Answers
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]
Answer:
A)2
Step-by-step explanation:
we would like to integrate the following definite Integral:
[tex] \displaystyle \int_{0} ^{1} 5x \sqrt{x} dx[/tex]
use constant integration rule which yields:
[tex] \displaystyle 5\int_{0} ^{1} x \sqrt{x} dx[/tex]
notice that we can rewrite √x using Law of exponent therefore we obtain:
[tex] \displaystyle 5\int_{0} ^{1} x \cdot {x}^{1/2} dx[/tex]
once again use law of exponent which yields:
[tex] \displaystyle 5\int_{0} ^{1} {x}^{ \frac{3}{2} } dx[/tex]
use exponent integration rule which yields;
[tex] \displaystyle 5 \left( \frac{{x}^{ \frac{3}{2} + 1 } }{ \frac{3}{2} + 1} \right) \bigg| _{0} ^{1} [/tex]
simplify which yields:
[tex] \displaystyle 2 {x}^{2} \sqrt{x} \bigg| _{0} ^{1} [/tex]
recall fundamental theorem:
[tex] \displaystyle 2 ( {1}^{2}) (\sqrt{1} ) - 2( {0}^{2} )( \sqrt{0)} [/tex]
simplify:
[tex] \displaystyle 2 [/tex]
hence
our answer is A
Related Questions
8. Write the equation for a line that has a slope of 5 and a y-intercept of
negative 12.
Answers
Answer:
[tex]y=5x-12[/tex]
Step-by-step explanation:
This is in slope-intercept form, [tex]y=mx+b[/tex] where [tex]m[/tex] stands for the slope and [tex]b[/tex] stands for the y-intercept.
Hope this is helpful.
Step-by-step explanation:
equation of the line is given by the equation
y=mx+c
in this question you are given the slope (m) as 5 and the y intercept (c) as -12
therefore the equation will be
y=5x+(-12)
y=5x-12
6. Write an equation of a line that is Parallel to the line: y = 3x -3
Answers
Answer:
3x - y -6 = 0
Step-by-step explanation:
We need to find the Equation of the line parallel to the given equation of line . The given equation of the line is ,
[tex]\rm\implies y = 3x - 3 [/tex]
Slope Intercept Form :-
[tex]\rm\implies y = mx + c [/tex]
where ,
m is slopec is y intercept .Therefore , the Slope of the line is 3 . Let the parallel line passes through ( 3,3) . We know that the parallel lines have same slope . Therefore the slope of the parallel line will also be 3 .
Using point slope form :-
[tex]\rm\implies y - y_1 = m ( x - x_1) \\\\\rm\implies y - 3 = 3( x - 3 ) \\\\\rm\implies y -3 = 3x -9 \\\\\rm\implies 3x -y -9+3=0\\\\\rm\implies \boxed{\rm\red{ 3x -y -6=0}}[/tex]
Given ACM, angle C=90º. AP=9, PM=12. Find AC, CM, AM.
Answers
Answer:
AM = 25, AC = 15, CM = 20
Step-by-step explanation:
The given parameters are;
In ΔACM, ∠C = 90°, [tex]\overline{CP}[/tex] ⊥ [tex]\overline{AM}[/tex], AP = 9, and PM = 16
[tex]\overline{AC}[/tex]² + [tex]\overline{CM}[/tex]² = [tex]\overline{AM}[/tex]²
[tex]\overline{AM}[/tex] = [tex]\overline{AP}[/tex] + PM = 9 + 16 = 25
[tex]\overline{AM}[/tex] = 25
[tex]\overline{AC}[/tex]² = [tex]\overline{AP}[/tex]² + [tex]\overline{CP}[/tex]² = 9² + [tex]\overline{CP}[/tex]²
∴ [tex]\overline{AC}[/tex]² = 9² + [tex]\overline{CP}[/tex]²
Similarly we get;
[tex]\overline{CM}[/tex]² = 16² + [tex]\overline{CP}[/tex]²
Therefore, we get;
[tex]\overline{AC}[/tex]² + [tex]\overline{CM}[/tex]² = 9² + [tex]\overline{CP}[/tex]² + 16² + [tex]\overline{CP}[/tex]² = [tex]\overline{AM}[/tex]² = 25²
2·[tex]\overline{CP}[/tex]² = 25² - (9² + 16²) = 288
[tex]\overline{CP}[/tex]² = 288/2 = 144
[tex]\overline{CP}[/tex] = √144 = 12
From [tex]\overline{AC}[/tex]² = 9² + [tex]\overline{CP}[/tex]², we get
[tex]\overline{AC}[/tex] = √(9² + 12²) = 15
[tex]\overline{AC}[/tex] = 15
From, [tex]\overline{CM}[/tex]² = 16² + [tex]\overline{CP}[/tex]², we get;
[tex]\overline{CM}[/tex] = √(16² + 12²) = 20
[tex]\overline{CM}[/tex] = 20.
