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3 years ago

13

A cylinder and a cone have the same measurements for height and radius. The cylinder has a volume of 45 cm ^ 3 . What is the vol

ume of the cone?

1 answer:

sweet [91]3 years ago

4 0

Answer:

91,125

Step-by-step explanation:

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If you rotate the point (2, 3) 90 degrees counterclockwise about the origin, what is the image of the point?

AlexFokin [52]

Rotation counterclockwise 90 degrees has the rule

(x,y) -> (-y,x)

So the image is obtained, according to the rule,
(2,3) -> (-3,2)

4 0

3 years ago

miss Akunina [59]

Answer:

4x=3/8

8×4x=3

32x=3

x=3/32. Ansss...

6 0

3 years ago

The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 38 feet and

forsale [732]

Answer:

Only truck 1 can pass under the bridge.

Step-by-step explanation:

So, first of all, we must do a drawing of what the situation looks like (see attached picture).

Next, we can take the general equation of an ellipse that is centered at the origin, which is the following:

$\frac{x^2}{a^2}+\frac{y^2}{b^2}$

where:

a= wider side of the ellipse

b= shorter side of the ellipse

in this case:

$a=\frac{38}{2}=19ft$

and

b=12ft

so we can go ahead and plug this data into the ellipse formula:

$\frac{x^2}{(19)^2}+\frac{y^2}{(12)^2}$

and we can simplify the equation, so we get:

$\frac{x^2}{361}+\frac{y^2}{144}$

So, we need to know if either truk will pass under the bridge, so we will match the center of the bridge with the center of each truck and see if the height of the bridge is enough for either to pass.

in order to do this let's solve the equation for y:

$\frac{y^{2}}{144}=1-\frac{x^{2}}{361}$

$y^{2}=144(1-\frac{x^{2}}{361})$

we can add everything inside parenthesis so we get:

$y^{2}=144(\frac{361-x^{2}}{361})$

and take the square root on both sides, so we get:

$y=\sqrt{144(\frac{361-x^{2}}{361})}$

and we can simplify this so we get:

$y=\frac{12}{19}\sqrt{361-x^{2}}$

and now we can evaluate this equation for x=4 (half the width of the trucks) so:

$y=\frac{12}{19}\sqrt{361-(8)^{2}}$

y=11.73ft

this means that for the trucks to pass under the bridge they must have a maximum height of 11.73ft, therefore only truck 1 is able to pass under the bridge since truck 2 is too high.

5 0

3 years ago

Please help ASAP 25 pts + brainliest to right/best answer

Galina-37 [17]

(f + g)(x) = f(x) + g(x)

(f + g)(x) = 3x + 5 + x^2 = x^2 + 3x + 5

Answer: Choice D

8 0

3 years ago

a food snack manufacturer samples 9 bags of pretzels off the assembly line and weights their contents. If the sample mean is 14.

gladu [14]

Answer:

<h2>13.7≤ $\mu$ ≤14.7</h2>

Step-by-step explanation:

The formula for calculating the confidence interval is expressed as shown;

CI = xbar ± Z(б/√n)

xbar is the sample mean

Z is the value at 95% confidence interval

б is the standard deviation of the sample

n is the number of samples

Given xbar = 14.2, Z at 95% CI = 1.96, б = 0.70 and n = 9

Substituting this values into the formula;

CI = 14.2 ± 1.96(0.70/√9)

CI = 14.2 ± 1.96(0.70/3)

CI = 14.2 ± 1.96(0.2333)

CI = 14.2 ± 0.4573

CI = (14.2-0.4573, 14.2+0.4573)

CI = (13.7427, 14.6537)

Hence, the 95% confidence interval of the true mean is within the range

13.7≤ $\mu$ ≤14.7 (to 1 decimal place).

6 0

3 years ago