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3 years ago

7

A sphere with a diameter of 16mm has the same surface area as the total surface area of a right cylinder with the base diameter

equal to the sphere diameter. How high is the cylinder?
A. 16 mm
B. 8 mm
C. 18 mm
D. 14 mm

2 answers:

miv72 [106K]3 years ago

8 0

$R_{sphere}= \frac{1}{2} *16=8[mm]\\
A_{sphere}=4 \pi R^{2}\\
A_{cylinder}=2 \pi R(R+h)\\\\

4\pi R^{2}=2 \pi R(r+h)\\
 \frac{4\pi R^{2}}{2 \pi R} =r+h\\
h= \frac{4\pi R^{2}}{2 \pi R}-R=2R-R=R\\
R=8[mm]$

So the answer is B. 8 mm

Softa [21]3 years ago

5 0

Answer:

8 mm

Step-by-step explanation:

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3 years ago

A county is considering rasing the speed limit on a road because they claim that the mean speed of vehicles is greater than 30 m

DochEvi [55]

Answer:

No, at alpha equals 0.10, we do not have enough evidence to support the county's claim.

Step-by-step explanation:

We are given that a county is considering raising the speed limit on a road because they claim that the mean speed of vehicles is greater than 30 miles per hour.

A random sample of 15 vehicles has a mean speed of 31 miles per hour and a standard deviation of 4.7 miles per hour.

<em><u>Let </u></em> $\mu$ <em><u> = true mean speed of the vehicles.</u></em>

SO, <u>Null Hypothesis</u>, $H_0$ : $\mu \leq$ 30 miles per hour {means that the mean speed of vehicles is lesser than or equal to 30 miles per hour}

<u>Alternate Hypothesis,</u> $H_A$ : $\mu$ > 30 miles per hour {means that the mean speed of vehicles is greater than 30 miles per hour}

The test statistics that will be used here is <u>One-sample t test statistics</u> as we don't know about the population standard deviation;

T.S. = $\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean speed of 15 vehicles = 31 mph

s = sample standard deviation = 4.7 mph

n = sample of vehicles = 15

So, <em><u>test statistics</u></em> = $\frac{31-30}{\frac{4.7}{\sqrt{15} } }$ ~ $t_1_4$

= 0.824

<u><em>Hence, the value of test statistics is 0.824.</em></u>

<em />

<em>Now at 0.10 significance level, the t table gives critical value of 1.345 at 14 degree of freedom for right-tailed test. Since our test statistics is less than the critical value of t as 0.824 < 1.345, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.</em>

<em />

Therefore, we conclude that the mean speed of vehicles is lesser than or equal to 30 miles per hour which means that the county's claim is not supported.

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4 years ago

What is the value for m and n?

Inga [223]

Answer:

M = 8 N = 10

Step-by-step explanation:

Multiplying exponents adds the exponent, meaning that inside of the brackets, it is a^4 * b^5. Multiply the exponents by two because you are squaring the entire equation. Therefore, m=8 and n=10

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3 years ago

Find the first partial derivatives of the function f(x,y,z)=4xsin(y−z)

Amanda [17]

Answer:

$f_x(x,y,z)=4\sin (y-z)$

$f_x(x,y,z)=4x\cos (y-z)$

$f_z(x,y,z)=-4x\cos (y-z)$

Step-by-step explanation:

The given function is

$f(x,y,z)=4x\sin (y-z)$

We need to find first partial derivatives of the function.

Differentiate partially w.r.t. x and y, z are constants.

$f_x(x,y,z)=4(1)\sin (y-z)$

$f_x(x,y,z)=4\sin (y-z)$

Differentiate partially w.r.t. y and x, z are constants.

$f_y(x,y,z)=4x\cos (y-z)\dfrac{\partial}{\partial y}(y-z)$

$f_y(x,y,z)=4x\cos (y-z)$

Differentiate partially w.r.t. z and x, y are constants.

$f_z(x,y,z)=4x\cos (y-z)\dfrac{\partial}{\partial z}(y-z)$

$f_z(x,y,z)=4x\cos (y-z)(-1)$

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Therefore, the first partial derivatives of the function are $f_x(x,y,z)=4\sin (y-z), f_x(x,y,z)=4x\cos (y-z)\text{ and }f_z(x,y,z)=-4x\cos (y-z)$ .

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4 years ago

Peggy is thinking of a number such that when twice the number is added to three times one more than the number she gets the same

mars1129 [50]

Answer:

-7

Step-by-step explanation:

Lets assume the number Peggy is thinking of be "x".

Now as given, when twice the number is added to three times one more than the number. We can write it as

∴ $2x+3(x+1)$ --- Equation 1

Again, it is given that Peggy gets the same result as when she multiplies four times one less than the number.

∴ $4(x-1)$ -- equation 2

Next, we can equate both the equation 1 and 2 as it is given that result is same.

$2x+3(x+1)= 4(x-1)$

Let´s distribute 3 into $(x+1)$ and 4 into $(x-1)$

⇒ $2x+3x+3=4x-4$

⇒ $5x+3=4x-4$

Subtract both side by 4x and 3

∴ $x=-7$

∴ Peggy was thinking of -7

4 0

3 years ago