The area under the curve y = x² + 4 on the interval [-3, 2] exists [tex]$\frac{95}{3}[/tex].
What is the area under the curve y = x² + 4 on the interval [-3, 2]?The area under a curve between two points exists seen by accomplishing a definite integral between the two points. To estimate the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b. This area can be estimated by utilizing integration with given limits.
The equation that represents the curve exists
y = x² + 4
To estimate the area under the curve in the interval of [-3, 2] will be
[tex]$&\text { area }=\int_{-3}^{2} x^{2}+4 d x \\[/tex]
[tex]$&=\left[\frac{x^{3}}{3}+4 x\right]_{-3}^{2} \\[/tex]
[tex]$&=\frac{1}{3}\left[x^{3}\right]_{-3}^{2}+4[x]_{-}^{2} _{3} \\[/tex]
simplifying the above equation, we get
[tex]$&=\frac{1}{3}\left[(2)^{3}(-3)^{3}\right]+4[(2)-(-3)] \\[/tex]
[tex]$&=\frac{1}{3}[8+27]+4[2+3] \\[/tex]
[tex]$&=\frac{1}{3}(35)+20 \\[/tex]
[tex]$&=\left(\frac{95}{3}\right)[/tex]
Therefore, the area under the curve y = x² + 4 on the interval [-3, 2] exists [tex]$\frac{95}{3}[/tex].
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The daily high temperature of Elk Creek drops by 1.2°C every day. What is the net change in the daily high temperature after two calendar weeks?
Answer:
Step-by-step explanation:
Answer: 16.8°C
Calculate the amount of heat (in kJ) released when 3.5 mol CH4 react. 4() + 22() → 2() + 22() + 890
The amount of heat (in KJ) released when 3.5 moles of CH₄ react is 3115 KJ
Balanced equationCH₄ + 2O₂ -> CO₂ + 2H₂O ΔH = 890 KJ
From the balanced equation above,
1 mole of CH₄ reacted to release 890 KJ of heat energy.
How to determine the heat energy released by 3.5 moles of CH₄From the balanced equation above,
1 mole of CH₄ reacted to release 890 KJ of heat energy
Therefore,
3.5 moles of CH₄ will react ro release = 3.5 × 890 = 3115 KJ of heat energy
Thus, 3115 KJ of heat energy were released from the reaction
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The area of triangle ABC is 4√2 m².
Work out the value of x.
Give your answer correct
to 3 significant figures.
Note: Please make sure your final line says x =
Answer:
x=1.08 (3SF)
Step-by-step explanation:
hope it helps!!!!
A bowling ball weighs 15 pounds on earth and weighs 4 pounds on the planet saturn. you could determine a 100–pound earthling's weight on saturn using the proportion: a. startfraction 15 over 4 endfraction = startfraction b over 100 endfraction c. startfraction 4 over 15 endfraction = startfraction 100 over b endfraction b. startfraction 15 over 4 endfraction = 100 over b endfraction d. either a or c
100–pound earthling's weight on Saturn using the proportion is (B)
15/4 = 100/x.
What is proportion?The size, number, or quantity of one object or group of things in comparison to another thing or group of things In our class, the ratio of guys to girls is two to one (2:1).To find the 100–pound earthling's weight on Saturn using the proportion:
Weight of ball on Earth = 15 poundsWeight of ball on Saturn= 4 poundsLet 100 pounds of earthling weight on Saturn be x pounds.Thus, the proportion is 15:4 = 100:x15/4 = 100/xTherefore, 100–a pound earthling's weight on Saturn using the proportion is (B) 15/4 = 100/x.
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The correct question is given below:
A bowling ball weighs 15 pounds on earth and weighs 4 pounds on the planet Saturn. you could determine a 100–pound earthling's weight on Saturn using the proportion:
a. start fraction 15 over 4 end fraction = start fraction x over 100 end fraction
b. startfraction 15 over 4 endfraction = 100 over x endfraction
c. startfraction 4 over 15 endfraction = startfraction 100 over x endfraction
d. either a or c
PLEASE HELP IM STUCK
Answer:
y=1
Step-by-step explanation:
Since you already found x,
We will only be needing one equation to find y..
