Answer:
The width of the conference room = 18 feet
Step-by-step explanation:
Given:
Scale drawing of a planned office space is represented as
1 in : 6 feet
To find the width of the conference room if the width in the drawing is 3 inches.
Solution:
Scale is the representation of ratio of lengths in the drawing to the actual length.
The scale given here means that 1 inch length in the drawing corresponds to 6 feet length actually.
Thus, in order to find the actual length of 3 inches, we can use unitary method
If 1 inch in drawing corresponds to = 6 feet
∴ 3 inches in drawing corresponds to = [tex]3\times 6 \ft[/tex] = 18 feet
Thus, width of the conference room = 18 feet
Celia made 3 1/2 cups of rice. A serving of rice is 2/3 cup. How many servings did ceila make?
Answer:
Celia make [tex]5\frac{1 }{4}[/tex] servings.
Step-by-step explanation:
Given:
Celia made 3 1/2 cups of rice.
A serving of rice is 2/3 cup.
Now, to find the number of servings Celia make.
Celia made [tex]3\frac{1}{2} =\frac{7}{2}\ cups.[/tex]
So, to get the number of servings we use unitary method:
If 2/3 cup of rice is of 1 serving.
So, 1 cup of rice is of = [tex]1\div\frac{2}{3}servings.[/tex]=[tex]\frac{3}{2}[/tex]
Then 7/2 cup of rice is of [tex]=\frac{7}{2} \times \frac{3}{2}[/tex]
[tex]=\frac{21}{4}=5\frac{1}{4}.[/tex]
Thus, 7/2 cup of rice is of [tex]5\frac{1 }{4}[/tex] servings.
Therefore, Celia make [tex]5\frac{1 }{4}[/tex] servings.
Ceila made 5.25 or 5 ¹/₄ servings of rice.
Ceila made 3 1/2 cups of rice. In improper fractions this is:
3 1 /2 = 7/2
The number of servings made by Ceila can be found by:
= Number of cups of rice Ceila made / Cups of rice in a serving
= 7 / 2 ÷ 2/3
= 7/2 × 3/2
= 21 / 4
= 5.25 servings
When dividing fractions, you can instead multiply the first fraction by the inverse of the second fraction.
In conclusion, Ceila made 5.25 or 5 ¹/₄ servings of rice.
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Beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle gym and the monkey bars. If Beth places the swings at point D, how could she prove that point D is equidistant from the jungle gym and monkey bars? If bisects , then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects. If bisects , then point D is equidistant from points A and B because congruent parts of congruent triangles are congruent. If bisects , then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects. If bisects , then point D is equidistant from points A and B because congruent parts of congruent triangles are congruent.
Point is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it makes up.
The angle bisector theorem states that a triangle's opposite side is divided into two halves by an angle bisector that is proportional to the triangle's other two sides.
A point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects, therefore if mACD = 90°, point D is equidistant from points A and B.
Any point on the perpendicular bisector is simply equal distance from both endpoints of the line segment on which it is drawn, according to the perpendicular bisector theorem.
The answer is that point is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it makes up.
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To prove that point D is equidistant from the jungle gym and monkey bars (points A and B), we would utilise the geometrical concept of congruent triangles. This involves drawing line segments from D to A and D to B, and if those segments are congruent, then point D is equidistant from points A and B. The process would encompass drawing a perpendicular bisector from point D to segment AB.
Explanation:To demonstrate that point D is equidistant from the jungle gym and the monkey bars, Beth would need to use specific concepts from geometry. First, she would need to identify points A and B as the jungle gym and monkey bars respectively. Point D is the location of the swings.
Next, she would draw line segments from D to A and D to B. If line segment DA is congruent to line segment DB, this means they have the same length, hence point D is an equal distance from both points A and B (the jungle gym and the monkey bars).
This can be proved through congruent triangles if a perpendicular bisector is drawn from point D to line segment AB. Such concept echoes that a point on a perpendicular bisector of a line segment is equidistant from the endpoints of the segment. The resulting triangles would be congruent, meaning every part, including the sides DA and DB, would be the same.
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A 2-liter bottle of soda (67.6 ounces) costs $1.89. A case of twelve 12 ounce
cans of the same soda costs $2.99. Calculate the unit price (price/ounce) of each
item and determine which is the better bargain.
