In circle A as shown below, segment DC is tangent to circle A at D. Also, DC = 4 and BC = 2

If f(x)=x2+10sinx, show that there is a number c such that f(c)=1000.

gayaneshka [121]

F(x) is continuous for all x.

Pick a point and show that f(x) is either negative or positive. Pick another point and show that f(x) is negative, if positive, or positive, if negative.

At x = 30, f(30) - 1000 = 900 + 10sin(30) - 1000 ≤ 0
Now, show at another point f(x) - 1000 is positive, and hence, there would be root between 30 and such point.

Let's pick 40.
At x = 40, f(40) - 1000 = 1600 + 10sin(40) - 1000 ≥ 0

Since f(x) - 1000 is continuous, there lies a root between 30 and 40, and hence, 30 ≤ c ≤ 40

7 0

2 years ago

The simplest radical form of the radicand 32

diamong [38]

Your answer is 4 radical 2.

5 0

2 years ago

Find the value of x .. assume that segments that appear to be tangent are tangent .

Rus_ich [418]

Answer:

sqrt(277) =x

x is approximately 16.64331698

Step-by-step explanation:

This is a right triangle since 14 is tangent to the circle and 9 is a radius

We can use the Pythagorean theorem to solve this problem

a^2 +b^2 =c^2

9^2+14^2 =x^2

81+196 = x^2

277 = x^2

Taking the square root of each side

sqrt(277) = sqrt(x^2)

sqrt(277) =x

6 0

2 years ago

Each year on the same day, Susan deposits $175 into a saving account that earns simple interest at a rate of 3.5%. She makes no

igomit [66]

The amount after time t will be given by simple interest formula given by:
A=prt/100
where:
principle,p=$175
rate, r=3.5%
time, t=5 years
thus the rate earned after 5 years will be:
A=(175*3.5/100*5)
A=$30.625
Answer: B] 30.65

3 0

2 years ago

The average number of traffic tickets issued in a city on any given day

Anton [14]

Answer:

The most tickets were written on Saturday .On Saturday 325 tickets were issued

Step-by-step explanation:

The average number of traffic tickets issued in a city on any given day Sunday-Saturday can be approximated by

$T(x) = -6x^2 + 84x + 37$