The provided integral may be expressed as follows using the following statement as a guide: 128/3 - 31 [tex]\sqrt{17}[/tex] /3
What is the definition of an integral?An integral in mathematics is either a number that depicts the area underneath the graph of a function over a specific period of time or a about before, the reversed of which includes the initial result (indefinite integral). To complete the whole, an essential component is required. The term crucial is a close synonym in this context. Integrals of functional and equations are a concept in mathematics. The word "aal" is derived from Middle English, which is derived from Latin Word integralis "thinking up unity," from Latin "with, entire."
To find [tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r$[/tex]
Put [tex]$16+r^2=t^2$[/tex]
[tex]$2 r d r=2 t d t$[/tex]
[tex]$r d r=d t$[/tex]
[tex]$r=0 \Rightarrow t=4$[/tex]
[tex]$r=1 \Rightarrow t=\sqrt{17}$[/tex]
[tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r=\int_4^{\sqrt{17}} \frac{t^2-16}{t} t d t$[/tex]
[tex]$=\left[\frac{t^3}{3}-16 t\right]_4^{\sqrt{7}}$[/tex]
[tex]$=\frac{(\sqrt{17})^3}{3}-16(\sqrt{17})-\frac{(4)^3}{3}+64$[/tex]
[tex]$=\frac{128}{3}-\frac{31 \sqrt{17}}{3}$[/tex]
[tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r=\frac{128}{3}-\frac{31 \sqrt{17}}{3}$[/tex]
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You go to a store to buy clothes. Shirts cost $10.25 each, and pants cost $17 each. Let x equal the number of shirts and y equal the number of pants you buy. You can only spend up to $50 at the store. Write an inequality that represents the number and each type of clothing you can buy.
The inequality which represents the number and each type of clothing you can buy is 10.25x + 17y ≤ 50
What does this inequality represent?This inequality represents the maximum amount of money you can spend at the store, given the cost of shirts and pants, and the number of each type of clothing you buy.
The x represents the number of shirts, and the y represents the number of pants. The inequality states that the total cost of the shirts (10.25x) plus the total cost of the pants (17y) must be less than or equal to $50.
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality.
Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
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given this information, in order to use her 4 hours of time spent studying to get the highest possible test score, how many hours should she have spent solving multiple choice problems, and how many hours should she have spent reviewing lecture notes? 0 hours working on problems, 4 hours reading 2 hours working on problems, 2 hours reading 3 hours working on problems, 1 hour reading 4 hours working on problems, 0 hours reading
The most effective way to use her 4 hours of study time to get the highest possibility or probability of test scores would be to spend 4 hours working on multiple-choice problems and 0 hours reviewing lecture notes.
From the information given, it is clear that working on multiple-choice problems is the most effective way to improve her test score. Therefore, the highest possibility or probability of test scores would be achieved by spending the most time working on multiple-choice problems.
The available time for studying is 4 hours, so the maximum time that can be spent working on multiple-choice problems is 4 hours. If she spends 4 hours working on multiple-choice problems, she will not have any time left to review lecture notes.
So, the most effective way to use her 4 hours of study time to get the highest possible test score would be to spend 4 hours working on multiple-choice problems and 0 hours reviewing lecture notes.
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9. The distance between a helicopter and its landing pad is 193 m. If the angle of
depression to its landing pad is 27° to its landing pad, at what altitude (height) is the
helicopter flying? Round your answer to the nearest whole number. [3 marks]
193 m
xm
Landing Pad
Using trigonometric ratio and the angle of depression, the altitude of the plane is 98m
What is Angle of DepressionThe angle of depression is an angle formed by a horizontal line and a line of sight from a point above that line to an object below that line. It is used in trigonometry to calculate the distance between the observer and the object of interest.
Using trigonometric ratio, we can calculate the height or altitude which the plane is flying.
Data;
angle = 27 degreesdistance = opposite = 193,height/ altitude = adjacent = xUsing tangent of the angle;
tan θ = opposite / adjacent
tan 27 = x / 193
x = 193 * tan27
x = 98m
The altitude is 98m
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Complete multiplication sentence
8/2=8 x 1/?
Answer:
1/2
Step-by-step explanation:
i hope it helps you all
The test scores for 9 students on the Unit 1 Test were 35, 25, 50, 95, 80, 60, 45, 100, and 90. What is the
value of the third quartile for this data set?
OA. 85
OB. 90
OC 92.5
OD. 95
The answer reads "40," is the correct response to the earlier question.
What is median ?
