Using implicit differentiation, it is found that the area of the square is increasing at a rate of:
A. 4.8 m²/minThe area of a square of side length l is given by:
[tex]A = l^2[/tex]
Applying implicit differentiation, the rate of change is given by:
[tex]\frac{dA}{dt} = 2l\frac{dl}{dt}[/tex]
The side is 3 m in length, hence [tex]l = 3[/tex].Growing at a rate of 0.8 m/min, hence [tex]\frac{dl}{dt} = 0.8[/tex]Then:
[tex]\frac{dA}{dt} = 2l\frac{dl}{dt} = 2(3)(0.8) = 4.8[/tex]
Hence, option A is correct.
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draw the graphs of the lines represented by the equations 3x-4y=1 and 4x-3y=6 in the same graph. also find the coordinates of the point where the two lines intersect
Answer:
I've attached the graph with it, the intersection point is,
x = 3, y = 2
if 1cm on a map represents 37 1/2 km what does a length of 2/5cm on the map represent
Answer:
15
Step-by-step explanation:
[tex]37 \frac{1}{2} \times \frac{2}{5} = \frac{75}{2} \times \frac{2}{5} = 15[/tex]
A train travelling in a circular track of 0.75 km of radíus at 22 km/hr. Find the angle in degrees through which it turns in one minute.
Step-by-step explanation:
Radius of circular track=r=0.75km
Circumference=2πr=2πkm
Speed of train=36 km\hr
Distance moved by train in 30 seconds =36×
3600
30
=
10
3
km
For 2π km, train turns 2π
c
∴ For
10
3
km, train turns
10
3
c
=
π
54
∘
1 minute of arc=
60
1
∘
Angle turned by train =(
π
54×60
) minutes of arc.
≃1031 minutes
Answer:
vận tốc22
chiềudai0.75
t=1/60
đ=111/30
The area of a segment of a circle is the area of the corresponding sector of the circle _____ the area of the corresponding triangle.
Answer:
The area of a segment of a circle is the area of the corresponding sector of the circle minus the area of the corresponding triangle.
Step-by-step explanation:
We know area of segment of a circle is the area of the corresponding sector of the circle minus the area of the corresponding triangle.
Help anyone can help me do this question,I will mark brainlest.
Answer:
Question 3: 220 centimeters
Question 4: 31.4 millimeters
Step-by-step explanation:
Question 3:
Formula for circumference: 2πr
2πr
Exchange π for 22/7
2 · (22/7) · r
Exchange r (radius) for 35
2 · (22/7) · 35
Simplify:
2 · (22/7) · 35
44/7 · 35
220; 220 centimeters
Question 4:
Formula for circumference: 2πr
2πr
Exchange π for 3.14
2 · 3.14 · r
Exchange r (radius) for 5
2 · 3.14 · 5
Simplify:
2 · 3.14 · 5
6.28 · 5
31.4; 31.4 millimeters
Answer:
220 cm31.4 mmStep-by-step explanation:
Concept:
Here, we need to know the idea of circumference.
The circumference is the perimeter of a circle. The perimeter is the curve length around any closed figure.
Circumference = 2πr
Solve:
Question # 1
r = 35 cm
π = 22/7
Circumference = 2πr
Circumference = 2 (22/7) (35)
Circumference = 2 (110)
Circumference = 220 cm
Question # 2
r = 5 mm
π = 3.14
Circumference = 2πr
Circumference = 2 (3.14) (5)
Circumference = 10 (3.14)
Circumference = 31.4 mm
Hope this helps!! :)
Please let me know if you have any questions
please help in indices
[tex] \frac{ {5}^{m + 2} - {5}^{m} }{ {5}^{m + 1} + {5}^{m} } \\ \\ \frac{ {4}^{m} + {4}^{m + 1} }{ {4}^{m + 2} - {4}^{m} } [/tex]
Step-by-step explanation:
Hey there!
Please see your required answer in picture.
Hope it helps!
Please find attached photograph for your answer.
Hope it helps.
Do comment if you have any query.
What is the solution set of 7x 2 + 3x = 0?
{0, 3/7}
{0, -3/7}
{0, -4/7}
Answer:
the answer is b when we have two positives it makes a negitive therefore its b
Step-by-step explanation:
please tell me what x =?
Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.
Remember: SOH-CAH-TOA
Looking from angle x, we know the opposite side and the adjacent side. Therefore, we should use the tangent function to solve.
tan(x) = 8/10
x = tan^-1(8/10)
x = 38.7 degrees
Hope this helps!
If you rolled a die, what is the probability that you would roll a 3 or a 9? Give your answer as a simplified fraction.
P(3 or 9) =
Answer: P (3 or 9) = 1/6
Step-by-step explanation:
Concept:
Here, we need to know the idea of probability.
Probability is a measure of the likelihood of an event to occur.
If you are still confused, please refer to the attachment below for a graphical explanation.