Length of a rope is 5 metre. What does it mean?
Answers
Step-by-step explanation:
Length of a rope is 5 meter. it means the rope is 5 meter long..
hope it helps.stay safe healthy and happy...instructions: state what additional information is required in order to know that the triangle in the image below are congruent for the reason given.
Given: SAS
Answers
Answer:
please I don't know can u please help me out
Answer:
The answer to your question where SAS is given
∠T ≈∠ W
Through any two points there is exactly one _____
space.
plane.
line.
point.
Answers
Answer:
C. Line
Is the correct answer
Find the measure of Angle B
Answers
Answer:
45
Step-by-step explanation:
Both angles have the same value, therefore, you can set your formula up as
5x-105=2x+30
5x = 2x + 30 + 105
5x - 2x = 135
3x = 135
x = 135/3
x = 45
Carla packed this box with one centimeter cubes what is the volume of the box plus is it cubic centimeters or just centimeters or is it square centimeters pls help you'll get brainlist
Answers
Cubic centimetres since they are cubes. Did you add any picture of the question? There seems to be none.
Calculate cos (theta) to two decimal places. PLS HELP ASAP
Answers
Answer:
B. -0.07
Step-by-step explanation:
Apply the Law of signs find θ.
Cos θ = (a² + b² - c²)/2ab
Where,
a = 7
b = 8
c = 11
Plug in the values
Cos θ = (7² + 8² - 11²)/2*7*8
Cos θ = (49 + 64 - 121)/112
Cos θ = -8/112
Cos θ = -0.0714285714
Cos θ = -0.07 (to 2 decimal places)
Please help me here. I've tried this one over and over and I'm unable to get the answer that was given. How do I find the area of this triangle?
Answers
Answer:
jjdjdjdj and technology and technology and technology and technology and technology
how do you find the arc length of a semi-circle?
Answers
the arc length is calculated by the formula [tex]\displaystyle\bf C=\frac{2\pi r}{360} \cdot\alpha[/tex] then [tex]\displaystyle\bf C=\frac{2\cdot 8 \pi }{360} \cdot180=8\pi=3,14\cdot8=25.12[/tex] or it can be calculated using the circumference of the circle since we have a semicircle the circumference 2πr must be divided by 2 С=2πr:2=πr =8π=25,12
Nathan is 1.55 meters tall. At 1 p.m., he measures the length of a tree's shadow to be 38.15 meters. He stands 32.9 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter .
Answers
Answer:
11.26 m
Step-by-step explanation:
The height of the tree is about 11.25 meters.
What are similar triangles?When the respective sides are proportional and the corresponding angles are congruent, two triangles are said to be similar.
Given that, the height of the person is 1.55 meters, the length of the tree's shadow is 38.15 meters, and the distance between the person and the tree is 32.9 meters.
Let the height of the tree be x.
Note that the scenario makes two similar triangles.
Since the ratio of the side lengths of similar triangles is proportional, it follows:
(38.15 - 32.9)/1.55 = 38.15/x
5.25/1.55 = 38.15/x
3.39 = 38.15/x
x = 38.15/3.39
x = 11.25
Hence, the height of the tree is about 11.25 meters.