The value of the middle observation found after the data are arranged in ascending order is referred to as the median of the data. In many cases, it is challenging to take all of the facts into account when representing something, and in these cases, median is helpful. The median is one of the simple to compute statistical summary metrics. The median is also known as the place average since it uses the data that is in the centre of a sequence to determine its value.
There are data of 9 students and we need to arrange them in ascending order to find our answer.
So, the arrangement looks like the following:
⇒ 25, 35, 45, 50, 60, 80, 90, 95, 100
We are aware that
In all cases, the middle value is the median.
Therefore, it is safe to say that the Median of the aforementioned arrangement is 60.
Hence, Median of the numbers on the left of the median is 60=35+45/2 = 40
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A group of individuals containing b boys and g girls is lined up in random order: that is, each of the (b + g)! permutations is assumed to be equally likely. What is the probability that the person in the i^th position, 1 lessthanorequalto i lessthanorequalto b + g is a girl?
The probability is g / (b + g).
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are.
Let Gi be the event that the person in the ith position is a girl.
let the simple space S is all the ways to order (b + g) people, where b for boys and g for girls.
then, P(Gi) = [tex]\frac{|Gi|}{|s|}[/tex]
|s| = (b + g)! / b! g!
for the purpose of this problems, individuals of the same sex are indistinguishable.
since, if we put a girl in the ith position, the other (b + g - 1) positions can be filled in randomly.
|Gi| = (b + g - 1)! / (g - 1)! b!
then, P(Gi) = [tex]\frac{|Gi|}{|s|}[/tex]
P(Gi) = [ (b + g - 1)! / (g-1)! b! ] / [ (b + g)! / b! g! ]
P(Gi) = g / (b + g)
Therefore, the probability is g / (b + g).
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Can someone please help me
In the rectangle given, the values of x and m<VUT are;
i. x = 6
ii. m<VUT = 64^o
Properties of a rectangle.A rectangle is a plane figure which is a family of quadrilateral since it has four straight sides. It has some properties which are:
i. the diagonals are equal and divides it into two equal parts
ii. the opposite sides are equal in length
iii. the measure its internal angles are right angle
These properties can be used to determine the values required in the given question.
i. RT = SU = 5x + 16
But,
2RV = RT
2(3x + 5) = 5x + 16
6x + 10 = 5x + 16
collect like terms
6x - 5x = -10 + 16
x = 6
ii. m<RUV + m<VUT = 90^o
But,
m<RUV = m<VRU = 26^o
So that,
m<RUV + m<VUT = 90^o
26^o + m<VUT = 90^o
m<VUT = 90^o - 26^o
= 64^o
m<VUT = 64^o
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find value of x if (125/27) * (125/27)^x = (5/3)^18
Answer: x=5
Step-by-step explanation:
[tex]\displaystyle(\frac{125}{27} )*(\frac{125}{27} )^x=(\frac{5}{3})^{18} \\\\(\frac{5^3}{3^3})*(\frac{5^3}{3^3})^x=(\frac{5}{3})^{18}\\\\(\frac{5}{3} )^3*((\frac{5}{3})^3)^x =(\frac{5}{3})^{18}\\\\(\frac{5}{3} )^3*(\frac{5}{3})^{3*x}= (\frac{5}{3} )^{18}\\\\(\frac{5}{3} )^3*(\frac{5}{3})^{3x}= (\frac{5}{3} )^{18}\\\\(\frac{5}{3})^{3x+3}= (\frac{5}{3} )^{18}\\\\Hence,\ \\\\3x+3=18\\\\3x+3-3=18-3\\\\3x=15\\\\[/tex]
Divide both parts of the equation by 3:
[tex]x=5[/tex]
PLSSS HELP IF YOU TURLY KNOW THISS
Answer: 2x + 3y + 1
Step-by-step explanation:
That is your answer
Please give brainliest
The expected value of a discrete random variable (a) is the outcome that is most likely to occur (b) can be found by determining the 50% value in the c.d.f. (c) equals the population median. (d) is computed as a weighted average of the possible outcome of that r able, where the weights are the probabilities of that outcome.
Therefore , the solution of the given problem of variable comes out to be where weights are the probability of that outcome.
Variable : What is it ?A variable is a quality that may be measured and take on several values. A few examples of variables are height, age, salary, province of birth, school grades, and kind of dwelling.
Here,
Given :
A discrete random variable's anticipated value
So, in order to determine the expected value of a discrete random variable,
we may infer from the provided data that it is calculated as a weighting factor of the potential outcomes of that variable,
where weights are the probability of that outcome.
Therefore , the solution of the given problem of variable comes out to be where weights are the probability of that outcome.
