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3 years ago

When is dot product zero?

Mathematics

1 answer:

blsea [12.9K]3 years ago

7 0

Answer:

explain

Step-by-step explanation:

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a 9ft ladder is placed 4.5 feet from the base of a wall. How high up will the ladder reach? Round to the nearest hundredth.

spin [16.1K]

Answer:

$\huge\boxed{7.79 \ \text{feet}}$

Step-by-step explanation:

We know that we have a 9 foot long ladder resting upon a wall, with an unknown height, but the ladder is 4.5 feet away from the wall.

This can be represented as a triangle, where x is the unknown side.

| \

x | \ 9

| \

|_____\

4.5

We can use The Pythagorean Theorem to find the value of x. The theorem states that $a^2+b^2=c^2$ , where a and b are the lengths of the legs and c is the length of the hypotenuse.

However, we already know the hypotenuse and one leg. Therefore we can substitute inside the equation to find the missing value.

$a^2 + 4.5^2 = 9^2\\\\a^2 + 20.25 = 81\\\\a^2 = 60.75\\\\a \approx 7.79$

Hope this helped!

7 0

2 years ago

A ramp is used to load suitcases on an airplane. If the cargo door is 7 feet from the ground and the angle formed by the end of

melisa1 [442]

Answer: $16.56\ ft$

Step-by-step explanation:

You must draw a right triangle as the one attached, where "x" is the lenght in feet of the ramp.

You need to use the following Trigonometric Identity:

$sin\alpha=\frac{opposite}{hypotenuse}$

In this case you can identify that:

$\alpha =25\°\\\\opposite=7\\\\hypotenuse=x$

Now you must substitute these values into $sin\alpha=\frac{opposite}{hypotenuse}$ :

$sin(25\°)=\frac{7}{x}$

Finally, you must solve for "x" in order to find its value.

This is:

$sin(25\°)=\frac{7}{x}\\\\xsin(25\°)=7\\\\x=\frac{7}{sin(25\°)}\\\\x=16.56$

6 0

2 years ago

Which of the following inequalities is correct?

almond37 [142]

Answer:

Step-by-step explanation:

because there variables represent 1 so 1 cant be bigger than one and the other two have real equations

6 0

2 years ago

The number of cubic units in the volume of a sphere is equal to the number of square units in the surface area of the sphere. Wh

viktelen [127]

Answer:

Radius of sphere is 3 units.

Step-by-step explanation:

Volume of sphere is given by $4/3 \pi r^3$

surface area of sphere is given by $4 \pi r^2$

where r is the radius of the sphere.

Given that

The number of cubic units in the volume of a sphere is equal to the number of square units in the surface area of the sphere.

we equate formula of Volume of sphere and surface area of sphere

assuming r as the radius.

thus,

$4/3 \pi r^3 = 4 \pi r^2\\\\4/3 \pi r^3/ 4 \pi r^2 = 1\\=>r/3 = 1\\=> r = 3$

Thus, radius of sphere is 3 units.

5 0

2 years ago

Mary sells to her father, robert, her shares in a corp for $55,000. the shares cost mary $80,000. how much loss may mary claim f

OverLord2011 [107]

Mary Purchase shares = $80,000
Mary Sells shares = $55,000

Loss she can claim for = $80,000 - $55,000
= $ 25,000

6 0

2 years ago