Answer:
The better bargain is the case of twelve 12 ounce cans.
Step-by-step explanation:
2-liter bottle of soda:
67.6 ounces cost $1.89, then
1 ounce costs
[tex]\$1.89\div 67.6\approx \$0.028[/tex]
A case of twelve 12 ounce cans:
[tex]12\times 12=144[/tex] ounces of the same soda cost $2.99, then
1 ounce costs
[tex]\$2.99\div 144\approx \$0.021[/tex]
The better bargain is the second choice, the case of twelve 12 ounce cans.
The probability that a truck will be going over the speed limit on I-80 between Cheyenne and Rock Springs is 75%. Suppose a random sample of 5 trucks is observed on this stretch of I-80.
a) What is the probability that exactly 2 trucks are going over the speed limits?
Answer:
The probability that exactly 2 trucks are going over the speed limit is 56.3% (rounding to the next tenth)
Step-by-step explanation:
1. Let's check all the information provided to us to answer the question correctly:
Probability that a truck will be going over the speed limit on I-80 between Cheyenne and Rock Springs = 75%.
Number of trucks in the random sample = 5
2. What is the probability that exactly 2 trucks are going over the speed limit?
Let's recall that two events are independent if the result of the second event is not affected by the result of the 1st event. If a first truck goes over the speed limit and a second truck does the same are independent events, the probability of both events occurring is the product of the probabilities of the individual events.
P (T₁ and T₂) = P (T₁) * P (T₂)
P (T₁ and T₂ ) = 0.75 * 0.75 = 0.5625
The probability that exactly 2 trucks are going over the speed limit is 56.3% (rounding to the next tenth)
Matt had instructions to take a box of nails to a classroom that has a number equal to the remainder of the division 2960÷9. matt took the nails to class room 17. without performing calculations, tell whether matt is correct. Explain your mathematical thinking.
Answer:
Matt is not correct
Step-by-step explanation:
The remainder from division by 9 will always be a number less than 9. The number 17 is not less than 9, so Matt made an error.
_____
Matt may have tried to find the remainder by adding the digits of the dividend:
2 + 9 + 6 + 0 = 17
Matt needs to continue this process until he gets a single digit:
1 + 7 = 8
8 is the remainder from the division.
Which of the following describes the placebo effect?
O
A. At least one block of subjects in an experiment receives only
placebos.
O
B. Subjects may respond to a treatment simply because they believe
it is affecting them.
C. Subjects receive inactive sugar pills instead of real medication.
O
D. An experiment is repeated many times with real drugs and
placebos
O
E. Subjects are prevented from knowing whether they are receiving
real drugs or placebos.
Answer:
b is the correct answer
The placebo effect describes how a person might show improvement simply because they believe a treatment is working, even if it's a dummy treatment. It's an essential aspect considered during clinical studies to distinguish between actual treatment effects and the impact of patients' expectations.
Explanation:The placebo effect is best described as the phenomenon in which a person experiences a perceived improvement in their condition or symptoms simply due to their belief in the efficacy of the treatment, even if the treatment is inactive or a 'dummy' treatment, such as a sugar pill. This is represented in the provided choices by option B. Subjects may respond to a treatment simply because they believe it is affecting them.
Notably, this effect is considered in the design of clinical trials and studies. This is typically done by using a control group that receives a placebo treatment, which allows researchers to separate the physiological effects of the treatment from psychological effects induced by expectations- a crucial aspect of medical and scientific research.
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Which explicit formula gives the nth term of the sequence
0, 3, 8, 15, 24,... ?
Answer: add over and over again
Step-by-step explanation:How do you get from 0 to 3? you add 3 to 0. Then, how do you get from 3 to 8? you add another 3 but then you a 2 too, so then 8. Lastly, my last example, how to get from 8 to 15. You take five, and then add 2 to it and add that number(then number you get when you add 5+1), 7 to 8.
Colin invests £4800 into his bank account.
He receives 3% per year compound interest.
How much will Colin have after 7 years?
Give your answer to the nearest penny where appropriate.
Answer:
$5903.39
Step-by-step explanation:
This can be solve using compound interest formula. The formula is:
[tex]F=P(1+r)^t[/tex]
Where
F is the future amount (what we are looking for)
P is the present amount (which is 4800)
r is the rate of compound interest per year, in decimal (3% per year, 3/100 = 0.03)
t is the time in years ( t = 7)
Now we substitute these values into the formula and find F:
[tex]F=P(1+r)^t\\F=4800(1+0.03)^7\\F=4800(1.03)^7\\F=5903.39[/tex]
So, Colin would have $5903.39 after 7 years, in his account.
