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Luda [366]
4 years ago
9

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:

<h2>1529.4 m³</h2>

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

We have the final answer as

<h3>1529.4 m³</h3>

Hope this helps you

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.

Hope this Helps!!!

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}

Let (1,2) be <em>x₁ </em>and <em>y₁ </em>and let (2.5,4) be <em>x₂ </em>and <em>y₂. </em>Therefore:

d=\sqrt{(2.5-1)^2+(4-2)^2}\\d=\sqrt{(1.5)^2+2^2}\\d=\sqrt{2.25+4}\\d=\sqrt{6.25}=2.5

Thus, r is 2.5.

Plugging these numbers into the equation, we have:

(x-h)^2+(y-k)^2=r^2\\(x-1)^2+(y-2)^2=2.5^2\\(x-1)^2+(y-2)^2=6.25

3 0
3 years ago
Help me I don't know what it is.
kotegsom [21]

Answer:

a is the correct answer

Step-by-step explanation:

-6-(-3)

-6+3

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8 0
3 years ago
The volume of a single layer in a rectangular prism is 18 cubic centimeters. There are 5 layers in this rectangular prism. What
sweet [91]

Answer: 90cm^3

Step-by-step explanation:

A rectangular prism is a three-dimensional solid.

A rectangular prism has six faces (each one of these faces are rectangles), eight vertices and twelve edges.

You know that this rectangular prism has 5 layers and the volume of one of these layers is 18 cubic centimeters (18cm^3).

Assuming that all these layers are equal, the volume of this rectangular prism can be calculated with:

V_{prism}=5*V_1

Where V_1 is the volume of one layer.

Substituting, you get:

V_{prism}=(5)(18cm^3)\\\\V_{prism}=90cm^3

8 0
3 years ago
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