Solve the attachment...
Answer:
2 ( Option A )
Step-by-step explanation:
The given integral to us is ,
[tex]\longrightarrow \displaystyle \int_0^1 5x \sqrt{x}\ dx [/tex]
Here 5 is a constant so it can come out . So that,
[tex]\longrightarrow \displaystyle I = 5 \int_0^1 x \sqrt{x}\ dx [/tex]
Now we can write √x as ,
[tex]\longrightarrow I = \displaystyle 5 \int_0^1 x . x^{\frac{1}{2}} \ dx [/tex]
Simplify ,
[tex]\longrightarrow I = 5 \displaystyle \int_0^1 x^{\frac{3}{2}}\ dx [/tex]
By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,
[tex]\longrightarrow I = 5 \bigg( \dfrac{2}{5} x^{\frac{5}{2}} \bigg] ^1_0 \bigg) [/tex]
On simplifying we will get ,
[tex]\longrightarrow \underline{\underline{ I = 2 }}[/tex]
X,Y and Z from a business with capitals Rs 5000,Rs.4500 and Rs.6500 respectively,after 6 month,X doubles has capital and after next 3 months Y trebles his capital .If the profit at the end of the year amount to RS.8300,find the profit obtained by each X,Y and Z.
Answer:
Profit obtained by X = Rs. 2,976.64
Profit obtained by Y = Rs. 2,545.58
Profit obtained by Z = Rs. 2,777.78
Step-by-step explanation:
Total capital for the first 6 months = Rs 5000 + Rs.4500 + Rs.6500 = Rs. 16,000
Total capital for the next 3 months = Rs. 16,000+ Rs 5000 = Rs. 21,000
Total capital for the last 3 months of the year = Rs. 21,000 + (Rs 4500 * 2) = Rs. 30,000
Share of profit of each partner is the sum of all the ratios of his capital to total capital of the business at each point in time multiply by the ratio of the numbers of months covered by each capital to 12 months and then multiply by RS.8300.
Profit obtained by X = ((Rs 5000 / 16,000) * (6 / 12) * Rs. 8300) + ((Rs 10,000 / 21,000) * (3 / 12) * Rs. 8300) + ((Rs 10,000 / 30,000) * (3 / 12) * Rs. 8300) = Rs. 2,976.64
Profit obtained by Y = ((Rs 4500 / 16,000) * (6 / 12) * Rs. 8300) + ((Rs 4500 / 21,000) * (3 / 12) * Rs. 8300) + ((Rs 13,500 / 30,000) * (3 / 12) * Rs. 8300) = Rs. 2,545.58
Profit obtained by Z = ((Rs 6500 / 16,000) * (6 / 12) * Rs. 8300) + ((Rs 6500 / 21,000) * (3 / 12) * Rs. 8300) + ((Rs 6,500 / 30,000) * (3 / 12) * Rs. 8300) = Rs. 2,777.78
Confirmation of total profit shared = Rs. 2,976.64 + = Rs. 2,545.58 + Rs. 2,777.78 = Rs. 8,300
TIMED HELP PLEASE. Determine whether the equation is an identity or not an identity.
Answer:
It's an identity
Step-by-step explanation:
The answer is an identity
I identity are composed by sin^2 and cos^2
Tan^2 can be simplified into those two sin n cos
Find the x and y intercept for the equation: − = 4
Answer:
x = (4,0)
y = (0,-4)
Step-by-step explanation:
x - y = 4
(0) - y = 4
-(-y) = -(4)
y = -4
x - (0) = 4
x = 4
x = (4,0)
y = (0,-4)
Answer:
x = 4 . 0
y = 0 . -4)
Step-by-step explanation:
f(x)=2x+3/4x+5
find f(-9)
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { f(-9)= 0.48}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]f(x) = \frac{2x + 3}{4x + 5} \\[/tex]
For [tex]f(-9)[/tex], put "[tex]-9[/tex]" for every value of "[tex]x[/tex]".
