get the height of the plane PA as;
PA/3000 = tan B
now angle B = 28 degrees from alternate angles postulate. Thus;
PA/3000 = tan 28
PA = 3000 * tan 28
PA = 3000 * 0.5317
PA = 1591 ft
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[tex]tan 28^o = \frac{PA}{3000}[/tex]
tan 28° · 3000= PA
(use a scientific calculator)
1595.128= PA
height = 1595
Nelson has half of his investments in stock paying a 6% dividend and the other half in a stock paying 9% interest. if his total annual interest is $660 how much does he have invested?
Given:
percent of dividend = 6%
percent of interest = 9%
Total annual interest = $ 660
Let the amount invested in both stocks be x and y.
Annual interest on 6% dividend gives:
[tex]\begin{gathered} =\text{ }\frac{6}{100}\text{ }\times\text{ x} \\ =\text{ 0.06x} \end{gathered}[/tex]Annual interest on 9% interest rate:
[tex]\begin{gathered} =\text{ }\frac{9}{100\text{ }}\times\text{ y} \\ =\text{ 0.09y} \end{gathered}[/tex]The total annual interest is $ 660. We can write:
[tex]0.06x\text{ + 0.09y =660}[/tex]We are given that Nelson divided his investment in half. This implies:
[tex]x\text{ = y}[/tex]Substituting, we have:
[tex]\begin{gathered} 0.06x\text{ + 0.09x = 660} \\ 0.15x\text{ = 660} \end{gathered}[/tex]Divide both sides by 0.15:
[tex]\begin{gathered} \frac{0.15x}{0.15}\text{ = }\frac{660}{0.15} \\ x\text{ = 4400} \end{gathered}[/tex]Hence, the amount Nelson has invested:
[tex]\begin{gathered} x\text{ = y = 4400} \\ \text{Amount invested = 4400 + 4400} \\ =\text{ 8800} \end{gathered}[/tex]Answer:
Nelson has $4400 invested in each investment
Determine whether the two figures are similar.
The two triangles are similar.
How to find similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
The side lengths of two similar triangles are proportional. That is, if ΔABC is similar to ΔDEF , then the following equation holds:
AB / DE = AC / DF = BC / EF
Hence,
6 / 3 = 10 / 5 = 8 / 4 = 2 / 1
This common ratio is called the scale factor .
The symbol ∼ is used to indicate similarity.
Therefore, the triangles are similar.
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a playground is rectangular and the length is 7/8 miles. if the area is 8/20 what is the width?
Answer:
so the width is 16/35 miles
Step-by-step explanation:
Length - 7/8 miles
Area - 8/20 miles
we know from the equation that area = Length x width
we need to rearrange so the width = Area ÷Length
width = 8/20 ÷ 7/8
= 8/20 × 8/7
= 16/35
chegg a spherical ball is measured to have a radius of 5 mm, with a possible measurement error of 0.1 mm. use the differential to estimate the possible change in volume (in mm3) resulting from the error in measuring the radius.
The possible change in volume that results from the error in measuring the radius is 32. 06 millimeters
How to determine the volume of the sphereIt is important to note that the formula for volume of a sphere is expressed by;
Volume = 4/3 πr³
Given that;
r is the radius of the sphereπ has the value 3.14Based on the information given, we have the measure of the radius to be 5 mm, with a possible measurement error of 0.1 mm
The original value of radius = 5mm
Radius after the measurement error = 5 + 0. 1 = 5. 01mm
Let's substitute the values into the formula
Volume = 4/ 3 (3.14)(5)³
We then expand the bracket
Volume = 4/ 3 (392.5)
Volume = 523. 3 cubic millimeters
For radius of the measurement error = 5.01mm
Volume = 4/ 3 (3.14)(5.1)³
Then, expand the bracket
Volume = 4/3 (416.52)
Volume = 555. 4 cubic millimeters
Change in volume = 555. 4 - 523. 3 = 32. 06 cubic millimeters
Hence, the change in volume is given as 32. 06 cubic millimeters
Learn more about volume here:
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What is (9^6 x7^-9)^-4=
Answer:
[tex] \dfrac{7^{36}}{9^{24}} [/tex]
Step-by-step explanation:
(9^6 x7^-9)^-4=
[tex] = (9^6 \times 7^{-9})^{-4} [/tex]
[tex] = 9^{-24} \times 7^{36} [/tex]
[tex] = \dfrac{7^{36}}{9^{24}} [/tex]
You have exactly 10 coins with a total
value is $1. Three of the coins are
quarters. What are the remaining coins?
The
Answer:
2 dimes and 5 pennies
Step-by-step explanation:
2 dimes (d) is 10 and 5 pennies (p) is 5
75+p+d=100
75+p=80
80+d=100
Answer: 3 quarters, 2 dimes, 1 nickel.
Step-by-step explanation: 3 quarters are worth 75 cents, 2 dimes are worth 20 cents, and 1 nickel is worth 5 cents! Hope this helps