I will take equation two: 3(2)+2y=8
Step Two: 6+2y=8 (then you minus 6 on each side)
Step Three: 2y=2 (divide)
y=1
Which point lies on the line described by the equation below? y+4=4(x-3
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies \begin{array}{llll} y+4=4(x-3)\implies y-(\stackrel{y_1}{-4})=\stackrel{m}{4}(x-\stackrel{x_1}{3})\\\\ ~\hfill (\stackrel{x_1}{3}~~,~~\stackrel{y_1}{-4}) \end{array}[/tex]
S=1 - 1/4 + 1/6 - 1/9 + 1/11 - 1/14..........infinity. Find the sum of series.
[tex]1+\frac{1}{6}+\frac{1}{11}+\cdots=\sum^{\infty}_{n=1} \frac{1}{5n-4} \\ \\ \frac{1}{4}+\frac{1}{9}+\cdots=\sum^{\infty}_{n=1} \frac{1}{5n-1} \\ \\ S=\sum^{\infty}_{n=1} \left(\frac{1}{5n-4} -\frac{1}{5n-1} \right) \\ \\ =\frac{\pi}{5} \sqrt{\frac{1}{5} (5+2\sqrt{5})}[/tex]
The price of a jacket is $500 and the price of a pair of jeans is $250.
(a) The price if the jacket is ____% if the pair of jeans.
(b) The price of the pair of jeans is ___% or the price of the jacket.
Answer:(a) 50% (b)5%
Step-by-step explanation:
For a, it's not really difficult because the price of a jacket is 1/2 more than jeans. So it's 50%.
For b, it's similar to no. (a) because the price of the jean is 1/2 less than a jacket. So u need to divide 250 by 500 and u will get 0.5 so if u want to put in % u need to multiply with 10, so u will get 5%.
Assume that thermometer readings are normally distributed with a mean of 0 C and a standard deviation of 1.00 C. A thermometer is randomly selected and tested. For the case below, draw a sketch, and find the probability of the reading. (The given values are in Celsius degrees.)
Between 1.50 and 2.25
1. Choose the correct graph
2.the probability of getting a reading between 1.50 and 2.25
The probability of getting a reading between 1.50 and 2.25 is; 0.00546
How to find the probability from z-score?We are given the following information in the question:
Mean; μ = 0 °C
Standard Deviation; σ = 1 °C
We are given that the distribution of thermometer readings is a bell shaped distribution that is a normal distribution.
Formula for z-score is;
z = (x' - μ)/σ
P(Between 1.50 degrees and 2.25 degrees) is expressed as;
P(1.5 ≤ x ≤ 2.25)
= P((1.5 - 0)/1 ≤ z ≤ (2.25 - 0)/1))
= P(z ≤ 2.25) - P(z < 1.5)
= 0.0546 = 5.46%
The graph that correctly describes this is the first graph
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Find the value of x. Degrees in an arc!! pls help i need this to study for my test!! pls show work thank you so much :)
Considering the angle of the arc, it is found that the value of x is of x = 12º.
What is the angle of the arc?It is twice the inside angle.
In this problem, the angle of the arc is of 102º, hence the inside angle is of 51º, which means that we can solve for x as follows:
4x + 3 = 51
4x = 48
x = 12º.
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Find the measure of two complementary angles of the measure of one angle is 3 more than the measure of its complement
ANSWER: 22.5 and 67.5
let, one angle be x then the another one is 3×(90-x)
x = 270 - 3x
x + 3x = 270
4x = 270
x = 270/4
x = 67.5 (first angle)
then, another angle = 90- 67.5 = 22.5
Geometry: complete this proof (ASAP!!!!! It’s urgent)
Answer:
1. Given.
2. Alternate Interior Angles Theorem.
3. m<2 + m<7 = 180 by definition of supplementary angles. By definition of congruent angles, m<2 = m<4 and m<5 = m<7, therefore m<4 + m<5 = 180 by substitution property of equality. By definition of supplementary angles, <4 is supplementary to <5.
4. Converse of Consecutive Angles Theorem.
A data set contains three points, and two of the residuals are 7 and -3. What 7
is the third residual?
The data set in discuss which contains three points and two of the residuals are 7 and -3 would have its third residual as; -4.
What is the third residual if the data set characterized as having 2 of its three residuals to be; 7 and -3?According.tinthe task content, the data set in discuss has three points and consequently should have three residuals.
Additionally, two of the three residuals have been given and on this note, it follows that the third residual must have a value such that the algebraic sum of all residuals is 0.