[tex]↬f( - 9) = \frac{2( - 9) + 3}{4( - 9) + 5}\\ [/tex]
[tex]↬ f(-9) = \frac{ - 18 + 3}{ - 36 + 5} \\[/tex]
[tex]↬ f(-9) = \frac{ - 15}{ - 31}\\ [/tex]
[tex]↬ f(-9)= \frac{15}{31}\\ [/tex]
[tex] ↬f(-9)= 0.48\\ [/tex]
[tex]\bold{ \green{ \star{ \red{Mystique35}}}}⋆[/tex]
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{f(x) = \dfrac{2x + 3}{4x + 5}}[/tex]
[tex]\mathsf{y = \dfrac{ 2x + 3}{4x + 5}}[/tex]
[tex]\mathsf{y = \dfrac{2(-9) + 3}{4(-9) + 5}}[/tex]
[tex]\mathsf{2(-9)}[/tex]
[tex]\mathsf{\bf = -18}[/tex]
[tex]\mathsf{y = \dfrac{-18 + 3} {4(-9) + 5}}[/tex]
[tex]\mathsf{-18 + 3}\\\mathsf{= \bf -15}[/tex]
[tex]\mathsf{y = \dfrac{ -15} {4(-9) + 5}}[/tex]
[tex]\mathsf{4(-9)}\\\mathsf{\bf = -36}[/tex]
[tex]\mathsf{y = \dfrac{-15}{-36 + 5}}[/tex]
[tex]\mathsf{-36 + 5}\\\mathsf{= \bf-31}[/tex]
[tex]\mathsf{y = \dfrac{-15}{ -31}\rightarrow\boxed{\bf \dfrac{15}{31}}}[/tex]
[tex]\boxed{\boxed{\huge\text{Answer: } \boxed{\bf f(-9) = \dfrac{15}{31}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
x + 2y when x = 1 and y = 4
Answer:
9
Step-by-step explanation:
x = 1
y = 4
x + 2y = 1 + 8 = 9
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
9
Step-by-step explanation:
x + 2y
subtitute:
1 + 2(4)
simplify:
1 + 8 = 9
Unit Test Unit Test Active 1 2 3 4 5 6 7 CO Given fix) = 17- x2, what is the average rate of change in f(x) over the interval [1, 5]? -6, -1/2, 1/4, 1
Answer:
Step-by-step explanation:
Average rate of change is the same thing as the slope. This is a quadratic so the slope is not something that is constant like it is in a line. Here you have the x coordinates of 1 and 5; each one of these x coordinates has a y coordinate that goes with it. If we draw a line from one of these coordinates to another, that line will have a slope. That is the slope we are trying to find. Thus, we need the y coordinates that go with each of these x coordinates. To do that, plug x into the equation and do the math to find y:
Let's start with x = 1.
f(1) = [tex]17-(1)^2[/tex] so
f(1) = 16 and the coordinate is (1, 16).
f(5) = [tex]17-(5)^2[/tex] so
f(5) = -8 and the coordinate is (5, -8). Now we apply the slope formula:
[tex]m=\frac{-8-16}{5-1}=\frac{-24}{4}=-6[/tex] So the answer is -6.
Drag each shape to the correct category. Identify which shapes are similar to shape A and which are not.
Evaluate without a calculator:
CSC -120°
Answer:
- [tex]\frac{2\sqrt{3} }{3}[/tex]
Step-by-step explanation:
Using the identity and the exact value
csc x = [tex]\frac{1}{sinx}[/tex] and sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]
- 120° is in the third quadrant where sin < 0 , then
csc - 120° = - sin60° , then
csc - 120°
= [tex]\frac{1}{-sin60}[/tex]
= - [tex]\frac{1}{\frac{\sqrt{3} }{2} }[/tex]
= - [tex]\frac{2}{\sqrt{3} }[/tex] ( rationalise the denominator )
= - [tex]\frac{2}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]
= - [tex]\frac{2\sqrt{3} }{3}[/tex]
The equivalent value of the trigonometric relation cosec ( -120 )° = 2√3/3
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
We know that the cosecant function is defined as the reciprocal of the sine function:
cosec (θ) = 1 / sin(θ)
Therefore, to evaluate cosec(-120°), we first need to find sin(-120°).