If you pute $2000 into an interest bearing account, where interest is compound quarterly (4 times a year) at 6%, how long will it take for your money to triple
Answer:
So it will take roughly 18.4471905815477 years.
(round appropriately if needed)
Step-by-step explanation:
A=P(1+r/n)^(nt)
6000=2000(1+0.06/4)^(4*t)
6000/2000 = (1+0.06/4)^(4*t)
3 = (1+0.06/4)^(4*t)
3 = (1.015)^(4*t)
log(3) = log((1.015)^(4*t))
log(3) = 4*t*log(1.015)
log(3)/(4*log(1.015)) = t
t = log(3)/(4*log(1.015))
t = 18.4471905815477
complete the synthetic division problem below -3|2 4 -4 6what is the quotient in polynomial form?
Answer:
2x^2-2x+2
Step-by-step explanation:
Solved through synthetic division
If you struggle with synthetic division you can use Math away a free calculator you can use on google.
After completing the synthetic division, the quotient in polynomial form is equal to: B. 2x² - 2x + 2.
What is synthetic division?Synthetic division can be defined as a simplified and specialized method that is used for the division of a polynomial by another polynomial of the first degree (x - n).
Also, you should use only the coefficients of the divided polynonial and its divisor and change the sign of the constant term in the divisor, in order to replace subtraction with addition.
Next, we would set up the synthetic division as follows:
-3 | 2 4 -4 6
|_________________
↓ -6 6 -6
|_________________
2 -2 2 0
Quotient = 2 -2 2 ⇒ 2x² - 2x + 2.
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What is the slope of the line through (−2,−6) and (2,2)
[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{(-6)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-2)}}}\implies \cfrac{2+6}{2+2}\implies \cfrac{8}{4}\implies 2[/tex]
The slope of the line passing through the points (−2,−6) and (2,2) is 2, calculated using the slope formula in mathematics. This means there is a rise of 2 on the y-axis for every 1 increase on the x-axis.
Explanation:Your task is to calculate the slope of a line passing through the points (−2,−6) and (2,2). In mathematics, slope is defined as the 'rise over run' - meaning, the change in the vertical axis (y-axis) for every unit increase in the horizontal axis (x-axis).
Conventionally, the slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1). Applying this formula to the given points:
m = (2 - (-6))/(2 - (-2))
m = (2 + 6)/(2 + 2) = 8/4 = 2.
So, the slope of the line that passes through points (-2,-6) and (2,2) is 2; this means there's a rise of 2 on the y-axis for every 1 increase on the x-axis when you move from point (-2, -6) to point (2, 2).
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Given that (4,7) is on the graph of f(x), find the
corresponding point for the function
f(x-2)
If [tex]P(4,7)\in G_f[/tex] where [tex]G_f=\{(x,f(x):\forall x\in\mathbb{R}\wedge f(x)\in\mathbb{R}\}[/tex] then [tex]f(x-2)[/tex] will shift the original function by 2 in the right resulting with new point [tex]P'(6,9)[/tex].
Hope this helps.
help? i dont understand.
Answer:
90-32 is the answer
Step-by-step explanation:
Because this is a right angle its total angle in degrees is 90 and if it is split in to then m1 and m2 must equal 90 degrees so if m2 is 32 degrees then m1 would be what's left which is 90-32
Oliver read for 450450450 minutes this month. His goal is to read for 10\%10%10, percent more minutes next month.
Answer: Oliver's goal is to read 45 minutes more next month
Step-by-step explanation:
Firstly, we need to know how much in minutes is the [tex]10\%[/tex] of [tex]450 min[/tex]:
[tex]450 min(10\%)=(450 min)(\frac{10}{100})=45 min[/tex]
This means Oliver wants to read 45 minutes more next month. If we add this number to the 450 minutes he read this month, we have a total of 495 minutes.