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the volume of a sphere is increasing at a constant rate of 2409 cubic inches per minute. at the instant when the radius of the sphere is 99 inches, what is the rate of change of the surface area of the sphere? the volume of a sphere can be found with the equation v
The rate of change of the surface area of the sphere is 1903784*pi cubic inches^2 per minute.
The volume of a sphere can be found using the equation V = 4/3 * pi * r^3, where V is the volume and r is the radius of the sphere.
The surface area of a sphere can be found using the equation A = 4 * pi * r^2, where A is the surface area.
To find the rate of change of the surface area, we can use the chain rule of calculus:
dA/dt = dA/dr * dr/dt
We know that dr/dt = 2409 cubic inches per minute (from the problem statement). To find dA/dr, we can take the derivative of the surface area equation with respect to r:
dA/dr = 8 * pi * r
Now we can substitute these values into the chain rule equation:
dA/dt = 8 * pi * r * dr/dt
When the radius of the sphere is 99 inches, we can substitute this value into the equation:
dA/dt = 8 * pi * 99 * 2409 cubic inches^2 per minute
So, the rate of change of the surface area of the sphere is 1903784*pi cubic inches^2 per minute.
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From the parent function, how has the equation y = (x+3)² been shifted?
Up 3
Down 3
Right 3
Left 3
The translation in y = (x + 3)² is of 3 units to the left. The correct option is the last one.
How has the equation been shifted?For a general function y = f(x), we define a horizontal translation of N units as:
g(x) = f(x + N)
if N > 0, the shift is to the left.if N < 0, the shift is to the right.Here the original function is y = x² and the translated one is:
y = (x + 3)²
So we just added 3 on the argument, so this is a shift of 3 units to the left, the correct option is the last one.
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In Exercises 1-4, find the exact values of the six trigono-
metric functions of the angle shown in the figure. (Use the
Pythagorean Theorem to find the third side of the triangle.)
1.
2.
0
8
6
0
13
5
Only number 1 and 2
Answer:
1. 10
2. 12
Step-by-step explanation:
1. 8² + 6² = y² (Taking the unknown side as y)
64 + 36 = 100
y² = 100
y = 10
2. 5² + x² = 13² (Taking the unknown side as x)
x² = 13² - 5²
= 169 - 25
= 144
x² = 144
x = 12
Water is poured into the top half of a spherical tank at a constant rate. If W(t) is the rate of increase of the depth of the water, then W is: O constant O linear and increasing O linear and decreasing O concave up
The rate of increase of the depth of the water (W(t)) is constant.
What is rate ?
In mathematics and physics, the rate is a measure of change of a certain quantity with respect to another quantity. The rate can be a number, a ratio or a derivative. It is often represented by the symbol "d" or "dx/dt" or "dy/dt" and it measures how fast a quantity is changing.
Water is poured into the top half of a spherical tank at a constant rate, this means that the rate of increase of the depth of the water (W(t)) is constant.
In this case, W(t) is constant.
It is important to keep in mind that the rate of change of the function doesn't indicate the shape of the function, it just tells us the change of the dependent variable with respect to the independent variable. The shape of the function can be visualized by creating a graph of the function.
So , The rate of increase of the depth of the water (W(t)) is constant.
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A group of 7 men can paint 42 square feet in a day. How many square feet would 20 men paint in a day?
Answer: If 7 men can paint 42 square feet in a day, then we can say that each man paints 42/7 = 6 square feet per day.
If 20 men paint, then they would paint 20 * 6 = 120 square feet per day.
Step-by-step explanation:
Rewrite the following equations in the form ax + by = c, where A is a positive integer.
y = x + 9
y = -6x - 5
y = 2/3x + 1
Answer:
y = x + 9 ==> x + (-y) = -9
y = -6x - 5 ==> 6x + y = -5
y = 2/3x + 1 ==> 2x/3 + (-y) = -1
Step-by-step explanation:
y = x + 9 ==> isolate the constant 9
**Don't subtract x on both sides as x has to be positive**
y - 9 = x ==> keep x positive by subtracting 9 on both sides
-9 = x - y ==> subtract y on both sides to isolate the constant
x + (-y) = -9 ==> make the equation in the form of ax + by = c
y = -6x - 5 ==> isolate the constant -5
y + 6x = -5 ==> isolate -5 by adding 6x on both sides, making x positive
6x + y = -5 ==> make the equation in the form of ax + by = c
y = 2x/3 + 1 ==> isolate the constant 9
**Don't subtract 2x/3 on both sides as x has to be positive**
y - 1 = 2x/3 ==> keep x positive by subtracting 1 on both sides
-1 = 2x/3 - y ==> subtract y on both sides to isolate the constant
2x/3 + (-y) = -1 ==> make the equation in the form of ax + by = c
A billiard ball is struck by a cue. It travels 1 0 0 cm 100cm before ricocheting off a rail and traveling another 1 2 0 cm 120cm into a corner pocket. The angle between the path as the ball approaches the rail and the path after it strikes the rail is 4 5 ∘ 45 ∘. How far is the corner pocket from where the cue initially struck the ball? Do not round during your calculations. Round your final answer to the nearest centimeter
The distance from the initial point to the corner pocket is 164 cm.
