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4 years ago

Find the angle between the given vectors to the nearest degree.

Mathematics

2 answers:

konstantin123 [22]4 years ago

6 0

Answer:

c. 108.4

Step-by-step explanation:

cos theta = (u dot v)/ (||u|| ||v||)

where dot stands for dot product and || || is the magnitude

u = (1,5) v= (7,-4)

u dot v = (1*7 + 5*-4) = 7-20 = -13

||u|| = sqrt( 1^2 +5^2) = sqrt(1+25) = sqrt(26)

||v|| = sqrt(7^2 + (-4)^2) = sqrt(49+16) = sqrt(65)

cos theta = -13/ sqrt(26) sqrt(65)

cos theta = -13 /sqrt(1690)

theta = arccos (-13/sqrt(1690))

theta = 108.43

VLD [36.1K]4 years ago

3 0

I believe the answer is c

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Find the volume of a pyramid with a square base, where the side length of the base is

ValentinkaMS [17]

Answer:

Step-by-step explanation:

Volume of a pyramid can be found by using the formula

$v = \frac{1}{3} \times a \times h \\$

a is the area of the base

h is the height

Since the base is a square we have

$v = \frac{1}{3} \times {15.3}^{2} \times 19.6 \\ = 78.03 \times 19.6 \\ = 1529.388$

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3 0

3 years ago

Luiza is jumping on a trampoline.

lyudmila [28]

Answer:

The second time when Luiza reaches a height of 1.2 m = 2 08 s

Step-by-step explanation:

Complete Question

Luiza is jumping on a trampoline. Ht models her distance above the ground (in m) t seconds after she starts jumping. Here, the angle is entered in radians.

H(t) = -0.6 cos (2pi/2.5)t + 1.5.

What is the second time when Luiza reaches a height of 1.2 m? Round your final answer to the nearest hundredth of a second.

Solution

Luiza is jumping on trampolines and her height above the levelled ground at any time, t, is given as

H(t) = -0.6cos⁡(2π/2.5)t + 1.5

What is t when H = 1.2 m

1.2 = -0.6cos⁡(2π/2.5)t + 1.5

0.6cos⁡(2π/2.5)t = 1.2 - 1.5 = -0.3

Cos (2π/2.5)t = (0.3/0.6) = 0.5

Note that in radians,

Cos (π/3) = 0.5

This is the first time, the second time that cos θ = 0.5 is in the fourth quadrant,

Cos (5π/3) = 0.5

So,

Cos (2π/2.5)t = Cos (5π/3)

(2π/2.5)t = (5π/3)

(2/2.5) × t = (5/3)

t = (5/3) × (2.5/2) = 2.0833333 = 2.08 s to the neareast hundredth of a second.

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4 0

3 years ago

Plz help with equation of the circle will award fastest CORRECT answer with brainliest

aliina [53]

Answer:

$(x-1)^2+(y-2)^2=6.25$

Step-by-step explanation:

The equation for a circle is given by:

$(x-h)^2+(y-k)^2=r^2$

Where (h,k) is the center and r is the radius.

The center is the red dot, which is (1,2). Thus, h=1 and k=2.

To find the radius, you need to use the distance formula. We are given two coordinates: the center (red dot) at (1,2) and a blue dot on the circle at (2.5,4). Find the radius by using the distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$