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Using the number line below, draw a box and whisker plot for the following data: 12,18,18,20,22,22,25,26,30,30,32,32,35,35,38,49,42
Answers
Answer:
Step-by-step explanation:
Population size: 17
Median: 30
Minimum: 12
Maximum: 49
First quartile: 21
Third quartile: 35
Interquartile Range: 14
Outliers: none
A parabola opens upward. The parabola goes through the point (3,-1),
and the vertex is at (2,-2).
Find the value of A for the parabola. Show your work. Use Part 1 and 2 to write the equation of the parabola.
Answers
Answer:
a=1
Step-by-step explanation:
Hopefully this helps :)
The equation of the parabola is: y = (x - 2)² - 2. Finding the value of A
The vertex of the parabola is at (2,-2). Since the parabola opens upward, the equation of the parabola will be of the form:
y = A(x - 2)² - 2
We can plug the point (3,-1) into this equation to find the value of A.
-1 = A(3 - 2)² - 2
Simplifying the right side of the equation, we get:
-1 = A - 2
Adding 2 to both sides of the equation, we get:
1 = A
Therefore, the value of A is 1.
Writing the equation of the parabola
The equation of the parabola is:
y = (x - 2)² - 2
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The answers to this question make no sense please help
Answers
Answer:
Step-by-step explanation:
each die has numbers 1-6 thus there are 36 (6*6) possible outcomes
a) 18 of the 36 are even = 1/2 = .5 = 50%
b) (1,2) and (2,1) are the only 3's 2/36 = 1/18 = .055
c) there are 10 combos that are LESS THAN 6 (2,3,4,5)
10/36 = .277 = 27.7%
2 3 4 5 6 7
3 4 5 6 7 8
4 5 6 7 8 9
5 6 7 8 9 10
6 7 8 9 10 11
7 8 9 10 11 12
∣1/12 − 5/6∣ − (2/5 + 1/10)
I WILL GIVE BRAINLYST
Answers
Answer:
forst mark me as a brainleast
What are the coordinates of points E, F, and GS
A. E (2, 3), F (8,5), G (5,8)
B. E (3, 2), F (8,3), G (5,6)
C. E (3, 2), F (8,4), G (5,7)
D. E (3, 3), F (9, 4), G (6,7)
Answers
Answer:
its a i think
Step-by-step explanation:
Battle is making fruit baskets, which include apples and bananas to send to some of her real estate clients. She wants each basket to have at least 12 pieces of fruit but the fruit should weigh no more than 80 ounces total. On average each apple weighs 5 ounces and each banana weighs 7 ounces.
Answers
Answer:
there are 2 apples in the basket
there are 10 banana in the basket
Step-by-step explanation:
According to the Question,
We have, Battle is making fruit baskets, which include apples and bananas to send to some of her real estate clients. She wants each basket to have at least 12 pieces of fruit.let x for apple And y for banana So, x+y=12---Equation 1
And, the fruit should weigh no more than 80 ounces total. On average each apple weighs 5 ounces and each banana weighs 7 ounces.Thus, 5x+7y=80 ----Equation 2
Now, (Equation 1) × 5 Subtract with (Equation 2) We get,
2y = 20 ⇒ y=10 (there are 10 banana in basket)
Put value of y=10 in Equation 2 we get5x+70=80 ⇔ x=2(there are 2 apples in basket)
2√4^3
find the rationalizing factor
Answers
Hello!
2√4³ =
2 × √4 ³ =
2 × 2³ =
2 × 8 = 16
Good luck! :)
HELP! how do I find the degrees for this problem
Answers
Answer:
90°
Step-by-step explanation:
m∠x+m∠y+m∠z=180°
m∠x+m∠y+90=180
m∠x+m∠y=180-90=90°
You're working as a floor rep in the local home improvement store. The store wants to increase its inventory. Last year, 40 lawn mowers cost $4,776. At the same cost, how much will 120 lawn mowers cost this year?
Answers
To set up this problem first you'll need to find out the price of one lawn mower.
