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2 years ago

Vector d is shown on a centimetre grid. Image attached.

Mathematics

1 answer:

nexus9112 [7]2 years ago

3 0

Answer:

see explanation

Step-by-step explanation:

A column vector has the form $\left[\begin{array}{ccc}x\\y\\\end{array}\right]$

Following the direction of the arrow , the x- displacement = - 3 and y- displacement = 2 , then column vector is

$\left[\begin{array}{ccc}-3\\2\\\end{array}\right]$

h + k

= $\left[\begin{array}{ccc}4\\-3\\\end{array}\right]$ + $\left[\begin{array}{ccc}-2\\-1\\\end{array}\right]$ ← add corresponding elements from each vector

= $\left[\begin{array}{ccc}4-2\\-3-1\\\end{array}\right]$

= $\left[\begin{array}{ccc}2\\-4\\\end{array}\right]$

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The dimensions of the tank are 50 cm by 32 cm by 20 cm. The tank is full of water and sand. The ratio of the volume of water to

Sauron [17]

Given:

Dimensions of a tank are 50 cm by 32 cm by 20 cm

The tank is full of water and sand

Ratio of volume of water to the volume of sand is 5:1

To find:

Volume of water in the tank in liters

Solution:

Without loss of generality, let,

Length of tank = 50 cm

Breadth of tank = 32 cm

Height of tank = 20 cm

Then, we have,

Total Volume of the tank = Length * Breadth * Height

$\Rightarrow$ Total Volume = 50*32*20 cc

$\Rightarrow$ Total Volume = 32000 cc

It is given that,

Volume of water : Volume of sand = 5:1

$\Rightarrow$ (Volume of water)/(Volume of sand) = 5/1

Cross multiplying, we have,

Volume of sand = (Volume of water)/5

It is also given that the tank is full of water and sand. This implies that,

Volume of water + Volume of sand = Total Volume

Using the value, we obtained, we get,

Volume of water + (Volume of water)/5 = Total Volume

$\Rightarrow$ (6 * Volume of water)/5 = Total Volume

Plugging in the value of total volume, we get,

$\Rightarrow$ (6 * Volume of water)/5 = 32000 cc

$\Rightarrow$ Volume of water = $\frac{32000*5}{6}$ cc

$\Rightarrow$ Volume of water $\approx$ 26,666.6667 cc

We know that,

1 cc = 0.001 liters

$\Rightarrow$ 26,666.6667 cc = (26666.6667 * 0.001) liters

$\Rightarrow$ 26,666.6667 cc $\approx$ 26.667 liters

Thus, Volume of water in the tank is approximately 26.667 liters

Final Answer:

Volume of water in the tank (in liters) is approximately 26.667 liters

4 0

2 years ago

Help with this question

Sholpan [36]

With some simplification,

cos⁻¹(x) - 5 cos⁻¹(x) - π/3 = 2π/3

becomes

-4 cos⁻¹(x) = π

cos⁻¹(x) = -π/4

However, the inverse cosine function has a range of 0 ≤ cos⁻¹(x) ≤ π, so there are no solutions to this equation.

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2 years ago

In a study of preferences in leafcutter ants, a researcher presented 20 randomly chosen ant colonies with leaves from the two mo

Rufina [12.5K]

Answer:

uyjytyhy

Step-by-step explanation:

tthtyi

tyujftyu

yijy

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3 years ago

What is the solution of the system.. explain what it means in the solution

UNO [17]

Answer:

The solution is (4,250)

Step-by-step explanation:

This means that when a member of either gym (A or B) signs up for a four-month membership, they pay the same amount - $250. Hope this helps :)

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2 years ago

Connected to the question before this

lesya [120]

Answer:

(4)Angle A is 63°

Step-by-step explanation:

To find angle A here is what you have to do

(1) triangle A is an Isosceles triangle which has two of its angles being equal.

(2) To find A we hv to look for the interior angles of the triangle. If u look carefully there is this angle outside the triangle .we can use a property called "Angles on a straight line

(3) " Angles on a straight line sum up to 180°" When u do that ur equation will look like this

126+(x)=180°. u may be wondering hw did we get the x?? well i named the angle we dont know with any valuable like T,F etc .when u group like terms ur equation should look like this (x)=180°-126°

if u subtract ur answer should be x=63°

(B) if u look closely u will see there are two triangles. The one to the far right is an Isosceles triangle why because there is this double stroke indicating it is an Isosceles triangle. Remember an Isosceles triangle has its bases being equal. so the the triangle has two angles of 30°. so If we want to find B we first have to find the interior angles of the Isosceles triangle . so our epuarion will be like this 30°+30°+(X)=180°

U group like terms so it will look like this x=180°-60° so,

x= 120°

So now T=120°

Now to find B

we write the equation like this T+(W)=180°

we put the value of T into the Equation w=180°-120 the answer is 60°

So to find B we find the interior angles of the triangle and the interior angles of the Isosceles triangle sum up to 180. so it will look like this B+90+60=180

Nb they should be in Degrees

finally u group like terms. ur equation should look like this B=180-150

ur answer should be B=30°

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3 years ago