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Setler [38]
4 years ago
11

Tito’s backyard measures 78 feet by 65 feet. Tito wants to expand the length and width of his backyard by the same amount so tha

t his new pet ferret has room to run. If Tito wants his backyard to have an area three times the current value, by how much should he extend the length and width?
Mathematics
1 answer:
almond37 [142]4 years ago
5 0
He should increase the length and width by a factor = sqrt 3.

so new length should be 78* sqrt3 = 135.1 - that is increase of 58.1 ft
and new width should be 65 * sqrt3 = 112,58  = increase of 47.58 ft
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) find a vector parallel to the line of intersection of the planes 5x − y − 6z = 0 and x + y + z = 1.
snow_tiger [21]
The cross product of the normal vectors of two planes result in a vector parallel to the line of intersection of the two planes.

Corresponding normal vectors of the planes are
<5,-1,-6> and <1,1,1>

We calculate the cross product as a determinant of (i,j,k) and the normal products

    i   j   k
   5 -1 -6
   1  1  1

=(-1*1-(-6)*1)i -(5*1-(-6)1)j+(5*1-(-1*1))k
=5i-11j+6k
=<5,-11,6>

Check orthogonality with normal vectors using scalar products
(should equal zero if orthogonal)
<5,-11,6>.<5,-1,-6>=25+11-36=0
<5,-11,6>.<1,1,1>=5-11+6=0

Therefore <5,-11,6> is a vector parallel to the line of intersection of the two given planes.
5 0
3 years ago
Janine is considering buying a water filter and a reusable water bottle rather than buying bottled water. Will doing so save her
prisoha [69]

Solution:

To save Some amount of money, Janine is considering buying a water filter and a reusable water bottle rather than buying bottled water.

To answer this question, we have to look at the thought process of Janine, that why she has done this?

The information that we need to answer this Question: is Written in Bold Letters

1. Amount of Water Drunk by Janine in a day= 4 × 16.9 Ounces= 67.6 Ounces= Approximately 2 Liter

2. Cost of 24-packs of 16.9 ounce bottles = $3.89

Cost of 4×6 packs of  16.9 ounce bottles =$3.89

Cost of 2 liter or 4 packs of  16.9 ounce bottles =\frac{3.89}{6}$

3. Cost of Reusable water bottle = $ 10

4. Time for which a reusable water bottle last= Infinitely

5. Cost of a faucet-mounted filter= $ 28

Cost of Refilling for a 3 pack filter=$ 33

So, Cost of Refilling a 1 pack filter= $11

1 filter will filter approximately =100 gallons of water=378 Liters

6. Cost of a water filter pitcher= $ 22

Now, coming to second part ,whether buying a water filter and a reusable water bottle rather than buying bottled water will save her money?

→Total cost of  water filter and a reusable water bottle = $28+$10+ $ (33÷3) ×(Number of times She refills the 3 filter pack)= $ 38 + $11 n

For, 1  water filter and a reusable water bottle total money spent = $ 49

→As the filter contains , 378 Liters of water, and Janine drinks Approx 2 liters of water daily, so 1 filter will last for 189 days.

→1 Liter = 33.81 Ounce

→Cost of 378 liters of water=\frac{3.89\times 189}{6}= $ 122.535

So, We can  Surely say that , buying a water filter and a reusable water bottle rather than buying bottled water will save Janine money.

7 0
3 years ago
Read 2 more answers
Pls help it for math
Morgarella [4.7K]
I think it’s 8

Hope it helps
7 0
3 years ago
Given sin theta=5/13 and cos theta=12/13, which of the following can be proven using a Pythagorean identity?
ZanzabumX [31]

Answer:

4th option

Step-by-step explanation:

given

sinΘ = \frac{5}{13} and cosΘ = \frac{12}{13} , then

( \frac{5}{13} )² + ( \frac{12}{13} )²

= \frac{25}{169} + \frac{144}{169}

= \frac{25+144}{169}

= \frac{169}{169}

= 1

showing sin²Θ + cos²Θ = 1

4 0
2 years ago
I really need help on this problem can i get help on how to solve the problem please
Jobisdone [24]
You cannot assume that the angles are equal. there is no angle measure and nothing to say the lines are parellel.
7 0
3 years ago
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