Answers
================================================
Work Shown:
Before we can use derivatives, we need to find the value of s when (x,y) = (15,20)
s^2 = x^2+y^2
s^2 = 15^2+20^2
s^2 = 225+400
s^2 = 625
s = sqrt(625)
s = 25
-----------
Now we can apply the derivative to both sides to get the following. Don't forget to use the chain rule.
s^2 = x^2 + y^2
d/dt[s^2] = d/dt[x^2 + y^2]
d/dt[s^2] = d/dt[x^2] + d/dt[y^2]
2s*ds/dt = 2x*dx/dt + 2y*dy/dt
2(25)*ds/dt = 2(15)*5 + 2(20)*(10)
50*ds/dt = 150 + 400
50*ds/dt = 550
ds/dt = 550/50
ds/dt = 11
-----------
Side note: The information t = 40 is never used. It's just extra info.
Related Questions
What is blank 8 3/4 - 2/3 - blank = 3 1/10
Answers
Answer:
151/30
Step-by-step explanation:
if you subsitute it you will get 3 1/10
Please help me with this question
Answers
Rewrite the equation by completing the square x^2+2x-3=0
Answers
Answer:
( x+1)^2 = 4
Step-by-step explanation:
x^2+2x-3=0
Add 3 to each side
x^2 +2x = 3
Take the coefficient of x
2
Divide by 2
2/2 =1
Square it
1^2 =1
Add to each side
x^2 +2x = 3
x^2 + 2x+1 = 3+1
( x+1)^2 = 4
Take the square root of each side
x+1 = ±2
Subtract 1 from each side
x+1-1 = -1 ±2
x = -1+2 x = -1-2
x =1 x = -3
How many inches apart will four bolts be along the circumference of the metal plate shown in the figure to the right
Answers
The number of inches apart that the four bolts will be along the circumference of the metal plate shown in the figure is 9.425 inches.
What is the circumference?The circumference refers to the total distance around a circle.
The circumference can determined using the following formula.
Circumference = 2πr
Diameter of the circle = 12 inches
Radius = 12/2 inches = 6 inches
Circumference = 2 x 22/7 x 6
= 37.7 inches
The number of bolts along the circumference = 4
Distance between the four bolts = 9.425 inches (37.8 ÷ 4)
Thus, using division operation, the distance apart of the four bolts is 9.425 inches.
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Which of these is the correct ratio of strawberries to blueberries for the fruit salad?
A. 8 strawberries: 30 blueberries
B. 8 strawberries: 8 blueberries
C. 4 strawberries: 30 blueberries
D. 32 strawberries: 30 blueberries
Answers
The ratio of the strawberries to the blueberries is 32 strawberries: 30 blueberries (option d).
What is the ratio?
Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s). The sign that is used to represent ratio is :.
The ratio of strawberries to blueberries - total number of strawberries : total number of blueberries.
(8 x 4) : 30
32 : 30
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Answer: A. 8 strawberries: 30 blueberries
Step-by-step explanation:
Find the value of 9y - 7 given that -2y + 1 = 7
Answers
Answer:
Brainleist! I need points see below
Step-by-step explanation:
-2y+1=7
-2y = 6
y = -3
now plug in
9 (-3) - 7
-27-7
-34
Need points! Because this useless mod deleted my answers for no reason
100 POINTS PLEASE HELP FAST
Select the correct answer.
The weight of a radioactive isotope was 96 grams at the start of an experiment. After one hour, the weight of the isotope was half of its initial weight. After two hours, the weight of the isotope was half of its weight the previous hour. If this pattern continues, which of the following graphs represents the weight of the radioactive isotope over time?
Answers
The top left graph represents the weight of the radioactive isotope over time.
How to define an exponential function?An exponential function has the definition presented according to the equation as follows:
\(y = ab^x\)
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The parameter values for the function in this problem are given as follows:
a = 96, b = 0.5.
Hence the function is given as follows:
\(y = 96(0.5)^x\)
Two points on the graph of the function are given as follows:
(1,48) and (2, 24).
Hence the top left graph represents the weight of the radioactive isotope over time.
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Answer:
Graph W
Step-by-step explanation:
The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.
Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).
The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.
Initial weight: 96 grams
After 1 hour: 96 / 2 = 48 grams
After 2 hours: 48 / 2 = 24 grams
After 3 hours: 24 / 2 = 12 grams
After 4 hours: 12 / 2 = 6 grams
After 5 hours: 6 / 2 = 3 grams
So, the points on the graph would be:
(0, 96), (1, 48), (2, 24), (3, 12), (4, 6), (5, 3)Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.