Solve:
The numbers on a dice: 1, 2, 3, 4, 5, 6
Total numbers = 6
Number of 3 = 1
Number of 9 = 0
P (3 or 9) = Favorable / Total (refer to the attachment below)
P (3 or 9) = (1 + 0) / (6)
P (3 or 9) = 1 / 6
Hope this helps!! :)
Please let me know if you have any questions
(2/3)^x-1=27/8, Find x. Please show a step-by-step explanation.
NB:x is an exponent.
[tex]( \frac{2}{3} ) {x - 1 = \frac{27}{8} }^{?} [/tex]
Answer:
x = -2
[tex](2/3)^{(x-1)} = \frac{27}{8}[/tex]
Step-by-step explanation:
you have to use logs here
[tex]ln((2/3)^{x} ) =ln(27/8)\\x ln((2/3) ) =ln(275/8)\\\\[/tex]
x-1 =ln(27/8)/ ln(2/3)
x -1 = -3
x = -2
Find the volume of this cylinder.
As soon as possible please..
Answer:
144
Step-by-step explanation:
V=PIr^2h
PI=3
V=3r^2h
r=2 h=12
V=3(2^2)12
V=3(4)12
V=12(12)
V=144in^3
Step-by-step explanation:
36 in ^3 is the volume of cylinder
Test
Subre
Which of these graphs represents a function?
1
2
1
45-43-2-1,
1 2 3 4 5
5-4-3-
-1:
1 2 3 4
2
3
4
.5
5
W.
X.
2
-2-1,
1 2 3 4
5-4-3-2-N 1 2 3 4 5
-3
.
Y
A w
B.
Х
Ос. Ү
OD. Z
arch
O
RI
99.
a
Answer:
88
Step-by-step explanation:
that's what I got and it was right
Using the theorem of the vertical line test, the graph c represents a function
How to determine the graph?For a graph to represent a function, the graph must pass the vertical line test
The above means that each x value must point to exactly one y value
Using the above as a guide, we can conclude that the graph c represents a function
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. Doanh nghiệp dự tính đầu tư góp vốn liên doanh với số tiền ban đầu là 500 trđ, trong vòng 4 năm, lãi suất dự kiến là 12%/năm. Tính tổng số lãi của hoạt động đầu tư liên doanh thu được sau khi kết thúc liên doanh ?
It cost 2.10 for a gourmet coffee shop to make a small latte.The price of a small latte is 2.94.What is the percent markup on the latte
Answer:
40%
Step-by-step explanation:
Given that :
Cost of production of small latte = 2.10
Sale price of small latte = 2.94
The Markup = Sale price of small latte - cost of production of small latte
The Markup = 2.94 - 2.10 = 0.84
Percentage Markup = (0.84 / 2.10) * 100%
Percentage Markup = 0.4 * 100% = 40%
Find the value of y. Round
the nearest tenth.
Answer: 178.3
Step-by-step explanation:
Use cos to find the value of x: cos(27)=350/x
You will find x = 392.81
Using this value, find sin(27): Sin(27)=y/392.81
You will find y=178.33
Rounding to the nearest tenth, you get 178.3
Find the missing segment in the image below
Answer:
? = 42
Step-by-step explanation:
24/8 = ?/14
cross mult
24/8 = x/14
336=8x
x = 42
The zero of the polynomial f(x) = 2x+7 is ___________.
Answer:
f(x)=2×+7 is=21
Step-by-step explanation:
i dont know that oh! i hope it helps for you
Can some some help me with this one?
Answer: 7.5 x 10^3 is the answer.
Step-by-step explanation: First, 7.5 x 10^9 is 7500000000. Next, if you convert it to kilometers you would get 7500. And, 7.5 x 10^3 = 7500. Thus, that is the answer.
Find the
Prove that sin theta tan theta= (1 + sec theta)(1 - cos theta)
Answer:
Step-by-step explanation:
RHS = (1 +Sec Ф)(1 - Cos Ф)
= 1*1 - 1*Cos Ф + Sec Ф *1 - Sec Ф *Cos Ф
= 1 - Cos Ф + Sec Ф - 1 {Sec Ф = [tex]\frac{1}{Cos \ theta}[/tex] )
=Sec Ф - Cos Ф
= [tex]\frac{1}{Cos \ theta}[/tex] - Cos Ф
[tex]= \frac{1}{Cos \ theta}-\frac{Cos \ theta*Cos \ theta}{Cos \ theta}\\\\= \frac{1-Cos^{2} \ theta}{Cos \ theta}\\\\= \frac{Sin^{2} \ theta}{Cos \ theta}\\\\=\frac{Sin \ theta*Sin \ theta}{Cos \ theta}\\\\= Sin \ theta*\frac{Sin \ theta}{Cos \ theta}[/tex]
= Sin Ф* tan Ф = LHS
The entrance fee to a local waterpark is $34 per person. At the waterpark, you can rent a raft for $1.50 per hour. Which expression is equivalent to the amount it would cost Leah for h hours in the park if she rented a raft?
Answer: 34+1.50h
Step-by-step explanation:
Algebraic Equation:
The entrance fee to the waterpark is the intial cost for Leah to get in the park. The amount of hours that Leah will spend at the park is a variable.
