(5a^4-3a^2) - (3a^2+3a)

The cone pictured has a surface area of ______ square centimeters. (Use 3.14 for π.)

Marina86 [1]

Assuming that the units are in cm
Given,

Diameter of the cone = 12 cm

Using the above, the radius of the cone can be determined, which is half the diameter of the cone

∴ Radius of the cone (r) = 12/2 = 6 cm
Height of the cone (h) = 7 cm

Using the above, slant height (s) = √(r² + h²) = √(6² + 7²) = √36 + 49 = √85 = 9.22 cm

π = 3.14

Now using the above values, we can calculate the total surface area of the cone.
Total surface area of the cone (A) = Lateral surface area of the cone (L) + Base surface area of the cone (B)

Lateral surface area of the cone (L) = π r s = 3.14 x 6 x 9.22 = 173.70 cm²
Base surface area of the cone (B) = π r² = 3.14 x 6² = 113.04 cm²

Total surface area of the cone = L + B = 173.70 + 113.04 = 286.74 cm²

6 0

3 years ago

I'm really stuck on these types of equations, can someone please help me solve this

guapka [62]

I just answered this question :)
If you any help on any others, just send me a message.
Or comment below.
The explanation is the image attached.

8 0

3 years ago

P(t) = 8 - 2(squareroot)2t + 4

BartSMP [9]

Step-by-step explanation:

P(t) = 8 − 2√(2t + 4)

The x-intercept(s) is where t = 0.

P(0) = 8 − 2√(0 + 4)

P(0) = 8 − 4

P(0) = 4

The y-intercept(s) is where P = 0.

0 = 8 − 2√(2t + 4)

2√(2t + 4) = 8

√(2t + 4) = 4

2t + 4 = 16

2t = 12

t = 6

So the intercepts are at (0, 4) and (6, 0).

The easiest way to tell if the function is increasing or decreasing is to graph it. Otherwise, we have to either use calculus to find the derivative, or assume the function is constantly increasing/decreasing and use limits.

lim(t→∞) P(t) = -∞

The function is decreasing.

6 0

3 years ago

Suppose a certain airline uses passenger seats that are 16.2 inches wide. Assume that adult men have hip breadths that are norma

Pachacha [2.7K]

Answer:

Each adult male has a 5.05% probability of having a hip width greater than 16.2 inches.

There is a 0.01% probability that the 110 adult men will have an average hip width greater than 16.2 inches.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by

$Z = \frac{X - \mu}{\sigma}$

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.

In this problem

Assume that adult men have hip breadths that are normally distributed with a mean of 14.4 inches and a standard deviation of 1.1 inches. This means that $\mu = 14.4, \sigma = 1.1$ .

What is the probability that any one of those adult male will have a hip width greater than 16.2 inches?

For each one of these adult males, the probability that they have a hip width greater than 16.2 inches is 1 subtracted by the pvalue of Z when X = 16.2. So:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{16.2 - 14.4}{1.1}$