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3 years ago

Given: AR ⊥ RS , TS ⊥ RS AT=26, RS=24 AR=12 Find: TS Answer: TS =

Mathematics

2 answers:

Olenka [21]3 years ago

6 0

Answer:

Solution -

Drawing a perpendicular from AQ to TS, we get a right angle triangle AQT

Using Pythagoras Theorem,

AT² = AQ² + QT²

⇒26² = 24² + QT² (∵ Due to symmetry AQ = RS)

⇒QT² = 676-576 = 100

⇒QT = 10

As TS = QT + QS = 12 + 10 = 22 ( ∵ Due to symmetry AR = QS )

∴ TS = 22 (ans)

kogti [31]3 years ago

4 0

Solution -

Drawing a perpendicular from AQ to TS, we get a right angle triangle AQT

Using Pythagoras Theorem,

AT² = AQ² + QT²

⇒26² = 24² + QT² (∵ Due to symmetry AQ = RS)

⇒QT² = 676-576 = 100

⇒QT = 10

As TS = QT + QS = 12 + 10 = 22 ( ∵ Due to symmetry AR = QS )

∴ TS = 22 (ans)

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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by

a_sh-v [17]

Answer:

Dimension of the box is $16.1\times 7.1\times 2.45$

The volume of the box is 280.05 in³.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the box?

Solution :

Let h be the height of the box which is the side length of a corner square.

According to question,

A sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

The length of the box is $L=21-2h$

The width of the box is $W=12-2h$

The volume of the box is $V=L\times W\times H$

$V=(21-2h)\times (12-2h)\times h$

$V=(21-2h)\times (12h-2h^2)$

$V=252h-42h^2-24h^2+4h^3$

$V=4h^3-66h^2+252h$

To maximize the volume we find derivative of volume and put it to zero.

$V'=12h^2-132h+252$

$0=12h^2-132h+252$

Solving by quadratic formula,

$h=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$h=\frac{-(-132)\pm\sqrt{132^2-4(12)(252)}}{2(12)}$

$h=\frac{132\pm72.99}{24}$

$h=2.45,8.54$

Now, substitute the value of h in the volume,

$V=4h^3-66h^2+252h$

When, h=2.45

$V=4(2.45)^3-66(2.45)^2+252(2.45)$

$V\approx 280.05$

When, h=8.54

$V=4(8.54)^3-66(8.54)^2+252(8.54)$

$V\approx -170.06$

Rejecting the negative volume as it is not possible.

Therefore, The volume of the box is 280.05 in³.

The dimension of the box is

The height of the box is h=2.45

The length of the box is $L=21-2(2.45)=16.1$

The width of the box is $W=12-2(2.45)=7.1$

So, Dimension of the box is $16.1\times 7.1\times 2.45$

6 0

4 years ago

A store is selling a mixture of apple granola and blueberry granola for $6.99 per pound. Blueberry granola costs $8.99 per pound

Alik [6]

Answer:the number of pounds of blueberry granola that she should put in the mixture is 10 pounds.

the number of pounds of apple granola that she should put in the mixture is 20 pounds

Step-by-step explanation:

Let x represent the number of pounds of blueberry granola that she should put in the mixture.

Let y represent the number of pounds of apple granola that she should put in the mixture.

She wants to make a 30 pounds mixture. This means that

x + y = 30

A store is selling a mixture of apple granola and blueberry granola for $6.99 per pound. This means that the cost of the 30 pound mixture would be

30 × 6.99 = $209.7

Blueberry granola costs $8.99 per pound and apple granola costs $5.99. This means that

8.99x + 5.99y = 209.7 - - - - - - - - - -1

Substituting x = 30 - y into equation 1, it becomes

8.99(30 - y) + 5.99y = 209.7

269.7 - 8.99y + 5.99y = 209.7

- 8.99y + 5.99y = 209.7 - 269.7

- 3y = - 60

y = - 60/ -3

y = 20

Substituting y = 20 into x = 30 - y, it becomes

x = 30 - 20 = 10 pounds

7 0

3 years ago

Identify a pair of similar triangles How can you tell the difference between Side-Side-Side, Side-Angle-Side, Angle-Side-Angle,

liberstina [14]

Step-by-step explanation:

SSS

SSS stands for "side, side, side" and means that we have two triangles with all three sides equal. For example: is congruent to: (See Solving SSS Triangles to find out more) If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent

SAS

The Side Angle Side postulate (often abbreviated as SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

ASA

ASA stands for "angle, side, angle" and means that we have two triangles where we know two angles and the included side are equal. For example: is congruent to: (See Solving ASA Triangles to find out more)

AAS

The Angle Angle Side postulate (often abbreviated as AAS) states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.

7 0

4 years ago

Plzzzz help! i will give brainliest 100 points! Let f(x) = 8x3 + 16x2 − 15 and g(x) = 2x + 1. Find f of x over g of x. A. 4 time

Blizzard [7]

Answer:

C. 4 times x squared plus 6 times x minus 3 minus 12 over the quantity 2 times x plus 1

Step-by-step explanation:

f(x) = 8x^3 + 16x^2 − 15

g(x) = 2x + 1.

f(x) / g(x) = (8x^3 + 16x^2 − 15) / (2x + 1)

Using long division

4 0

4 years ago

Stanley noticed that he is both the 10th tallest and the 10th shortest student in his class. If everyone in the class is at a di

STALIN [3.7K]

the answer for this question is B.20

6 0

4 years ago