Answer:
The goal is 945 minutes
Step-by-step explanation:
Find the x- and y-intercepts of the equation -5x+y=30
Answer:
x-intercept: -6y-intercept: 30Step-by-step explanation:
You can put the equation into intercept form by dividing by 30:
-5x/30 + y/30 = 1
x/(-6) + y/30 = 1
Intercept form is ...
x/(x-intercept) +y/(y-intercept) = 1
This lets us recognize the x-intercept as -6 and the y-intercept as 30.
The table represents a linear equation. A two column table with 5 rows. The first column, x, has the entries, negative 4, negative 2, 6, 10. The second column, y, has the entries, negative 11, negative 6, 14, 24. Which equation correctly uses point (–2, –6) to write the equation of this line in point-slope form? y – 6 = y minus 6 equals StartFraction 5 Over 2 EndFraction left-parenthesis x minus 2 right parenthesis.(x – 2) y – 6 = negative StartFraction 2 Over 5 EndFraction. (x – 2) y + 6 = y plus 6 equals StartFraction 2 Over 5 EndFraction left-parenthesis x plus 2 right parenthesis.(x + 2) y + 6 = y plus 6 equals StartFraction 5 Over 2 EndFraction left-parenthesis x plus 2 right parenthesis.(x + 2)
Answer:
[tex]y+6=\frac{5}{2}(x+2)[/tex]
y plus 6 equals StartFraction 5 Over 2 EndFraction left-parenthesis x plus 2 right parenthesis.
Step-by-step explanation:
we have the ordered pairs
[tex](-4,-11),(-2,-6),(6,14),(10,24)[/tex]
step 1
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
take the points
[tex](-4,-11),(-2,-6)[/tex]
substitute the given values
[tex]m=\frac{-6+11}{-2+4}[/tex]
[tex]m=\frac{5}{2}[/tex]
step 2
Find the equation in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{5}{2}[/tex]
[tex](x1,y1)=(-2,-6)[/tex]
substitute in the equation
[tex]y-(-6)=\frac{5}{2}(x-(-2))[/tex]
[tex]y+6=\frac{5}{2}(x+2)[/tex]
Nick has to build a brick wall. Each row of the wall requires 6^2 bricks. There a
the wall?
10²x6
10^6
6^10
10×6^2
Answer:
D. [tex]10\times 6^2[/tex]
Step-by-step explanation:
Please consider the complete question.
Nick has to build a brick wall. Each row of the wall requires [tex]6^2[/tex] bricks. There are 10 rows in the wall. How many bricks will Nick require to build the wall?
To find the number of total bricks required to make the wall, we will divide bricks used to make one row [tex](6^2)[/tex] by total number of rows that is 10.
[tex]\text{Number of total bricks required}=10\times 6^2[/tex]
Therefore, Nick will require [tex]10\times 6^2[/tex] bricks to make the wall and option D is the correct choice.
Find the range of these numbers:
15,2,3,7,8,4,3,2,16,2,4
What is the area of a triangle for one of the legs being 3in and the hypotenuse being 9in
The area of a triangle for one of the legs being 3 inches and the hypotenuse being 9 inches is 12.727 square inches
Solution:
Given that to find area of a triangle for one of the legs being 3 inches and the hypotenuse being 9 inches
From given information,
Let "c" = hypotenuse = 9 inches
Let "a" = length of one of the leg of triangle = 3 inches
To find: area of triangle
The area of triangle when hypotenuse and length of one side of triangle is given:
[tex]A = \frac{1}{2} a \sqrt{c^2 - a^2}[/tex]
Where, "c" is the length of hypotenuse
"a" is the length of one side of triangle
Substituting the given values we get,
[tex]A = \frac{1}{2} \times 3 \times \sqrt{9^2 - 3^2}[/tex]
[tex]A =\frac{1}{2} \times 3 \times \sqrt{81-9}\\\\A =\frac{1}{2} \times 3 \times \sqrt{72}\\\\A =\frac{1}{2} \times 3 \times 8.48528\\\\A = \frac{1}{2} \times 25.45584\\\\A = 12.727[/tex]
Thus area of triangle is 12.727 square inches
Which of the lines has a slope of -1/2 and a y-intercept of 3?
Liner systems of equations
Answer:
8 years
Step-by-step explanation:
x years later type A and type B will have the same height
Type A = Type B: 10 + (8/12)*X = 6 + (14/12)*X
multiply 12 each side
120 + 8x = 72 + 14x
14x - 8x = 120 - 72
6x = 48
x = 8
check: A: 10 x 12 + 8 x 8 = 184
B: 6 x 12 + 14 x 8 = 184
The solution to the system of equations is x = -3 and y = 2
To solve the given system of linear equations, use the method of elimination by multiplying the equations to eliminate y, solving for x, substituting the value of x back into one of the equations to solve for y, and checking the solution.