We know that sine is an odd function, which means that sin(-θ) = -sin(θ). Therefore,
sin(-120°) = -sin(120°)
We can now use the fact that the sine function has a period of 360 degrees, which means that sin(120°) is the same as sin(120° - 360°) = sin(-240°).
Using the same logic as before, we get:
sin(-240°) = -sin(240°)
Now , from the trigonometric relations , we get
Now, we can use the fact that sin(240°) = sin(240° - 360°) = sin(-120°), which means that:
sin(-240°) = -sin(-120°)
Therefore, we have:
sin(-120°) = -sin(120°) = -sin(-240°) = sin(240°)
Now, we can use the unit circle or trigonometric identities to find sin(240°). One way to do this is to draw a 30-60-90 degree triangle in the third quadrant of the unit circle, with the angle of 240° as the reference angle:
In this triangle, the opposite side (O) has a length of √3, the adjacent side (A) has a length of -1, and the hypotenuse (H) has a length of 2.
Therefore, sin(240°) = O/H = (√3)/2.
Finally, we can use the definition of the cosecant function to find cosec(-120°):
cosec(-120°) = 1/sin(-120°) = 1/sin(240°) = 1/((√3)/2) = 2/√3 = (2√3)/3.
Hence , cosec(-120°) is equal to (2√3)/3.
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if you are good at graphs this is good but please help it would mean a lot, I will give brain thingy
Answer:
(5, -6)
Step-by-step explanation:
The solution is where the lines cross.
Answer:
(5,-6)
Step-by-step explanation:
The solution to the system is where the two graphs intersect.
The graphs intersect at (5,-6)
find the coefficient of variation from the following data mean=4 variance=25
4x^2+22x factor the polynomial
Answer:
2x(2x+11)
Step-by-step explanation:
4x^2 +22x
Factor out 2x
2x*2x +2x*11
2x(2x+11)
does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?
Answer:
Inside
Step-by-step explanation:
Given equation of the Circle is ,
[tex]\sf\implies x^2 + y^2 = 25 [/tex]
And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,
[tex]\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2[/tex]
Here we can say that ,
• Radius = 5 units
• Centre = (0,0)
Finding distance between the two points :-
[tex]\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }[/tex]
Here we can see that the distance of poiñt from centre is less than the radius.
Hence the point lies within the circle
A²,b²,c² are consecutive perfect squares.How many natura numbers are lying between a² and c², if a>0
Answer:
The quantity of natural numbers between [tex]a^{2}[/tex] and [tex]c^{2}[/tex] is [tex]2\cdot (a + b) + 1[/tex].
Step-by-step explanation:
If [tex]a^{2}[/tex], [tex]b^{2}[/tex] and [tex]c^{2}[/tex] are consecutive perfect squares, then both [tex]a[/tex], [tex]b[/tex] and [tex]c[/tex] are natural numbers and we have the following quantities of natural numbers:
Between [tex]b^{2}[/tex] and [tex]c^{2}[/tex]:
[tex]c^{2} = (b+1)^{2}[/tex]
[tex]c^{2} = b^{2}+2\cdot b + 1[/tex]
[tex]c^{2}-b^{2} = 2\cdot b + 1[/tex]
And the quantity of natural numbers between [tex]b^{2}[/tex] and [tex]c^{2}[/tex] is:
[tex]c^{2}-b^{2}-1 = 2\cdot b[/tex]
Between [tex]a^{2}[/tex] and [tex]b^{2}[/tex]:
[tex]b^{2} = (a + 1)^{2}[/tex]
[tex]b^{2} = a^{2} +2\cdot a + 1[/tex]
[tex]b^{2}-a^{2} = 2\cdot a + 1[/tex]
And the quantity of natural numbers between [tex]a^{2}[/tex] and [tex]b^{2}[/tex] is:
[tex]b^{2}-a^{2}-1 = 2\cdot a[/tex]
And the quantity of natural numbers between [tex]a^{2}[/tex] and [tex]c^{2}[/tex] is:
[tex]Diff = 2\cdot a + 2\cdot b + 1[/tex]
Please observe that the component +1 represents the natural number [tex]b^{2}[/tex]
solve for x. Round to the nearest tenth, if necessary.
