When the height of a triangle is 4 cm and the area is 12 square cm, with the height increasing at 2 cm/min and the area increasing at 12 square cm/min, then the base of the triangle is changing at a rate of 5 cm/min.
Explanation:The subject of this question is Mathematics and is at the High School level. This question deals with the concept of related rates in calculus. First and foremost, remember the formula for the area of a triangle, which is A = 1/2bh, where A is the area, b is the base, and h is the height. Since we're given the rate of change of the height (dh/dt=2 cm/min) and the area (dA/dt=12 square cm/min), we can use this information in combination with the formula for the area of a triangle to derive an implicit function representing the rate of change of the base. By differentiating with respect to time t, we get dA/dt = 1/2b dh/dt + 1/2h db/dt. Plugging in the given values and solving for db/dt (the rate of change of the base length), we get db/dt = (2*dA/dt/h) - dh/dt. Then input the specific values at the given point, h = 4 cm and dA/dt = 12 square cm/min, dh/dt = 2 cm/min. The calculation results in db/dt = 5 cm/min. Therefore, the base of the triangle changes at a rate of 5 cm/min when the height is 4 cm and the area is 12 square cm.
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Divide the amounts in the ratio stated £40 in the ratio 2:3
A race car travels at a constant speed of 31m/s along a circular arc of radius 22m. What is the centripetal acceleration? a.) 1.41 m/s2 b.) 0.710 m/s2 c.) 43.7 m/s2 d.) 15.6 m/s2.
Answer:
C
The equation for this is a=v^2/r
when you plug in it is a=31^2/22=961/22=43.7m/s^2
Step-by-step explanation:
PLZ HELP.ONLY ANSWER IF YOUR 100% SURE. which equation represents a non proportional situation? A. y = 4x B. y = 5x - 1 C. y = 16x D. y = -8x
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if 100 envelopes cost 70 cents, how much would 250 cost?
Identify the reflection rule on a coordinate plane that verifies that triangle A(-1,7), B(6,5), C(-2,2) and A'(-1,-7), B'(6,-5), C'(-2,-2) triangle are congruent when reflected over the x-axis.
Final answer:
The reflection rule over the x-axis is when a point (x, y) reflects to (x, -y). Applying this rule to triangle A(-1,7), B(6,5), C(-2,2) gives us the reflected points that match the coordinates of A'(-1,-7), B'(6,-5), C'(-2,-2), proving the triangles are congruent.
Explanation:
The student is querying about the reflection of a triangle over the x-axis on a coordinate plane, specifically within the domain of Mathematics. To demonstrate that triangles A(-1,7), B(6,5), C(-2,2) and their reflected counterparts A'(-1,-7), B'(6,-5), C'(-2,-2) are congruent, we will use the reflection rule associated with reflections over the x-axis.
The reflection rule states that when a point (x, y) is reflected over the x-axis, the resulting point will be (x, -y). Applying this rule:
For point A(-1, 7), the reflection over the x-axis would be A'(-1, -7).
For point B(6, 5), the reflection would be B'(6, -5).
For point C(-2, 2), the reflection would be C'(-2, -2).
The reflected points A', B', and C' match the coordinates given for the congruent triangle, thus confirming the triangles are congruent using the reflection rule over the x-axis.
in the science center there were 236 butterflies in the fall and 128 more butterflies in the winter. in the spring ,there were 85 fewer butterflies .how many butterflies are in the science center now
If a equals James's present age write an expression for his age seven years from now
Which is a better buy? 20-ounce box of cereal for $3.60 or 28 ounce for $4.20?
At the beginning of soccer practice a water cooler contained 5 gallons of water at the end of soccer practice the water cooler is only 1/4 full how many gallons of water are in the cooler at the end of practice explain
what is the probability of randomly picking a girl without brown hair
A cell phone uses a 3.0 V battery. The circuit board it uses needs a 0.05 A current. What size resistor is needed to generate this current?
___ Ω
Answer:
the answer is 60.
Step-by-step explanation:
the school library has 97 books about space. John and 3 of his friends, each check out 9 books. how many space books are still in school libarary?
A car rental agency charges $16.00 per day plus $.15 per mile. Jim's bill for 4 days was $79.00. How many miles did he drive?
Answer:
Jim drove 100 miles
Step-by-step explanation:
the average number of minutes that it took jermaine to complete his homework assignments for a week in september was 27 minutes, with a mean absolute deviation of 4 minutes. with this informatiom, which statement is true. Pls someone help me
Answer:
On average, Jermaine spent between 23 and 31 minutes on his homework.
On average, Jermaine spent between 23 and 31 minutes on his homework.