Hence, we have; -3 + 7 +x = 0;
x = 3-7 = 4.
Ultimately, the third residual is; -4.
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Aakash has a fever. His body temperature during the day was 99.2°F. By evening, his body temperature has increased by 3.4°F.
His body temperature in the evening is
°F.
His body temperature in the evening is 102.6 °F
How to determine his body temperature?The given parameters are:
Temperature in the morning = 99.2°F.
Temperature increase = 3.4°F.
His body temperature in the evening is calculated as:
New = Temperature in the morning + Temperature increase
So, we have
New = 99.2°F + 3.4°F
Evaluate the sum
New = 102.6 °F
Hence, his body temperature in the evening is 102.6 °F
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Force equals mass times acceleration.
F = ma
Solve the equation for the
acceleration, a.
-A
Answer:
m = F / a is the answer
Step-by-step explanation:
F = ma
m = F / a
A pygmy hippo and a regular hippo were recently born. The pygmy hippo had a mass of 5 1/2 kg at birth. The regular hippo had a mass of 24 1/2 kg at birth. Complete the comparison. At birth, the regular hippo massed ? times as much as the pygmy hippo.
The mass of the regular hippo at birth to that of the pygmy hippo is 49/11
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
The pygmy hippo had a mass of 5 1/2 kg at birth = 5.5 kg.
The regular hippo had a mass of 24 1/2 kg at birth = 24.5 kg
Hence:
Ratio of regular hippo to pygmy hippo = 24.5 / 5.5 = 49/11
The mass of the regular hippo at birth to that of the pygmy hippo is 49/11
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Answer:
49/11 or 4 5/11
Step-by-step explanation:
just did it on khan Academy.
using point Q as the center of dilation.
Point Q is the center of dilation. Line segment A B is dilated to create line segment A prime B prime. The length of Q A is 1.25 and the length of A A prime is 1.25.
What is the scale factor?
1
1.25
2
2.5
Answer:
(c) 2
Step-by-step explanation:
The dilation scale factor multiplies the distance from the center of dilation.
Distance from QWe are given that QA = 1.25, and that AA' = 1.25. By the segment sum theorem, we have ...
QA' = QA +AA'
QA' = 1.25 +1.25 = 2.50
Scale factorThe scale factor multiplies the original distance:
QA' = k·QA . . . . . . . . . . where k is the dilation scale factor
2.50 = k·1.25 . . . . . . . . using the known lengths
2.50/1.25 = k = 2 . . . . divide by the coefficient of k
The scale factor is 2.
Factor the polynomial completely
10³ -25r² - 12r + 30
To calculate the height of a tower Mary measures the angle of elevation from a point A, to be
10. She then walks 100m directly towards the tower, and finds the angle of elevation from the
new point B to be 20°. What is the height of the tower to the nearest tenth of a metre?
If Mary measures the angle of elevation from a point A, to be 10°. She then walks 100m directly towards the tower, and finds the angle of elevation from the new point B to be 20°, the height of the tower comes out to be 37 meters.
Given Information and Formula Used:
The angle of elevation of the tower from point A (a in figure) = 10°
The angle of elevation of the tower from point B (b in figure) = 20°
The distance AB (ab n figure) = 100m
In right triangle adc, tan 10° = cd / ad ....... (1)
In right triangle bdc, tan 20° = cd / bd ......... (2)
Here, cd is the height of the tower.
Let the distance bd be x, then the ad = x + 100
Substituting this value of of ad in equation (1), we get,
tan 10° = cd / (x+100)
x+100 = cd / tan 10°
x+100 = cd / 0.18
x+100 = 5.6 cd ....... (3)
From equation (2),
tan 20° = cd / x
x = cd / tan 20°
x = cd / 0.34
x = 2.9 cd
Putting this value of x in equation (3), we obtain the height cd (or CD) as,
2.9 cd + 100 = 5.6 cd
(5.6 - 2.9)cd = 100
2.7cd = 100
cd = 100/2.7
cd ≈ 37m (To the nearest tenth of a meter)
Therefore, the height of the tower is calculated to be 37 meters.
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Match each quadratic equation with its solution set. 2x2 − 32 = 0 4x2 − 100 = 0 x2 − 55 = 9 x2 − 140 = -19 2x2 − 18 = 0
Correct match for the quadratic equation are:
A. {-4, 4}
B. {-5, 5}
C. {-8, 8}
D. {-11, 11}
E. {3,-3}
What is a quadratic equation ?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.
