A cylindrical vase has a volume of 192.5 cubic centimeters. The height of this vase is 5 centimeters. The formula for the volume of the cylinder is πr^2h where r is the radius and h is the height of the vase. Find the radius of this vase.(Given that π ≈ 22 / 7 )

Hi there!

[tex]\large\boxed{\text{9 quarters}}[/tex]

We can let x = dimes and y = quarters.

We know that one dime = $0.10 and a quarter = $0.25, so:

$3.05 = $0.10x + $0.25y

And:

17 = x + y

Solve the system of equations. We can rearrange the bottom equation to create an expression equal to y:

17 - x = y

Substitute this into the top equation for y:

3.05 = 0.10x + 0.25(17 - x)

Distribute and simplify:

3.05 = 0.10x + 4.25 - 0.25x

3.05 = 4.25 - 0.15x

Solve for x:

-1.2 = -0.15x

x = 8

Find y using the above expression:

17 - 8 = y

y = 9

Suppose there is a function f(x), the definite integral of the function is the difference between the upper and lower x-values.

There are three relationships between the definite integral and the area of the region. The relationships are:

Positive function

The area between the function itself and the x-axis represents the definite integral.

Negative function

The area between the function itself and the x-axis, multiplied by -1 represents the definite integral.

Region between two functions

The definite integral of the function is the difference between the region of both functions.

See attachment for further illustration

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Answer:

A. Zero.

Step-by-step explanation:

Technically, the correct answer is "undefined", as there will be infinite change in the slope amount. However, of all the given choices, Zero should be the best answer. However, if it is wrong, do ask your teacher, and state that undefined should be the answer choice, and that credit should be rewarded for such.

Answer:

9--7

Step-by-step explanation:

Answer:

[tex](x^{-3})^2[/tex]

Step-by-step explanation:

applying the exponent rule to the inside of the bracket, x^3 x x^-6 = x^-3 since you add the exponents

The slope of the tangent line to the curve at a point (x, y) is dy/dx. By the chain rule, this is equivalent to

dy/dθ × dθ/dx = (dy/dθ) / (dx/dθ)

where y = r(θ) sin(θ) and x = r(θ) cos(θ). Then

dy/dθ = dr/dθ sin(θ) + r(θ) cos(θ)

dx/dθ = dr/dθ cos(θ) - r(θ) sin(θ)

Given r(θ) = cos(3θ), we have

dr/dθ = -3 sin(3θ)

and so

dy/dx = (-3 sin(3θ) sin(θ) + cos(3θ) cos(θ)) / (-3 sin(3θ) cos(θ) - cos(3θ) sin(θ))

When θ = π/3, we end up with a slope of

dy/dx = (-3 sin(π) sin(π/3) + cos(π) cos(π/3)) / (-3 sin(π) cos(π/3) - cos(π) sin(π/3))

dy/dx = -cos(π/3) / sin(π/3)

dy/dx = -cot(π/3) = -1/√3

The correct statement is test is reliable and authentic as the probability of no false positives is more than 0.5

Given that

[tex]H_o:P= 0.50\\\\H_1:P>0.50[/tex]

Now following calculations to be done to reach the conclusion:

There is no false positive as

= 100 - 5.5

= 94.5%

[tex]\hat P =0.945, n = 12[/tex]

Now

[tex]z = \frac{\hat P - P}{\sqrt\frac{P(1-P)}{n} }\\\\=\frac{0.945-0.5}{\sqrt\frac{0.5\times0.5}{12} } \\\\= 3.08[/tex]

So

P value = P(z >3.08) = 0.0010

Therefore we can conclude that test is reliable and authentic as the probability of no false positives is more than 0.5

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Answer:

216

Step-by-step explanation:

Volume of prism = BH

B -> Base area

Area of base:

b = 10 mi

h = 3.6mi

Area of the triangular base = [tex]\dfrac{1}{2}*b*h[/tex]