Divide the amount if lawn mowers bought last year with the cost to get the cost of one lawn mower
Take the number you get and multiply that bu the amount of lawn mowers this year (120)
answer: $14,328
Write 8 as the ratio of two integer
Answers
Answer:
Step-by-step explanation: 7 1 16 37
8/1 8 divided by 1
16/2 16 divided by 2
24/3 24 divided by 3 I could go on, but won't
What is a set ? Give an example of a set .
Answers
Answer: 24
Step-by-step explanation:
The temperature of a chemical solution is originally 21^\circ\text{C}21 ∘ C21, degrees, start text, C, end text. A chemist heats the solution at a constant rate, and the temperature of the solution is 75^\circ\text{C}75 ∘ C75, degrees, start text, C, end text after 121212 minutes of heating. The temperature, TTT, of the solution in ^\circ\text{C} ∘ Cdegrees, start text, C, end text is a function of xxx, the heating time in minutes. Write the function's formula. T=
Answers
Answer:
T(x) = 21 + 4.5x
Step-by-step explanation:
Given :
Original temperature = 21°C
Final temperature = 75°C
Time, x = 12 minutes
The temperature, T as a function of x, heating time in minutes :
We need to obtain the constant heating rate per minute :
Final temperature = initial temperature + (constant rate change,△t * time)
75 = 21 + 12△t
75 - 21 = 12 △t
54 = 12 △t
△t = 54 / 12
△t = 4.5°C
Hence, temperature change is 4.5°C per minute.
Hence,
T(x) = 21 + 4.5x
Answer:
T= 21+4.5x
Step-by-step explanation:
I got it right on Khan Academy
PLEASE MARK BRAINLIEST
A boat has a ladder that's ten feet long, and hangs off the side of the boat,
with its last two feet submerged in water. If the ocean tide rises five feet,
how much of the ladder will be underwater?
Answers
Answer:
2ft
Step-by-step explanation:
The tide doesn't effect the part of ladder that is underwater that is always 2ft
How much of the ladder that will be underwater is 7 ft.
Since the ladder is 10 ft long and its last two feet are submerged under water, this implies that 2 ft of the ladder are submerged under water.
When the tide rises by five feet, the part of the ladder that would be under water is 2 ft + 5ft = 7ft.
So, how much of the ladder that will be underwater is 7 ft.
Learn more about tide here:
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Write the product as a single power. 6^(5) * 6^(2) * 6^(5)
Answers
Answer:
6^12
Step-by-step explanation:
add up all the exponents
[tex]\displaystyle\bf \boxed{a^m\cdot a^n=a^{m+n}}\\\\6^5\cdot 6^2\cdot6^5=6^{5+2+5}=\boxed{6^{12} }[/tex]
How many marbles do you need to be able to arrange them into the shape of an equilateral triangle with 75 rows
Answers
Answer:
2850
Step-by-step explanation:
1+2+3+4+5+6+7...74+75
just add up all the numbers from 1 to 75
Solve 4x + 11 = k for x.
O A. x= -11
O B. x=-11
O C. x = 4k - 44
D. x= k-7
Answers
Answer:
4x + 11 = k
<=> 4x = k - 11
<=>
[tex]x = \frac{k - 11}{4} [/tex]
Find the area of the triangle with vertices A(-3,2), B(1,-2), and c(1,3)
Answers
Answer:
[tex]A(-3,2)\: B(-1,-2)\: C(1,3)[/tex]
[tex]A=1/2[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)][/tex]
[tex]=1/2[-3(-2-3)(+1(3-2)+1(2-(-2))][/tex]
[tex]=1/2(15+1+4)[/tex]
[tex]=1/2(20)[/tex]
[tex]=10[/tex]
[tex]ANSWER: 10 ~units^{2}[/tex]
------------------------------
hope it helps...
have a great day!!
The area of triangle with vertices A(-3,2), B(1,-2), and c(1,3) is 12 units^2.
What is area of triangle?The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.
The green line represents the height of the triangle = 4 units
The red line represents the base of the triangle = 6 units
Area of the triangle = 1/2 x 6 x 4 = 12 units^2
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La potencia que se obtiene de elevar a un mismo exponente un numero racional y su opuesto es la misma verdadero o falso?
