Answer:
dA/dt = 31 in²/ sec
Step-by-step explanation:
The area of the triangle is:
A(t) = (1/2)*b*h where b is the base and h the height
Differentiation on both sides of the equation we obtain
dA/dt = (1/2)* db/dt * h + (1/2)* dh/dt * b (1)
db/dt = 3 in/sec
dh/dt = 2 n/sec
b = 10 in
h = 14 in
By substitution in (1)
dA/dt = 0,5* 3*14 + 0,5* 2*10
dA/dt = 21 in² /sec + 10 in²/sc
dA/dt = 31 in²/ sec
What is the greatest common factor of the two terms
24x^6 and 18x^4
30x^3y^5 and 25x^2y
24x⁶ and 18x⁴ —> 6x⁴
30x³y⁵ and 25 x²y —> 5x²y
find the area of the figure. round your answer to the nearest hundredth
Answer:
im sorry i cant these numbers
Step-by-step explanation:
Determine the following indefinite integrals. Check your work by differentiation.
∫4x^1/3-x^-1/3dx
Answer:
[tex]\displaystyle \int { \Big( 4x^\bigg{\frac{1}{3}} - x^\bigg{\frac{-1}{3}} \Big) } \, dx = 3x^\bigg{\frac{4}{3}} - \frac{3x^\bigg{\frac{2}{3}}}{2} + C[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
IntegralsIndefinite IntegralsIntegration Constant CIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int { \Big( 4x^\bigg{\frac{1}{3}} - x^\bigg{\frac{-1}{3}} \Big) } \, dx[/tex]
Step 2: Integrate
[Integral] Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle \int { \Big( 4x^\bigg{\frac{1}{3}} - x^\bigg{\frac{-1}{3}} \Big) } \, dx = \int {4x^\bigg{\frac{1}{3}}} \, dx - \int {x^\bigg{\frac{-1}{3}}} \, dx[/tex][1st Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int { \Big( 4x^\bigg{\frac{1}{3}} - x^\bigg{\frac{-1}{3}} \Big) } \, dx = 4\int {x^\bigg{\frac{1}{3}}} \, dx - \int {x^\bigg{\frac{-1}{3}}} \, dx[/tex][Integrals] Reverse Power Rule: [tex]\displaystyle \int { \Big( 4x^\bigg{\frac{1}{3}} - x^\bigg{\frac{-1}{3}} \Big) } \, dx = 4 \bigg( \frac{3x^\bigg{\frac{4}{3}}}{4} \bigg) - \frac{3x^\bigg{\frac{2}{3}}}{2} + C[/tex]Simplify: [tex]\displaystyle \int { \Big( 4x^\bigg{\frac{1}{3}} - x^\bigg{\frac{-1}{3}} \Big) } \, dx = 3x^\bigg{\frac{4}{3}} - \frac{3x^\bigg{\frac{2}{3}}}{2} + C[/tex]Step 3: Check
Differentiate the answer.
Rewrite [Derivative Property - Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx} \bigg[ 3x^\bigg{\frac{4}{3}} \bigg] - \frac{d}{dx} \bigg[ \frac{3x^\bigg{\frac{2}{3}}}{2} \bigg] + \frac{d}{dx} \bigg[ C \bigg][/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle 3\frac{d}{dx} \bigg[ x^\bigg{\frac{4}{3}} \bigg] - \frac{3}{2}\frac{d}{dx} \bigg[ x^\bigg{\frac{2}{3}} \bigg] + \frac{d}{dx} \bigg[ C \bigg][/tex]Basic Power Rule: [tex]\displaystyle 3 \bigg( \frac{4}{3}x^\bigg{\frac{1}{3}} \bigg) - \frac{3}{2} \bigg( \frac{2}{3}x^\bigg{\frac{-1}{3}} \bigg)[/tex]Simplify: [tex]\displaystyle 4x^\bigg{\frac{1}{3}} - x^\bigg{\frac{-1}{3}}[/tex]∴ we have found the answer.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
Help me please I’m begging worth 40 points!!!!!
round 8,437 to the nearest whole number
Answer:
the answer is 8,000.
Step-by-step explanation:
The ceiling of Stacy's living room is a square that is 25 ft long on each side. Stacy
knows the diagonal of the ceiling from corner to corner must be longer than 25 ft,
but she doesn't know how long it is.
Solve for the length of the diagonal of Stacy's ceiling in two ways:
(a) Using the Pythagorean Theorem.
(b) Using trigonometry.
Round each answer to the nearest whole number and make sure to show all your
work. (Hint: the answers should be the same!)
Please help !!!
Answer:
The answer is below
Step-by-step explanation:
a) Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It states that the square of the hypotenuse is equal to the sum of the square of the legs of the triangle.
