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Rudik [331]
3 years ago
12

Line "AB" and line "CD" are perpendicular and intersect at point P. What is the measure of angle APC?​ ​

Mathematics
1 answer:
mojhsa [17]3 years ago
6 0

Answer:

APC is 90 degrees

Step-by-step explanation:

When lines intersect and are perpendicular. that means the angle of intersection is 90 degrees.

APC is 90 degrees

You might be interested in
4 1/2 ​ ÷(−1 3/7​ ) please help and hurry
myrzilka [38]

Hi! I'm happy to help!

To first solve this, we need to make those mixed numbers improper fractions.

To make 4 1/2 an improper fraction, you have to turn 4 into halves (multiply four by 2) then add the extra half, giving you 9/2.

\frac{9}{2}​ ÷(−1\frac{3}{7}​ )

Now, we turn 1 3/7 into an improper fraction. We turn 1 into sevenths (multiply 1 by 7) then add the other 3 sevenths, giving you 10/7.

\frac{9}{2}​ ÷(−\frac{10}{7}​ )

From here, we need to turn this problem into a multiplication problem in order to solve. Since multiplication is the opposite of division, we need to get the opposite of something, so we use our second fraction and flip it.

\frac{9}{2}​ ×(−\frac{7}{10}​ )

Now, we multiply the top by the top, and the bottom by the bottom. (any positive multiplied by a negative gives a negative)

-\frac{63}{20}

<u>Since we cannot simplify, our final answer is -63/20.</u>

I hope this was helpful, keep learning! :D

6 0
3 years ago
Read 2 more answers
Patrice Matson works for a company that uses a
Sergeeva-Olga [200]

Answer:

hello your question is incomplete below is the complete question

Patrice Matson works for a company that uses a percentage method to compute income tax withheld. Patrice is single and claims two allowances. Each allowance is $63.46 each week. She earns $480 per week. Find the amount of income tax withheld.

answer: $35.3

Step-by-step explanation:

using the percentage method The percentage of Patrice  income to be withheld as tax based on his weekly income  = 10% of taxable income

Gross income per week = $480

Allowances = $63.46 * 2 = $126.92

Taxable income = $480 - $126.92 = $353.08

amount to be withheld as tax = 10.% * $353.08 = $35.3

5 0
3 years ago
(a) Find the unit tangent and unit normal vectors T(t) and N(t).
andrey2020 [161]

Answer:

a. i. (i + tj + 2tk)/√(1 + 5t²)

ii.  (-5ti + j + 2k)/√[25t² + 5]

b. √5/[√(1 + 5t²)]³

Step-by-step explanation:

a. The unit tangent

The unit tangent T(t) = r'(t)/|r'(t)| where |r'(t)| = magnitude of r'(t)

r(t) = (t, t²/2, t²)

r'(t) = dr(t)/dt = d(t, t²/2, t²)/dt = (1, t, 2t)

|r'(t)| = √[1² + t² + (2t)²] = √[1² + t² + 4t²] = √(1 + 5t²)

So, T(t) = r'(t)/|r'(t)| = (1, t, 2t)/√(1 + 5t²)  = (i + tj + 2tk)/√(1 + 5t²)

ii. The unit normal

The unit normal N(t) = T'(t)/|T'(t)|

T'(t) = dT(t)/dt = d[ (i + tj + 2tk)/√(1 + 5t²)]/dt

= -5ti/√(1 + 5t²)⁻³ + [-5t²j/√(1 + 5t²)⁻³] + [-10tk/√(1 + 5t²)⁻³]

= -5ti/√(1 + 5t²)⁻³ + [-5t²j/√(1 + 5t²)⁻³] + j/√(1 + 5t²)+ [-10t²k/√(1 + 5t²)⁻³] + 2k/√(1 + 5t²)

= -5ti/√(1 + 5t²)⁻³ - 5t²j/[√(1 + 5t²)]⁻³ + j/√(1 + 5t²) - 10t²k/[√(1 + 5t²)]⁻³ + 2k/√(1 + 5t²)

= -5ti/√(1 + 5t²)⁻³ - 5t²j/[√(1 + 5t²)]⁻³ - 10t²k/[√(1 + 5t²)]⁻³ + j/√(1 + 5t²) + 2k/√(1 + 5t²)

= -(i + tj + 2tk)5t/[√(1 + 5t²)]⁻³ + (j + 2k)/√(1 + 5t²)

We multiply by the L.C.M [√(1 + 5t²)]³  to simplify it further

= [√(1 + 5t²)]³ × -(i + tj + 2tk)5t/[√(1 + 5t²)]⁻³ + [√(1 + 5t²)]³ × (j + 2k)/√(1 + 5t²)

= -(i + tj + 2tk)5t + (j + 2k)(1 + 5t²)

= -5ti - 5²tj - 10t²k + j + 5t²j + 2k + 10t²k

= -5ti + j + 2k

So, the magnitude of T'(t) = |T'(t)| = √[(-5t)² + 1² + 2²] = √[25t² + 1 + 4] = √[25t² + 5]

So, the normal vector N(t) = T'(t)/|T'(t)| = (-5ti + j + 2k)/√[25t² + 5]

(b) Use Formula 9 to find the curvature.

The curvature κ = |r'(t) × r"(t)|/|r'(t)|³

since r'(t) = (1, t, 2t), r"(t) = dr'/dt = d(1, t, 2t)/dt  = (0, 1, 2)

r'(t) = i + tj + 2tk and r"(t) = j + 2k

r'(t) × r"(t) =  (i + tj + 2tk) × (j + 2k)

= i × j + i × 2k + tj × j + tj × 2k + 2tk × j + 2tk × k

= k - 2j + 0 + 2ti - 2ti + 0

= -2j + k

So magnitude r'(t) × r"(t) = |r'(t) × r"(t)| = √[(-2)² + 1²] = √(4 + 1) = √5

magnitude of r'(t) = |r'(t)| = √(1 + 5t²)

|r'(t)|³ = [√(1 + 5t²)]³

κ = |r'(t) × r"(t)|/|r'(t)|³ = √5/[√(1 + 5t²)]³

8 0
3 years ago
Rolling two die, how many ways can a five show up on at least one die
IRINA_888 [86]
Total possibilities would be: 

(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)
(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)
(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)
(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)
(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)
(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)

You want 5 on at-least one, so mark 5th column & 5th raw.
There are 6 in both lines with 1 common = (5,5)

In short, Your Answer would be 11

Hope this helps!
3 0
3 years ago
I need helppp pleasee
gogolik [260]
50p=c
So $50 x the number of people = the price in dollars
So for 11 people it would cost $550
I hope this helped :)
8 0
2 years ago
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