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3 years ago

Find the measures of the acute angles of the right triangle shown

Mathematics

1 answer:

yanalaym [24]3 years ago

7 0

9514 1404 393

Answer:

2x° = 64°
(x-6)° = 26°

Step-by-step explanation:

The acute angles in a right triangle are complementary:

2x° +(x -6)° = 90°

3x = 96 . . . . . . . . . divide by °, add 6

x = 32 . . . . . . . . . divide by 3

(x-6)° = (32 -6)° = 26°

2x° = 2(32)° = 64°

The acute angles have measures 26° and 64°.

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if $5,250 is invested at 4.5% compounded monthly, what is the amount accumulated at the end of 10 years?

Romashka [77]

Answer:

In 10 years, you will have $793,789.89

Step-by-step explanation:

Counted with compound interest, i would need to know what was the initial but the answ is $793,789.89

6 0

3 years ago

A cylinder has a radius of 4x + 3 and a height of 3x + 6. Which polynomial in standard form best

MrRa [10]

Answer:

Step-by-step explanation:

R=4x+3

H=3x+6

Volume of a cylinder= Πr²h

inserting the parameters

v=π(4x+3)²(3x+6)

v=π(16x²+24x+9)(3x+6)

V=π[3x(16x²+24x+9) +6(16x²+24x+9)]

v=Π(48x³+72x²+27x+96x²+144x+54)

v=π(48x³+168x²+171x+54)m³

8 0

3 years ago

Find the arc length of the given curve between the specified points. x = y^4/16 + 1/2y^2 from (9/16), 1) to (9/8, 2).

lutik1710 [3]

Answer:

The arc length is $\dfrac{21}{16}$

Step-by-step explanation:

Given that,

The given curve between the specified points is

$x=\dfrac{y^4}{16}+\dfrac{1}{2y^2}$

The points from $(\dfrac{9}{16},1)$ to $(\dfrac{9}{8},2)$

We need to calculate the value of $\dfrac{dx}{dy}$

Using given equation

$x=\dfrac{y^4}{16}+\dfrac{1}{2y^2}$

On differentiating w.r.to y

$\dfrac{dx}{dy}=\dfrac{d}{dy}(\dfrac{y^2}{16}+\dfrac{1}{2y^2})$

$\dfrac{dx}{dy}=\dfrac{1}{16}\dfrac{d}{dy}(y^4)+\dfrac{1}{2}\dfrac{d}{dy}(y^{-2})$

$\dfrac{dx}{dy}=\dfrac{1}{16}(4y^{3})+\dfrac{1}{2}(-2y^{-3})$

$\dfrac{dx}{dy}=\dfrac{y^3}{4}-y^{-3}$

We need to calculate the arc length

Using formula of arc length

$L=\int_{a}^{b}{\sqrt{1+(\dfrac{dx}{dy})^2}dy}$

Put the value into the formula

$L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4}-y^{-3})^2}dy}$

$L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4})^2+(y^{-3})^2-2\times\dfrac{y^3}{4}\times y^{-3}}dy}$

$L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4})^2+(y^{-3})^2-\dfrac{1}{2}}dy}$

$L=\int_{1}^{2}{\sqrt{(\dfrac{y^3}{4})^2+(y^{-3})^2+\dfrac{1}{2}}dy}$

$L=\int_{1}^{2}{\sqrt{(\dfrac{y^3}{4}+y^{-3})^2}dy}$

$L= \int_{1}^{2}{(\dfrac{y^3}{4}+y^{-3})dy}$

$L=(\dfrac{y^{3+1}}{4\times4}+\dfrac{y^{-3+1}}{-3+1})_{1}^{2}$

$L=(\dfrac{y^4}{16}+\dfrac{y^{-2}}{-2})_{1}^{2}$

Put the limits

$L=(\dfrac{2^4}{16}+\dfrac{2^{-2}}{-2}-\dfrac{1^4}{16}-\dfrac{(1)^{-2}}{-2})$

$L=\dfrac{21}{16}$

Hence, The arc length is $\dfrac{21}{16}$

6 0

3 years ago

Select the correct answer.

mixer [17]

Answer:

Step-by-step explanation:

find 6%

429.99*6/100= 25.7994

Total cause of the laptop

429.99+25.7994= 455.79

4 0

3 years ago

Read 2 more answers

Which function represents g(x), a reflection of f(x) = 4

mel-nik [20]

Answer: Correct answer is C -I just took the test

we have the function f(x) = 4(1/2)x, and we want to reflex it over the x-axis.

you can see in the graph that the reflex over this axis changes the sign of f(x) in all the points (where f(0) = 4, g(0) = -4, f(1) = 2, g(1) = -2, and so on), then the reflex, g(x) is equal to -f(x)

now we have:

g(x) = -f(x) = - 4(1/2)x

then the right answer is the third option:

g(x) = -4(1/2)x

Step-by-step explanation:

7 0

3 years ago