Can someone help please!!

From a square piece of cardboard paper of area size 9 m2 , squares of the same size are cut off from each corner of the paper. T

levacccp [35]

Answer:

Max vol = 2 cubic metres

Step-by-step explanation:

Given that from a square piece of cardboard paper of area size 9 m2 , squares of the same size are cut off from each corner of the paper.

Side of the square = 3m

If squares are to be cut from the corners of the cardboard we have the dimensions of the box as

3-2x, 3-2x and x.

Hence x can never be greater than or equal to 1.5

V(x) = Volume = $V(x) = x(3-2x)^2\\= 9x+4x^3-12x^2$

We use derivative test to find the maxima

$V'(x) = 9+12x^2-24x\\V"(x) = 24x-24\\$

Equate I derivative to 0

$9+12x^2-24x=0\\x=1/2,3/2$

If x= 3/2 box will have 0 volume

So this is ignored

V"(1/2) <0

So maximum when x =1/2

Maximum volume

= $9(1/2)+4(1/2)^3-12(1/2)^2\\=2$ cubic metres

6 0

2 years ago

Jonathan is going to the movies. A ticket to the movies cost $12.95. He decides to invite 6 of his friends. How much will he pay

mamaluj [8]

Answer:

77.70 dollars or 77.7

Step-by-step explanation:

12.95 x 6 = 77.7 dollars

12.95 + 12.95 + 12.95 + 12.95 + 12.95 = 77.70

Hope this helps

7 0

2 years ago

Read 2 more answers

Dear Math Helper,

valentina_108 [34]

Answer:

n = 98, that is, she scored at the 98th percentile.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

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

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

The Z-score measures how many standard deviations the measure is from the mean. 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, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

She scored 38, so $X = 38$

Test scores are normally distributed with a mean of 25 and a standard deviation of 6.4.

This means that $\mu = 25, \sigma = 6.4$

Find the percentile:

We have to find the pvalue of Z. So

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

$Z = \frac{38 - 25}{6.4}$

$Z = 2.03$

$Z = 2.03$ has a pvalue of 0.98(rounding to two decimal places).

So n = 98, that is, she scored at the 98th percentile.

5 0

2 years ago

20 points!! Pls help

Studentka2010 [4]

Answer:

Step-by-step explanation:

-x-3=y, therefore x = -y-3

-3x - 8y = 4

Find the value of y

Substitute the x in -3x - 8y = 4 with -y-3

We get

-3·(-y-3) - 8y = 4

3y + 9 - 8y = 4

-5y = 4-9

-5y = -5

_______________

Find the value of x

x = -y-3

x = -1-3

_______________

Answer (x, y) =

_____________________

#IndonesianPride - kexcvi

5 0

3 years ago

Read 2 more answers

below is a graph of a logarithmic function, identify it key characteristics. match accordingly.that is the question and can you

Zolol [24]

End behavior: f. As x -> 2, f(x) -> ∞; As x -> ∞, f(x) -> -∞

x-intercept: a. (3, 0)

Range: p. (-∞, ∞)

The range is the set of all possible y-values

Asymptote: x = 2

Transformation: l. right 2

with respect to the next parent function:

$g(x)=\log _{\frac{1}{3}}(x)$

Domain: g. x > 2

The domain is the set of all possible x-values

4 0

1 year ago