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3 years ago

4. A rectangle has a diagonal of 8 cm. The diagonal creates a 60° angle at the base of the rectangle.

Mathematics

1 answer:

tamaranim1 [39]3 years ago

7 0

9514 1404 393

Answer:

a) see attachment

b) base: 4, height: 4√3

c) area: 16√3

Step-by-step explanation:

a) The figure is drawn in the attachment

b) The side lengths of a 30-60-90 right triangle have the ratio ...

1 : √3 : 2

Multiplying these by 4 gives the side lengths of each triangle created by the diagonal. The base (short leg) is 4 units; the height (long leg) is 4√3 units.

c) The area is the product of base and height:

A = bh

A = 4(4√3) = 16√3 . . . . square units

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An aeroplane X whose average speed is 50°km/hr leaves kano airport at 7.00am and travels for 2 hours on a bearing 050°. It then

Zigmanuir [339]

Answer:

(a)123 km/hr

(b)39 degrees

Step-by-step explanation:

Plane X with an average speed of 50km/hr travels for 2 hours from P (Kano Airport) to point Q in the diagram.

Distance = Speed X Time

Therefore: PQ =50km/hr X 2 hr =100 km

It moves from Point Q at 9.00 am and arrives at the airstrip A by 11.30am.

Distance, QA=50km/hr X 2.5 hr =125 km

Using alternate angles in the diagram:

$\angle Q=110^\circ$

(a)First, we calculate the distance traveled, PA by plane Y.

Using Cosine rule

$q^2=p^2+a^2-2pa\cos Q\\q^2=100^2+125^2-2(100)(125)\cos 110^\circ\\q^2=34175.50\\q=184.87$ km$

SInce aeroplane Y leaves kano airport at 10.00am and arrives at 11.30am

Time taken =1.5 hour

Therefore:

Average Speed of Y

$=184.87 \div 1.5\\=123.25$ km/hr\\\approx 123$ km/hr (correct to three significant figures)$

(b)Flight Direction of Y

Using Law of Sines

$\dfrac{p}{\sin P} =\dfrac{q}{\sin Q}\\\dfrac{125}{\sin P} =\dfrac{184.87}{\sin 110}\\123 \times \sin P=125 \times \sin 110\\\sin P=(125 \times \sin 110) \div 184.87\\P=\arcsin [(125 \times \sin 110) \div 184.87]\\P=39^\circ $ (to the nearest degree)$

The direction of flight Y to the nearest degree is 39 degrees.

7 0

3 years ago

What is the value of x? <br> a. 2/3b) 4/3c) 4d) 6?

oksian1 [2.3K]

Value of x=6....
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8 0

3 years ago

Pleaseeeeee solveee 25 points pleaze help geometry

tatiyna

Answer:

(-3/2, 6)

Step-by-step explanation:

(-3,8) (6,-4)

As we move along the line segment with endpoints (-3,8) and (6,-4) from (-3,8) to (6,-4) x increases by 9 units (from -3 to 6) and y decreases by -12 units (from 8 to -4).

for ratio of 1:5

Since 1+5=6, the point we are looking for is 1/6 of the way from (-3,8) to (6,-4).

So, the desired point is

(-3 + (1/6)(9), 8 - (1/6)(12) )

= (-3 + 3/2 , 8 - 2)

= ( (-6 + 3)/2, 6)

= (-3/2, 6)

for map reference see the image below

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3 years ago

What degree is -4^4xy^4

Viktor [21]

Answer:

Step-by-step explanation:

The degree is 5

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a_sh-v [17]

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