List the terms of the polynomial. Give the coefficient of the second term. -4y5 + 6x4 +9w³ - 4w - 1 Separate terms using commas. Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c . Make sure your variables match those in the question. Terms Coefficient
Answers
The coefficient of the second term, 6x⁴, is 6.
The terms of the polynomial are:
-4y⁵, 6x⁴, 9w³, -4w, -1
The coefficient of the second term, which is 6x⁴, we look at the number in front of the variable term.
The coefficient is 6.
Therefore, the list of terms is:
-4y⁵, 6x⁴, 9w³, -4w, -1
Each term represents a separate component of the polynomial, where the variable is raised to a certain power and multiplied by its coefficient.
The coefficients indicate the scalar value by which each term is multiplied.
The polynomial's terms are -4y5, 6x4, 9w3, -4w, and -1.
Looking at the number in front of the variable term, we can determine the second term's coefficient, which is 6x4.
There is a 6 coefficient.
As a result, the terms are as follows: -4y5, 6x4, 9w3, -4w, and -1.
Each term represents a different part of the polynomial, where the variable is multiplied by its coefficient and raised to a given power.
The scalar value by which each phrase is multiplied is shown by the coefficients.
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What is a tessellation, how are tessellations used, and what must happen at vertices in order for polygons to tessellate?
Answers
A tessellation is a pattern made by repeating geometric shapes without any gaps or overlaps. These shapes, called tiles or polygons, fit together perfectly to cover a plane or a surface. Tessellations can be found in various forms of art, architecture, and design. They are used to create visually appealing patterns and decorations, as well as to explore mathematical concepts.
Tessellations are utilized in various practical applications, such as tiling floors, walls, and pavements, designing mosaics and quilts, and creating computer graphics and textile patterns. They are also studied in mathematics to understand concepts like symmetry, geometry, and transformations.
For polygons to tessellate, certain conditions must be met at their vertices. At each vertex, the angles formed by the polygons must add up to a whole number of degrees, typically 360 degrees. In other words, the sum of the interior angles of each polygon meeting at a vertex must be a multiple of 360 degrees.
This ensures that the polygons can fit together seamlessly without leaving any gaps or overlaps. Examples of polygons that tessellate include equilateral triangles, squares, and hexagons, as their angles add up to 360 degrees at each vertex.
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The net of a triangular prism isgiven below. Find the surfacearea of the triangular prism.
Answers
Given:
Height of the prism = 9 cm
Dimensions of the base triangle are:
height of the triangle = 3 cm
Base length = 4 cm
Required:
Find the area of the triangular prism.
Explanation:
The surface area of the triangular prism is given by the formula:
\(A=(Perimeter\text{ of the base}\times length\text{ of the prism\rparen+\lparen2}\times base\text{ area\rparen}\)Substitute the given values in the formula.
\(A=[(4+4+4)\times9]+2(\frac{1}{2}\times4\times3)\)\(\)What are the values of x that satisfy the equation x2 + 4x - 1 = 0?
O A-
45
O B 4+13
OC -2 13
D. 2+5
Answers
Step1: write out the equation
\(x^2+4x-1=0^{}\)Looking at the equation it cannot be factorized, hence we use the quadratic formula method
Step2: write out the quadratic formula
\(\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \end{gathered}\)where a=coefficient ofx²=1
b=coefficient of x=+4
c= constant =-1
Step3: Substitute the values into the formula above
\(x=\frac{-4\pm\sqrt[]{4^2-4(1)(-1)}}{2(1)}\)\(\begin{gathered} x=\frac{-4\pm\sqrt[]{16+4}}{2} \\ =\frac{-4\pm\sqrt[]{20}}{2} \end{gathered}\)Hence, by splitting the denominator we have
\(\begin{gathered} x=\frac{-4}{2}\pm\frac{\sqrt[]{20}}{2} \\ =-2\pm\frac{\sqrt[]{4\times5}}{2} \\ =-2\pm\frac{2\sqrt[]{5}}{2} \\ =-2\pm\sqrt[]{5} \end{gathered}\)x=-2±√5
Therefore the right option is c
An angle that measures 133º.