                        [tex]=\dfrac{1}{2}*10*3.6\\\\= 18 \ mi^{2}[/tex]

H = 12 mi

Volume of prism = 18 * 12 = 216  cubic mi

Answer:

this is the answer of this question

hoping it will help u

Answer:

8.49

Step-by-step explanation:

there is a little formula related to the famous formula of Pythagoras.

it says that the height of a triangle is the square root of the product of both segments of the baseline (the segments the height splits the baseline into).

so, x is actuality the height of the triangle.

x = sqrt(3×24) = sqrt(72) = 8.49

Step-by-step explanation:

Therefore, the degree of polynomial √3 is zero.

[tex]\sf\huge\underline\color{pink}{༄Answer:}[/tex]

[tex]\tt{\sqrt{3}}[/tex] is a polynomial of degree 0

[tex]\sf\huge\underline\color{pinl}{༄Note:}[/tex]

[tex]\color{pink}{==========================}[/tex]

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-༄⁂✰Park Hana Moon

Answer:

48 minutes

240 at 60mph = 4 hrs.

240 at 50 mph = 4.8 hrs.

it would take an extra 60*.8 or 48 minutes

Step-by-step explanation:

The trip will be of 48 minutes longer when the speed is decreased by 10 miles per hour.

What is the formula for time?

The time is given by distance/speed. The unit of time is minutes or seconds.

When distance of 240 miles is cover by the speed of 60 miles per hour then the time take to travel this distance will be 240/60=4 hours

When distance of 240 miles is cover by the speed of 50 miles per hour then the time take to travel this distance will be 240/50=4.8 hours

The difference between 4.8 hours and 4 hours is of 0.8 hours or 0.8*60=48 minutes.

Therefore, the trip will be of 48 minutes longer.

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Answer:

16 units

Step-by-step explanation:

period = length of an interval that contains exactly one copy of the repeating pattern, so from one peak to another peak.

in this graph its the peaks are 1 and 17, hence the period is 16

Answer:  Choice A

[tex]\tan(\alpha)*\cot^2(\alpha)\\\\[/tex]

============================================================

Explanation:

Recall that [tex]\tan(x) = \frac{\sin(x)}{\cos(x)}[/tex] and [tex]\cot(x) = \frac{\cos(x)}{\sin(x)}[/tex]. The connection between tangent and cotangent is simply involving the reciprocal

From this, we can say,

[tex]\tan(\alpha)*\cot^2(\alpha)\\\\\\\frac{\sin(\alpha)}{\cos(\alpha)}*\left(\frac{\cos(\alpha)}{\sin(\alpha)}\right)^2\\\\\\\frac{\sin(\alpha)}{\cos(\alpha)}*\frac{\cos^2(\alpha)}{\sin^2(\alpha)}\\\\\\\frac{\sin(\alpha)*\cos^2(\alpha)}{\cos(\alpha)*\sin^2(\alpha)}\\\\\\\frac{\cos^2(\alpha)}{\cos(\alpha)*\sin(\alpha)}\\\\\\\frac{\cos(\alpha)}{\sin(\alpha)}\\\\[/tex]

In the second to last step, a pair of sine terms cancel. In the last step, a pair of cosine terms cancel.

All of this shows why [tex]\tan(\alpha)*\cot^2(\alpha)\\\\[/tex] is identical to [tex]\frac{\cos(\alpha)}{\sin(\alpha)}\\\\[/tex]

Therefore, [tex]\tan(\alpha)*\cot^2(\alpha)=\frac{\cos(\alpha)}{\sin(\alpha)}\\\\[/tex] is an identity. In mathematics, an identity is when both sides are the same thing for any allowed input in the domain.

You can visually confirm that [tex]\tan(\alpha)*\cot^2(\alpha)\\\\[/tex] is the same as [tex]\frac{\cos(\alpha)}{\sin(\alpha)}\\\\[/tex] by graphing each function (use x instead of alpha). You should note that both curves use the exact same set of points to form them. In other words, one curve is perfectly on top of the other. I recommend making the curves different colors so you can distinguish them a bit better.