The given system of linear equations is:
x − 7y = -11
5x + 2y = -18
To solve this system of equations, we can use the method of substitution or elimination. I will demonstrate the method of elimination:
Multiply the first equation by 5 and the second equation by 1 to make the coefficients of y in both equations the same.Add the two equations together to eliminate y and solve for x.Substitute the value of x back into one of the original equations to solve for y.Check the solution by substituting the values of x and y into both equations to ensure they satisfy both equations.The solution to the system of equations is x = -3 and y = 2.
complete question given below:
Liner systems of equations
x−7y=−11
5x+2y=−18
A rectangle has a length that is 4 units longer than the width. If the width is increased by 7 units and the length increased by 5 units, write and equivalent expression for the area of the rectangle
Answer:
The expression for Area of rectangle is [tex]x^2+16x+63[/tex].
Step-by-step explanation:
Given:
A rectangle has a length that is 4 units longer than the width.
Let the width of the rectangle be 'x' Units.
Length of rectangle will be = [tex]x+4\ Units[/tex]
If the width is increased by 7 units.
New Width of the rectangle = [tex]x+7\ Units[/tex]
Also the length increased by 5 units,
New Length of rectangle will be = [tex]x+4+5 = x+9\ Units[/tex]
We need to write an equivalent expression for area of the rectangle.
Area of rectangle is given by length times width.
framing in expression form we get;
Area of rectangle = [tex](x+7)\times(x+9)[/tex]
On Solving the equation we get;
Area of rectangle = [tex]x^2+9x+7x+63=x^2+16x+63[/tex]
Hence the expression for Area of rectangle is [tex]x^2+16x+63[/tex].
The ratio of girls to boys at a movie is 7:3 if there are 9 boys how many girls are at the movie
Work is provided in the image attached.
Final answer:
Using the ratio of 7 girls to 3 boys and knowing that there are 9 boys, we find that there are 21 girls at the movie by setting up a proportion and solving for the number of girls.
Explanation:
To find out the number of girls at the movie, we need to use the ratio given, which is 7 girls to 3 boys or 7:3. Since there are 9 boys, we can set up a proportion to solve for the number of girls (G):
7 girls : 3 boys = G girls : 9 boys
Now we cross multiply and solve for G:
7 * 9 = 3 * G
63 = 3 * G
Divide both sides by 3 to find the number of girls:
G = 63 / 3
G = 21
Therefore, there are 21 girls at the movie.
A swimming pool is being drained so it can be cleaned. The amount of water in the pool is changing according to the función f(t)= 80,000 - 16,000t , where t = time in hours and f(t) = amount of water in liters. What is the domain of this function in this situation? Explain how you found your answer.
Answer:
0 ≤ t ≤ 5.
Step-by-step explanation:
In the function [tex]f(t)[/tex], [tex]t[/tex] is the independent variable. The domain of [tex]f[/tex] is the set of all values of [tex]t[/tex] that this function can accept.
In this case, [tex]f(t)[/tex] is defined in a real-life context. Hence, consider the real-life constraints on the two variables. Both time and volume should be non-negative. In other words,
[tex]t \ge 0[/tex].[tex]f(t) \ge 0[/tex].The first condition is an inequality about [tex]t[/tex], which is indeed the independent variable.
However, the second condition is about [tex]f[/tex], the dependent variable of this function. It has to be rewritten as a condition about [tex]t[/tex].
[tex]\begin{aligned} f(t) &\ge 0 &&\text{Assumption} \cr 80000 - 16000\, t& \ge 0 && \text{Definition of} ~ f \cr 80000 & \ge 16000\, t && \begin{aligned}&\text{Add $16000\, t$} \\[-0.5em] & \text{to both sides of the inequality}\end{aligned} \cr 5 &\ge t &&\begin{aligned}&\text{Divide both sides of} \\[-0.5em] & \text{the inequality by $16000$}\end{aligned} \cr t &\le 5 && \text{Flip the inequality}\end{aligned}[/tex].
Hence, t ≤ 5.
