I need somebody help on this test i am Taking

What’s the answer to this?

inna [77]

Since the triangle is equilateral, all its angles are equal to 60°

AO is the bisector⇒∠OAD = 30°

AO is the hypotenuse, ∠OAD = 30°⇒

OD=5*2=10m

By the Pythagorean theorem

$10^2=AD^2+5^2\\AD=\sqrt{100-25} \\AD=\sqrt{75}$

$AC=AD+DC=2\sqrt{75}=10\sqrt{3}$

$S=\frac{a^2\sqrt{3} }{4}$

$S=\frac{(10\sqrt{3})^2\sqrt{3} }{4} =\frac{300\sqrt{3} }{4} =75\sqrt{3} m^2$

Answer: A) $S=75\sqrt{3}$ m²

P.S. Hello from Russia and sorry for my bad english :^)

3 0

2 years ago

If anyone knows about definite integrals for calculus then please I request help! I

kicyunya [14]

Answer:

$\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{1}{8} \bigg( e^\Big{\frac{4}{25}} - e^\Big{\frac{4}{81}} \bigg)$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

U-Substitution

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution.

Set u: $\displaystyle u = 4x^{-2}$
[u] Differentiate [Basic Power Rule, Derivative Properties]: $\displaystyle du = \frac{-8}{x^3} \ dx$
[Bounds] Switch: $\displaystyle \left \{ {{x = 9 ,\ u = 4(9)^{-2} = \frac{4}{81}} \atop {x = 5 ,\ u = 4(5)^{-2} = \frac{4}{25}}} \right.$

Step 3: Integrate Pt. 2

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}\int\limits^9_5 {\frac{-8}{x^3}e^\big{4x^{-2}}} \, dx$
[Integral] U-Substitution: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}\int\limits^{\frac{4}{81}}_{\frac{4}{25}} {e^\big{u}} \, du$
[Integral] Exponential Integration: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}(e^\big{u}) \bigg| \limits^{\frac{4}{81}}_{\frac{4}{25}}$
Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8} \bigg( e^\Big{\frac{4}{81}} - e^\Big{\frac{4}{25}} \bigg)$
Simplify: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{1}{8} \bigg( e^\Big{\frac{4}{25}} - e^\Big{\frac{4}{81}} \bigg)$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

4 0

2 years ago

Factor 20a + 45.............................................

Delvig [45]

Answer:5(4a+9)

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Please response ASAP! 2+3= 9+2= 0+1= 7+4=

Stolb23 [73]

2+3=5

9+2=11

0+1=1

7+4=11

3 0

2 years ago

Read 2 more answers

Which values for x and y make the statement (x + 5)(y - 6) = 0 true?

-BARSIC- [3]

$||Solving \ for \ x. ||$ 

$(x + 5)(y - 6) = 0$

$(x + 5)(y - 6) = 0 :x$

$
x+5=0
 
$ $|Divide \ both \ sides \ by \ y-6|$

$
x=-5
 
$ $|Subtract \ 5 \ from \ both \ sides|$

$||Solving \ for \ y. ||$

$
y-6=0
 
$ $|Divide \ both \ sides \ by \ x+5|$

$
y=6
 
$

$Solution =\ \textgreater \ x = -5, y = 6$

6 0

3 years ago