A box of 7 items costs $20.73 find the cost of each item

The radius of a right circular cone is increasing at a rate of 1.5 in/s while its height is decreasing at a rate of 2.1 in/s. At

givi [52]

Answer:

The volume of the cone is changing at a rate of approximately 8670.796 cubic inches per second.

Step-by-step explanation:

Geometrically speaking, the volume of the right circular cone ( $V$ ), in cubic inches, is defined by the following formula:

$V = \frac{1}{3}\cdot \pi \cdot r^{2}\cdot h$ (1)

Where:

$r$ - Radius, in inches.

$h$ - Height, in inches.

Then, we derive an expression for the rate of change of the volume ( $\dot V$ ), in cubic inches per second, by derivatives:

$\dot V = \frac{1}{3}\cdot \pi \cdot (2\cdot r\cdot h \cdot \dot r + r^{2}\cdot \dot h)$ (2)

Where:

$\dot r$ - Rate of change of the radius, in inches per second.

$\dot h$ - Rate of change of the height, in inches per second.

If we know that $r = 120\,in$ , $\dot r = 1.5\,\frac{in}{s}$ , $h = 107\,in$ and $\dot h = -2.1\,\frac{in}{s}$ , then the rate of change of the volume is:

$\dot V \approx 8670.796\,\frac{in^{3}}{s}$

The volume of the cone is changing at a rate of approximately 8670.796 cubic inches per second.

8 0

2 years ago

How do I graph the inequality of this equation. y > x + 2

ZanzabumX [31]

-- For just a minute, make it an Equality . . . y = x + 2 .

-- Graph the Equality. That graph is a straight line.

-- The INequality says that 'y' is LESS than x+2,
and THAT's everything UNDER the line.
(But not the points on the line itself.)

4 0

2 years ago

Solve for x: 3x²-243

mylen [45]

3x²–243=0 —> 3 (x²–81) = 0 —>

x²–81=0 —> (x-9)(x+9)=0

x-9=0 —> x=9

x+9=0 —> x=–9

I hope I helped you^_^

7 0

2 years ago

Solve for x | 2x-1| +4 = 8

Brums [2.3K]

Answer:

x = 2 1/ 2 , − 1 1/2

Step-by-step explanation:

5 0

2 years ago

A major retail clothing store is interested in estimating the difference in mean monthly purchases by customers who use the stor

faust18 [17]

Answer:

Critical value is t = 1.9901

Step-by-step explanation:

We are given the results of the sampling :

In-House Credit Card National Credit Card Sample Size : 32 50

Mean Monthly Purchases : $45.67 $39.87

Standard Deviation : $10.90 $12.47

Also, the managers wished to test whether there is a statistical difference in the mean monthly purchases by customers using the two types of credit cards, using a significance level α of 0.05.

Firstly, we will specify our null and alternate hypothesis;

Let $\mu_1$ = Mean Monthly Purchases of In-House Credit Card

$\mu_2$ = Mean Monthly purchases of National Credit Card

So, Null Hypothesis, $H_0$ : $\mu_1-\mu_2$ = 0 {means that there is no difference in the mean monthly purchases by customers using the two types of credit cards}

Alternate Hypothesis, $H_0$ : $\mu_1-\mu_2\neq$ 0 {means that there is statistical difference in the mean monthly purchases by customers using the two types of credit cards}

The test statistics that will be used here is Two-sample t-test statistics;

T.S. = $\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }$ ~ $t_n___1+n_2-_2$

where, $\bar X_1$ = Sample mean Purchases of In-House Credit Card = $45.67

$\bar X_2$ = Sample mean Purchases of National Credit Card = $39.87

$s_p$ = pooled variance

$n_1$ = In-house credit card sample = 32

$n_2$ = National credit card sample = 50

So, degree of freedom of t-value here is (32 + 50 - 2) = 80

Now, at 0.05 significance level, t table gives critical value of t = 1.9901 at 80 degree of freedom.

Therefore, the critical value assuming the population standard deviations are not known but that the populations are normally distributed with equal variances is t = 1.9901.

3 0

2 years ago