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3 years ago

15

Marian has a goal of running 18 1/2 miles during track practice this week. On Monday she ran 2 1/2 miles, on Tuesday 2.9 miles,

on Wednesday 3 3/4 miles, and on Thursday 5 1/4 miles. How far does she need to run on Friday to reach her goal?

1 answer:

velikii [3]3 years ago

7 0

Answer:

4.1

Step-by-step explanation:

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What is the slope of a line that goes through the points (-1,2) and (1, 4)?

oksian1 [2.3K]

Answer:

1

Step-by-step explanation:

We can use the slope formula

m = ( y2-y1)/(x2-x1)

= ( 4-2)/(1 - -1)

= (4-2)/(1+1)

= 2/2

= 1

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3 years ago

What is the order biggest to least.<br><br> 6/40 -4 3/4 -9/20

OlgaM077 [116]

Answer:

.15, -.45, -4.75

Step-by-step explanation:

put all of them into a ti84 calculator and convert to decimals and then you get your answer.

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3 years ago

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A cardboard box without a lid is to have a volume of 19,652 cm3. Find the dimensions that minimize the amount of cardboard used.

Effectus [21]

Answer:

The dimension of the cardboard is 34 cm by 34 cm by 17 cm.

Step-by-step explanation:

Let the dimension of the cardboard box be x cm by y cm by z cm.

The surface area of the cardboard box without lid is

f(x,y,z)= xy+2xz+2yz.....(1)

Given that the volume of the cardboard is 19,652 cm³.

Therefore xyz =19,652

$\Rightarrow z=\frac{19652}{xy}$ ......(2)

putting the value of z in the equation (1)

$f(x,y)=xy+2x(\frac{19652}{xy})+2y(\frac{19652}{xy})$

$\Rightarrow f(x,y)=xy+\frac{39304}{y})+\frac{39304}{x}$

The partial derivatives are

$f_x=y-\frac{39304}{x^2}$

$f_y=x-\frac{39304}{y^2}$

To find the dimension of the box set the partial derivatives $f_x=0$ and $f_y=0$ .Therefore $y-\frac{39304}{x^2}=0$

$\Rightarrow y=\frac{39304}{x^2}$ .......(3)

and $x-\frac{39304}{y^2}=0$

$\Rightarrow x=\frac{39304}{y^2}$ .......(4)

Now putting the x in equation (3)

$y =\frac {39304}{(\frac{39304}{y^2})^2}$

$\Rightarrow y=\frac{y^4}{39304}$

$\Rightarrow y^3= 39304$

⇒y=34 cm

Then $\Rightarrow x=\frac{39304}{34^2}$ =34 cm.

Putting the value of x and y in the equation (2)

$z=\frac{19652}{34 \times 24}$

=17 cm.

The dimension of the cardboard is 34 cm by 34 cm by 17 cm.

4 0

3 years ago

What is 103,727,495 in word from

natima [27]

One hundred and three million, seven hundred and twenty seven thousand, four hundred and ninety five.

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3 years ago

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What is the value of y?<br><br><br> A. y = -1<br><br> B. y = 0<br><br> C. y = 1<br><br> D. y = 3

OverLord2011 [107]

Step-by-step explanation:

The centroid divides the length of each median in 2:1 ratio.

The length of the part between the vertex and the centroid is twice the length between the centroid and the mid-point of the opposite side.

In case of median KM,

K is the vertex and M is the midpoint of the side JL

KT = 2× TM

5y+3 = 2(y+3)

5y+3= 2y +6

5y-2y= 6-3

3y = 3

y= 1

6 0

3 years ago