Answer:
44.4
Step-by-step explanation:
Sin=opposite/hypotenuse
Sin40=x/69
x=69sin40
x=44.4 rounded from 44.352
PLEASE HURRY Aline has a slope of -1/2 and a y-intercept of -2. What is the x-intercept of the line?
Answer:
x- intercept = - 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - [tex]\frac{1}{2}[/tex] and c = - 2 , then
y = - [tex]\frac{1}{2}[/tex] x - 2 ← equation of line
To find the x- intercept let y = 0
0 = - [tex]\frac{1}{2}[/tex] x - 2 ( add 2 to both sides )
2 = - [tex]\frac{1}{2}[/tex] x ( multiply both sides by - 2 to clear the fraction )
- 4 = x
The x- intercept is - 4
Given P(A) = 0.36, P(B) = 0.2 and P(ANB) = 0.122, find the value of P(AUB), rounding to the nearest thousandth, if necessary.
Answer:
The value of P(AUB) = 0.438
Step-by-step explanation:
Given:
P(A) = 0.36
P(B) = 0.2
P(A∩B) = 0.122
Find:
The value of P(AUB)
Computation:
P(AUB) = P(A) + P(B) - P(A∩B)
The value of P(AUB) = 0.36 + 0.2 - 0.122
The value of P(AUB) = 0.56 - 0.122
The value of P(AUB) = 0.438
Which of the following is an example of an exponential equation?
y=(3x)^2
y=x/2
y=x^4
y=2(3)^x
Answer:
Option D
Step-by-step explanation:
y = 2(3)^x is the example of exponential equation.
Solve for x. Round to the nearest tenth, if necessary.
A loan of 28,000 is made at 4% interest, compounded annually. After how many years will the amount due reach 48000 or more?
Answer:
The time is 13.7 years.
Step-by-step explanation:
principal, P = 28000
Rate of interest , R = 4 % annually
Amount, A = 48000
Let the time is t.
Use the formula of the compound interest.
[tex]A = P\times \left ( 1+\frac{r}{100} \right )^t\\\\48000 = 28000\times \left ( 1+\frac{4}{100} \right )^t\\\\1.71 = 1.04^t\\\\log 1.71 = t log 1.04\\\\t =\frac{0.233}{0.017}\\\\t = 13.7 years[/tex]
Hermes says that the opposite of 9 is 9 since
each number is 9 units from zero on the number line. Is Hermes correct?
Explain why or why not
Hermes is incorrect. The opposite of 9 is -9 if Hermes says that the opposite of 9 is 9 since each number is 9 units from zero on the number line.
What is a number line?It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.
To find the same distance away from zero in the opposite direction to determine the opposite number.
The distance from zero in this situation is 9. nine times in the opposite direction from zero.
Thus, Hermes is incorrect. The opposite of 9 is -9 if Hermes says that the opposite of 9 is 9 since each number is 9 units from zero on the number line.
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Please help me I really can't do these
Answer:
[tex]110 in^{2}[/tex]
Step-by-step explanation:
[tex]===========================================[/tex]
Formulas:
Area of a rectangle/square:
[tex]A=lw[/tex]
[tex]===========================================[/tex]
Squares(2):
5*5=25
Multiply by 2
50 in.
Rectangles(4):
5*3=15
Multiply by 4.
60 in.
Total:
Add.
50+60= 110 in2
I hope this helps!
I tried figuring it out but its kinda hard not knowing what to make as an equation?
