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3 years ago

15

Alison is preparing for a math contest. Each day she works on multiplication problems for 20 minutes and division problems for 1

0 minutes. How many minutes does Alison practice multiplication and division problems in 15 days

1 answer:

Alexxandr [17]3 years ago

6 0

600 minutes (10 hours)

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1 year ago

Three security cameras were mounted at the corners of a triangles parking lot. Camera 1 was 110 ft from camera 2, which was 137

Nata [24]

Answer:

<em>Camera 2nd has to cover the maximum angle, i.e. </em> $78.70^\circ$ .

Step-by-step explanation:

Please have a look at the triangular park represented as a triangle $\triangle ABC$ with sides

a = 110 ft

b = 158 ft

c = 137 ft

1st camera is located at point C, 2nd camera at point B and 3rd camera at point A respectively.

We can use law of cosines here, to find out the angles $\angle A, \angle B, \angle C$

As per Law of cosine:

$cos C = \dfrac{a^{2}+b^2-c^2 }{2ab}\\cos B = \dfrac{a^{2}+c^2-b^2 }{2ac}\\cos A = \dfrac{b^{2}+c^2-a^2 }{2bc}$

Putting the values of a,b and c to find out angles $\angle A, \angle B, \angle C$ .

$cos C = \dfrac{110^{2}+158^2-137^2 }{2\times 110 \times 158}\\\Rightarrow cos C = \dfrac{12100+24964-18769 }{24760}\\\Rightarrow cos C =0.526\\\Rightarrow C = 58.24^\circ$

$cos B = \dfrac{110^{2}+137^2-158^2 }{2\times 110 \times 137}\\\Rightarrow cos B = \dfrac{12100+18769 -24964}{30140}\\\Rightarrow cos B = \dfrac{5905}{30140}\\\Rightarrow cos B =0.196\\\Rightarrow B = 78.70^\circ$

$cos A = \dfrac{158^{2}+137^2-110^2 }{2\times 158 \times 137}\\\Rightarrow cos A = \dfrac{24964+18769-12100}{43292}\\\Rightarrow cos A = \dfrac{31633}{43292}\\\Rightarrow cos A = 0.731\\\Rightarrow A = 43.05^\circ$

<em>Camera 2nd has to cover the maximum angle</em>, i.e. $78.70^\circ$ .

6 0

3 years ago

A rock is thrown at 0 seconds from a height of 6 feet. If the parabola representing the height as a function of time has a verte

Korolek [52]

Answer:

The correct option is;

The graph will have a height of 6 feet at 16 seconds

Step-by-step explanation:

The given parameters are;

The start time for throwing the rock = 0 s

The height from which the rock is thrown = 6 ft

The vertex of the parabola = 8 seconds

Given that the vertex is the axis of symmetry, then the time it takes the rock to reach the vertex (8 seconds) from the point (0, 6) will be the same time it takes the rock to reach the point on the other side of the parabola at the same 6 feet which will then have coordinates (8 + 8, 6) or (16, 6) which will be 6 feet in 16 seconds.

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3 years ago