Combine the two inequalities to obtain the domain:
0 ≤ t ≤ 5.
Graph - 2x + 4y = 4 4 for the domain D:{-8,-4,0,4,8}
Answer:
C
Lined up with the points
Rewrite 27+36 using GCF and the Distributive property
Answer:9(3+4)
Step-by-step explanation:
GCF=9 27/9=3 36/9=4
The GCF will be 9 and the expression using distributive property will be 9 ( 3 + 4 ) .
An expression 27 + 36 is given in the question.
We have to simplify the expression by using distributive property.
What is the distributive property ?
The distributive property is given by ; A ( B+ C) = AB + AC , where A, B and C are three different values.
As per the question ;
the expression is 27 + 36
Here ;
We need to find the GCF in between 27 and 36.
The greatest common factor in 27 and 36 is 9.
∵ According to the distributive property ;
A ( B + C ) = AB + AC
so ;
the expression in distributive property can be written as ;
(9 × 3) + (9 × 4)
that will be equal to ;
9 ( 3 + 4 )
So ;
27 + 36 = (9 × 3) + (9 × 4) = 9 ( 3 + 4 )
Thus , the GCF will be 9 and the expression using distributive property will be 9 ( 3 + 4 ) .
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The volume of a sphere is increasing at a rate of 6π cubic centimeters per hour. At what rate, in centimeters per hour, is its diameter increasing with respect to time at the instant the radius of the sphere is 3 centimeters.
A: 1/3
B: 1
C: √6
D: 6
Answer: Diameter is increasing as [tex]\frac{1}{3}[/tex] centimeter per hour.
Step-by-step explanation:
Alright, lets get started.
The formula for volume of sphere is given as V : [tex]\frac{4}{3}\pir^3[/tex]
The volume of a sphere is increasing at a rate of [tex]6\pi[/tex] cubic centimeters per hour.
It means : [tex]\frac{dV}{dt}=6\pi[/tex]
[tex]V=\frac{4}{3}\pi r^3[/tex]
Taking derivative with respect to t
[tex]\frac{dV}{dt}=\frac{4}{3}\pi \times 3r^2 \frac{dr}{dt}[/tex]
[tex]6\pi=4\pi r^2 \frac{dr}{dt}[/tex]
at the instant the radius of the sphere is 3 centimeters, means
[tex]\frac{dr}{dt}= \frac{6}{4 \times 3^2}[/tex]
[tex]\frac{dr}{dt}=\frac{1}{6}[/tex]
As [tex]radius = \frac{diameter}{2}[/tex]
[tex]\frac{1}{2}\frac{dD}{dt}=\frac{1}{6}[/tex]
[tex]\frac{dD}{dt} =\frac{1}{3}[/tex]
Hence diameter is increasing as [tex]\frac{1}{3}[/tex] centimeter per hour. : Answer
Hope it will help :)
The volume of a sphere is increasing at a rate of 6π cubic centimeters per hour. The rate at which its diameter is increasing with respect to time at the instant with the radius of the sphere 3 centimeters is: [tex]\mathbf{\dfrac{1}{3}}[/tex]
Option A is correct.
The volume of a sphere can be represented by using the formula:
[tex]\mathbf{V = \dfrac{4}{3}\pi r^3}[/tex]
Now, by differentiation, if we differentiate the rate at which the volume is increasing with time, we have:
[tex]\mathbf{\dfrac{dV}{dt} = \dfrac{4}{3}\pi r^3 \ \dfrac{dr}{dt}}[/tex]
[tex]\mathbf{\dfrac{dV}{dt} = 4 \pi r^2 \ \dfrac{dr}{dt}}[/tex]
Given that:
[tex]\mathbf{\dfrac{dV}{dt}= 6 \pi cm^3/ sec}[/tex] radius (r) = 3 cmReplacing the values into the differentiated equation, we have:
[tex]\mathbf{6 \pi= 4 \pi (3)^2 \ \dfrac{dr}{dt}}[/tex]
[tex]\mathbf{\ \dfrac{dr}{dt}=\dfrac{6 \pi}{4 \pi (3)^2}}[/tex]
[tex]\mathbf{\ \dfrac{dr}{dt}=\dfrac{6 }{4 \times 9}}[/tex]
[tex]\mathbf{\ \dfrac{dr}{dt}=\dfrac{1 }{6}\ cm/sec}[/tex]
Recall that radius = d/2∴
[tex]\mathbf{\dfrac{1}{2} \dfrac{dr}{dt} =\dfrac{1}{6} }[/tex]
[tex]\mathbf{ \dfrac{dr}{dt} =\dfrac{1}{6} \times \dfrac{2}{1}}[/tex]
[tex]\mathbf{ \dfrac{dr}{dt} =\dfrac{1}{3}}[/tex]
Therefore, we can conclude that the rate at which its diameter is increasing with respect to time at the instant with the radius of the sphere 3 centimeters is [tex]\mathbf{\dfrac{1}{3}}[/tex]
Learn more about spheres here:
https://brainly.com/question/11374994?referrer=searchResults
There are two spinners. The first spinner has three equal sectors labeled 1, 2, and 3. The second spinner has four equal sectors labeled 3, 4, 5, and 6. Spinners are spun once.
