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1 year ago

Asap! find the length of the arc

Mathematics

1 answer:

Fantom [35]1 year ago

6 0

Answer:

A. $\frac{21}{4} \pi\ \space\ in$

Step-by-step explanation:

The formula for arc length is:

arc length = rθ

where:

r is the radius = 7 in

θ is the central angle in radians = 135 × $\frac{ \space\ \pi\ }{180}$ = 3/4 π

Substituting these values into the formula:
arc length = 7 in × 3/4 π

= $\frac{21}{4} \pi\ \space\ in$

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A country has 32 parks that allow camping and 43 parks that have playgrounds. Of those, 10 parks both allow camping and have pla

Olenka [21]

Answer:

Step-by-step explanation:

Given:

32 parks allow camping

43 parks allow playgrounds

10 parks both allow camping and playgrounds

110 total parks

First, we need to add 32, 43, and 10

32 + 43 + 10 = 85

Then, we find the difference of 110 and 85

110 - 85 = 25

Since it isn't a decimal, there is no point in rounding.

8 0

3 years ago

Prove that if b is a square matrix then b+b^t is symmetric

WARRIOR [948]

A matrix $\mathbf X$ is symmetric if $\mathbf X=\mathbf X^\top$ . We have

$(\mathbf B+\mathbf B^\top)^\top=\mathbf B^\top+(\mathbf B^\top)^\top=\mathbf B^\top+\mathbf B=\mathbf B+\mathbf B^\top$

and so $\mathbf B+\mathbf B^\top$ is indeed symmetric.

6 0

3 years ago

What is the value of x in the equation 3(4x+6) =21 A) 1/4 B) 13/4 C) 4/13 D) 12/7

nata0808 [166]

3 (4x + 6) = 21
4x + 6 = 21/3
4x + 6 = 7
4x = 7 - 6
4x = 1
x = 1/4

8 0

2 years ago

What is the horizontal asymptote for y(t) for the differential equation dy dt equals the product of 2 times y and the quantity 1

marta [7]

First, we need to solve the differential equation.
$\frac{d}{dt}\left(y\right)=2y\left(1-\frac{y}{8}\right)$
This a separable ODE. We can rewrite it like this:
$-\frac{4}{y^2-8y}{dy}=dt$
Now we integrate both sides.
$\int \:-\frac{4}{y^2-8y}dy=\int \:dt$
We get:
$\frac{1}{2}\ln \left|\frac{y-4}{4}+1\right|-\frac{1}{2}\ln \left|\frac{y-4}{4}-1\right|=t+c_1$
When we solve for y we get our solution:
$y=\frac{8e^{c_1+2t}}{e^{c_1+2t}-1}$
To find out if we have any horizontal asymptotes we must find the limits as x goes to infinity and minus infinity.
It is easy to see that when x goes to minus infinity our function goes to zero.
When x goes to plus infinity we have the following:
$$$\lim_{x\to\infty} f(x)$$=y=\frac{8e^{c_1+\infty}}{e^{c_1+\infty}-1} = 8$
When you are calculating limits like this you always look at the fastest growing function in denominator and numerator and then act like they are constants.
So our asymptote is at y=8.

3 0

2 years ago

Which ordered pairs lie on the graph of the exponential function f(x)=−3^2x+5 ? Select each correct answer. (−2, 76) (

In-s [12.5K]

Plugging in values, we get that (1,-4) works.

$f(1)=-3^{2*1}+5=-3^2+5=-9+5=-4$

3 0

2 years ago

Read 2 more answers