Answers
Answer:
The angle is a Obtuse Angle
The water usage at a car wash is modeled by the equation W(x) = 5x3 + 9x2 − 14x + 9, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours. Write a function, C(x), to model the water used by the car wash on a shorter day. C(x) = 5x3 + 7x2 − 14x − 6 C(x) = 4x3 + 7x2 − 14x + 6 C(x) = 4x3 + 7x2 − 14x − 6 C(x) = 5x3 + 7x2 − 14x + 6
Answers
W(x) - C(x) = 2(W(x) - C(x))
Solving this equation for C(x), we get:
C(x) = (W(x) - 2W(x))
= W(x)(1 - 2)
= (5x3 + 9x2 - 14x + 9)(1 - 2)
= (5x3 + 7x2 - 14x + 6)
Therefore, the function C(x) to model the water used by the car wash on a shorter day is:
C(x) = (5x3 + 7x2 - 14x + 6)
Find the area of rhombus shaped field, if the length of each side be 1.8 dm and the altitude be 14 cm. * a)252 cm² b)224 cm² c)242 cm²
Answers
We have
1.8 dm to centimters it is 18 cm
Then for the area we will use
\(A=a\cdot h\)a is the side and h is the height
a=18 cm
h=14 cm
we substitute
\(A=18\cdot14=252\text{ cm}^2\)ANSWER
a)252 cm²
The graph below could be the graph of which exponential function?
||||
5
5
Answers
The graph could be the graph of exponential function of option b)
\(F(x) = 2 • (0.5)^{x} \)
The general form of an exponential function is
\(f(x) = {ab}^{x} \)
Here, a is the function's starting value and b is its growth factor.
F(x) is an increasing function if b > 1, and if b<1, then f(x) is a decreasing function
The function's initial value is 2 as can be seen from the provided graph. Therefore, a has a value of 2.
Given that the graph indicates that the function is decreasing, b must be less than 1.
It indicates that the necessary function is in the form of
\(f(x) = 2(b)^{x} \)
Where it is b<1
By checking option B, b=0.5<1. Hence, option B is the correct answer
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Note that the full question is:
(check the attached image)
find the point p that partitions the line segment AB given the ratio. A(3,5)B(4,3) with the ratio. 3:1
Answers
The coordinates of p which divides the line AB in ratio 3:1 is (3.75, 3.5).
What is section Formula?The section formula provides the coordinates of a point that, either internally or externally, divides the line connecting two locations in a ratio.
P ( x , y ) = ( c ⋅ m + a ⋅ n m + n , d ⋅ m + b ⋅ n m + n ) .
Ratio of line = 3:2
m and n represents the ratios 3:2
let the coordinates of p(x, y).
using Section formula
= [ (3(4) + 1(3) / (3+1), 3(3) + 1(5) / 3+ 1]
= (15/ 4, 14/4)
= (3.75, 3.5)
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2. Kasie lives in Seattle. She can see her house from the observation deck of the Seattle Space Needle. The
observation deck is 520 feet above the ground and the angle of depression from the deck to her house
is 70. What is the direct distance from the base of the Space Needle to Kasie's house? Round your
answer to the nearest foot.
Answers
Direct distance from the base of the Space Needle to Kasie's house = 1429 feet.
What is angle of depression?The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.
Given,
Height of the observation deck AB = 520 feet
Angle of depression = 70°
Distance of the Space needle base to house BC = ?
By the figure,
tan70° = AB/BC
BC = tan70°(AB)
BC = 2.7475(520)
BC = 1428.7 feet
Distance of the Space needle base to house to nearest foot = 1429 feet
Hence, 1429 feet is the distance between base of the Space Needle to Kasie's house.
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Time sensitive! Please get back to me within the next 30 minutes :)
At a bakery, a latte costs three times as much as a bagel. I bought a latte and a bagel, and the
total cost was $5.00. How much does a latte cost, and how much does a bagel cost?
Answers
Answer:
bagel $1.25
latte: $3.75
Step-by-step explanation:
Let the price of a bagel = b.
A latte costs 3 times as much as a bagel, so the price of a latte is 3b.
b + 3b = 5
4b = 5
b = 1.25
3b = 3.75
Answer:
bagel $1.25
latte: $3.75
Answer: A bagel cost 1.25$ and a latte cost 3.75$
Step-by-step explanation:
Let a latte be y
Let a bagel be x
3x = y Total cost = 5$
A bagel is x, plus the 3x
4x = 5
x = 1.25
Sub back into 3x = y
3*1.25 = 3.75
Solve for x.