Answers
Answer:
Falso.
Step-by-step explanation:
Sea [tex]d = \frac{a}{b}[/tex] un número racional, donde [tex]a, b \in \mathbb{R}[/tex] y [tex]b \neq 0[/tex], su opuesto es un número real [tex]c = -\left(\frac{a}{b} \right)[/tex]. En el caso de elevarse a un exponente dado, hay que comprobar cinco casos:
(a) El exponente es cero.
(b) El exponente es un negativo impar.
(c) El exponente es un negativo par.
(d) El exponente es un positivo impar.
(e) El exponente es un positivo par.
(a) El exponente es cero:
Toda potencia elevada a la cero es igual a uno. En consecuencia, [tex]c = d = 1[/tex]. La proposición es verdadera.
(b) El exponente es un negativo impar:
Considérese las siguientes expresiones:
[tex]d' = d^{-n}[/tex] y [tex]c' = c^{-n}[/tex]
Al aplicar las definiciones anteriores y las operaciones del Álgebra de los números reales tenemos el siguiente desarrollo:
[tex]d' = \left(\frac{a}{b} \right)^{-n}[/tex] y [tex]c' = \left[-\left(\frac{a}{b} \right)\right]^{-n}[/tex]
[tex]d' = \left(\frac{a}{b} \right)^{(-1)\cdot n}[/tex] y [tex]c' = \left[(-1)\cdot \left(\frac{a}{b} \right)\right]^{(-1)\cdot n}[/tex]
[tex]d' = \left[\left(\frac{a}{b} \right)^{-1}\right]^{n}[/tex]y [tex]c' = \left[(-1)^{-1}\cdot \left(\frac{a}{b} \right)^{-1}\right]^{n}[/tex]
[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c = (-1)^{n}\cdot \left(\frac{b}{a} \right)^{n}[/tex]
[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c' = \left[(-1)\cdot \left(\frac{b}{a} \right)\right]^{n}[/tex]
[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c' = \left[-\left(\frac{b}{a} \right)\right]^{n}[/tex]
Si [tex]n[/tex] es impar, entonces:
[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c' = - \left(\frac{b}{a} \right)^{n}[/tex]
Puesto que [tex]d' \neq c'[/tex], la proposición es falsa.
(c) El exponente es un negativo par.
Si [tex]n[/tex] es par, entonces:
[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c' = \left(\frac{b}{a} \right)^{n}[/tex]
Puesto que [tex]d' = c'[/tex], la proposición es verdadera.
(d) El exponente es un positivo impar.
Considérese las siguientes expresiones:
[tex]d' = d^{n}[/tex] y [tex]c' = c^{n}[/tex]
[tex]d' = \left(\frac{a}{b}\right)^{n}[/tex] y [tex]c' = \left[-\left(\frac{a}{b} \right)\right]^{n}[/tex]
[tex]d' = \left(\frac{a}{b} \right)^{n}[/tex] y [tex]c' = \left[(-1)\cdot \left(\frac{a}{b} \right)\right]^{n}[/tex]
[tex]d' = \left(\frac{a}{b} \right)^{n}[/tex] y [tex]c' = (-1)^{n}\cdot \left(\frac{a}{b} \right)^{n}[/tex]
Si [tex]n[/tex] es impar, entonces:
[tex]d' = \left(\frac{a}{b} \right)^{n}[/tex] y [tex]c' = - \left(\frac{a}{b} \right)^{n}[/tex]
(e) El exponente es un positivo par.
Considérese las siguientes expresiones:
[tex]d' = \left(\frac{a}{b} \right)^{n}[/tex] y [tex]c' = \left(\frac{a}{b} \right)^{n}[/tex]
Si [tex]n[/tex] es par, entonces [tex]d' = c'[/tex] y la proposición es verdadera.
Por tanto, se concluye que es falso que toda potencia que se obtiene de elevar a un mismo exponente un número racional y su opuesto es la misma.