The angle between the path as the ball approaches the rail and the path after it strikes the rail is 45 degrees.
We know that the ball traveled 100cm before ricocheting off the rail and another 120cm into the corner pocket.
We can use the Pythagorean Theorem to find the distance from where the cue initially struck the ball to the corner pocket.
Let x be the distance from the initial point to the corner pocket.
x^2 = 100^2 + 120^2 - 2100120*cos(45^{\circ})
x = \sqrt{28000} = \sqrt{700*40} = \sqrt{28000} = 164.856
Rounded to the nearest centimeter, the distance from the initial point to the corner pocket is 164 cm.
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What is the value of 1 − 2 × 3 + 4 ÷ 5 ?
Answer: -4.2
Step-by-step explanation:
=1-6+0.8
=-4.2
fill in the blank: if the factor (x-a)^n shows up in the complete factorization of a polynomial, then the multiplicity of a is____.
a. n
b. a
c. a-n
d. x-a
If the factor (x - a)^n shows up in the complete factorization of a polynomial, then the multiplicity of a is: A. n.
What is a polynomial function?In Mathematics, a polynomial function can be defined as a type of mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations.
This ultimately implies that, a polynomial graph touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.
In this context, we can logically deduce that the graph of a polynomial function would touch the x-axis (x-coordinate) and turns around at r when the value of r is a zero of even multiplicity.
In conclusion, the multiplicity of a must be n since the factored form in the complete factorization of this polynomial function is (x - a)^n.
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PLEASE HELP 50 POINTS URGENT
Is the system of equations consistent and independent, consistent and dependent, or inconsistent?
y = 3x + 4
y = 3x + 3
ok yx goes opposite side do cross multiplication
Answer:
The answer is Inconsistent.
Step-by-step explanation:
There is no solution.
If lil uzi had 69,420 dollhairs and John Xina wanted 69 percent of it how much money does John Xina want???
The amount of money that John Xina wants would be = $47,899.8
What is percentage?Percentage is defined as the part of the value that can be expressed as per 100 of the whole given value. This can be represented with a symbol such as %.
The amount of money Uzi has = $69,420
The percentage of money John wants from uzi = 69%
The amount of money that is 69% of Uzi's money;
= 69/100×69,420
= 4789980/100
= $47,899.8.
Therefore, the amount of money that John wants from Uzi would be = $47,899.8.
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ANSWER im just writing random thing because i needed to type 20 character please solve question
The given hypotheses of the thing will be 9.7cm.
What is Pythagoras theorem?
The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC2 = AB2 + AC2 in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.
b²=h²-p²
given b=5.2cm
p=8.2cm
h²=l²+b²
h²=8.2²+5.2² = 94.28
h = 9.7 cm
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Which of the following represent a multiplicative relationship? Select THREE correct answers.
Answer:
Bicycle workout, Andrea, and Wendy
Step-by-step explanation:
In the bicycle workout it is a multiplicative relationship because there is a constant increase of 15 / hour
Andrea's is multiplicative because the constant increase of $20 / month
Wendy's is as well because of the constant increase of 2 miles / day
Yeah pls help been trying for tens of minutes
Answer:
34
Step-by-step explanation:
They gave us -3+5i.
The conjugate of -3+5i is
-3 - 5i
You use the same numbers -3 and 5i, but with a minus sign instead of a plus.
Then multiply them together.
(-3 + 5i)(-3 - 5i)
-3•-3 + 15i - 15i - 25i^2
= 9 - 25i^2
Remember i^2 is -1.
= 9 - 25(-1)
= 9 + 25
= 34
Shortcut version:
When you multiply a complex number and its conjugate, square both numbers and add them together.
3^2 + 5^2
= 9 + 25
= 34
Out of 120 high school boys and 80 high school girls, 45 students tried out for track. Twelve of those 45 students were girls. Use this information to complete the two-way table. Enter your answer by filling in the boxes to complete the table.
As per the question, 33 boys tried the track and 87 boys didn't, whereas 12 girls tried the track and 68 girls didn't.
