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2 years ago

I need help with this geometry question

Mathematics

1 answer:

UNO [17]2 years ago

6 0

Answer:

radius ≈ 15.5

Step-by-step explanation:

the radius is RS

the angle between a tangent and the radius at the point of contact is 90°

then Δ RST is a right triangle

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , then

RS² + ST² = RT² ( substitute values )

RS² + 7² = 17²

RS² + 49 = 289 ( subtract 49 from both sides )

RS² = 240 ( take square root of both sides )

RS = $\sqrt{240}$ ≈ 15.5 ( to 1 dec. place )

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find a formula for the nth term of the arithmetic sequence the first term is -2 and the common difference is 8

Rudiy27

Answer:

a(n) = -2 + 8(n - 1)

Step-by-step explanation:

General formula is a(n) = a(1) + d(n - 1), where d is the common difference.

Here a(n) = -2 + 8(n - 1)

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3 years ago

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Vera_Pavlovna [14]

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3 years ago

How to integrate with steps:<br><br> (4x2-6)/(x+5)(x-2)(3x-1)

joja [24]

$\displaystyle\int\frac{4x^2-6}{(x+5)(x-2)(3x-1)}\,\mathrm dx$

You have a rational expression whose numerator's degree is smaller than the denominator's. This tells you you should consider a partial fraction decomposition. We want to rewrite the integrand in the form

$\dfrac{4x^2-6}{(x+5)(x-2)(3x-1)}=\dfrac a{x+5}+\dfrac b{x-2}+\dfrac c{3x-1}$

$\implies4x^2-6=a(x-2)(3x-1)+b(x+5)(3x-1)+c(x+5)(x-2)$

You can use the "cover-up" method here to easily solve for $a,b,c$ . It involves fixing a value of $x$ to make 2 of the 3 terms on the right side disappear and leaving a simple algebraic equation to solve for the remaining one.

If $x=-5$ , then $94=112a\implies a=\dfrac{47}{56}$
If $x=2$ , then $10=35b\implies b=\dfrac27$
If $x=\dfrac13$ , then $-\dfrac{50}9=-\dfrac{80}9c\implies c=\dfrac58$

So the integral we want to compute is the same as

$\displaystyle\frac{47}{56}\int\frac{\mathrm dx}{x+5}+\frac{10}{35}\int\frac{\mathrm dx}{x-2}+\frac58\int\frac{\mathrm dx}{3x-1}$

and each integral here is trivial. We end up with

$\displaystyle\int\frac{4x^2-6}{(x+5)(x-2)(3x-1)}\,\mathrm dx=\frac{47}{56}\ln|x+5|+\frac27\ln|x-2|+\frac5{24}\ln|3x-1|+C$

which can be condensed as

$\ln\left|(x+5)^{47/56}(x-2)^{2/7}(3x-1)^{5/24}\right|+C$

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3 years ago

HELP 50pts And Brainleist. I need the Answers ...

Anvisha [2.4K]

Let us assume that the first company the cab flat rate is 5$ and the cap driver charges 2$ per mile .for the second company the cab flat rate is 3$ and the cab driver charges 3$ per mile.
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y-intercept which is the cab flat rate .
y=mx+b
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x. is the milage
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3 years ago

A test has 20 questions. If Peter gets 80% correct, how many questions did Peter miss?

Oduvanchick [21]

Answer:

Step-by-step explanation:

20 x 0.80

16 - 20

3 0

3 years ago

Read 2 more answers