What is Mean absolute deviation?This is defined as the average of the absolute deviations from a central point.
In this scenario, the mean absolute deviation
= 27 ± 4 minutes
= 27+4 or 27 - 4
= 31 or 23 minutes.
Therefore we can infer that Jermaine spent between 23 and 31 minutes on his homework.
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which of the following must be true?
check ALL that apply,
Jean adds 35 and 9. How can she solve using only equations to model her thinking?
What is the value of a for the following circle in general form? x^2+y^2+ax+by+c=0
The 'a' in the equation refers to the coefficient influencing the horizontal shift of a circle's center. To find 'a', you often need specifics about the circle, such as its center or radius. When such information is provided, the quadratic formula can be used to solve it.
Explanation:The given equation x2+y2+ax+by+c=0 represents the general form of a circle equation. The value of 'a' is a coefficient that impacts the horizontal shift of the circle along the x-axis. Unfortunately, without specific values attached, it is impossible to directly calculate 'a'. Nevertheless, if the equation is compared to the completed square form of a circle equation, i.e., (x-h)2+(y-k)2=r2, you can ascertain that 'a' would be -2h, where h is the x-coordinate of the circle's center.
In specific examples, for instance, if a = 1, b = 0.0211, and c = -0.0211, we can solve for x using the quadratic formula -b ± √b² - 4ac divided by 2a yielding -0.0211 ± √(0.0211)2 − 4(1)(−0.0211)/2(1), where 'a', 'b', 'c' are the coefficients from the equation of a circle in its general form.
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Dr. Adama is a botanist . She measures thhe daily hieght of a particular variety of sunflower,Sunny yellow,begining when thesunflower is 60 days old. At 60 days,the height of the sunflower is 205 centimeters. Dr. Adama finds that the growty rate ofthis sunflower is 2 centimeters per day after the first 60 days.
At Central High School, there are 60 football players and 25 cheerleaders. What is the ratio of cheerleaders to football players? please slimlfy
Answer:
The answer is 5:12
Step-by-step explanation:
Milton got a paperweight like the one shown below. He needs to fill it with sand to give it weight.
If a = 2 inches, what is the volume of the paperweight?
A.24 in3
B.56 in3
C.16 in3
D.32 in3
Solution:
Given that, Milton got a paperweight like the one shown in the figure.
The Paper Weight is in the shape of a cuboid and a cube.
Length and breadth of cuboid is a and height of the cuboid is 2a, whereas side of cube is a.
The volume of sand required to fill in the Paper Weight , is equal to the volume of the Paper weight,
Volume of Paper Weight = Volume of cube + Volume of cuboid
We know that, Volume of cube =[tex] (side)^{3} [/tex]
and , Volume of Cuboid = [tex] length \times breadth \times height [/tex]
Volume of Paper Weight = [tex] a^{3}+ (a\times a \times2a)= a^{3} +2a^{3} = 3a^{3} [/tex]
Given that , a = 2 inches , then Volume of Paper Weight = [tex] 3 \times (2)^{3}= 3\times 8 = 24 [/tex]
[tex] 24 \: in^{3} [/tex] is the volume of the paperweight.
Option A is the correct solution.
Four sets of data are shown in box-and-whisker plots. Which set has the largest MEDIAN?
Answer:
It’s c
Step-by-step explanation:
Kim is reading a book with 380 pages. She read 20 pages each day until she reached Part 2 of the book. Part 2 of the book is 160 pages long. She uses the equation 380−20d=160 to represent the number of days, d, it took her to read Part 1. How many days did it take Kim to read Part 1 of the book?
part 1 of the book took 19 days
Lee ann paid in advance for 20 hours of day care. After one week, she had used 12 3/4 hours. How many hours of day care does she have left!
PLZZZ HELP!!!! 15POINTS
In the coordinate plane, what is the length of the line segment that connects points at (4, −1) and (9, 7) ? Enter your answer in the box. Round to the nearest hundredth. units
Answer:
9.43 is correct I've taken the test on k-12
Step-by-step explanation:
8n^2-4(7m^3+5n^2)
help
Find the value of x°
25°
85°
75°
105°
Tetsuo's savings account has a balance of $1192. After 22 years, what will the amount of interest be at 1.5% compounded annually?
a.
$2622.40
c.
$467.98
b.
$450.98
d.
$461.98
Triangle DEF is congruent to triangle GHI. Side DE measures 52. Side GH measures 10x-13. Side HI measures 12x-16 find the value of x
PLZ HELP
The price of a technology stock was 9.83
yesterday. Today, the price fell to 9.72
. Find the percentage decrease. Round your answer to the nearest tenth of a percent.
@nilbert