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3 years ago

A triangular pyramid is formed from three right triangles as shown below.

Mathematics

1 answer:

Lady bird [3.3K]3 years ago

7 0

ΔADC is a right angle triangle, we will use the Pythagorus Theorem to find the length CD.

Formula of the Pythagorus Theorem :

⇒ a² + b² = c²

⇒ AD² + CD² = AC²

The value of AD is 54 and the value of AC is 90:

54² + CD² = 90²

Solve for CD:

54² + CD² = 90²

CD² = 90² - 54²

CD² = 5184

CD = √5184

CD = 72

ΔADC is also a right angle triangle, we will use the Pythagorus Theorem to find the length BD.

Formula of the Pythagorus Theorem :

⇒ a² + b² = c²

⇒ BD² + CD² = BC²

The value of CD is 72 and the value of BC is 97:

BD² + 72² = 97²

Solve for BD:

BD² = 97² - 72²

BD² = 4225

BD = √4225

BD = 65

Answer: The length of BD is 65 units.

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The math club needs to raise more than $552.50 for a trip to state competition. The club has raised more than 12% of the funds.

VLD [36.1K]

Need to pay less than 88% of $552.50 -> $486.20
Split between 7 of them -> $69.45
They have to pay less than 69.45, or A. m <$69.45

5 0

3 years ago

What is 5900 rounded to the nearest thousand on a number line

Vaselesa [24]

6000 do i really have to explain. lol

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3 years ago

Read 2 more answers

The curves r1(t) = 4t, t2, t3 and r2(t) = sin(t), sin(5t), 2t intersect at the origin. find their angle of intersection, θ, corr

san4es73 [151]

First get the tangent vectors by differentiating r1 and r2
$r_1 '(t) = (4,2t,3t^2) \\ \\ r_2'(t) = (cos (t), 5 cos(5t), 2)$
Evaluate at t=0
$r_1' = (4,0,0) \\ \\ r_2' = (1,5,2)$

Use identity for angle between 2 vectors:
$u*v = |u| |v| cos \theta$

Evaluate dot product and unit vectors:
$u*v = (4,0,0)*(1,5,2) = 4 \\ \\ |u| = \sqrt{4^2 +0^2+0^2} = 4 \\ \\ |v| = \sqrt{1^2 + 5^2+2^2} = \sqrt{30}$

Sub into identity and solve for theta:
$4 = 4 \sqrt{30} cos \theta \\ \\ cos\theta = \frac{1}{\sqrt{30}} \\ \\ \theta = 79.48$

Answer:
Angle of intersection is about 79 degrees.

5 0

3 years ago

Which of the following lines best fits the data shown in the scatter plot

xenn [34]

Answer:

Im pretty sure its A

Step-by-step explanation:

4 0

3 years ago

3(m - 1) = 5m +3 -2m please help me solve this step by step asap!

cupoosta [38]

Answer:

0 = 6

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3(m−1)=5m+3−2m

(3)(m)+(3)(−1)=5m+3+−2m (Distribute)

3m+−3=5m+3+−2m

3m−3=(5m+−2m)+(3) (Combine Like Terms)

3m−3=3m+3

Step 2: Subtract 3m from both sides.

3m−3−3m=3m+3−3m

−3=3

Step 3: Add 3 to both sides.

−3+3=3+3

0=6

3 0

3 years ago