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3 years ago

NOTE: Angles not necessarily drawn to scale.

Mathematics

2 answers:

Anastasy [175]3 years ago

7 0

The answer is 13!! :)

AVprozaik [17]3 years ago

3 0

The entire plane is 360°
Each side (top & bottom) is 180°
Each 1/4 section is 90°
With the information given that the angle opposite to x is 77°
And the total angle of that quadrant is 90°
By using the laws of angles.

Then you can calculate 90°-77°=x
So x=13°

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The diagram shows a 9cm x 7cm rectangle-based pyramid. all the diagonal sides - TA, TB, TC, AND TD- are length 12cm. M is the mi

lakkis [162]

Answer:

∠TAC is approximately equal to 61.6°

Step-by-step explanation:

The given parameters for the pyramid are;

The dimension for the rectangular base are; Length = 9 cm, width = 7 cm

The length of the diagonal sides, TA, TB, TC, and TD = 12 cm each

The midpoint of the rectangular base = Point M

The diagonal AC = AM + MC

AM = MC as given M is the midpoint of the rectangular base

∴ AC = AM + MC = 2·AM

By Pythagoras' theorem, AC = √(9² + 7²) = √130

AC = √130 cm

∴ AM = AC/2 = (√130)/2 cm

Alternatively, AM = √((9/2 cm)² + (7/2 cm)²) = √(32.5) cm

∠TAC = ∠TAM

By trigonometric ratios, we have;

$cos (\theta) = \dfrac{Length \ of \ adjacent \ side \ to \ angle }{Length \ of \ hypotenuse\ side \ to \ angle}$

$\therefore cos (\angle TAM) = cos (\angle TAC) = \dfrac{\left (\dfrac{\sqrt{130} }{2} \right )}{12} = \dfrac{\sqrt{130} }{2 \times 12} = \dfrac{\sqrt{130} }{24}$

$\angle TAC = arccos \left ( \dfrac{\sqrt{130} }{24} \right ) \approx 61.6 ^{\circ} \ to 1 \ decimal \ place$

6 0

3 years ago

A cyclist rides at an average speed of 18 miles per hour. if she wants to bike 212 km, how long (in hours) must she ride?

SOVA2 [1]

The cyclist would ride 7.31836 to travel 212 km.

8 0

3 years ago

Read 2 more answers

Line segment AB has endpoints A(1, 2) and B(5, 3). Find the coordinates of the point that divides the line segment directed from

Tanzania [10]

Answer:

The coordinates of the point that divides the line segment directed from A to B in the ratio of 1:3 is P ( 2 , 2.25 ).

Step-by-step explanation:

Given:

Let Point P ( x , y ) divides Segment Am in the ratio 1 : 3 = m : n (say)

point A( x₁ , y₁) ≡ ( 1 , 2)

point B( x₂ , y₂) ≡ (5 , 3)

To Find:

point P( x , y) ≡ ?

Solution:

IF a Point P divides Segment AB internally in the ratio m : n, then the Coordinates of Point P is given by Section Formula as

$x=\frac{(mx_{2} +nx_{1}) }{(m+n)}\\ \\and\\\\y=\frac{(my_{2} +ny_{1}) }{(m+n)}\\\\$

Substituting the values we get

$x=\frac{(1\times 5 +3\times 1) }{(1+3)}\\ \\and\\\\y=\frac{(1\times 3 +3\times 2) }{(1+3)}\\\\\therefore x = \frac{8}{4}=2 \\\\and\\\therefore y = \frac{9}{4}=2.25 \\\\\\\therefore P(x,y) = (2 , 2.25)$