You need to add the intial cost and the variable amounts together.
34+h
You put the h in the equation because you don't know how long Leah will spend on the raft. You will be multiply by the rate per hour for a raft.
34+1.50h
Therefore the cost for Leah is 34+1.50.
34 + 1.50h
Therefore, Leah’s cost is 34 + 1.50h.
State if the triangles are similar. If so, how do you know they are similar and complete the similarity statement.
ΔFED
~ ____
Answer:
FED ~ MLF
Step-by-step explanation:
∠L = ∠E
∠F = ∠F
Since both angles are congruent, that would mean all angles are congruent.
If all angles are congruent, then the triangles are always similar no matter the length of the sides.
The complete statement is [tex]\triangle FED\sim \triangle FLM[/tex].
What are the similar triangles?Similar triangles are the triangles that have the same shape, but their sizes may vary.
What is AA or angle angle similarity rule?If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.
What are vertically opposite angles?When two lines intersect each other, then the opposite angles are formed due to intersection are called vertical angles or vertically opposite angles.
According to the given question.
We have two triangles LMF and EDF
In triangles LMF and EFD we have
∠MLF = ∠DEF (given)
Also, ∠MFL = ∠DFE (vertically opposite angles)
Since, we know that " if any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other".
Therefore, by AA similarity criteria triangle FED is similar to FLM.
Hence, the complete statement is [tex]\triangle FED\sim \triangle FLM[/tex].
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Find X
Round to the nearest tenth
Answer:
x=437.3 ft
Step-by-step explanation:
cos(29)=B/H, cos(29)=x/500. x=437.3 ft
In a random sample of 190 people, 151 said that they watched educational television. Find the 90% confidence interval of the true proportion of people who watched educational television. Round intermediate answers to at least five decimal places. Round your final answers to at least three decimal places.
Answer:
(0.7465 , 0.8429 )
Step-by-step explanation:
Confidence Level - "P" values
90% 1.645
Confidence Interval - "P" values
(0.7465 , 0.8429 )
which exponential expression is equivalent to
Answer:
B
Step-by-step explanation:
(y^(4))^(1/5)=y^(4/5)
Please help i do not understand this question!
Answer:
Distributive property
Step-by-step explanation:
The rule being shown here is the distributive property, because the first binomial is taken apart and separately multiplied with the other binomial.
instruction Find m<HFG
Answer:
∠ HFG = 79°
Step-by-step explanation:
The inscribed angle HFG is half the measure of its intercepted arc, that is
∠ HFG = [tex]\frac{1}{2}[/tex] × 158° = 79°
Solve for x.
A) -9
C) -5
B) -11
D) 10
Answer:
here's the answer to your question
Answer: D. 10
Step-by-step explanation:
Concept:
Here, we need to know the triangle sum theorem.
The Triangle Sum Theorem states that the sum of the three interior angles in a triangle is always 180°.
If you are still confused, please refer to the attachment below for a graphical explanation.
Solve:
According to the Triangle Sum Theorem:
∠1 + ∠2 + ∠3 = 180
Substitute the angle values
(60) + (50) + (7x) = 180
Combine like terms
110 + 7x = 180
SUbtract 110 on both sides
110 + 7x - 110 = 180 - 110
7x = 70
Divide 7 on both sides
7x / 7 = 70 / 7
x = 10
Hope this helps!! :)
Please let me know if you have any questions
Please help me solve this guys
Answer:
Factored Form: y=(x+1) ( x+3)y=(x+1)(x+3)
X-intercepts: (-1,0), (-3,0)(−1,0),(−3,0)
Axis of Symmetry: x= -2x=−2
Vertex: (-2,-1)(−2,−1)
Domain: (\begin{gathered}(-\infty , \infty ), ( x | x ER)\\\end{gathered}
(−∞,∞),(x∣xER)
Range: y > =-1y>=−1
Given the following coordinates complete the glide reflection transformation.
hopefully this answer can help you to answer the next question.
If the ratio between the radii of two spheres is 3:7, what is the ratio of
their volumes?
A. 27:343
B. 9:49
C. 9:7
D. 21:49
Answer:
A
Step-by-step explanation:
Ratio of volume is ratio of the radius raised to the power 3.
The ratio of the volume of the spheres is 27 : 343
What is a Sphere?A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.
The Surface Area of a Sphere = 4πr²
The Volume of a Sphere = ( 4/3 ) πr³
where r is the radius of the sphere
Given data ,
The ratio of the radii of two spheres is 3:7.
Therefore, if the smaller sphere has a radius of 3x, then the larger sphere has a radius of 7x.
The ratio of the volumes of the two spheres is given by:
(Volume of smaller sphere) : (Volume of larger sphere) = (4/3)π(3x)³ : (4/3)π(7x)³
Simplifying the above expression, we get:
(Volume of smaller sphere) : (Volume of larger sphere) = 27 : 343
Hence , the ratio of the volumes of the two spheres is 27 : 343
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