Let x be the length of the hypotenuse, using Pythagoras:
x² = 25² + 25²
x² = 1250
x = 35 (to the nearest whole number)
b) Using sine rule:
[tex]\frac{x}{sin(90)} =\frac{25}{sin(45)} \\\\x=\frac{25}{sin(45)} *sin(90)\\\\x=35(to \ nearest\ whole\ number)[/tex]
Find the values of X and Y. Show your work.
Answer:
x = 6
y = 24
Step-by-step explanation:
Recall: length of corresponding sides of similar figures are proportional to each other.
Thus:
4/12 = x/18 = 8/y
Find x:
4/12 = x/18
1/3 = x/18
Cross multiply
3x = 18
3x/3 = 18/3
x = 6
Find y:
4/12 = 8/y
1/3 = 8/y
Cross multiply
y = 8*3
y = 24
Please help!
What is g(x)?
Answer:C
Step-by-step explanation:
Which set of coordinates satisfies the system of equations y = x − 3 and y = -2x + 1?
A.
B.
C.
D.
Answer:
C
It is the only point that connects the two lines
The probability that a student is accepted to a prestigious college is 0.3. If 5 students from the same school apply, what is the probability that at most 4 are accepted
Answer:0.849185
Step-by-step explanation:
Binomial probability formula we will use:
[tex]$P(x)=\frac{n !}{x !(n-x) !} p^{x} q^{n-x}$[/tex]
where,
[tex]n=5$\\$\mathrm{P}$ (probability of success) $=0.3$\\q=1-p[/tex]
The computation of the probability will be :
[tex]$P(x \leq 2 ; 5,0.3)=P(x=0 ; 5,0.3)+P(x=1 ; 5,0.3)+P(x=2 ; 5,0.3)+P(x=3 ; 5,0.3)$\\$=\left[\frac{5 !}{5 !(5-0) !}(0.3)^{0}(1-0.3)^{5-0}\right]+\left[\frac{5 !}{5 !(5-1) !}(0.3)^{1}(1-0.3)^{5-1}\right]$$+\left[\frac{5 !}{5 !(5-2) !}(0.3)^{2}(1-0.3)^{5-2}\right]$$++\left[\frac{5 !}{5 !(5-3) !}(0.3)^{3}(1-0.3)^{5-3}\right]$$++\left[\frac{5 !}{5 !(5-4) !}(0.3)^{4}(1-0.3)^{5-4}\right]$\\$=0.1681+0.3601+0.3087+0.006615+0.00567$\\$\Rightarrow 0.849185$[/tex]
The probability that at most 4 are accepted = 0.849185
The ceiling of Stacy's living room is a square that is 25 ft long on each side. Stacy
knows the diagonal of the ceiling from corner to corner must be longer than 25 ft,
but she doesn't know how long it is.
Solve for the length of the diagonal of Stacy's ceiling in two ways:
(a) Using the Pythagorean Theorem.
(b) Using trigonometry.
Round each answer to the nearest whole number and make sure to show all your
work. (Hint: the answers should be the same!)
Please help !!!
Answer:
A. 35 ft.
B. 35 ft
Step-by-step explanation:
Please see attached photo for diagram.
A. Determination of the diagonal using pythagorean theorem.
A square has all sides equal. Thus, the diagonal of the square can be obtained as follow:
Ist leg (L₁) = 25 ft
2nd leg (L₂) = 25 ft
Diagonal (d) =?
d² = L₁² + L₂²
d² = 25² + 25²
d² = 625 + 625
d² = 1250
Take the square root of both side
d = √1250
d = 35 ft
B. Determination of the diagonal using trigonometry.
Since all the sides in a square are equal, the angle between each leg will be 90°. Thus, the diagonal will bisect the angle between the two leg equally i.e
Angle between Diagonal and each leg = 90/2 = 45°
Finally, we shall determine the length of the diagonal. This can be obtained as follow:
Angle θ = 45°
Opposite = 25 ft
Hypothenus = d
Sine θ = Opposite / Hypothenus
Sine 45 = 25 / d
0.7071 = 25 / d
Cross multiply
0.7071 × d = 25
Divide both side by 0.7071
d = 25 / 0.7071
d = 35 ft
Answer for brainlest
Answer:
∠1 = ∠5
Step-by-step explanation:
The reason is because corresponding angles are equal! :)
Rachel ate 1 4/6 brownies, and brandy ate 6/7 of a brownie. how many brownies did they eat altogether?
Answer:
53/21 OR 2 11/21
Step-by-step explanation:
1 4/6 + 6/7
Change 1 4/6 into an improper fraction
1 4/6 6x1= 6+4= 10/6
Simplify 10/6 --> 5/3
5/3+ 6/7
find a common denominator (21)
35/21+18/21= 53/21
mixed number form is 2 11/21
Answer:
[tex]2 \frac{11}{21}[/tex]
Step-by-step explanation:
1 4/6 + 6/7 = 2 11/21
Hi I need help plz help
Answer: 120
Step-by-step explanation:
5/3 X 4/3 X 2= 40/9
40/9 Divided by 1/3
40/3
What is the meaning of amplitude and period in math?