According to the given Information:First equation:2x² - 32 = 0
Adding thirty-two to both sides of the equation:
2x² = 32
Dividing between two on both sides of the equation:
x² = 322
x² = 16
Applying square root to eliminate the exponent:
x = ±√16
x = ±4
Second equation:4x² - 100 = 0
Adding hundred to both sides of the equation:
4x² = 100
Dividing between four on both sides of the equation:
x² = 100/4
x² = 25
Applying square root to eliminate the exponent:
x = ±√25
x = ±5
Third equation:x² - 55 = 9
Adding fifty-five to both sides of the equation:
x² = 9 + 55
x² = 64
Applying square root to eliminate the exponent:
x = ±√64
x = ±8
Fourth equation:x² - 140 = -19
Adding one- fourty to both sides of the equation:
x² = -19 + 140
x² = 121
Applying square root to eliminate the exponent:
x = ±√121
x = ±11
Fifth equation:2x² - 18 = 0
Adding eighteen to both sides of the equation:
2x² = 18
Dividing between two on both sides of the equation:
x² = 182
x² = 9
Applying square root to eliminate the exponent:
x = ±√9
x = ±3
Correct match for the quadratic equation are: A. {-4, 4},B. {-5, 5},
C. {-8, 8},D. {-11, 11},E. {3,-3}
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I understand that the question you are looking for is:
Match each quadratic equation with its solution set.
A. 2x2 - 32 = 0 {-8, 8}
B. 4x2 - 100 = 0 {-4, 4}
C. x2 - 55 = 9 {-5, 5}
D. x2 - 140 = -19 {-11, 11}
E. 2x2 - 18 = 0 {3,-3}
Write down the next two numbers in each of the following sequences. 40 POINTS
a) 0.04,0.1,0.16, __ , __
b)3,9,27 , __,__
c)0.3,1/3,11/30,__,__
Answer:
Below in bold.
Step-by-step explanation:
a) 0.04, 0.1, 0.16
You add 0.06 to get the next term:
The next 2 are: 0.22, 0.28.
b) 3, 9, 27
You multiply by 3 to get next term
Next 2 are: 81, 243.
c) 0.3, 1/3, 11/30
1/3 - 0.3 = 1/30
11/30 - 1/3 = 1/30
So common difference = 1/30
The next 2 terms are 12/30 and 13/30
= 2/5 , 13/30.
The model of a trinomial is shown.
An algebra tile configuration. 0 tiles are in the Factor 1 spot and 0 tiles are in the Factor 2 spot. 24 tiles are in the Product spot: 1 is labeled + x squared, 7 are labeled negative x, the 2 tiles below + x squared are labeled + x, and the 14 tiles below the negative x tiles are labeled negative.
What are the factors of the trinomial? Select two options.
x – 14
x + 7
x – 7
x – 2
x + 2
The factors of the trinomial are:
x – 7x + 2Options C and E
This is further explained below.
What is trinomial?Generally, A trinomial is a kind of polynomial that is used in basic mathematics. It is composed of three components, also known as monomials.
In conclusion, The following expressions are the components of the trinomial: x - 7, x + 2
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The geometry of the hybrid orbitals about a central atom with sp3d hybridization is:________
For sp3d hybridized central atoms, the only possible molecular geometry is trigonal bipyramidal.
Hybridisation (or hybridization) is a process of mathematically combining two or more atomic orbitals from the same atom to form an entirely new orbital different from its components and hence being called as a hybrid orbital.
In this case, if all the bonds are in place, the shape is also trigonal bipyramidal.
In chemistry, a trigonal bipyramid formation is a molecular geometry with one atom at the center and 5 more atoms at the corners of a triangular bipyramid.