We know at centroid medians bisect each other in the ratio 2:1.

[tex]\\ \sf\longmapsto TY=2x[/tex]

[tex]\\ \sf\longmapsto 2x=30[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{30}{2}[/tex]

[tex]\\ \sf\longmapsto x=15[/tex]

Answer:

A

Step-by-step explanation:

On the median TW the distance from the vertex to the centroid is twice the distance from the centroid to the midpoint , then

YW = [tex]\frac{1}{2}[/tex] × TY = [tex]\frac{1}{2}[/tex] × 30 = 15

Answer:

Yes

Step-by-step explanation:

Plugging in the values in the equation, we have

1=3*(2)-5, 1=1 which is TRUE

Answer:

D) is your correct answer

Answer:

Hello,

do you mean factorise but not solve ?

Just one formula:

[tex]\boxed{a^2-b^2=(a-b)(a+b)}[/tex]

Step-by-step explanation:

[tex]g)\\\\16x^3y-81xy^5\\\\=xy(16x^2-81y^4)\\\\=xy(4x^2+9y^2)(4x^2-9y^2)\\\\=xy(2x-3y)(2x+3)(4x^2+9y^2)\\\\\\\\h)\\\\x^8-y^8\\\\=(x^4+y^4)(x^4-y^4)\\\\=(x^4+y^4)(x^2+y^2)(x^2-y^2)\\\\=(x-y)(x+y)(x^2+y^2)(x^4+y^4)\\[/tex]

Answer:

here only one formula to use in both question

a^2+b^2= (a+b)(a-b)

Answer:

1st option

1st graph has the centre on (-1,-2) and the distance of the circumference from the centre is 2

Answered by GAUTHMATH

Answer:

The two substances will have the same volume after approximately 3.453 hours.

Step-by-step explanation:

The volume of substance A (measured in cubic centimeters) increases at a rate represented by the equation:

[tex]\displaystyle \frac{dA}{dt} = 0.3 A[/tex]

Where t is measured in hours.

And substance B is represented by the equation:

[tex]\displaystyle \frac{dB}{dt} = 1[/tex]

We are also given that at t = 0, A(0) = 3 and B(0) = 5.

And we want to find the time(s) t for which both A and B will have the same volume.  

You are correct in that B(t) is indeed t + 5. The trick here is to multiply both sides by dt. This yields:

[tex]\displaystyle dB = 1 dt[/tex]

Now, we can take the integral of both sides:

[tex]\displaystyle \int 1 \, dB = \int 1 \, dt[/tex]

Integrate. Remember the constant of integration!

[tex]\displaystyle B(t) = t + C[/tex]

Since B(0) = 5:

[tex]\displaystyle B(0) = 5 = (0) + C \Rightarrow C = 5[/tex]

Hence:

[tex]B(t) = t + 5[/tex]

We can apply the same method to substance A. This yields:

[tex]\displaystyle dA = 0.3A \, dt[/tex]

We will have to divide both sides by A:

[tex]\displaystyle \frac{1}{A}\, dA = 0.3\, dt[/tex]

Now, we can take the integral of both sides:

[tex]\displaystyle \int \frac{1}{A} \, dA = \int 0.3\, dt[/tex]

Integrate:

[tex]\displaystyle \ln|A| = 0.3 t + C[/tex]

Raise both sides to e:

[tex]\displaystyle e^{\ln |A|} = e^{0.3t + C}[/tex]

Simplify:

[tex]\displaystyle |A| = e^{0.3t} \cdot e^C = Ce^{0.3t}[/tex]

Note that since C is an arbitrary constant, e raised to C will also be an arbitrary constant.