Answer:
See below
Step-by-step explanation:
For a wave function, the amplitude is the distance from the maximum or minimum of the function to the midline. The period is the length of which the wave cycle repeats (for example y=sinx has a period of 2pi).
Answer:
Amplitude is the height from the mean, or rest,value of the function to its maximum or minimum . ...The period is the distance required for the function to complete one full cycle. For the sin function, the amplitude is given by and the period is defined as. The same is true for a cosine function.
Step-by-step explanation:
☆hope it is helpful to you ☆
[tex]nisha[/tex]
Kobe drinks
cup of juice each day. He has
juice left. For how many days will it last?
Show your answer as a multiplication
equation with 1/3 as a factor. Remember,
you can write 2 1/3 as a fraction.
1/6 _12/85/907 4456
first put h then a then aaaaaaaaaaaaaaaaaaaaaaa then hah
PLEASE HELPPPP MEEEEE, JUSTFIY PLZZ
Answer:
a. Unsure
b. True
c. Unsure
d. True
A - False
B - True
C- False
D- True
Whenever she visits Allenville, Maureen has to drive 48 miles due north from home. Whenever she visits Weston, she has to drive 14 miles due east from home. How far apart are Allenville and Weston, measured in a straight line?
Answer:
34 i belive not 100% sure but what grade level is this
Step-by-step explanation:
can someone please help me with this
Answer:
Surface Area = 139.4 (rounded to nearest tenth)
i need this done fast
Answer: 1) V≈1244.07 in 2) V≈54286.72 ft 3) V≈23816.41 yd
Step-by-step explanation:
What is the perimeter of a square whose area is 64 square kilometers?
.
A 16 km
B.32 km
c. 64 km
D.256 km
Confusion .. help please
Answer:
2
Step-by-step explanation:
We are to determine the value of KM which is adjacent to angle 35. we also have the value for the hypotenuse. Thus we would use COS
Cos 35 = adjacent /hypotenuse
0.8192 = adjacent / 123
adjacent = 0.8192 x 123 = 100.7557 cm
100.8 cm
the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero
additive inverse of -33
Additive Inverse of -33
༆ANSWER:—————————————————
[tex]\purple{\boxed{\boxed{\tt\pink{➢33}}}}[/tex]
The additive inverse of -33 is 33.Remember!»The opposite of the given integer is called its additive inverse. The sum of a number and its additive inverse is zero. For example, the additive inverse of -4 is 4, so when you add the two integer they sum will be zero.
Given f(x) = 3 and g(x) = cos(x). What is lim [F(x) - g(x)]?
x = -TT
2
4
DNE
Answer:
4
Step-by-step explanation:
[tex]\lim_{n \to \ -\pi } (f(x) - g(x))\\\\ = \lim_{n \to \ -\pi } (3 - cos x)\\\\ = 3 - cos( - \pi) = 3 - cos(\pi)\\\\ = 3 - (-1) = 3 + 1 = 4[/tex]
A car is 3 times as old as its tires were when it was as old as the tires Are now.
When it’s tires are as old as the car is now,the car will be a year older than the tires are now.
What are the present ages of car and tires?
Answer:
Present age of the car = 1.5 years and the tires are 0.5 years old.
Step-by-step explanation:
Let the present age of the car be x years and that of the tires be y years.
x = 3y
x = y + 1
3y = y + 1
2y = 1
y = 0.5.
x = 3*0.5 = 1.5.
the circle below is centered at (-1,1) and has a radius of 3. what is its equation?
Answer:
[tex](x+1)^2 + (y-1)^2 = 9\\\\or\\\\x^2 + y^2 +2x -2y -7 = 0[/tex]
Step-by-step explanation:
[tex](x +1 )^2 + (y -1)^2 = 3^2\\\\x^2 +2x +1 + y^2 + 1 -2y = 9\\\\x^2 + y^2 +2x -2y +2 -9 = 0\\\\x^2 + y^2 +2x -2y -7 = 0[/tex]
Make congruent angles. Write down the ratios.
Answer:
Ratio=BG/RT=RA/BA=TA/AG
Step-by-step explanation:
Slope Formula
What is the slope of the line with points (-3, -3) and (-1, - 2)?
Answer:
1/2
Step-by-step explanation:
Slope can be expressed with the formula below
Which is is the difference in y axis over that of x axis
m=( y2 - y1)/(x2 - x1)
( x1 y1) = (-3, -3)
x2 y2)= (-1, - 2)
= ( -2+3)/(-1+3)
m= 1/2
Hence, the slope of the line is 1/2
The two way table shows the results of a survey that asked high school students whether they have a job.
I NEEED HELPPPPPPPPP!!!!!