How many outcomes do not show an even number on the first spinner and show a 6 on the second spinner?
2
3
5
7
Answer:
2
Step-by-step explanation:
There are three numbers on the first spinner. Two are not even (1 and 3).
So there are 2 possible outcomes that work: 1 and 6 or 3 and 6.
Final answer:
There are two outcomes that meet the criteria of the question: not showing an even number on the first spinner and showing a 6 on the second spinner.
Explanation:
The question asks how many outcomes result in an odd number on the first spinner and show a 6 on the second spinner. The first spinner has three equal sectors labeled 1, 2, and 3, of which two are odd (1 and 3). The second spinner has four equal sectors labeled 3, 4, 5, and 6, but we are only interested in the outcome when the spinner shows a 6.
Since we want the first spinner to show an odd number, we ignore the 2, leaving us with 1 and 3 as the possible outcomes for the first spinner. For the second spinner, we are only interested in the outcome of 6. This means we multiply the two outcomes from the first spinner (1 and 3) by the one outcome from the second spinner (6), resulting in two possible outcomes: (1,6) and (3,6).
Therefore, the correct answer is there are two outcomes that do not show an even number on the first spinner and show a 6 on the second spinner.
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Answer:
Therefore,
Distance between XY is 878 ft and YB is 524 ft.
Step-by-step explanation:
Given:
BW = 1612 ft
∠ Y = 72°
∠ X = 49°
To Find:
XY = ?
YB = ?
Solution:
In right angle Triangle Δ WBY Tangent identity,
[tex]\tan Y= \frac{\textrm{side opposite to angle Y}}{\textrm{side adjacent to angle Y}}[/tex]
Substituting we get
[tex]\tan 72= \frac{WB}{YB}=\frac{1612}{BY}[/tex]
[tex]\therefore BY=\frac{1612}{3.077}=523.88=524\ ft...(approximate)[/tex]
Similarly,
In right angle Triangle Δ WBX Tangent identity,
[tex]\tan X= \frac{\textrm{side opposite to angle X}}{\textrm{side adjacent to angle X}}[/tex]
Substituting we get
[tex]\tan 49= \frac{WB}{XB}=\frac{1612}{XB}[/tex]
[tex]\therefore XB=\frac{1612}{1.15}=1401.73=1402\ ft...(approximate)[/tex]
Now For
[tex]XB = XY +BY[/tex].............Addition Property
Substituting we get
[tex]1402 = XY +524\\\\\therefore XY=1402-524=878\ ft[/tex]
Therefore
Distance between XY is 878 ft and YB is 524 ft.
The graph, of quadratic function f has x-intercepts of (-7,0)and(-4,0).
Which equation could represent function f?
A. f(x) = (x-7)(x-4)
B. f(x) = 2(x+7)(x-4)
C. f(x) = -3(x+7)(x+4)
D. f(x) = -1/2(x-7)(x+4)
Answer:
C. f(x)=-3(x+7)(x+4)
Step-by-step explanation:
x-intercept means the value of x where the functions touches the x axis.
The function touches x axis at two places, x=-7 and x=-4 ie. both -7 and -4 are the roots of the equation.
And the terms (x+7) and (x+4) are the factors of the function f(x),
Only one such case exists where (x+7) and (x+4) are there as factors, ie. Option C.
Therefore, C.-3(x+7)(x+4).
Answer:
C. f(x)=-3(x+7)(x+4)
Step-by-step explanation:
Got it right on the test