By definition:

[tex]\displaystyle A(t) = \pm C e^{0.3t} = Ce^{0.3t}[/tex]

Since A(0) = 3:

[tex]\displaystyle A(0) = 3 = Ce^{0.3(0)} \Rightarrow C = 3[/tex]

Therefore, the growth model of substance A is:

[tex]A(t) = 3e^{0.3t}[/tex]

To find the time(s) for which both substances will have the same volume, we can set the two functions equal to each other:

[tex]\displaystyle A(t) = B(t)[/tex]

Substitute:

[tex]\displaystyle 3e^{0.3t} = t + 5[/tex]

Using a graphing calculator, we can see that the intersect twice: at t ≈ -4.131 and again at t ≈ 3.453.

Since time cannot be negative, we can ignore the first solution.

In conclusion, the two substances will have the same volume after approximately 3.453 hours.

Answer:

535 students passed and 107 students failed

Step-by-step explanation:

Create a system of equations where p is the number of students who passed and f is the number of students who failed:

p + f = 642

p = 5f

Solve by substitution by plugging in 5f as p into the first equation, then solving for f:

p + f = 642

5f + f = 642

6f = 642

f = 107

So, 107 students failed.

Find how many students passed by multiplying this by 5:

107(5)

= 535

535 students passed and 107 students failed.

Answer:

[tex]4 \sqrt{122} \sqrt{12} \\ (4 \times 2) \times ( \sqrt{12} \times \sqrt{12} ) \\ (4 \times 2) \times 12 \\ 8 \times 12 \\ 96[/tex]

Answer:

Step-by-step explanation:

The idea here is to find the area of the circle and then subtract from it the area of the triangle. That will give you the area of what's left in the circle (the shaded part). The area of a circle is:

[tex]A_c=\pi r^2[/tex] so

[tex]A_c=(3.14)(12.4)^2[/tex]   where 12.4 is the radius.

[tex]A_c=482.81[/tex] rounded to the nearest tenth. I used 3.14 for pi.

Now for the area of the triangle. The formula is

[tex]A_t=\frac{1}{2}bh[/tex] where h is the height of 12.4 and the base is the diameter which is 12.4 * 2 = 24.8

[tex]A_t=\frac{1}{2}(24.8)(12.4)[/tex] so

[tex]A_t=153.76[/tex]

Now subtract the triangle's area from the circle's area:

482.81 - 153.76 = 329.05 mm²

Answer:

x=4sqrt3 a=4 b=3  ,y=8sqrt3 c=8 d=3

Step-by-step explanation:

because this is a 30-60-90 triangle, it is easy to find the side lengths. the longer leg is sqrt(3) times the shorter leg so x= 12/sqrt(3) or 4sqrt(3). the hypotenuse is 2 times the shorter leg so y= 8sqrt(3)

[tex]\\ \sf\longmapsto (m-8)+(m-8)+(m-8)+(m-8)+(m-8)+(m-8)=12[/tex]

[tex]\\ \sf\longmapsto 6(m-8)=12[/tex]

[tex]\\ \sf\longmapsto 6m-48=12[/tex]

[tex]\\ \sf\longmapsto 6m=12+48[/tex]

[tex]\\ \sf\longmapsto 6m=60[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{60}{6}[/tex]

[tex]\\ \sf\longmapsto m=10[/tex]

Answer:

M=14

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

(whole secant) x (external part) = (tangent)^2

(48+x) * 48 = 60^2

(48+x)48=3600

Divide each side by 48

48+x =75

Subtract 48

48+x-48 = 75-48

x =27

The expression that represents the amount of money Deion would have saved in w weeks is 95 + 7w and the total savings after 6 weeks will be $137.

A statement expressing the equality of two mathematical expressions is known as an equation.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

As per the given,

Initial fixed money = $95

Per week saving $7/week

Total money = fixed money + money in w weeks.

⇒ 95 + 7w

For 6 weeks, w = 6

⇒ 95 + 7× 6 = $137.

Hence "The expression that represents the amount of money Deion would have saved in w weeks is 95 + 7w and the total savings after 6 weeks will be $137".

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