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2 years ago

AB and BC form a right angle at point B. If A=(-3,-1) and B=(4,4), what is the equation of BC

Mathematics

1 answer:

poizon [28]2 years ago

7 0

Answer:

Step-by-step explanation:

We look for the equation of the line AB

We have then:

y-yo = m (x-x0)

m = (y2-y1) / (x2-x1)

m = (4 - (- 1)) / (4 - (- 3))

m = 5/7

We choose an ordered pair:

(xo, yo) = (4, 4)

Substituting:

y-4 = (5/7) (x-4)

y = (5/7) x-20/7 + 4

7y = 5x - 20 + 28

7y = 5x + 8

y = (5/7) x + 8/7

The equation of the perpendicular line is:

-7x - 5y = -48

Answer:

the equation of BC is:

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In this question,We have to group the given expression to get 5 as the final answer .

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$5^3 \div (5+20)$

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3 years ago

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3 years ago

Find the volume and surface area of the square pyramid

Montano1993 [528]

The volume and surface area of the pyramid will be 392 / 3 cubic units and 189 square units. Then the correct option is A.

The complete question is attached below.

<h3>What is the volume and surface area of the pyramid? </h3>

Suppose the base of the pyramid has length = L units, width = W units, slant height = K units, and the height of the pyramid is of H units.

Then the volume of the pyramid will be

V = (L × B × H) / 3

The surface area of the pyramid will be

SA = 2(1/2 × B × K) + 2(1/2 × L × K) + (L × B)

Then the volume will be

V = (7 × 7 × 8) / 3

V = 392/3 cubic units

Then the surface area will be

SA = 2(1/2 × 7 × 10) + 2(1/2 × 7 × 10) + (7 × 7)

SA = 189 square units

Then the correct option is A.

More about the volume and surface area of the pyramid link is given below.

brainly.com/question/23302816

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2 years ago

Find the function r that satisfies the given condition. r'(t) = (e^t, sin t, sec^2 t): r(0) = (2, 2, 2) r(t) = ()

lesantik [10]

Answer:

r(t) = (e^t +1, -cos(t) + 3, tan(t) + 2)

Step-by-step explanation:

A primitive of e^t is e^t+c, since r(0) has 2 in its first cooridnate, then

e^0+c = 2

1+c = 2

c = 1

Thus, the first coordinate of r(t) is e^t + 1.

A primitive of sin(t) is -cos(t) + c (remember that the derivate of cos(t) is -sin(t)). SInce r(0) in its second coordinate is 2, then

-cos(0)+c = 2

-1+c = 2

c = 3

Therefore, in the second coordinate r(t) is equal to -cos(t)+3.

Now, lets see the last coordinate.

A primitive of sec²(t) is tan(t)+c (you can check this by derivating tan(t) = sin(t)/cos(t) using the divition rule and the property that cos²(t)+sin²(t) = 1 for all t). Since in its third coordinate r(0) is also 2, then we have that

2 = tan(0)+c = sin(0)/cos(0) + c = 0/1 + c = 0

Thus, c = 2

As a consecuence, the third coordinate of r(t) is tan(t) + 2.

As a result, r(t) = (e^t +1, -cos(t) + 3, tan(t) + 2).

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Eddi Din [679]

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