Bond angle(s): 90°, 120°
Coordination number: 5
Point group: D3h
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A gardener has 520 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing.
garden bordered by a river
What dimensions would guarantee that the garden has the greatest possible area?
shorter side: _____ft (feet)
longer side: ____ft (feet)
greatest possible area: ___ft2 (square-feet)
The shortest side is 130 feet, the longest side is 260 feet and the greatest possible area is 33800 square feet
What dimensions would guarantee that the garden has the greatest possible area?The given parameter is
Perimeter, P = 520 feet
Represent the shorter side with x and the longer side with y
One side of the garden is bordered by a river:
So the perimeter is:
P = 2x + y
Substitute P = 520
2x + y = 520
Make y the subject
y = 520 - 2x
The area is
A = xy
Substitute y = 520 - 2x in A = xy
A = x(520 - 2x)
Expand
A = 520x - 2x^2
Differentiate
A' = 520 - 4x
Set to 0
520 - 4x = 0
Rewrite as:
4x= 520
Divide by 4
x= 130
Substitute x= 130 in y = 520 - 2x
y = 520 - 2 *130
Evaluate
y = 260
The area is then calculated as:
A = xy
This gives
A = 130 * 260
Evaluate
A = 33800
Hence, the shortest side is 130 feet, the longest side is 260 feet and the greatest possible area is 33800 square feet
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How to factorise completely please help this is algebra
Answer:
Below in bold.
Step-by-step explanation:
9t^2 - u^2 (the difference of 2 squares)
= (3t - u) (3t + u).
2c - 4d - pc + 2pd
= 2(c - 2d) - p(c - 2d)
c -2d is common to both parts so the factors are:
(2 - p)(c - 2d)
The real solutions to the quadratic -x² - 2x+5=0 are:
2± √√29
2
-1±-√6
No real solutions.
None of the choices are correct.
Answer:
No real solutions.
Step-by-step explanation:
To solve this, we need to use Quadratic Formula.
Quadratic Formula:
[tex]x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ [/tex]
in the form of:
[tex]a {x}^{2} + bx + c[/tex]
Given information from the question, we can deduce:
a = -1
b = -2
c = 5
Let's substitute these values into the formula.
[tex]x = \frac{ - ( - 2) + - \sqrt{ {( - 2)}^{2} - 4( - 1)( -5)} }{2( - 1)} \\ = no \: real \: solutions[/tex]
if you punch these into the calculator.
The table represents an exponential function. what is the multiplicative rate of change of the function? a. 1/5 b. 2/5 c. 2 d. 5
Después de 15 meses de haber prestado un capital al 5% de rédito, tengo que pagar de interés Q468.75. ¿Qué capital se ha prestado?
The capital borrowed, or the principal when the interest was Q468.75 is Q7500.
The principal P, amount borrowed, at a certain rate of interest R%, for a time of T years, giving an interest of I, can be calculated using the formula:
P = (I * 100)/(R * T).
In the question, we are asked to find the capital borrowed, that is, the principal, when the user pays Q468.75 after 15 months at 5% of income.
Thus, Interest (I) = Q468.75, rate of interest (R) = 5%, and time (T) = 15 months = 15/12 years = 1.25 years.
Thus, the principal P, can be calculated by substituting the values in the formula: P = (I * 100)/(R * T).
P = (468.75*100)/(5*1.25),
or, P = 46875/6.25,
or, P = 7500.
Thus, the capital borrowed, or the principal when the interest was Q468.75 is Q7500.
The provided question is in Spanish. The question in English is:
"After 15 months of having borrowed capital at 5% of income, I have to pay Q468.75 in interest. What capital has been borrowed?"
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Help asap brb.asap asap will give max points
Answer:
[tex]3^{3}[/tex]
Step-by-step explanation:
Note: When you divide exponents with the same constant, the exponent will be subtracted, and vice-versa, when you multiply exponents with the same constant, the exponents will be added.
[tex]\frac{3^{-9} }{3^{-12} } \\= 3^{-9-(-12)} \\=3^{-9+12} \\=3^{3}[/tex]
In the expression (ax+b)*(cx^2+dx+e), find two set of values of a,b,c,d and e so that the coefficient of x^3and x terms after expansion are 4and 10 respectively.
Answer:
2, 0, 2, 3, 5
1, 2, 4, 0, 5
Step-by-step explanation:
(ax + b)(cx² + dx + e)
acx³ + adx² + aex + bcx² + bdx + be
2(2)x³ + 2(3)x² + 2(5)x + 0 + 0 + 0
4x³ + 6x² + 10x
a = 2
b = 0
c = 2
d = 3
e = 5
1(4)x³ + 1(0)x² + 1(10)x + 2(4)x² + 0 + 10
4x³ + 8x² + 10x + 10
a = 1
b = 2
c = 4
d = 0
e = 5