-7/8x=-5
Ox= 4 3/8
Ox=-4 3/8
Ox=5 5/7
Help please
Answers
Answer: \(x=5\frac{5}{7}\)
Step-by-step explanation:
\(-\frac{7}{8} x=-5\)
multiply both sides by \(-\frac{8}{7}\)
\((-\frac{8}{7})( -\frac{7}{8}) x=-5(-\frac{8}{7} )\\x=\frac{40}{7\\}\\x=5\frac{5}{7}\)
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is 15 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles. Do not include the degree symbol in your answer.
Answers
Answer:
x = 45
y = 60
z = 75
Step-by-step explanation:
We can create three different equations with the given variables:
x + y + z = 180
y + z = 3 x
z = y + 15
then we can use this last equation to substitute for 'z" in the second equation:
y + z = 3x
y + y + 15 = 3 x
2 y + 15 = 3 x
x = 2/3 y + 5
Then we can re-write the first equation in terms of y and solve for this unknown:
2/3 y + 5 + y + y + 15 = 180
2/3 y + 2 y = 160
8/3 y = 160
y = 3 * 160 /8
y = 60
Then x = 2/3 (60) + 5 = 45
so x = 45
and finally: z = 60 + 15 = 75
so z = 75
What is the solution? 4p – 12 = 8 + 4p + 5p
a. 16
b. 6
c. -5
d. -4
Answers
Answer:
d. -4
Step-by-step explanation:
4p – 12 = 8 + 4p + 5p4p – 12 = 8 + 9p4p – 9p = 8 + 12– 5p = 20p = 20 ÷ (– 5)p = – 4What is the solution? 4p – 12 = 8 + 4p + 5p
a. 16
b. 6
c. -5
d. -4
Answer:-Option d. -4
Explanation:-=> 4p – 12 = 8 + 4p + 5p
=> 4p - 4p - 5p = 8 + 12
=> -5p = 20
=> p = 20/(-5)
=> p = -4
paula bought an electric drill at 75% of the regular price.She paid 32.90 for the drill. What was the regular price?(round to the nearest cent)
Answers
Answer:
$43.87.
Step-by-step explanation:
let the regular price be x, then
0.75x = 32.9
x = 32.9 / 0.75 = $43.87
Answer:
43.87
Step-by-step explanation:
Let the regular price be T
T x 75% = 32.903T/4 = 32.903T = 4 x 32.903T = 131.60T = 43.87100 points. You earned $1600 in interest in your savings account over 10 years at a rate of 8%. How much money did you originally deposit into your savings account?
Answers
A = p(1+r)^t
1600 = p(1+0.08)¹⁰
P = 1600/2.1589
P= 741.12
741.12 dollar money did you originally deposit into your savings account!
Answer:
Simple interest: Principal = $2000
Annual compound interest: Principal = $1380.59
Step-by-step explanation:
As the question does not stipulate which type of interest was applied, please find below calculations for both simple interest and annual compound interest.
Simple Interest Formula
I = Prt
where:
I = interest accruedP = principalr = interest rate (in decimal form)t = time (in years)Given:
I = $1600r = 8% = 0.08t = 10 yearsSubstitute the given values into the formula and solve for P:
\(\implies \sf 1600=P(0.08)(10)\)
\(\implies \sf 1600=0.8P\)
\(\implies \sf P=\dfrac{1600}{0.8}\)
\(\implies \sf P=2000\)
Therefore, the initial deposit (principal) was $2000.
.....................................................................................................
Annual Compound Interest Formula
\(\large \text{$ \sf I=P\left[\left(1+r\right)^{t} -1\right]$}\)
where:
I = interest accruedP = principal amountr = interest rate (in decimal form)t = time (in years)Given:
I = $1600r = 8% = 0.08t = 10 yearsSubstitute the given values into the formula and solve for P:
\(\implies \sf 1600=P\left[\left(1+0.08)^{10}-1\right]\)
\(\implies \sf 1600=P\left[\left(1.08)^{10}-1\right]\)
\(\implies \sf 1600=P\left[2.15892...-1\right]\)
\(\implies \sf 1600=P\left[1.15892...\right]\)
\(\implies \sf P=\dfrac{1600}{1.15892...}\)
\(\implies \sf P=1380.5897...\)
Therefore, the initial deposit (principal) was $1380.59 (nearest cent).