HELP 20 points Congruence by SSS AND SAS NO LINKS
Answer:
where is the question oooo
Help please
If the measure of angle 6 is 140 degrees and the measure of angle 7 is (x + 30) degrees, what value of x will guarantee n ∥ m?
Answer:
x = 10
Step-by-step explanation:
If n // m , then angle 6 and angle 7 are co interior angles and they are supplementary.
∠6 + ∠7 = 180
140 + x +30 = 180
x + 170 = 180
x = 180 - 170
x = 10
What is the scale factor from abc to xyz?
Answer:
C
Step-by-step explanation:
The scale factor is the ratio of corresponding sides, image to original, so
scale factor = [tex]\frac{XY}{AB}[/tex] = [tex]\frac{9}{45}[/tex] = [tex]\frac{1}{5}[/tex] → C
The scale factor will be equal to 1 / 5. the correct option is C.
What is a scale factor?The scale factor is defined as the proportion of the new image's size to that of the previous image. Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.
In the given image all the angles are the same and the sides are dilated so the scale factor will be calculated as below,
Scale factor = Original size / dilated size
Scale factor = XY / AB
Scale factor = 9 / 45
Scale factor = 1 / 5
Therefore, the scale factor will be equal to 1 / 5. the correct option is C.
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Write the equation of the line in Slope-Intercept Form given the information below.
Slope =−7/4
Y-Intercept =5
Answer:
y = -7/4 x + 5
Step-by-step explanation:
A sequence has a common ratio of Three-halves and f(5) = 81. Which explicit formula represents the sequence?
Answer:
[tex]f(n) = \frac{32}{3}(\frac{3}{2})^n[/tex]
Step-by-step explanation:
Given
[tex]r = \frac{3}{2}[/tex]
[tex]f(5) = 81[/tex]
Required
The geometric sequence
A geometric sequence is represented as:
[tex]f(n) = ar^{n-1}[/tex]
Replace n with 5
[tex]f(5) = ar^{5-1}[/tex]
[tex]f(5) = ar^4[/tex]
Substitute values for f(5) and r
[tex]81 = a* (\frac{3}{2})^4[/tex]
Open bracket
[tex]81 = a* \frac{81}{16}[/tex]
Make a the subject
[tex]a = \frac{81 * 16}{81}[/tex]
[tex]a = 16[/tex]
So, the explicit function is:
[tex]f(n) = ar^{n-1}[/tex]
[tex]f(n) = 16 * (\frac{3}{2})^{n-1}[/tex]
Split
[tex]f(n) = 16 * (\frac{3}{2})^n \div (\frac{3}{2})[/tex]
Convert to multiplication
[tex]f(n) = 16 * (\frac{3}{2})^n * \frac{2}{3}[/tex]
[tex]f(n) = \frac{32}{3}(\frac{3}{2})^n[/tex]
Answer:
f(x) = 16*(3/2)^(x-1)
Step-by-step explanation:
right on edge
what is 50000000000000000000000000000 cubed
Answer:
50000000000000000000000000000*50000000000000000000000000000*50000000000000000000000000000=1.25e+86
Hope This Helps!!!
Help me with the diagram please!!!
Answer:
(B) 30
Step-by-step explanation:
Imagine you drew a line from Point T until it touched Line PR. Let's call that point where it touched Line PR "Point Z".
That line (called Line TZ) would be perpendicular to PR, forming a 90 degree angle.
Now, TZW is a triangle.
To find x, we need to find the angle measurment of Angle ZTW.
This is where we use the hexagon.
A hexagon's interior angle sum is 720, meaning each interior angle is equal to 120 degrees. So Angle UTS would equal 120 degrees.
However, Line TZ bisects that 120 degree angle, so Angle ZTW would equal 60 degrees (because 120/2 = 60).
Now we have two angles of the triangle: 90 & 60.
A triangle's interior angle sum is 180.
Add 90 & 60, which is 150, and subtract 150 from 180.
The result is 30, which is the angle measurement of x.
Hope it helps (●'◡'●)
