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NeTakaya
3 years ago
13

Over the last 3  evenings, Keisha received a total of 81  phone calls at the call center. The first evening, she received 6  few

er calls than the second evening. The third evening, she received 3  times as many calls as the first evening. How many phone calls did she receive each evening
Mathematics
1 answer:
tensa zangetsu [6.8K]3 years ago
8 0

Answer:

First: 15

Second: 21

Third: 45

Step-by-step explanation:

In order to create the equation we need to represent the evenings with an alebraic term, in thsi case we are going to represent the second evening with an X

Second evening:x

The first night she got 6 fewer calls than the second: Second-6=x-6

The third night she received 3 times the first: 3(first night)=3(x-6)

The equation is First Night plus second night plus third night equals 81.

First+second+third=81\\x+(x-7)+3(x-6)=81\\x+x-7+3x-18=81\\5x=81+21+6\\5x=105\\x=\frac{105}{5} \\x=21

So the first evening he received 15 calls, the second he received 21 and the third one he received 45.

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3 years ago
A hoop, a uniform solid cylinder, a spherical shell, and a uniform solid sphere are released from rest at the top of an incline.
Serjik [45]

Answer:

Step-by-step explanation:

Given

Hoop, Uniform Solid Cylinder, Spherical shell and a uniform Solid sphere released from Rest from same height

Suppose they have same mass and radius

time Period is given by

t=\sqrt{\frac{2h}{a}} ,where h=height of release

a=acceleration

a=\frac{g\sin \theta }{1+\frac{I}{mr^2}}

Where I=moment of inertia

a for hoop

a=\frac{g\sin \theta }{1+\frac{mr^2}{mr^2}}

a=\frac{g\sin \theta }{2}

a for Uniform solid cylinder

a=\frac{g\sin \theta }{1+\frac{mr^2}{2mr^2}}

a=\frac{2g\sin \theta }{3}

a for spherical shell

a=\frac{g\sin \theta }{1+\frac{2mr^2}{3mr^2}}

a=\frac{3g\sin \theta }{5}

a for Uniform Solid

a=\frac{g\sin \theta }{1+\frac{2mr^2}{5mr^2}}

a=\frac{5g\sin \theta }{7}

time taken will be inversely proportional to the square root of acceleration

t_1=k\sqrt{2}=1.414k

t_2=k\sqrt{\frac{3}{2}}=1.224k

t_3=k\sqrt{\frac{5}{3}}=1.2909k

t_4=k\sqrt{\frac{7}{5}}=1.183k

thus first one to reach is Solid Sphere

second is Uniform solid cylinder

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3 years ago
Pls be right will give brainliest :3
Vedmedyk [2.9K]
A:5

I hope this helps you
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2 years ago
See attachment below
KatRina [158]

Answer: Third Option

x=1.469743

Step-by-step explanation:

We have the following exponential equation

3^{x+1}=15

We must solve the equation for the variable x

To clear the variable x apply the log_3 function on both sides of the equation

log_3(3^{x+1})=log_3(15)

Simplifying we get the following:

x+1=log_3(15)

To simplify the expression log_3 (15) we apply the base change property

log_b(y)=\frac{log(y)}{log(b)}

This means that:

log_3 (15)=\frac{log(15)}{log(3)}

Then:

x+1=\frac{log(15)}{log(3)}

x=\frac{log(15)}{log(3)}-1

x=1.469743

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