Total number of boys = 120
Total number of girls = 80
Students who tried out for track = 45
Students that were girls = 45
If 12 were girls, therefore,
Total number of boys -
= 45 - 12
= 33
This means that 33 boys tried the track
Now, since 12 girls tried the track
Boys who did not try the track -
= 120 - 33
= 87
Girls who did not try the track -
= 80 - 12
= 68
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The area of trapezoid ABCD is 60. One base is 4 units longer than the other, and the height of the trapezoid is 5. Find the length of the median of the trapezoid.
The length of the median of the trapezoid is 12.
The area of a trapezoid is given by the formula (1/2)h(b1+b2), where h is the height and b1 and b2 are the lengths of the bases. We know that the area is 60, the height is 5 and b1 = b2 + 4.
So, we can write the equation as follows:
(1/2) * 5 * (b1 + b2) = 60
To find the length of the median of a trapezoid, we need to find the length of the mid-segment. The mid-segment of a trapezoid connects the midpoints of the non-parallel sides. The length of the midsegment is the average of the lengths of the bases.
So, the length of the median is (b1 + b2) / 2.
We can substitute the value of the area to find the lengths of the bases and then use that to find the length of the median.
(1/2) * 5 * (b1 + b2) = 60
(1/2) * 5 * (b1 + b2) = 60
b1 + b2 = 24
b1 = b2 + 4
b2 = 24 - b1
b1 = (24 - b1) + 4
b1 = 24 - b1 + 4
b1 = 28 - b1
b1 = 28 - (24 - b1)
b1 = 4 + b1
b1 = b2 + 4
b1 = b1
So, the lengths of the bases are equal to 14 and 10.
Length of median = (14 + 10) / 2 = 12.
Therefore, The length of the median of the trapezoid is 12.
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There are 840 people sitting at tables at a
conference. If each table holds 12 people, there are ____ people at each table.
Answer:
The answer would be 70
Step-by-step explanation:All you have to do is divide 840 by 12 and you get 70 Hope this helps and have a great week:)
Answer:
70
Step-by-step explanation:
This is because 840/12=70
Hope it helps you
PLS RATE AS BRAINLIEST ANSWER
Ryan is making a fruit drink. The directions say to mix 3 cups of water with 1 1/2 scoops of powdered fruit mix.
1. how many cups of water should he use with 6 scoops of fruit mix?
2. Rate needed
3. What is the unit rate?
4. Interpretation of unit rate?
12 cups of water should be mixed to 6 scoops of fruit mix and the unit rate is 0.5 scoops per cup
What is the unit rate?Unit rate is the ratio of two different units, with denominator as 1. For example, kilometer/hour, meter/sec, miles/hour, salary/month, etc. Arithmetic is probably the most basic and ancient branch of mathematics and is quite commonly used in our day-to-day life.
Given here: Ryan is making a fruit drink. The directions say to mix 3 cups of water with 1 1/2 scoops of powdered fruit mix.
Thus the ratio of the number of cups of water to scoops of powdered fruit mix is equal to 3:3/2=2:1
∴ With 6 scoops of fruit mix we will be required to mix 12 cups of water.
Again unit rate ( scoops of fruit mix / cup of water)= 1.5/3
=0.5 scoops/cup of water
The unit rate means the number of scoops that are required to be mixed with a cup of water.
Hence, 12 cups of water should be mixed to 6 scoops of fruit mix and the unit rate is 0.5 scoops per cup
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Peter has to subtract (x² - 2x - 4) from (x² + 3x + 5)
Here is his working
(x² + 3x + 5) - (x² - 2x - 4)
= x² + 3x +5-x² - 2x - 4
= x + 1
Explain what is wrong with Peter's working.
Answer:
Grouping of like terms.
Step-by-step explanation:
(x² - 2x - 4) - (x² + 3x + 5)
= x² - 2x - 4 - x² + 3x + 5
Grouping of like terms
= x² - x² - 2x + 3x- 4 + 5
= x + 1.
Can you guys help me to figure out the area and explain to me pls
Answer:
123.2
Step-by-step explanation:
First find area of the square ABCD, then the triangle AMN.
Find CD:
sin30 = CD/20
CD = 20(sin30) = 10
CD = AD = 10
Find MD:
cos30 = MD/20
MD = 20(cos30) = 17.32
AM = MD - AD = 17.32 - 10 = 7.32
Area of ABCD = (10)(10) = 100
Find height of triangle AMN: AN
cos30 = AN/7.32
AN = cos30(7.32) = 6.34
Area of triangle ANM = 1/2(7.32(6.34) = 23.2
Total Area of the shape = 100 + 23.2 = 123.2
