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3 years ago

Given: KLMN is a trapezoid m∠K = 90°, m∠N = 45° LK = LM = 10 Find: KN, Area of KLMN

Mathematics

1 answer:

Ilya [14]3 years ago

5 0

Let KLMN be a trapezoid (see added picture). From the point M put down the trapezoid height MP, then quadrilateral KLMP is square and KP=MP=10.
A triangle MPN is right and <span>isosceles, because
</span>m∠N=45^{0}, m∠P=90^{0}, so m∠M=180^{0}-45^{0}-90^{0}=45^{0}.Then PN=MP=10.
The ttapezoid side KN consists of two parts KP and PN, each of them is equal to 10, then KN=20 units.
Area of KLMN is egual to $A= \frac{LM+KN}{2} *MP= \frac{10+20}{2} *10=150$ sq. units.

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Laney builds a tower with wooden cubes. The bottom cube's edges are 8 centimeters long. The middle cube's edges are 2 centimeter

Mazyrski [523]

Answer: The total volume of the the cubes in the tower is 792 cubic centimetres (792 cm³)

Step-by-step explanation: We shall call the volume of the cube at the bottom VB, the volume of the cube at the middle VM, and the volume of the cube at the top VT. The tower is made up of cubes at different levels and at the bottom the cube measures 8 centimetres. The cube at the middle measures 2 cm less than the bottom cube, hence middle cube equals 8 minus 2 which equals 6 cm. The top cube measures 2 cm less than the middle cube, hence the top cube equals 6 minus 2 which equals 4 cm. The volume of each cube is given as;

Volume = L³

The length of a cube measures the same on all sides, that is, length, width and height. The length on all sides therefore of the bottom cube is 8 cm. The volume equals;

VB = 8³

VB = 512 cm³

The length on all sides of the middle cube is 6 cm (measures 2 cm shorter than the bottom cube). The volume of the middle cube equals;

VM = L³

VM = 6³

VM = 216 cm³

The length on all sides of the top cube is 4 cm (measures 2 cm shorter than the middle cube). The volume of the top cube equals;

VT = L³

VT = 4³

VT = 64

From the calculations shown, the total volume of the cubes in the tower is given as;

Total volume = VB + VM + VT

Total volume = 512 + 216 + 64

Total volume = 792 cm³

Total volume is 792 cubic centimetres.

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2 years ago

Read 2 more answers

Donald has x twenty dollar bills and one ten dollar bill how much money does Donald have

Paha777 [63]

In equation form that would be X20+10. He has X amount of 20 dollar bills, then a 10 dollar bill. We have to multiply X by 20 first, then add that to 10.

~Deceptiøn

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2 years ago

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Develop an estimate for each of the following situations.(at) The cost of a 500-mile automobile trip, if gaso-line is $4 per gal

Olin [163]

Answer:

The answer is below

Step-by-step explanation:

develop an estimate for each of the following situations.

(a) The cost of a 500- mile automobile trip, if gasoline is $4.00 per gallon, vehicle wear and tear is $0.65 per mile, and our vehicle gets 25 miles per gallon.

(b) The total number of hours in the average human life, if the average life is 75 years.

(c) The number of days it takes to travel around the equator using a hot air balloon, if the balloon averages 100 miles per day, the diameter of the earth is ~4,000 miles.

Solution:

a) The total trip = 500 mile

Cost of wear and tear = $0.65 per mile = $0.65 * 500 mile = $325

25 miles takes 1 gallon of gasoline at a cost of $4 per gallon

Cost of gasoline = $4 per gallon * 500 miles / 25 miles per gallon = $80

cost of a 500-mile automobile trip = Cost of wear and tear + Cost of gasoline = $325 + $80 = $405

b) Average life of human = 75 years.

1 year = 365 days, 1 day = 24 hours

Average life of human in hours = 75 years * 365 days * 24 hours =657000 hours

c) Diameter of earth = 4000 miles

Distance of equator = diameter of earth = 4000 miles

100 mile per day

number of days for the balloon to travel round the earth = 4000 miles / (100 mile per day) = 40 days

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2 years ago

Suppose an ant walks counterclockwise on the unit circle from the point to the endpoint of the radius that forms an angle of rad

serg [7]

Answer:

$\frac{4\pi}{3}$

Step-by-step explanation:

The original questions is suppose an ant walks counterclockwise on a unit circle from the point (1,0) to the endpoint of the radius that forms an angle of 240 degrees with the positive horizontal axis.

To find the distance ant walked we find the arc length of the sector with central angle 240 degree and radius =1 (unit circle)

arc length of a sector = $\frac{centralangle}{360} \cdot 2\pi r$

arc length of a sector = $\frac{240}{360} \cdot 2\pi(1)$

arc length of a sector = $\frac{2}{3} \cdot 2\pi$

$\frac{4\pi}{3}$

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3 years ago

Evaluate the line integral for x^2yds where c is the top hal fo the circle x62 _y^2 = 9

natulia [17]

Parameterize $C$ by

$\mathbf r(t)=\langle x(t),y(t)\rangle=\langle3\cos t,3\sin t\rangle$

where $0\le t\le\pi$ . Then the line integral is

$\displaystyle\int_Cx^2y\,\mathrm dS=\int_{t=0}^{t=\pi}x(t)^2y(t)\left\|\frac{\mathrm d\mathbf r(t)}{\mathrm dt}\right\|\,\mathrm dt$
$=\displaystyle\int_{t=0}^{t=\pi}(3\cos t)^2(3\sin t)\sqrt{(-3\sin t)^2+(3\cos t)^2}\,\mathrm dt$
$=\displaystyle3^4\int_{t=0}^{t=\pi}\cos^2t\sin t\,\mathrm dt$

Take $u=\cos t$ , then

$=\displaystyle-3^4\int_{u=1}^{u=-1}u^2\,\mathrm du$
$=\displaystyle3^4\int_{u=-1}^{u=1}u^2\,\mathrm du$
$=\displaystyle2\times3^4\int_{u=0}^{u=1}u^2\,\mathrm du$
$=54$

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3 years ago