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The power P that must be delivered by a car's engine varies directly as the distance dthat the car moves and inversely as the time t required to move that distance. To move the car 1,400ft in 70s, the engine must deliver 112kilowatts (kW) of power. Find the distance (in feet) the car moves when 148kW of power is delivered for 90s. Enter the answer as an integer. Round to the nearest whole unit, if needed.
Answers
Answer:
P ∝ d
P ∝ 1/t
Using this information, we can establish a formula:
P = Kd/t , where K is some constant
We need to determine that constant using the initial conditions.
d = 2100 ft
t = 70 s
P = 180 KW
K = Pt/d
K = [(180 kW)(70s)] / 2100 ft
K = 6 kW s / ft
We can now find the distance of the car when P = 204 kW and t = 90s
P = Kd/t
d = Pt/K
d = [(204 kW)(90 s)] / (6 kWs /ft)
d = 3060 ft
One jar of spaghetti sauce is made with 1/4 of a cup of tomatoes. How many full jars of spaghetti sauce can be made with 3 cups of tomatoes?
Answers
Answer:
you can make 12 cans of them
Please help I’m stuck and keep getting the wrong answer
Answers
The time spent higher than 26 meters above the ground is 0.42 minutes. Answer: 0.42
A Ferris wheel is 30 meters in diameter and boarded from a platform that is 4 meters above the ground.
The six o'clock position on the Ferris wheel is level with the loading platform.
The wheel completes 1 full revolution in 2 minutes.
We have to find how many minutes of the ride are spent higher than 26 meters above the ground.
So, let's start with some given data,Consider the height of a person at the six o'clock position = 4 meters
So, the height of a person at the highest point = 4 + 15 = 19 meters (since the diameter is 30 meters, the radius will be 15 meters)
Also, the height of a person at the lowest point = 4 - 15 = -11 meters
Therefore, the Ferris wheel completes one cycle from the lowest point to the highest point and back to the lowest point.
So, the total distance travelled will be = 19 + 11 = 30 meters.
Also, we are given that the wheel completes 1 full revolution in 2 minutes.
We need to calculate the time spent higher than 26 meters above the ground.
So, the angle between the 6 o'clock position and 2 o'clock position will be equal to the angle between the 6 o'clock position and the highest point.
This angle can be calculated as follows:
Angle = Distance travelled by the Ferris wheel / Circumference of the Ferris wheel * 360 degrees
Angle = 30 / (pi * 30) * 360 degrees
Angle = 360 degrees / pi
= 114.59 degrees
So, the total angle between the 6 o'clock position and the highest point is 114.59 degrees.
Now, we need to find out how much time is spent at an angle greater than 114.59 degrees.
This can be calculated as follows:
Time = (Angle greater than 114.59 degrees / Total angle of the Ferris wheel) * Total time taken
Time = (180 - 114.59) / 360 * 2 minutes
Time = 0.42 minutes
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Is x^-3-5y^-2 a polynomial
Answers
Answer:
Yes, it is.
Step-by-step explanation:
A polynomial is a mathematical expression containing two or more terms.
For example, a+b is a polynomial. 2a-23b+c is also a polynomial.
Hope this helps :)
Answer:
Yes x^-3-5y^-2 is a polynomial
Step-by-step explanation:
Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer. For example, 3x+2x-5 and x^-3-5y^-2 is a polynomial.
What is the circumference of the circle?
Answers
Answer:
c=40.192
Step-by-step explanation:
c=2pir
c=2*pi*6.4
c=12.8pi
c=12.8*
c=40.192
Isabel works as a tutor for $8 an hour and as a waitress for $9 an hour. This month, she worked a combined total of 93 hours at her two jobs. Let t be the number of hours Isabel worked as a tutor this month. Write an expression for the combined total dollar amount she earned this month.
Answers
We know that t is the number of hours Isabel worked as a tutor, and that she worked for a total of 93 hours. This means that the number of hours she worked as a waitress is 93 - t hours.
Now, for each of the t hours she worked as a tutor, she earned $8, so the total amount Isabel earned from that job is 8t dollars.
For each of the 93 - t hours Isabel worked as a waitress, she earned $9, so the amount she earned from her job as a waitress is 9(93 - t) dollars.
Therefore, the total amount she earned is 8t + 9(93 - t) dollars. This can be simplified to 837 - t dollars.
NEED HELP ON THIS ASAP
Answers
Answer:
CosF=A/H
CosF=24/25
CosF=0.96
F=Cos^-1(0.96)
F=16°